SPM MM KERTAS 1

13. Table shows the results based on the grades 15. Diagram shows a pie chart that represents the
obtained by a group of Form 5 students in a test. points obtained by each of the sports houses in a
Given the students with grades A, B or C are cross country event.
considered to have passed. Rajah menunjukkan satu carta pai yang mewakili
Jadual menunjukkan keputusan mengikut gred yang jumlah mata yang diperoleh setiap rumah sukan
diperoleh sekumpulan pelajar Tingkatan 5 dalam dalam acara merentas desa di sebuah sekolah.
suatu ujian. Diberi pelajar yang memperoleh
gred A, B dan C dianggap lulus.

Grade ABCD
Gred 6 20 x 22

Number Of Candidates
Bilangan Calon

Table/Jadual

If a pie chart is drawn to represent the given

information, the angle of the sector that represents

the students with grade B is 144°. Given the second place was won by the house with
570 points.
The number of Form 5 students that passed the test Calculate the points received by the house that won
the event.
is Diberi bahawa tempat kedua dimenangi oleh
rumah yang memperoleh 570 mata.
Jika sebuah carta pai dilukis untuk mewakili Hitung jumlah mata yang diperoleh rumah yang
menjadi johan acara itu.
maklumat itu, sudut sektor yang mewakili pelajar A 720
B 740
yang memperoleh gred B ialah 144°. C 760
D 780
Bilangan pelajar Tingkatan 5 yang lulus dalam
16. The pie chart in Diagram shows the number of
ujian itu ialah stamps collected by four students.
Carta pai dalam Rajah menunjukkan bilangan
A 26 C 40 setem yang dikumpul oleh empat orang pelajar.

B 28 D 50

14. The incomplete Table shows the scores of 25
competitors in a Mathematics quiz. Given the mode
score is 3 and 36% of the competitors achieve
scores less than the mode score.
Jadual yang tidak lengkap menunjukkan skor yang
diperoleh sekumpulan 25 orang peserta dalam satu
kuiz Matematik. Diberi skor mod
ialah 3 dan 36% daripada peserta itu memperoleh
skor kurang daripada skor mod.

Scores 12345
Skor

Competitors 8n3 Given the ratio of the number stamps collected by
Bilangan
peserta Chia to the number of stamps collected by Ben is 5

Table/Jadual : 2.

If the total number of stamps of the four students is

Find the value of n. 600, calculate the number of stamp, collected by
Cari nilai n.
A2 Ben.
B3
C4 Diberi nisbah bilangan setem Chia kepada
D5
bilangan setem Ben ialah 5 : 2.

Jika jumlah bilangan setem empat orang pelajar itu

ialah 600 keping, hitung bilangan setem Ben.

A 60 C 200

B 100 D 250

SMK BUKIT JALIL PANITIA MATEMATIK 51

17. Diagram below is a pictograph showing the sales of
pineapples on Wednesday. The sales on Monday
and Tuesday are not shown.
Rajah di bawah ialah piktograf yang menunjukkan
jualan nanas pada hari Rabu. Jualan pada hari
Isnin dan Selasa tidak ditunjukkan.

Calculate the value of x.

Hitung nilai x.

A 240 B 216

C 210 D 205

represents 20 pineapples 19. Diagram below is a pictogram which shows the
mewakili 20 nanas sales of mineral water in May. The sales for June
and July are not shown.
The sales of pineapples on Monday, Tuesday and Rajah di bawah ialah piktogram yang menunjukkan
jualan air mineral dalam bulan Mei. Jualan dalam
bulan Jun dan Julai tidak ditunjukkan.

Wednesday are in the ratio 5 : 1 : 3.

Find the difference in the number of pineapples May
Mei
sold on Monday and Tuesday.
June
Jualan nanas pada hari Isnin, Selasa dan Rabu Jun

adalah dalam nisbah 5 : 1 : 3. July
Julai
Cari beza antara bilangan nanas yang dijual pada
represents 144 bottles
hari Isnin dengan bilangan nanas yang dijual pada mewakili 144 botol

hari Selasa. Diagram/Rajah

A 40 B 120

C 160 D 240

18. Diagram (a) is a bar chart showing the number of The sales of mineral water in May, June and July
workers in three factories, P, Q and R.
Diagram (b) is a pie chart showing the number of are in the ratio 2 : 1 : 5.
workers in the three factories according to gender.
Rajah (a) ialah carta palang yang menunjukkan Find the difference in number of bottles of mineral
bilangan pekerja di tiga kilang, P, Q dan R.
Rajah (b) ialah carta pai yang menunjukkan water sold between Jun and July.
bilangan pekerja di tiga kilang mengikut jantina.
Jualan air mineral dalam bulan Mei, Jun dan Julai

adalah dalam nisbah 2 : 1 : 5.

Cari beza bilangan botol air mineral yang dijual

antara bulan Jun dan Julai.

A 1 152 B 2 304

C 3 456 D 4 608

SMK BUKIT JALIL PANITIA MATEMATIK 52

7. Algebraic Expression 5. , express x in terms of p and y.
Ungkapan Algebra Given , ungkapkan x dalam sebutan p

Easy / Senang Diberi
1. dan y.

Given express q in terms of p.

Diberi ungkapkan q dalam sebutan p.

A 5p – 1 C 5(p – 1)
2

B p–1 D 5p – 1
2 2

2. , express x in terms of y. 6. Given 6 – 2(m – 3) = m, then m =
Given , ungkapkan x dalam sebutan y. Diberi 6 – 2(m – 3) = m, maka m =

Diberi A0 C3

A x = 4 – y B1 D4
y

B x =4 y y 7. Given 6q – 2(p + 3) = 10, then p =
–
Diberi 6q – 2(p + 3) = 10, maka p =
y– 4
C x = y A 3q – 2 6q – 7
C 2

D x =4 y y B 3q – 8 D 6q – 13
– 2

3. Given q = 2(h + k), express k in terms of h and q. 8. Given 3 – (k – 1) = k, then k =

Diberi q = 2(h + k), ungkapkan k dalam sebutan h Diberi 3 – (k – 1) = k, maka k =

dan q. A –4 C2

A k =2h − q B –2 D4
2

B k =q − 2h 9. Given 5p2 = 3r + 4q. Express q in terms of p and r.
2 Diberi 5p2 = 3r + 4q. Ungkapkan q dalam sebutan

C k = 2(q – 2h) p dan r.

D k = 2(2h – q)

4.
=

A p2 C p3
q q

B p2 D p3 10.
q3 2q2

SMK BUKIT JALIL PANITIA MATEMATIK 53

11. Given , express n in terms of k. 4.
Given
, express T in terms of R and W.

Diberi , ungkapkan n dalam sebutan k.

2 2 Diberi , ungkapkan T dalam sebutan R
k –
A n = B n = k 1 dan W.

C n = 2 D n = 2 – k A 2
+ k R2 + W
k 1
4
B R2 – W

12. Given 3m = 2n2 – 5, express n in terms of m. C 4
Diberi 3m = 2n2 – 5, ungkapkan n dalam sebutan R2 + W
m.
D 4
AB R2 + W2

CD 5.
Given (p – 2) = (2 – p), find the value of p.

Moderate / Sederhana Diberi (p – 2) = (2 – p), cari nilai p.
1. A1
,express Q in terms B2
Given , ungkapkan Q dalam C3
of m and P. D4

Diberi 6. , express h in terms of k.
sebutan m dan P. Given

Diberi , ungkapkan h dalam sebutan k.

2. Given x + 4 = 3xy + 5, express x in terms of y. 7. express x in terms of h and y.
Diberi x + 4 = 3xy + 5, ungkapkan x dalam sebutan Given ungkapkan x dalam sebutan
y.
54
Diberi
h dan y.

3. , express T in terms of p.
Given

Diberi , ungkapkan T dalam sebutan p.

A T= 1–p C T= 3p
3p 1–p

B T= 1+p D T= 3p
3p 1+p

SMK BUKIT JALIL PANITIA MATEMATIK

8. then p = 15.
Given
maka p =
Diberi C –4
A –12 D –3
B –9

9. then k = 16. Given then n =
Given maka n =
maka k = Diberi
Diberi C –3 A
D –5 B (2p + 3)2 + 9
A0 C 4p(p – 3)
B –2 D 4p2 – 12p – 18

10. then x = 17.
Given Given

Diberi maka x = , then p =

A – 1 C 1 Diberi , maka p =
3 3
m2q
B –1 D1 A m2(q − 1) C 4

11. B m2q D m2q
Given 2 1 + m2
then m =

Diberi maka m = 18. then k =
A (4r + 5)2 Given
B (4r + 2)2
C (4r – 4)2 Diberi maka k =
D (4r – 7)2
q−h 2 h
h (q - h)2
A C

12. then k = B q2 - h2 D
Given h

Diberi maka k =

A 3 – 3h 19.
Given
B 7 – 3h then T =

C 7 – 3h
2
Diberi maka T =
3h – 5
D 2 3 − 2r 2 9 − r2
r 4r2
A C

13. Given mp – 2(m – p) = m, then m = B 2r 2 D 9 + 1
Diberi mp – 2(m – p) = m, maka m = 3−r 4r2

A 2p C 2p
3–p 3+p
20.
B 2p D 2p Given , then m =
1–p 1+p

14. Diberi , maka m =
Given (m + 3) = 4 – 2(m + 5), then m =
4f 2 − 3
Diberi (m + 3) = 4 – 2(m + 5), maka m = A f+3 C f
C –1 4f 2
A –3
B –2 D0 B 4f − 3 2 D 4f 2
f f+3

SMK BUKIT JALIL PANITIA MATEMATIK 55

21. Given 10x – 3 = –5(x – 3) + 12. Difficult / Sukar
1.
Find the value of x. then r =
Diberi 10x – 3 = –5(x – 3) + 12. Given maka r =

Cari nilai x. C2 Diberi
A –1

B1 D3

22.
Given
Find the value of x.

Diberi

Cari nilai x.

A 7 1 C − 2 2.
2 5 Given

B 3 D − 5 , then T =
4 6

23. Diberi , maka T =

A w+3 2 C 8
w+1 w2 − 1

B 9 − w2 D w2 + 9
w2 − 1 w2 + 1

3. Given then w =
Diberi maka w =

24. A v2 − 9 C v−3 2
Given v2 − 4 v−2
, then q =
4v 4v 2
B (v + 2)2 D v+2

Diberi , maka q =

A p C −p 4.
7p + 1 7p − 1 Given
then p =
B p D p
7p − 1 −7p − 1
Diberi maka p =

25. Given 2 – = m – 2, then m = A k² C − 1
= m – 2, maka m = k2 − 1 k2
Diberi 2 –
A6 B k² − 1 D 1
B3 k2 k2
C0
D -3

SMK BUKIT JALIL PANITIA MATEMATIK 56

8. Algebra 9.
Algebra

Easy / Senang 10. (4m – 5n)(5m + 4n) =
A 20m2 + 9mn – 20n2
1. B 20m2 – 9mn – 20n2
7pq – (6 – 9pq) = C 20m2 – 41mn – 20n2
A 10pq – 2 D 20m2 – 41mn + 20n2
B –10pq – 18

C 4pq 2
D –2pq – 2

2. (2m – 7)(4m + 5) = 11. Express as a single fraction in its
A 8m2 – 18m – 35 simplest form.
B 8m2 – 18m + 35
C 8m2 + 18m – 35
D 8m2 + 18m + 35

3. 4x2 – x(3 – 2x) = Ungkapkan sebagai satu pecahan
A 2x2 – 3x
B 2x2 – 3 C 6x2 – 3 tunggal dalam bentuk termudah.
D 6x2 – 3x

4. p2 + (3q + p)(3q − p) = A p2 – 4p – 6
A 9q2 p2
B 2p2 + 9q2
C 2p2 − 6pq B p2 + 4p – 6
D 2p2 + 6pq + 9q2 p2

C p2 + 6
p2

5. p2 – 6
D p2

12. Given 10 = x2 – 2xy, express y in terms of x.

Diberi 10 = x2 – 2xy, ungkapkan y dalam sebutan x.

A y= 10 – x2
2x

6. 2(3x – y)2 + 6xy = B y= 10 + x2
A 18x2 + 2y2 + 6xy 2x
B 9x2 + y2 + 3xy
C 18x2 – 6xy + 2y2 C y= x2 – 10
D 9x2 – 3xy + y2 2x

7. D y= x – 10
2

13. (y + 2x)(3y – x) = B 3y2 – 5xy – 2x2
A 3y2 + 4xy – 2x2 D 3y2 – 4xy – 2x2
C 3y2 + 5xy – 2x2

14. as a single fraction in its
Express
8. simplest form.

Ungkapkan sebagai satu

pecahan tunggal dalam bentuk termudah.

A 7d – 2 B 5d – 2

4d2 4d2
C 7d – 1 D 5d – 1

2d2 2d2

SMK BUKIT JALIL PANITIA MATEMATIK 57

15. Given y = 5x2 + 4, express x in terms of y. Moderate / Sederhana
Diberi y = 5x2 + 4, ungkapkan x dalam sebutan y. 1. (3h + 4)(2h – 5) =
AB
A 6h2 – 7h + 20
CD B 6h2 – 7h – 20
C 6h2 – 23h + 20
D 6h2 – 23h – 20

16. Express as a single fraction in its 2. as a single fraction in its
simplest form. Express
simplest form.

Ungkapkan sebagai satu pecahan Ungkapkan sebagai satu pecahan

tunggal dalam bentuk termudah. tunggal dalam bentuk termudah.

A n = 2 B n = k 2 1 pm − 3m − p
k – A 3m2

C n = 2 D n = 2 – k pm − 3m + p
+ k 3m2
k 1 B

17. Express as a single fraction in its C 4p − 3
simplest form. 3m

D −2p − 3
3m

Ungkapkan sebagai satu pecahan

tunggal dalam bentuk termudah. 3. 3x2 – x(1 – x) =
A 2x2 – 1
5mn – 1 + m B 2x2 – x
A n2 C 4x2 – 1
D 4x2 – x
B 5mn – 1 – m
n2
4.
5mn – 1 + m Simplify .
C n – n2

D 5mn – 1 – m
n – n2
Ringkaskan .

18. as a single fraction in its A m B m
Express sebagai satu n n2
simplest form.
C m2 D 3m2
Ungkapkan n2 4n

pecahan tunggal dalam bentuk termudah 5. (2x – y)2 – x(x – y) =
A 3x2 – 3xy + y2
A 3p2 – 9p – 6 B 3x2 – 5xy + y2
6p2 C 3x2 + xy – y2
D 3x2 – 5xy – y2
B 3p2 – 9p + 6
6p2

C p2 – 3p – 2
2p2

D p2 – 3p + 2
2p2

SMK BUKIT JALIL PANITIA MATEMATIK 58

6. A 4m + m2
Express
as a single fraction in its 2−m
simplest form.
B 4 + m2
2−m

C 4 + 2m
2−m
Ungkapkan sebagai satu pecahan
4+m
tunggal dalam bentuk termudah. D 2−m

−3 − p − p2 11. 3(x + 2) – (1 – 2x)2 =
Ap A 1 + 3x – 4x2
B 1 + 7x + 4x2
B −3 − p − p2 C 5 + 3x + 4x2
p2 D 5 + 7x – 4x2

C −3 + p − p2 12.
p Express
simplest form.
D −3 + p − p2 as a single fraction in its
p2

7. 5pq – 2(1 – pq) = Ungkapkan sebagai satu pecahan
A 3pq – 2
B 4pq – 2 tunggal dalam bentuk termudah.
C 6pq – 2
D 7pq – 2 A −p2 + 6p + 2
6p
8. as a single fraction in
Express −p2 − 6p + 2
B 6p
its simplest form.
p2 − p + 1
C 3p

Ungkapkan sebagai satu p2 − p + 3
D 3p
pecahan tunggal dalam bentuk termudah.

A h2 − h − 10 B h2 − 2h − 10 13. 4x(x + y) – (–x – 3y)2 =
h2 h2 A 3x2 – 2xy – 9y2
B 3x2 – 2xy – 3y2
C h2 − h − 13 D h2 − 2h − 13 C 5x2 – 2xy + 9y2
h2 h2 D 5x2 – 2xy + 3y2

9. (2e + 3)(h – 1) + (e – 1)(h – 2) = 14. as a single fraction

A 3eh – 4h + 5 Express
B 3eh + 4h – 5 in its simplest form.
C 3eh – 4e + 2h – 1
D 3eh – 4e – 2h + 1 Ungkapkan sebagai satu

10. pecahan tunggal dalam bentuk termudah.
Express
simplest form. as a single fraction in its A 3m (3 + n)

m+2

B 3m (3 - n)

m+2

Ungkapkan sebagai satu pecahan C __m + 2__

tunggal dalam bentuk termudah. 3m (3 - n)

D __m + 2__

3m (3 + n)

SMK BUKIT JALIL PANITIA MATEMATIK 59

15. (p – q)(p + q) + p(p – q) = 3. (3x – y)2 – (x + 2y)(x – 3y) =
A 2p2 – q2 – q A 8x2 – 7xy – 5y2
B 2p2 – q2 – pq B 8x2 – 7xy + 5y2
C 2p2 – q2 + i C 8x2 – 5xy – 7y2
D 2p2 + q2 – pq D 8x2 – 5xy + 7y2

16. as a single fraction in its 4. (2t – k)(t + 3k) – 4kt =
Express A (2t – 3k)(t – k)
simplest form. B (2t – 3k)(t + k)
C (2t + 3k)(t – k)
Ungkapkan sebagai satu pecahan D (2t + 3k)(t + k)

tunggal dalam bentuk termudah. 5. Factorise (h – 2)(k + 1) – (k + 1) completely.
Faktorkan (h – 2)(k + 1) – (k + 1) selengkapnya.
A 2(q + 1) A (h – 3)(k + 1)
B 2(q + p) B (h – 2)(k + 2)
C 2q + pm C (h – 1)(k + 1)
D (h + 1)(k + 1)
m
D 2q + 2m 6. Factorise 12a – 3ab2 completely.
Faktorkan 12a – 3ab2 selengkapnya.
m A 3a(4 – b2)
B 3a(2 – b)2
17. Given p = 5q – r, express q in terms of p and r. C 3a(2 + b)(2 – b)
Diberi p = 5q – r, ungkapkan q dalam sebutan p D 9a2(4 – b2)

dan r. 7. (2h + 3)(k – 2) + (h + 1)(k – 1) =
A 3hk – 5h + 4k – 7
A q= p+r B 3hk – 5h + 2k – 7
5 C 3hk – 3h + 4k – 5
D 3hk – 3h – 4k – 7
B q= p–r
5 8. 2x(2x – 3y) – (2x – 3y)2 =
A 6xy – 9y2
C q= p + r B 6xy + 9y2
5 C 8x2 + 6xy – 9y2
D 8x2 – 6xy – 9y2
D q= p – r
5

Difficult / Sukar
1.

2. as a single fraction in its
Express

simplest form.

Ungkapkan sebagai satu pecahan

tunggal dalam bentuk termudah.

A 2n C 3n + 2
n2– 1 n2 – 1

B 2+n D 2n2 + n
n2– 1 n2– 1

SMK BUKIT JALIL PANITIA MATEMATIK 60

FORM 4 / TINGKATAN 4 10. Express 138 000 in standard form.
Chapter 1 Standard Form
Bab 1 Bentuk Piawai Ungkapkan 138 000 dalam bentuk piawai.
A 1.3 × 103
Easy / Senang B 1.3 × 104
C 1.38 × 104
1. Round off 241 356 to 3 significant figures. D 1.38 × 105

Bundarkan 241 356 kepada 3 angka bererti.

A 240 000 C 241 300 11. Round off 0.05893 correct to two significant

B 241 000 D 241 400 figures.

2. Round off 44 550 to 3 significant figures. Bundarkan 0.05893 betul kepada dua angka

Bundarkan 44 550 kepada 3 angka bererti. bererti.

A 44 500 C 44 600 A 0.05 C 0.058

B 44 550 D 44 700 B 0.06 D 0.059

3. Round off 0.1423 to 2 significant figures. 12. Express 0.00001001 in standard form

Bundarkan 0.1423 kepada 2 angka bererti. Ungkapkan 0.00001001 dalam bentuk piawai.
A 1.001 × 10–6
A 0.14 C 0.1420 B 1.001 × 10–5 C 1.001 × 105
D 1.001 × 106
B 0.1400 D 0.1500

4. Express 321 000 in standard form. 13. Round off 0.4673 correct to two significant figures.
Bundarkan 0.4673 betul kepada dua angka bererti.
Ungkapkan 321 000 dalam bentuk piawai. A 0.40
A 3.21 × 10–6 B 0.46
B 3.21 × 10–5 C 3.21 × 105 C 0.47
D 3.21 × 106 D 0.50

5. Express 3 860 000 in standard form. 14. Express 0.000307 in the standard form.
Ungkapkan 0.000307 dalam bentuk piawai.
Ungkapkan 3 860 000 dalam bentuk piawai. A 3.07 × 10–4
A 3.86 × 10 3 B 3.07 × 10–1
B 3.86 × 10 5 C 3.07 × 103
C 3.86 × 106 D 3.07 × 104
D 3.86 × 107

6. Express 1.52 × 10–5 as a single number. 15. Round off 80 746 to three significant figures.
Ungkapkan 1.52 × 10–5 sebagai nombor tunggal. Bundarkan 80 746 kepada tiga angka bererti.
A 0.00152 A 80 700
B 0.000152 B 80 740
C 0.0000152 C 80 750
D 0.00000152 D 80 800

7. Express 7.207 × 104 as a single number. 16. Express 6.483 × 10–5 as a single number.
Ungkapkan 7.207 × 104 sebagai nombor tunggal. Ungkapkan 6.483 × 10–5 sebagai satu nombor
tunggal.
A 72 000 C 72 100 A 0.06483
B 0.006483
B 72 070 D 72 170 C 0.0006483
D 0.00006483
8. Express 0.0000502 in standard form.

Ungkapkan 0.0000502 dalam bentuk piawai.
A 5.02 × 10–7 C 5.02 × 10–5
B 5.02 × 10–6 D 5.02 × 10–2

9. Round off 0.03642 to 3 significant figures. 17. Express 0.00000704 in the standard form.
Bundarkan 0.03642 kepada 3 angka bererti. Ungkapkan 0.00000704 dalam bentuk piawai.
A 0.036 A 7.04 × 10–6
B 0.0364 B 7.04 × 10–5
C 0.03640 C 7.04 × 105
D 0.03642 D 7.04 × 106

SMK BUKIT JALIL PANITIA MATEMATIK 61

18. Round off 0.004707 correct to three significant 2. 0.072 =

figures. 12 000 000 C 6 × 10–7
Bundarkan 0.004707 betul kepada tiga angka A 6 × 10–6 D 6 × 10–9
bererti. B 6 × 10 –8

A 0.004 C 0.00470 3. 0.000034 – 2.2 × 10–6 =
B 0.005 D 0.00471 A 3.18 × 10–6
C 3.18 × 105
19. Express 4.98 × 10–2 as a single number. B 3.18 × 10–5 D 3.18 × 106
Ungkapkan 4.98 × 10–2 sebagai satu nombor
tunggal. 4. 0.0054 – 6 × 10–5 = C 5.34 × 10–3
A 0.00498 A 5.34 × 10–5 D 5.34 × 102
B 0.0498 B 5.34 × 10–4

C 498 5. 5.3 × 1016 + 4.2 × 1017 =
D 4 980
A 4.73 × 1016 C 4.73 × 1020
20. Round off 19.959 correct to three significant B 4.73 × 1017 D 4.73 × 1033

figures.

Bundarkan 19.959 betul kepada tiga angka bererti. 6.

A 19.9

B 19.96

C 20

D 20.0

21. Round off 0.08604 correct to three significant

figures.

Bundarkan 0.08604 betul kepada tiga angka

bererti. The diagram shows a water tank.
A 0.100
B 0.0861 If 40% of the tank is filled with water, calculate the
C 0.0860 volume, in cm 3 , of water in the tank.
D 0.086
22. Round off 70 932 correct to three significant Rajah di atas menunjukkan sebuah tangki air.
figures.
Bundarkan 70 932 betul kepada tiga angka bererti. Jika 40% daripada tangki itu diisi dengan air,
hitung isi padu, dalam cm 3, air di dalam tangki

tersebut.

A 709 C 70 900

B 710 D 70 930

23. Express 461 000 in standard form. A 2.36 × 105 C 3.52 × 105
B 3.48 × 105 D 3.68 × 106
Ungkapkan 461 000 dalam bentuk piawai.
C 4.61 × 10–3
A 4.61 × 103 D 4.61 × 10–5
B 4.61 × 105
7. 3.36 × 10–8 – 1.9 × 10–9
A 3.19 × 10–2
24. Round off 0.7863 correct to two significant figures. B 3.11 × 10–3

Bundarkan 0.7863 betul kepada dua angka bererti. C 3.17 × 10–8

A 0.7 D 3.17 × 10 –9

B 0.78

C 0.79 8. 3.75 × 10-3 =
D 0.8 (5 × 10-4)-2

Moderate / Sederhana C 3.87 × 105 A 5.5 × 10–2
1. 3.7 × 105 + 18 000 = D 3.88 × 105 B 9.3 × 10–3
C 9.37 × 10–8
A 3.68 × 104 D 9.375 × 10–10
B 3.88 × 104

SMK BUKIT JALIL PANITIA MATEMATIK 62

9. 4.8 × 1012 – 9.6 × 1011 = 18. 8.2 × 106 – 1.3 × 105 =
A 6.9 × 105
A 3.84 × 1011 C 4.8 × 1011 B 6.9 × 106
B 3.84 × 1012 D 4.8 × 1012 C 8.07 × 105
D 8.07 × 106
10. 2.7 × 10–5 – 0.0000048 =
A 2.1 × 10–6 19. Find the value of (1 – 0.638) ÷ 20 and round off the
B 2.1 × 10–5
C 2.22 × 10–6 answer correct to two significant figures.
D 2.22 × 10–5 Cari nilai bagi (1 – 0.638) ÷ 20 dan bundarkan

jawapan itu betul kepada dua angka bererti.

11. 0.0072 = A 0.01 C 0.019
800 000
A 9 × 10–9 B 0.018 D 0.02
B 9 × 10–8
C 9 × 108 20. 9.4 × 1012 – 4.6 × 1011 =
D 9 × 109
A 5.8 × 1011 C 8.94 × 1011
B 5.8 × 1012 D 8.94 × 1012

12. 6.25 × 10–5 = 21. C 3.525 × 108
(5 × 10–2)2 = D 3.525 × 1012
A 1.25 × 10–7
B 1.25 × 101 A 2.82 × 10–9
C 2.5 × 10–10 B 2.82 × 1012
D 2.5 × 10–2
22. Find the value of 4 × (6 582 + 4 709) and round off

13. 4.37 × 10–6 – 8.5 × 10–7 = the answer correct to three significant figures.

A 3.13 × 10–7 C 3.52 × 10–7 Cari nilai bagi 4 × (6 582 + 4 709) dan bundarkan

B 3.13 × 10–6 D 3.52 × 10–6 jawapan itu betul kepada tiga angka bererti.

A 31 000 C 45 100

B 31 100 D 45 200

14. (4.2 × 104)2 = 23. 5.9 × 10−4 − 9.4 × 10−5 =
1.4 × 10–2 A 4.96 × 10−5
A 3 × 106 B 4.96 × 10−4
B 3 × 1010 C 3.5 × 10−5
C 1.26 × 1010 D 3.5 × 10−6
D 1.26 × 1011
24. 4.3 × 10−5 + 2.4 × 10−6 =
15. 0.0007 + 3.5 × 10–4 = A 4.54 × 10−6
A 1.05 × 10–3 B 4.54 × 10−5
B 1.05 × 10–4 C 4.54 × 10−2
C 7.35 × 10–3 D 4.54 × 10−1
D 7.35 × 10–4
25. 9.4 × 1012 – 4.6 × 1011 =

16. 12 000 = A 4.8 × 1011 C 8.94 × 1011
4.8 × 106 B 4.8 × 1012 D 8.94 × 1012
A 2.5 × 10–4
B 2.5 × 10–3 Difficult / Sukar
C 4 × 102 1. Given that the speed of light is 3 × 105 km s–1, find
D 4 × 102
the distance, in km, travelled by light in 22
17. 0.0000036 – 2.4 × 10–8 =
A 1.2 × 10–6 minutes. Express the answer in standard form.
B 1.2 × 10–7
C 3.576 × 10–6 Diberi bahawa laju cahaya ialah
D 3.576 × 10–7 3 × 105 km s–1, cari jarak, dalam km, yang dilalui

oleh cahaya dalam masa 22 minit.

Nyatakan jawapan dalam bentuk piawai.

A 3.96 × 106 C 3.96 × 109
B 3.96 × 10 8 D 39.6 × 109

SMK BUKIT JALIL PANITIA MATEMATIK 63

2. Diagram shows an empty cylinder with a radius of 5. Diagram below shows a square PQTU and a
70 cm and a height of 200 cm. rectangle QRST.
Rajah menunjukkan sebuah silinder kosong yang Rajah di bawah menunjukkan sebuah segi empat
berjejari 70 cm dan tinggi 200 cm. sama PQTU dan sebuah segi empat tepat QRST.

Diagram/Rajah

A worker fills up 75% of the cylinder with water. Diagram /Rajah
Calculate the volume, in cm3, of the water in the
Calculate the area, in m2, of the rectangle QRST.
cylinder. Hitung luas, dalam m2, segi empat tepat QRST.
A 2.75 × 109
Seorang pekerja memasukkan air ke dalam silinder B 2.75 × 1010
C 5 × 108
itu sehingga 75% penuh. D 5 × 109
Hitung isi padu, dalam cm3, air di dalam silinder

itu.

A 2.31 × 106 C 4.4 × 106 6. A rectangular field is 45 m long and 25 m wide.
B 2.31 × 108 D 4.4 × 108 Calculate the total length, in cm, of wire fence

required to enclose the field.

3. A rectangular floor has a length of 36 m and a Sebuah padang yang berbentuk segi empat tepat

width of 28 m. Find the number of square tiles of berukuran 45 m panjang dan 25 m lebar.

side 30 cm that are required to cover the whole Hitung jumlah panjang, dalam cm, pagar dawai

floor. yang diperlukan untuk memagar padang itu.
Suatu lantai yang berbentuk segi empat tepat A 1.4 × 103
mempunyai panjang 36 m dan lebar 28 m. Cari B 1.4 × 104
bilangan jubin yang berbentuk segi empat sama C 7.0 × 103
dengan sisi 30 cm, yang diperlukan untuk menutupi D 7.0 × 104

seluruh lantai itu.

A 1.12 × 104 7. Given H = mq2, find the value of m if H =
B 1.12 × 105 4.6 × 107 and q = 2.5 × 102.
C 3.36 × 104 Diberi H = mq2, cari nilai m jika H = 4.6 × 107
D 3.36 × 105 dan q = 2.5 × 102.
A 1.84 × 103
4. A rectangular floor has a length of 32 m and a B 1.84 × 102
width of 28 m. The floor will be covered with tiles. C 7.36 × 102
D 7.36 × 103

Each tile is a square of side 16 cm. Calculate the

number of tiles required to cover the whole floor. 8.

Suatu lantai yang berbentuk segi empat tepat

mempunyai panjang 32 m dan lebar 28 m. Lantai

itu akan ditutupi dengan jubin. Setiap jubin A 2.82 × 10–9
B 2.82 × 1012
berbentuk segi empat sama bersisi 16 cm. C 3.525 × 108
D 3.525 × 1012
Hitung bilangan jubin yang diperlukan untuk

menutupi seluruh lantai itu.

A 3.5 × 104 C 5.6 × 104
B 3.5 × 108 D 5.6 × 108

SMK BUKIT JALIL PANITIA MATEMATIK 64

9. 14. Diagram shows a cylinder.

Calculate the value of , and round off the Rajah menunjukkan sebuah silinder.

answer correct to three significant figures.

Hitung nilai , dan bundarkan jawapan itu

betul kepada tiga angka bererti.

A 0.014 C 0.0141

B 0.015 D 0.0142

10.

Calculate the value of , and round off the

answer correct to three significant figures. Diagram/Rajah

Hitung nilai , dan bundarkan jawapan itu Using π = 3.142, find its volume, in cm3, correct to

betul kepada tiga angka bererti. four significant figures.
[Volume of a cylinder = πr2h]
A 0.31 C 0.312
Dengan menggunakan π = 3.142, cari isi padunya,
B 0.32 D 0.313 dalam cm3, betul kepada empat angka bererti.
[Isi padu silinder = πj2t]
11. Calculate the value of 0.064 ÷ (1.6 – 1.06), and
A 4 948 C 19 794
round off the answer correct to three significant
B 4 949 D 19 795
figures.
Hitung nilai 0.064 ÷ (1.6 – 1.06), dan bundarkan 15. The radius of a hemisphere is 9 cm. Using π =
3.142, find its total surface area, in cm2, correct to
jawapan itu betul kepada tiga angka bererti.

A 0.11 C 0.119 three significant figures.
[Total surface area of a hemisphere = 3πr2]
B 0.118 D 0.12

12. Diagram shows a cuboid. Jejari sebuah hemisfera ialah 9 cm. Dengan
Rajah menunjukkan sebuah kuboid.
menggunakan π = 3.142, cari jumlah luas
permukaannya, dalam cm2, betul kepada tiga

angka bererti.
[Jumlah luas permukaan hemisfera = 3πj2]

A 28.2 C 763

B 28.3 D 764

16. The speed of a comet is 64 200 km s-1. Calculate

the distance, in km, travelled by the comet in 2.5

minutes. Give the answer in two significant figures.

The height of the cuboid is half of its length. [Speed = Distance × Time]
Find the volume, in cm3, of the cuboid correct to Laju suatu komet ialah 64 200 km s-1. Hitung jarak,

three significant figures. dalam km, yang dilalui komet itu dalam 2.5 minit.

Tinggi kuboid itu adalah setengah daripada Berikan jawapan dalam dua angka bererti.

panjangnya. [Laju = Jarak × Masa]
Cari isi padu, dalam cm3, kuboid itu betul kepada
A 160 000 C 9 600 000

tiga angka bererti. B 160 500 D 9 630 000

A 294 C 331

B 295 D 332

13. A cube has edges of 8.5 cm. Find its total surface
area, in cm2, correct to two significant figures.

Sebuah kubus mempunyai tepi 8.5 cm. Cari luas
permukaannya, dalam cm2, betul kepada dua

angka bererti.

A 430 C 610

B 440 D 720

SMK BUKIT JALIL PANITIA MATEMATIK 65

17. Diagram shows an empty cuboidal tank, with 20. The volume of diesel carried by six lorry tankers is
length 400 cm, width 200 cm and height 700 cm. 1.2 × 106 litres. The volume of diesel carried by
Rajah menunjukkan sebuah tangki kosong four of the lorry tankers is 1.4 × 104 litres.
berbentuk kuboid berukuran 400 cm panjang, 200
cm lebar dan 700cmtinggi. Find the volume, in litres, of diesel in the other two

lorry tankers.

Isi padu diesel yang dibawa oleh enam buah lori
tangki ialah 1.2 × 106 liter. Isi padu diesel yang

dibawa oleh empat buah lori tangki ialah
1.4 × 104 liter.

Cari isi padu, dalam liter, diesel di dalam dua buah

lori tangki lagi. C 0.016 × 106
A 0.016 × 104 D 1.186 × 106
B 1.186 × 104

21. A company buys 3500 shares at RM0.35 per share
from Mr Lai, then sells 3.1 × 103 shares at RM0.55

per share and the rest at RM0.45 per share.

If 75% of the tank is filled with water, calculate the Calculate the profit from the transaction.
volume, in cm3, of water in the tank.
Sebuah syarikat membeli 3500 saham pada

Jika 75% daripada tangki diisi dengan air, hitung harga RM0.35 sesaham daripada Encik Lai,
isi padu, dalam cm3, air di dalam tangki itu. kemudian menjual 3.1 × 103 saham pada

A 4.2 × 106 C 5.6 × 106 harga RM0.55 sesaham dan selebihnya pada

B 4.2 × 107 D 5.6 × 107 harga RM0.45 sesaham.

Hitung keuntungan daripada urus niaga itu.

18. Perihelion occurs on 3 January when the distance A RM0.66 × 102 C RM0.66 × 104
of the Earth from the Sun is 1.47 ×108 km whereas B RM6.6 × 102 D RM6.6 × 104

Afelion occurs on 4 July when the distance of the 22. The energy, E joules, produced by a nuclear
reaction is given by E = mc2.
Earth from the Sun is 1.52 ×108 km.

Find the difference, in km, between the distances of Calculate the energy, in joules, produced if
m = 0.004 kg and c = 2 × 108 m s-1.
the Earth from the Sun on 3 January and 4 July.
Tenaga, E joule, yang dihasilkan oleh tindak balas
Perihelion berlaku pada 3 Januari nuklear diberi dengan E = mc2.

apabila jarak Bumi dari Matahari ialah Hitung tenaga, dalam joule, yang dihasilkan

1.47 ×108 km manakala Afelion berlaku jika m = 0.004 kg dan c = 2 × 108 m s-1.

pada 4 Julai apabila jarak Bumi dari Matahari A 1.6 × 1018 C 1.6 × 1014

ialah 1.52 ×108 km. B 0.8 × 1018 D 0.8 × 1014

Cari beza, dalam km,antara jarak Bumi dari

Matahari pada 3 Januari dan pada 4 Julai. 23. A snail moves 0.75 cm in one second.

A 5 × 108 C 0.5 × 107 Find the distance, in mm, of the snail after 6

B 5 × 106 D 2.99 × 108 minutes.

19. A rectangular floor has a length of 3 600 cm and a Seekor siput bergerak 0.75 cm dalam satu saat.

width of 2 700 cm. The floor will be covered with Cari jarak, dalam mm, siput itu selepas 6 minit.

square tiles with sides of 30 cm. A 2.7 × 102 C 2.7 × 103
B 4.5 × 102 D 4.5 × 103
Calculate the number of tiles required to cover the

floor completely.

Suatu lantai yang berbentuk segi empat tepat

berukuran panjang 3 600 cm dan lebar 2 700

cm. Lantai itu akan ditutupi dengan jubin yang

berbentuk segi empat sama dengan sisi 30 cm.

Hitung bilangan jubin yang diperlukan untuk

menutupi seluruh lantai itu.

A 1.08 × 104 C 1.08 × 105
B 3.24 × 104 D 3.24 × 105

SMK BUKIT JALIL PANITIA MATEMATIK 66

24. Diagram below shows a tank in the form of a Chapter 2 Quadratic Equations
cuboid with a length of 8 m, a width of 7.5 m and Bab 2 Persamaan Kuadratik
a height of 6 m.
Rajah di bawah menunjukkan satu tangki Easy / Senang C x2 – 3
berbentuk kuboid dengan panjang 8 m, lebar 7.5 1. x(x – 3) = D x2 + 3x
m dan tinggi 6 m.
A x – 3x
B x2 – 3x

2. 5y(1 – 2y) = C 5y – 10y2
A 5y – 2 D 5y2 – 10
B 5y – 2y2

3. (7 – k)k = C 7k2 – k
A 7 – k2 D 7k2 – k2
B 7k – k2

Diagram 4. (2r – 1)(r – 1) = C 2r2 – 3r + 1
Rajah A 2r 2 + 1 D 2r 2 + 3r – 1
B 2r 2 – r + 1

75% of the tank is filled up with water. 5. (t + 1)(t – 3) = C t2 + 2t + 3
Find the volume, in cm3, of the water. A t 2 – 2t – 3 D 2t 2 – t – 3
B t2+t+3
75% daripada tangki itu diisi dengan air.

Cari isi padu, dalam cm3, air itu.

A 2.7 × 105 B 2.7 × 106 6. Expand 4p(1 – p).
C 2.7 × 107 D 2.7 × 108
Kembangkan 4p(1 – p).
25. The speed of light is 3 × 108 m s–1. A 4p – p2
Find the distance travelled, in m, by light in B 4p – 4p2
5 hours. C 4p2 – 2p
Laju cahaya ialah 3 × 108 m s–1. D 4p2 – 4p
Cari jarak yang dilalui, dalam m, bagi
cahaya dalam masa 5 jam. 7. (3x – 1)(x – 5) =
A 3x2 – x + 5
A 1.5 × 109 B 3x2 – 2x + 5
B 9.0 × 109 C 3x2 – x + 5
C 5.4 × 109 D 3x2 – 16x + 5
D 5.4 × 1012
8. 2q(q – 3) =
A 2q2 – 5q
B 2q2 – 4q
C 2q2 – 6q
D 2q2 – 6q – 5

9. (r – 1)(3 – r) =
A –r2 + 4r – 3
B –r2 – 5r + 2
C r 2 – 3r – 4
D r2 – 4r + 1

10. Expand (2y – 1)2.
Kembangkan (2y – 1)2.
A 4y2 + 1
B 4y2 + 2
C 4y2 + 2y – 1
D 4y2 – 4y + 1

SMK BUKIT JALIL PANITIA MATEMATIK 67

11. Factorise 2x2 – 5x + 3. 20. 100m2 − 36 = C 4(5m – 3)(5m + 3)
Faktorkan 2x2 – 5x + 3. A 2(50m2 − 18) D 4(5m – 3)2
A (x – 3)(2x + 1) B 4(25m2 − 9)
B (2x – 3)(x – 1)
21. x2 − 12x + 36 = C (x + 3)(x – 12)
C (2x + 1)(x + 3) A (x – 6)2 D (x − 9)(x + 4)
B (x – 6)(x + 6)
D (2x + 3)(x + 1)

12. Factorise t 2 – 4t – 21. 22. Which of the equations below is not a quadratic
Faktorkan t2 – 4t – 21.
equation in one unknown?
A (t – 4)(t + 3)
B (t + 4)(t – 7) Antara persamaan berikut, yang
C (t + 3)(t – 7)
D (t – 21)(t + 1) manakah bukan suatu persamaan kuadratik dalam

satu pemboleh ubah?

A p2 − 5p = 14 C 6m2 − 11n + 4 = 0

13. Solve the quadratic equation (p + 1)(p – 2) = 0. B x² + 10 =x D 10q = 5q2
7
Selesaikan persamaan kuadratik (p + 1)(p – 2) = 0.

A p = –1, p = 2 C p = 2, p = 0 23. Express 2y2+ 2y = 13y − 15 in the general form.
Ungkapkan 2y2+ 2y = 13y – 15 dalam bentuk am.
B p = 1, p = –3 D p = 2, p = 1

14. Solve the quadratic equation x(9x – 1) = 0. A 2y2 − 11y + 15 C 15 + 11y – 2y2
Selesaikan persamaan kuadratik x(9x – 1) = 0. B 2y2 − 11y + 15 D 2y2 + 15 − 11y

A x = 0, x = 9 24. Which of the values of x below is a root of the
quadratic equation 8x2+ 2x – 3 = 0?
B x = 0, x = 1
9 Antara nilai x berikut, yang manakah merupakan
punca bagi persamaan kuadratik 8x2+ 2x – 3 = 0?
C x = 1, x = 9
D x = –1, x = –9

15. Solve the quadratic equation 2p2 – 3p = 0. A x = − 1 C x = −3
Selesaikan persamaan kuadratik 2p2 – 3p = 0. 2

A p = 0, p = 3 C p = 1, p = 1 B x= 1 D x=3
2 3 2

B p = 0, p = –3 D p = 2, p = –3 25. Find the values of x for the quadratic equation (x +
3)(x – 5) = 0.
16. Which of the following is not a quadratic
Cari nilai-nilai x bagi persamaan kuadratik (x +
expression?
3)(x – 5) = 0.
Antara yang berikut, yang manakah bukan satu
A 3, 5 C 3, −5
ungkapan kuadratik?
A (x – 3)(x + 5) C 1 B −3, −5 D −3, 5
y
B 4x² – 5x – 12 + 2y²

D 8 – y² Moderate / Sederhana
1. Factorise 3x2 – x(2x –1).
17. (p + 3)(p − 7) = C p² + 4p − 4
A p² + 4p – 21 D p² – 4p – 4 Faktorkan 3x2 – x(2x – 1).
B p² – 4p – 21
A x(x + 1)
18. 4x2− 3x(3 – x) = B (x + 1)(x – 1)
A x2 – 9 C (x – 1)(x – 2)
B x2 – 9x D (x + 2)(x – 1)

C 7x2 – 9 2.
D 7x2 – 9x

19. 16w2 − 72w = C 4w(4w – 18)
A 8(2w2− 9w) D 2w(8w – 36)

B 8w(2w – 9)

SMK BUKIT JALIL PANITIA MATEMATIK 68

The diagram shows a trapezium PQRS. If the area 10. C 3x2 – 3x + 9
of trapezium is 15 cm2, form a quadratic equation (x – 3)(4x + 6) = D 3x2 – 3x – 9
in terms of x.
Rajah di atas menunjukkan sebuah trapezium A 2x2 – 3x + 9 C 6x2 – x
PQRS. Jika luas trapezium itu B 2x2 – 3x – 9 D 6x2 + x
ialah 15cm 2, bentukkan satu persamaan kuadratik
dalam sebutan x. 11. x + 2x(3x – 2) = C (x + 3)(6x – 7)
A 2x2 + 3x = 0 A 6x2 – 3x D (2x + 3)(3x – 7)
B 2x2 + 6x – 15 = 0 B 6x2 + 3x
C 2x2 – 5x – 42 = 0 C 3(2y + 1)(5y – 2)
D 2x2 + 7x – 48 = 0 12. 6x2 − 5x – 21 = D 3(2y – 1)(5y + 2)
A (2x – 3)(3x − 7)
3. Find the values of k in the following quadratic B (x – 3)(6x – 7)
equation.
Cari nilai k dalam persamaan kuadratik yang 13. 30y2 – 3y – 6 =
berikut. A (6y – 3)(5y + 2)
B 15y + 6)(2y – 1)

k+4 = 3 14. 36 + 5k – k2 =
2 k+3
A (4 – k)(9 + k)
A k = –1, k = 1 B (4 + k)(9 – k) C (4 − k)(k – 9)
B k = –6, k = –1 D (4 − k)(k − 9)
C k = –3, k = 1
15. in the
D k = 2, k = 3
Rewrite the quadratic equation
4. Factorise 4x2 – x – 5. general form.
Faktorkan 4x2 – x – 5.
Tulis semula persamaan kuadratik dalam
A (4x – 1)(5x – 1) bentuk am.
B (4x – 1)(x + 5)
C (4x – 5)(x + 1) A x2 – 2x – 24 = 0 C x2 – 2x – 4 = 0
D (4x + 1)(x – 5) B 24 – x2 + 2x = 0 D x2 – 2x + 24 = 0

5. (x – 3)2– 4x = 16. Express (2x + 4)(x – 5) = 5 – 2x, in the general

A (x – 1)(x + 9) form.
B (x – 9)(x – 1) Ungkapkan (2x + 4)(x – 5) = 5 – 2x, dalam sebutan
C (9x – 1)(x – 1)
D (9x – 1(x – 1) am. C 3x2 – 4x – 25 = 0
A 2x2 – 4x – 25 = 0 D 3x2 – 6x – 25 = 0
6. Solve (k + 4)(k – 4) = 9. B 2x2 – 6x – 25= 0

Selesaikan (k + 4)(k – 4) = 9. 17.
Express
A k = –4, k = 5 C k = –5, k = 5

B k = 4, k = –4 D k = –9, k = 9 , in the general form.

7. 4(y + 2) – (1 – 3y)2 = C 7 – 2y + 9y2 Ungkapkan , dalam sebutan am.
A 7 + 10y + 9y2 D 7 – 2y – 9y2 A 4m2 – 7m + 3= 0 C 4m2 – 7m – 3 = 0
B 7 + 10y – 9y2 B 4m2 + 7m + 3= 0 D 4m2 + 7m – 3 = 0

8. 6(2x – 1)(x – ) = C 2x2 − 10x + 2 18.Solve the quadratic equation 2q2 + 3q – 2 = 0.
A 12x2 − 10x + 2 D 2x2 − 10x – 2 Selesaikan persamaan kuadratik 2q2 + 3q – 2 = 0.
B 12x2 − 10x – 2 C 4x2 + 6x – 20
D 4x2 + 6x + 20 A q= 1 , 2 C q= 1 , −2
9. 2(x – 2)(x + 5) = 2 2
A 4x2 + 14x – 20
B 4x2 – 14x + 20 B q= 1 , −2 D q= 1 , 2
2 2

SMK BUKIT JALIL PANITIA MATEMATIK 69

19.Solve the quadratic equation 3m2 + 23m – 8 = 0. 4. Diagram shows a triangle.
Rajah menunjukkan sebuah segi tiga.
Selesaikan persamaan kuadratik 3m2 + 23m – 8 = 0.

A m = 8, 1 C m= −8, 1
3 3

B m = −8, − 1 D m = 8, − 1
3 3

20. Diagram/Rajah
Solve the quadratic equation

Form a quadratic expression, in terms of h, for the

Selesaikan persamaan kuadratik area of the triangle.

A k = −4, −9 C k = −3, 12 Bentuk satu ungkapan kuadratik, dalam sebutan h,

B k = −4, 9 D k = 3, −12 bagi luas segi tiga itu. C 2h2 + 3h
A 2h2 + 3 D 4h2 + 6h
Difficult / Sukar B 2h2 + 6

1.

5. A car travels from Sitiawan to Bukit Merah in
(2t – 6) hours.

If the average speed of the car is 30t km/h, form a

quadratic expression, in terms of t, to represent the

total distance travelled by the car.

The table shows three types of stationery and their Sebuah kereta bertolak dari Sitiawan ke Bukit
respective prices. Halim bought 4 pens, 4 rulers and Merah dalam masa (2t – 6) jam.
(x – 1) note books.
If the total amount of money spent was RM15.00, Jika purata laju kereta itu ialah 30t km/j, bentuk

find the value of x. satu ungkapan kuadratik, dalam sebutan t, untuk
Jadual di atas menunjukkan tiga jenis alat tulis dan
mewakili jumlah jarak yang dilalui oleh kereta itu.

A 60t2 – 90 C 60t2 – 180
B 60t2 + 90t D 60t2 – 180

harga masing-masing. Halim membeli 4 batang

pen, 4 batang pembaris dan (x – 1) buah buku nota. 6. A carpet measuring 4 m × 2 m is placed on the

Jika jumlah wang yang dibelanjakan floor of a rectangular room as shown in Diagram.

ialah RM15.00, cari nilai x. Sebidang permaidani yang berukuran

A2 C5 4 m × 2 m diletakkan di atas lantai sebuah bilik

B3 D8 yang berbentuk segi empat tepat seperti yang

ditunjukkan dalam Rajah.

2. The difference of two numbers is 5 and their

product is 126.

Find the value of the bigger number.

Beza bagi dua nombor ialah 5 dan hasil darab dua

nombor tersebut ialah 126.

Cari nilai nombor yang lebih besar itu.

A 9 C 14

B 10 D 16

3. Pak Ali‟s age is w years. His son, Ahmad‟s age is Diagram/Rajah

35 years younger.

Find the product of their age in terms of w. Find the area of the floor not covered by the carpet,

Pak Ali berumur w tahun. Anak lelaki in terms of x.

beliau, Ahmad 35 tahun lebih muda daripada Cari luas lantai yang tidak ditutupi oleh

beliau. permaidani itu, dalam sebutan x.

Cari hasil darab umur mereka dalam sebutan w. A 3x2 + 5x – 4 C 4x2 + 6x – 4

A w2 – 35w C w2 – 35 B 3x2 + 5x – 6 D 4x2 + 6x – 6
B w2 + 35w D w2 + 35

SMK BUKIT JALIL PANITIA MATEMATIK 70

7. Factorise: The area of the rectangle is 45 cm2.

Faktorkan: Form a quadratic equation in terms of k.

6x2 + 10x – 25 Luas segi empat tepat itu ialah 45 cm2.

A 2(3x – 4)(x + 3) C 2(2x – 4)(x + 3) Bentuk satu persamaan kuadratik dalam sebutan k.

B 2(3x – 4)(x – 3) D 2(2x – 4)(x – 3) A 6k + k + 57 = 0 C 6k2 − k + 57 = 0

B 6k2 − k – 57 = 0 D 6k2 + k − 57 = 0

8. Factorise:

Faktorkan: 14. Express (x – 3)(x + 5) = 2x2 + 4, in the general

k2 – 9(k – 2) form.
Ungkapkan (x – 3)(x + 5) = 2x2 + 4, dalam sebutan
A (k – 3)(k – 6) C (9k + 2)(k – 1)

B (k + 1)(k – 2) D (k – 1)(9k – 2) am. C x2 − 2x – 19 = 0
A x2 − 2x − 11= 0 D x2 − 2x + 19 = 0
9. Factorise: B x2 − 2x + 11= 0

Faktorkan: 15. The total of a number and its square is 56.
Find the number which is a positive integer.
6t2 − 15t – 9 Jumlah satu nombor dan kuasa duanya ialah 56.
Cari nombor itu yang merupakan integer positif.
A (6t – 3)(t + 3) C 3(t – 3)(2t + 1) A5 C7
B6 D8
B (6t + 1)(t – 9) D 3(t – 1)(t + 9)

10. Factorise:
Faktorkan:

A 4q(q – 36) C 4(q2 + 9) 16. The growth rate of a type of bacteria is (3x + 8) per
B 4q(q – 9) D 4(q – 3)(q + 3) second. Given the number of bacteria after a period
of 5xseconds is 130.
11. Factorise: t2 + 3(t2 – 12) Form a quadratic equation in terms of x.
Faktorkan: Kadar pertumbuhan sejenis bakteria ialah
C 4(t2 + 3) (3x + 8) sesaat. Diberi bilangan bakteria
A 3t(t – 6) D 4(t – 3)(t + 3) selepas 5x saat ialah 130.
B 3t(t – 9) Bentuk persamaan kuadratik dalam sebutan x.
A 2x2 + 4x – 26 = 0 C 3x2 + 4x – 26 = 0
B 2x2 + 8x – 26 = 0 D 3x2 + 8x – 26 = 0

12. A positive integer is 7 more than another integer, x. 17. Express (y – 5)2 = 9, in the general form.
The product of the two integers is 144. Ungkapkan (y – 5)2 = 9, dalam bentuk am.
Form a quadratic equation in terms of x. A y2 – 10y + 16 = 0 C y2 – 10y – 34 = 0
Suatu integer positif ialah 7 lebih besar daripada B y2 – 25y + 10 = 0 D y2 – 25y + 34 = 0
integer yang satu lagi, x. Hasil darab kedua-dua
integer itu ialah 144. 18. Solve the quadratic equation (x – 4)2 = 9.
Bentuk satu persamaan kuadratik dalam sebutan x.
A x2+ 7x – 144 = 0 C x2 + 7x + 144 = 0 Selesaikan persamaan kuadratik (x – 4)2 = 9.
B x2 − 7x – 144 = 0 D x2 − 7x + 144 = 0
A x = −1, −7 C x = −1, 7

B x = 1, 7 D x = 1, −7

13. Diagram shows a rectangle. 19. Solve the equation (3m – 2)2 = m2.
Rajah menunjukkan sebuah segi empat tepat. Selesaikan persamaan (3m – 2)2 = m2.

A m= 1 , 1 C m= 1 , 2
3 2

B m= 1 , 1 D m = 2, −1
2

SMK BUKIT JALIL PANITIA MATEMATIK 71

Chapter 3 : Sets 5.
Bab 3 : Set

Easy / Senang
1.

The Venn diagram shows the elements of the
universal set ξ, set P and set Q. List all the elements

of set Q'.

Gambar rajah Venn di atas menunjukkan unsur set
semesta ξ, set P dan set Q. Senaraikan semua unsur

The Venn diagram shows the universal set ξ, set P bagi set Q'.
and set Q. List all the elements in the set (P ∪ Q)'. A {1, 2, 5}
B {1, 3, 4}
Gambar rajah Venn di atas menunjukkan set C {1, 2, 3, 4}
semesta ξ, set P dan set Q. Senaraikan semua unsur D {1, 3, 5, 6}
dalam set (P ∪Q)'.

A {a, b, f} 6. In Diagram below, the Venn diagram shows the
B {d, g, i} number of elements of sets J,K and L.
C {c, e, h} Dalam Rajah di bawah, gambar rajah Venn
D {d, g, h, i} menunjukkan bilangan unsur bagi set J, K dan L.

2. Given ξ = K ∪ L, which of the following Venn
diagrams represents set K ⊂ L?
Diberi ξ = K ∪ L, gambar rajah Venn yang
manakah mewakili set K ⊂ L?

3. List all the subsets of set Y = {1, 8}. Diagram /Rajah
Senaraikan semua subset bagi set Y = {1, 8}.
A {1}, {8} Given ξ = J ∪ K ∪ L and n(ξ) = 36, find the value
B {1}, {8}, { } of x.
C {1}, {8}, {1, 8} Diberi ξ = J ∪ K ∪ L dan n(ξ) = 36, cari nilai bagi
D {1}, {8}, {1, 8}, { } x.
A3 C5
4. Given the universal set ξ = M ∪ N,M = {3, 7, 9} B4 D7
and N = {2, 7, 8}, find the value of n(ξ).
7. In Diagram below, the Venn diagram shows the
Diberi set semesta ξ = M ∪ N, M = {3, 7, 9} dan elements of the universal set ξ.
N = {2, 7, 8}, cari nilai n(ξ). Dalam Rajah di bawah, gambar rajah Venn
A3 menunjukkan unsur-unsur dalam set semesta ξ.
B5
C6 n(P' ∩ Q) = Diagram /Rajah
D8 A2
B4 C5
SMK BUKIT JALIL PANITIA MATEMATIK D7

72

8. Given the universal set ξ = P ∪ Q ∪ R, which of the 11. Diagram is a Venn diagram which shows the

following Venn diagrams represents the set universal set, ξ, set E and set F.

(P ∩ Q)∪ R? Rajah ialah gambar rajah Venn yang menunjukkan

Diberi set semesta ξ = P ∪ Q ∪ R, antara gambar set semesta, ξ, set E dan set F.

rajah Venn berikut, yang manakah mewakili
set (P ∩ Q) ∪ R?

9. Diagram is a Venn diagram showing the elements Diagram/Rajah
of the universal set, ξ, set P and set Q.
The shaded region represents set
Rajah ialah gambar rajah Venn yang menunjukkan Rantau yang berlorek mewakili set
unsur-unsur set semesta, ξ, set P dan set Q. A E ∩ F'
B E' ∩ F
C E∩F
D (E ∩ F)'

Diagram/Rajah 12. List all the subsets of set R = {p, q}.
Senaraikan semua subset bagi set R = {p, q}.
List all the elements of set P'. A { }, {p, q}
Senaraikan semua unsur bagi set P'. B {p}, {q}
C {p}, {q}, {p, q}
D {p, q}, {p}, {q}, { }

13. Diagram below shows the number of elements in
the universal set, ξ, set A and set B.
Rajah di bawah menunjukkan bilangan unsur
dalam set semesta, ξ, set A dan set B.

A {k} Diagram /Rajah
B {h, m}
C {a, e, u} Cari n(A ∩ B)'. Find n(A ∩ B)'.
D {h, k, m} A7
B 12 C 13
10. Given the universal set, ξ = Q ∪ R, set D 14
Q = {1, 2, 3, 4} and set S = {2, 4, 6}, find n(ξ).
Diberi set semesta, ξ = Q ∪ R, set
Q = {1, 2, 3, 4} dan set R = {2, 4, 6}, cari n(ξ).
A2
B5
C6
D7

SMK BUKIT JALIL PANITIA MATEMATIK 73

14. Diagram below is a Venn diagram showing the 18. Which of the following sets is an empty set?
universal set, ξ, set P, set Q and set R. Antara set berikut, yang manakah set kosong?
A R = {x : x is a multiple of 13 and 85 < x < 90}
Rajah di bawah ialah gambar rajah Venn yang R = {x : x ialah gandaan 13 dan 85 < x < 90}
menunjukkan set semesta, ξ, set P, set Q dan set R. B Q = {x : x is a prime number and
115 < x < 120}
Diagram /Rajah Q = {x : x ialah nombor perdana dan
115 < x < 120}
The shaded region is represented by C P = {x : x is a perfect cube and 60 < x < 70}
P = {x : x ialah kuasa tiga sempurna dan
Rantau berlorek diwakili oleh 60 < x < 70}
A (P ∩ Q) ∩ R D S = {x : x is a factor of 185 and 35 < x < 40}
B R' ∩ (P ∩ Q) S = {x : x ialah satu faktor bagi 185 dan
C (P ∩ Q) ∪ R 35 < x < 40}
D (P ∩ Q)' ∩ R
19. The following statements are true except
15. It is given that set M = {3, 4, 5}, set N = {3, 5, 6, 7} Pernyataan-pernyataan berikut adalah
benar kecuali
and set P = {3, 4}. A {cuboid} ⊄ {polygons}
{kuboid} ⊄ {poligon}
Which of the following is true? B {multiples of 4} ⊂ {multiples of 10}

Diberi bahawa set M = {3, 4, 5}, set {gandaan 4} ⊂ {gandaan 10}
C {May, June} ⊂ {months of the year}
N = {3, 5, 6, 7} dan set P = {3, 4}.
{Mei, Jun} ⊂ {bulan dalam setahun}
Antara berikut, yang manakah benar? D {odd numbers} ⊄ {prime numbers}

A P⊂N C P⊂M {nombor ganjil} ⊄ {nombor perdana}

B N⊂M D M⊂N

16. “A set of multiples of 4 which are less than 32.” 20. Given P = {a, e, i, o, u}, the number of subsets

Write the following set in set notation. for P is
“Satu set gandaan 4 yang kurang daripada 32.”
Diberi P = {a, e, i, o, u}, bilangan subset bagi P
Tulis set yang berikut dalam tatatanda set.
ialah

A 25 C 30

B 28 D 32

A {8, 12, 16, 20, 24, 28} 21. List all the subset for the set W = {2, 3, 5}.
B {4, 8, 12, 16, 20, 24, 28} Senaraikan semua subset bagi set W = {2, 3, 5}.
C {8, 12, 16, 20, 24, 28, 32} A {2}, {3}, {5}, {2, 3}, {3, 5}, {2, 3, 5}
D {4, 8, 12, 16, 20, 24, 28, 32} B { }, {2}, {3}, {5}, {2, 3}, {2, 5}, {3, 5}
C {2}, {3}, {5}, {2, 3}, {2, 5}, {3, 5}, {2, 3, 5}
17. The following statements are true except D { }, {2}, {3}, {5}, {2, 3}, {2, 5}, {3, 5},
Pernyataan-pernyataan berikut adalah {2, 3, 5}
benar kecuali
A 51 ∈ {multiples of 3} 22. Which of the following is a possible universal set
51 ∈ {gandaan 3}
B 2 ∉ {prime numbers} for the set G = {multiples of 6}?
2 ∉ {nombor perdana}
C semicircle ∉ {polygons} Antara set berikut, yang manakah ialah set semesta
semi bulatan ∉ {poligon}
D 7 ∈ {factors of 28} yang mungkin bagi set G = {gandaan 6}?
7 ∈ {faktor-faktor 28}
A {multiples of 3} C {multiples of 9}

{gandaan 3} {gandaan 9}

B {multiples of 8} D {multiples of 12}

{gandaan 8} {gandaan 12}

SMK BUKIT JALIL PANITIA MATEMATIK 74

23. It is given that set A = {1, 3, 5, 7, 9}, set 2. In the Venn diagram, ξ = {Form 3 students},
P = {students who play football} and
B = {2, 3, 5, 7} and set C = {3, 6, 9}. Q = {students who play volleyball}.
Find A ∩ B ∩ C. Dalam gambar rajah Venn di bawah,
ξ = {pelajar Tingkatan 3},
Diberi bahawa set A = {1, 3, 5, 7, 9}, set P = {pelajar yang bermain bola sepak} dan
Q = {pelajar yang bermain bola tampar}.
B = {2, 3, 5, 7} dan set C = {3, 6, 9}.
Cari A ∩ B ∩ C.

A {3} C {3, 5, 7, 9}

B {3, 7} D {1, 2, 3, 5, 6, 7, 9}

24. Diagram is a Venn diagram which shows the Given n(ξ) = 36, n(P) = 24, n(Q) = 15
elements of set P, set Q and set R. and n(P ∩ Q) = 9, find the number of students who
Rajah ialah gambar rajah Venn yang menunjukkan
unsur bagi set P, set Q dan set R. do not play the two games.
Diberi n(ξ) = 36, n(P) = 24, n(Q) = 15 dan
n(P ∩ Q) = 9, cari bilangan pelajar yang tidak

bermain dua permainan itu.

A5 C8

B6 D9

Find P ∩ Q. C {f, k, m} 3.
Cari P ∩ Q. D {f, g, h, k, m}
The diagram shows a Venn diagram with the
A {j, l} universal set ξ = K ∪ L. Given n(L) = 25, n(K) = 20
and n(K ∩ L) = 4, find n(ξ).
B {g, h} Rajah di atas menunjukkan gambar rajah Venn
dengan set semesta, ξ = K ∪ L. Diberi n(L) = 25,
25. It is given that set J = {11, 12, 13, 14, 15}, set n(K) = 20 dan n(K ∩ L) = 4, cari n(ξ).
A 20
K = {12, 15, 18} and set L = {12, 14, 16, 18}. B 25
Find J ∪ K ∪ L. C 32
D 41
Diberi bahawa set J = {11, 12, 13, 14, 15}, set
4. The Venn diagram shows the number of students in
K = {12, 15, 18} dan set L = {12, 14, 16, 18}. the sets P, Q and R.
Cari J ∪ K ∪ L. Gambar rajah Venn di bawah menunjukkan
bilangan pelajar dalam set P, Q dan R.
A {12} Given/Diberi
ξ = P ∪ Q ∪ R,
B {11, 15, 16, 18} P = {students who play football},
P = {pelajar yang bermain bola sepak},
C {12, 14, 15, 8} Q = {students who play basketball} and
Q = {pelajar yang bermain bola keranjang} dan
D {11, 12, 13, 14, 15, 16, 18} R = {students who play badminton}.
R = {pelajar yang bermain badminton}.
Moderate / Sederhana
1.

The diagram shows a Venn diagram with the
universal set ξ = E ∪ F ∪ G. Which of the

regions, A, B, C or D, represents the
set E ∩ F' ∩ G'?

Rajah di atas menunjukkan gambar rajah Venn
dengan set semesta ξ = E ∪ F ∪ G. Antara

kawasan A, B, C danD, yang manakah mewakili
set E ∩ F' ∩ G'?

SMK BUKIT JALIL PANITIA MATEMATIK 75

If the number of students who play both football A 65
and basketball is 10, find the number of students B 78
who play only one type of game. C 88
Jika bilangan pelajar yang bermain kedua-dua D 91
bola sepak dan bola keranjang ialah 10, cari
bilangan pelajar yang bermain hanya sejenis 8. Given the universal set, ξ = P ∪ Q ∪ R, which
permainan. Venn diagram represents P ⊂ Q, Q ∩ R ≠ ø
A 27 and P ∩ R = ø?
B 30 Diberi set semesta, ξ = P ∪ Q ∪ R, gambar rajah
C 36 Venn manakah yang mewakili
D 43 P ⊂ Q, Q ∩ R ≠ ø dan P ∩ R = ø?

5. Given/Diberi
ξ = {x : 10 < x < 70, x is an integer},
ξ = {x : 10 < x < 70, x ialah integer},

set K = {x : x is a multiple of 4} and

set K = {x : x ialah gandaan 4} dan

set L = {x : x is a perfect square}.

set L = {x : x ialah kuasa dua sempurna}.
Find n(K ∩ L)
Cari n(K ∩ L).

A2 C4

B3 D5

6. Diagram is a Venn diagram showing the elements
of the universal set, ξ, set P and set Q.

Rajah ialah gambar rajah Venn yang menunjukkan
unsur-unsur set semesta, ξ, set P dan set Q.

List all the elements of set P' ∪ Q.

Senaraikan semua unsur bagi set P' ∪ Q. 9. Diagram is a Venn diagram with the universal set,
ξ = P ∪ Q ∪ R.
A {n, r} C {m, n, r, s, t}
Rajah ialah gambar rajah Venn dengan set
B {n, r, s, t} D {j, k, l, m, s, t} semesta, ξ = P ∪ Q ∪ R.

7. Diagram shows a Venn diagram with the universal

set, ξ = M ∪ P.
Rajah menunjukkan gambar rajah Venn dengan set

semesta, ξ = M ∪ P.

Given n(M ∩ P) = 13, n(M) = 38 and n(P) = 53, Which of the regions, A, B, C or D, represents the
find n( ξ,). set Q' ∩ R'?
Diberi n(M ∩ P) = 13, n(M) = 38 dan Antara rantau, A, B, C dan D, yang manakah
n(P) = 53, cari n( ξ,). mewakili set Q' ∩ R'?

SMK BUKIT JALIL PANITIA MATEMATIK 76

10. It is given that the universal set, 13. Diagram below is a Venn diagram that shows the
ξ = {x : 31 < x ≤ 40, x is an integer} and number of elements in set F, set G and set H.
set P = {x : x is a number such that the product of Rajah di bawah ialah gambar rajah Venn yang
its two digits is an even number}. menunjukkan bilangan unsur dalam set F, set G
Find set P'. dan set H.
Diberi bahawa set semesta,
ξ = {x : 31 < x ≤ 40, x ialah integer} dan Diagram /Rajah
set P = {x : x ialah nombor dengan keadaan hasil
darab dua digitnya ialah nombor genap}. Given the universal set ξ = F ∪ G ∪ H,
Cari set P'. find n(F ∩ G ∩ H').
A {32, 34, 36, 38} Diberi set semesta ξ
B {31, 33, 35, 37, 39} = F ∪ G ∪ H, cari n(F ∩ G ∩ H').
C {33, 35, 37, 39, 40} A4 C8
D {31, 33, 35, 37, 39, 40} B 6 D 10

11. Diagram below shows a Venn diagram with the 14. It is given that ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10},
universal set, ξ = T ∪ W. set P = {even numbers} and set Q = {4, 8}.
Rajah di bawah menunjukkan gambar rajah Venn Which Venn diagram represents the relationship
dengan set semesta, ξ = T ∪ W. between the universal set, ξ, set P and set Q?
Diberi bahawa ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10},
Diagram /Rajah set P = {nombor genap} dan set
Q = {4, 8}. Gambar rajah
Given n(ξ) = 180, n(T) = 120 and n(W) = 105, Venn yang manakah mewakili hubungan antara set
find n(T ∩ W). semesta, ξ, set P dan set Q?
Diberi n(ξ) = 180, n(T) = 120 dan n(W) = 105,
cari n(T ∩ W).
A 15
B 45
C 60
D 75
12. Diagram below is a Venn diagram which shows the
universal set ξ = K ∪ L ∪ M.
Rajah di bawah ialah gambar rajah Venn yang
menunjukkan set semesta ξ = K ∪ L ∪M.

Which of the following sets is represented by the
shaded region?
Antara set berikut, yang manakah diwakili oleh
rantau berlorek itu?

A M' ∪(K ∪ L) C M' ∪ (K ∩ L)
B M' ∪ (K ∩ L) D K ∩ L ∩M

SMK BUKIT JALIL PANITIA MATEMATIK 77

15. It is given that the universal set, 18. It is given that the universal set,
ξ ={x : 50 < x ≤ 65, x is an integer} and ξ = {x : 6 ≤ x ≤ 17, x is an integer}and
set R = {x : x is a prime number}. set P = {x : x is a prime number}.
Find the value of n(R'). List all the elements of set P'.
Diberi bahawa set semesta, Diberi bahawa set semesta,
ξ = {x : 50 < x ≤ 65, x ialah integer} dan ξ = {x : 6 ≤ x ≤ 17, x ialah integer} dan
set R = {x : x ialah nombor perdana}. set P = {x : x ialah nombor perdana}.
Cari nilai bagi n(R'). Senaraikan semua unsur bagi set P'.
A 3 C 10 A {6, 8, 10, 12, 14, 15, 16}
B 5 D 12 B {6, 8, 9, 10, 12, 14, 15, 16}
C {7, 11, 13, 17}
16. Diagram below shows a Venn diagram with the D {7, 9, 11, 13, 17}
universal set, ξ, set P, set Q and set R.
Rajah di bawah menunjukkan gambar rajah Venn 19. Diagram below is a Venn diagram which shows the
dengan set semesta, ξ, set P, set Q dan set R. universal set, ξ, set M and set N.
Rajah di bawah ialah gambar rajah Venn yang
menunjukkan set semesta, ξ, set M dan set N.

The shaded region represents

Kawasan yang berlorek mewakili

Diagram /Rajah A M ∩ N' C M∩N

List all the elements of set (P ∩ Q)'. B M' ∩ N D M' ∩ N'
Senaraikan semua unsur bagi set (P ∩ Q)'.
A {3, 5} 20. Which of the following Venn diagrams
B {1, 4, 6, } represents P ∩ Q ≠ ϕ, P ∩ R = ϕ and R ⊂ Q such
C {1, 4, 6, 7, 8, 9, 12, 14} that the universal set, ξ =P ∪ Q ∪ R?
D {1, 3, 4, 6, 7, 8, 9, 12, 14} Antara gambar rajah Venn berikut, yang manakah
mewakili P ∩ Q ≠ ϕ, P ∩ R = ϕ dan R ⊂ Q dengan
17. Diagram below is a Venn diagram showing the keadaan set semesta, ξ = P ∪ Q ∪ R?
number of elements in sets P, Q and R.
Rajah di bawah ialah gambar rajah Venn yang
menunjukkan bilangan unsur dalam set P, Q dan R.

Diagram /Rajah 78

Given the universal set, ξ = P ∪ Q ∪ R, find the
value of n(Q ∪ R ∩ P).
Diberi bahawa set semesta,
ξ = P ∪ Q ∪ R, cari nilai bagi n(Q ∪ R ∩ P).
A3 C7
B5 D9

SMK BUKIT JALIL PANITIA MATEMATIK

21. Diagram below is a Venn diagram showing 24. Diagram below is a Venn diagram which shows the
set B and set V. It is given that elements of sets ξ, P and Q.
B = {badminton players}, V = {volleyball players}
Rajah di bawah ialah gambar rajah Venn yang
and the universal set, ξ = B ∪ V. menunjukkan unsur-unsur bagi set ξ, P dan Q.
Rajah di bawah ialah gambar rajah Venn yang
menunjukkan set B dan set V. Diberi bahawa
B = {pemain badminton},
V = {pemain bola tampar} dan set semesta,

ξ = B ∪ V.

If n(B) = 10, n(V) = 17 and n(B ∩ V) = 3, find the Diagram / Rajah
Find the value of n(P ∩ Q)'.
value of n(B ∪ V). Cari nilai bagi n(P ∩ Q)'.
A5
Jika n(B) = 10, n(V) = 17 dan n(B ∩ V) = 3, cari B7
C9
nilai bagi n(B ∪ V). C 30 D 11
A 24 D 33
B 27 25. It is given that set E = {2, 4}, set
F ={2, 3, 4, 5} and set G = {1, 3, 5, 7, 9}.
22. It is given that the universal set, Which of the following Venn diagram represents
ξ = {x : 11 ≤ x < 21, x is an integer} and the relationship between the sets E, F and G?
set R = {x : x is a number such that the sum of its Diberi bahawa set E = {2, 4}, set F = {2, 3, 4, 5}
digits is an odd number}. dan set G = {1, 3, 5, 7, 9}.
List all the elements of set R'. Antara gambar rajah Venn berikut, yang manakah
Diberi bahawa set semesta, mewakili hubungan antara set E, F dan G?
ξ = {x : 11 ≤ x < 21, x ialah integer} dan
set R = {x : x ialah nombor yang hasil tambah Difficult / Sukar
digitnya ialah nombor ganjil}. 1. Given
Senaraikan semua unsur bagi set R'.
A {11, 13, 15, 17, 19} ξ = {x : 12 ≤ x ≤ 36, x is an integer},
B {11, 13, 15, 17, 19, 20} E = {x : x is a number such that the sum of its
C {12, 14, 16, 18} digits is 8} and F = {x : x is a multiple of 2}.
D {13, 15, 17, 19, 20} Find n(E ∩ F).

23. Given ξ = {x : 10 ≤ x ≤ 20, x is an integer}, Diberi
set P = {x : x is an odd number) and set ξ = {x : 12 ≤ x ≤ 36, x ialah integer},
Q ={x : x is a prime number}. E = {x : x ialah nombor yang hasil tambah
digitdigitnya ialah 8} dan
Find the elements of set P ∩ Q'. F = {x : x ialah gandaan 2}. Cari n(E ∩ F).
Diberi ξ = {x : 10 ≤ x ≤ 20, x ialah integer}, A1 C3
set P = {x : x ialah nombor ganjil} dan set B2 D5
Q ={x : x ialah nombor perdana}.

Cari unsur-unsur bagi set P ∩ Q'.
A {15}
B {11, 15}
C {15, 19}
D {11, 13, 17 19}

SMK BUKIT JALIL PANITIA MATEMATIK 79

2. Given/Diberi 5. Diagram is a Venn diagram showing the number of
ξ = {x : 30 ≤ x ≤ 60, x is an integer}, students in sets P, Q and R. It is given that set
ξ = {x : 30 ≤ x ≤ 60, x ialah integer}, P = {English Society members}, set
Q = {Astronomy Society members}, set
K = {x : x is a multiple of 6} and R = {Mathematics Society members} and the
K = {x : x ialah gandan 6} dan
universal set, ξ = P ∪ Q ∪ R.
L = {x : x is a multiple of 8}. Rajah ialah gambar rajah Venn yang menunjukkan
L = {x : x ialah gandaan 8}. bilangan pelajar bagi set P, Q dan R. Diberi
Find n(K ∪ L). bahawa set P = {ahli Persatuan Inggeris}, set
Cari n(K ∪ L). Q = {ahli Persatuan Astronomi}, set
A4 R = {ahli Persatuan Matematik} dan set semesta,
B9
C6 ξ = P ∪ Q ∪ R.
D 10

3. Given the universal set ξ = {x : 25 ≤ x ≤ 35, x is an If the number of students who join both the
integer} and set T = {x : x is a number such that the
product of its two digits is an odd number}. Astronomy Society and the Mathematics Society is
Find set T'.
Diberi set semesta ξ = {x : 25 ≤ x ≤ 35, x ialah 11, find the number of students who join only two
integer} dan set T = {x : x ialah nombor di mana
hasil darab digit-digitnya ialah nombor societies.
ganjil}. Cari set T'.
A {25, 26, 27, 28, 30} Jika bilangan pelajar yang menyertai kedua-dua
B {31, 32, 33, 34, 35}
C {25, 26, 27, 28, 29, 30, 2, 34} Persatuan Astronomi dan Persatuan Matematik
D {27, 28, 29, 30, 31, 33, 34, 35}
ialah 11, cari bilangan pelajar yang menyertai dua
4. In Diagram below, the Venn diagram shows
sets X, Y and Z. Given the universal set ξ persatuan sahaja.
= X ∪Y ∪ Z.
Dalam Rajah di bawah, gambar rajah Venn A 12 C 16
menunjukkan set X, Y dan Z.Diberi set semesta ξ
= X ∪ Y ∪ Z. B 14 D 22

6. Diagram is a Venn diagram showing the number of
elements of sets P, Q and R.
Rajah ialah gambar rajah Venn yang menunjukkan
bilangan unsur bagi set P, Q dan R.

Diagram /Rajah

Which of the following is represented by the

shaded region?

Antara berikut, yang manakah diwakili oleh

kawasan yang berlorek?

A X∪Y∩ Z C X∩Y∩Z

B (X ∩ Y)' ∩ Z' D X ∩ Y ∪ Z' It is given that the universal set,
ξ = P ∪ Q ∪ R and n(R') = n(Q ∩ R).
SMK BUKIT JALIL PANITIA MATEMATIK Find the value of y.
Diberi bahawa set semesta, ξ = P ∪ Q ∪ R dan
n(R') = n(Q ∩ R).
Cari nilai y.

80

A9 9. Table below shows data obtained from a survey of
B 10 90 students. Diagram below is a Venn diagram that
C 11 represents part of the information in Table below.
D 12 Jadual di bawah menunjukkan data yang diperoleh
daripada satu kaji selidik ke atas 90 orang pelajar.
7. Diagram below is a Venn diagram showing the Rajah di bawah ialah gambar rajah Venn yang
number of students in sets C, M and S. It is given mewakili sebahagian maklumat dalam Jadual di
that set C = {Chess Club members}, bawah.
set M = {Computer Club members},
set S = {Swimming Club members} and universal
set, ξ = C ∪ M ∪ S.
Rajah di bawah ialah gambar rajah Venn yang
menunjukkan bilangan pelajar dalam set C, M dan
S. Diberi bahawa set C = {ahli Kelab Catur},
set M = {ahli Kelab Komputer},
set S = {ahli Kelab Renang} dan set semesta,
ξ = C ∪ M ∪ S.

If the number of students who join only two clubs Find the number of students who like all the three
is 18, find the number of students who join the
three clubs. food.
Jika bilangan pelajar yang menyertai dua kelab
sahaja ialah 18, cari bilangan pelajar yang Cari bilangan pelajar yang menyukai ketiga-tiga
menyertai tiga kelab itu.
A3 makanan itu.
B6
C 12 A 12 C 21
D 18
B 19 D 35
8. Given the universal set,
ξ = {x : x is a positive integer less than 20}, 10. Diagram below shows a Venn diagram with
set R = {x : x is a multiple of 2}, universal set, ξ = {Form Four students}, set P =
set S = {x : xis a multiple of 3} and
set T = {x : x is a perfect square}, find the elements {members of Red Crescent Society}, set Q =
of the set T ∪ (R' ∩ S).
Diberi set semesta {members of Police Cadet} and set R = {members
ξ = {x : x ialah integer positif kurang
daripada 20}, of Traffic Society}.
set R = {x : x ialah gandaan 2},
set S = {x : x ialah gandaan 3} dan Rajah di bawah menunjukkan gambar rajah Venn
set T = {x : x ialah kuasa dua sempurna} dengan set semesta, ξ = {pelajar Tingkatan
Cari unsur bagi set T ∩ (R' ∩ S).
A 1, 3, 9, 15 Empat}, set P = {ahli Persatuan Bulan Sabit
B 1, 3, 4, 9, 15
C 1, 3, 4, 9, 16 Merah}, set Q = {ahli Kadet Polis} dan set R =
D 1, 3, 4, 9, 15, 16
{ahli Persatuan Trafik}.

SMK BUKIT JALIL PANITIA MATEMATIK 81

It is given that n(P) = 115, n(Q) = 95, n(R) = 48 12. It is given that the universal set ξ = {x : 20 < x
and n(Q ∩ R) = 36. The number of Form Four < 50, x has at least a digit 3}, set P = {x : x is
divisible by 3}, set Q= {x : x is an odd number} and
students who are not a member of any of the three set R = {x : x is a prime number}
Find (P′ ∪Q) ∩ R.
societies is 18. Diberi bahawa set semesta ξ = {x : 20 < x < 50, x
mengandungi sekurang-kurangnya satu digit 3}, set
Find the total number of Form Four students. P = {x : xboleh dibahagi tepat dengan 3}, set Q =
{x : x ialah nombor ganjil} dan set R = {x : x ialah
Diberi bahawa n(P) = 115, n(Q) = 95, n(R) = nombor perdana}.
48 dan n(Q ∩ R) = 36. Bilangan pelajar Cari (P′ ∪Q) ∩ R.
A {30, 33, 36, 3 }
Tingkatan Empat yang bukan ahli mana-mana tiga B {23, 31, 37, 43}
C {23, 31, 33, 35, 37, 39, 43}
persatuan itu ialah 18 orang. D {23, 31, 32, 33, 34, 35, 37, 38, 39, 43}

Cari jumlah pelajar Tingkatan Empat. 13. It is given that the universal set ξ = {x : 11 < x <
26}, set E = {multiples of 4}, set F = {perfect
A 218 C 240 squares}, set G ={a two-digit numbers where the
product of the digits is less than 7} and ξ
B 234 D 294 = E ∪F ∪G.
Find n(E ∩ F′)∪G′.
11. Diagram is a Venn diagram showing the number of Diberi bahawa set semesta ξ = {x : 11 < x <
students in a group who read three types of reading 26}, set E = {gandaan 4}, set F = {kuasa
materials during leisure time. dua sempurna}, set G ={nombor dua digit dengan
Rajah ialah gambar rajah Venn yang menunjukkan keadaan hasil darab digit-digitnya adalah kurang
bilangan pelajar dalam suatu kumpulan yang daripada 7} dan ξ = E ∪F ∪G.
membaca tiga jenis bahan bacaan semasa waktu Cari n(E ∩ F′)∪G′.
lapang. A6 C8
B7 D9

It is given that the universal set ξ = {all the students 14. Diagram shows a Venn diagram with the universal
set ξ = {Form Four Students}, set R ={Members of
in the group}, set C = {students who read comics},
the Red Crescent Society}, set S = {Members of the
set M = {students who read magazines}, set N
= {students who read newspapers} and n(ξ) = 50. Scouts} and set C = {Members of the Co-operative

Find the number of students who read only two Society}.

types of reading materials. Rajah menunjukkan gambar rajah Venn dengan set
Diberi bahawa ξ = {semua pelajar dalam semesta ξ = {Pelajar Tingkatan Empat}, set T

kumpulan itu}, set C = {pelajar yang membaca = {Ahli Persatuan Bulan Sabit Merah}, set S

komik}, set M = {pelajar yang membaca = {Ahli pengakap} dan set C = {Ahli Persatuan

majalah}, set N = {pelajar yang membaca surat Koperasi}.
khabar} dan n(ξ) = 50.

Cari bilangan pelajar yang membaca dua jenis

bahan bacaan sahaja.

A 5 C 12
B 9 D 14

SMK BUKIT JALIL PANITIA MATEMATIK 82

It is given that n(R) = 34, n(S) = 48, n(C) = 16. Table shows data obtained from a survey of 95
65, n(S ∩ C) = 19 and n(ξ) = 153. LCD viewers. Diagram is a Venn diagram which
represents part of the information in Table.
Find the number of Four Four students who are not
Jadual menunjukkan data yang diperoleh daripada
members of any of the three societies. satu kaji selidik ke atas 95 orang penonton LCD.
Rajah ialah gambar rajah Venn yang mewakili
Diberi bahawa n(R) = 34, n(S) = 48, n(C) = sebahagian maklumat dalam Jadual.
65, n(S ∩ C) = 19 dan n(ξ) = 153.

Cari bilangan pelajar Tingkatan Empat yang

bukan ahli mana-mana tiga persatuan itu.

A 6 C 25

B 13 D 44

15. Diagram is a Venn diagram which shows the Games watched Number of
Permainan yang ditonton viewers
number of students who took part in track Bilangan
Football penonton
events during heats in an athletic meet. Given the Bola Sepak 58
Badminton
set T = {200 metres}, set F = {400 metres}, set E Badminton 52
= {800 metres} and universal set ξ = T∪F ∪E . Football and Badminton only
Bola Sepak dan Badminton 17
Rajah ialah gambar rajah Venn yang menunjukkan
bilangan pelajar yang mengambil bahagian dalam sahaja 9
Football and Golf only
acara balapan semasa saringan dalam suatu Bola Sepak dan Golf sahaja 29

temasya olahraga. Diberi set T = Football only 24
Bola Sepak sahaja
{200 meter}, set F = {400 meter}, set E Badminton only
= {800 meter} dan set semesta ξ = T ∪F ∪E. Badminton sahaja

Table/Rajah

Diagram/Rajah

If the number of students who took part in both the

200 metres and 400 metres events is 11, find the

number of students who took part in only two

events.

Jika bilangan pelajar yang mengambil bahagian

dalam kedua acara 200 meter

dan 400 meter ialah 11 orang, cari bilangan Find the number of viewers who watched football

pelajar yang mengambil bahagian dalam dua or golf and also badminton games.

acara sahaja. Cari bilangan penonton yang menonton bola sepak

A 16 C 18 atau golf dan juga menonton

B 17 D 19 permainan badminton.

A 26 C 37

B 28 D 66

SMK BUKIT JALIL PANITIA MATEMATIK 83

17. Diagram is a Venn diagram which shows the 19. It is given that the universal set
elements of sets T, U and V. ξ = {x : 10 ≤ x ≤ 30, x is an integer},

Rajah ialah gambar rajah Venn yang menunjukkan set P = {x : x has digit 2 or 7},
unsur-unsur set T, set U dan set V.
set Q = {x : x is a prime number} and

set R = {x : x is a number with the sum of the digits
equal to 5}. Find n(P ∪Q ∪R).

Diberi bahawa set semesta
ξ = {x : 10 ≤ x ≤ 30, x ialah integer},

set P = {x : x mempunyai digit 2 atau 7},

set Q = {x : x ialah nombor perdana} dan

set R = {x : x ialah nombor dengan hasil tambah
digit-digit sama dengan 5}. Cari n(P ∪Q ∪R).

A 12 C 18

B 16 D 21

Diagram/Rajah 20. It is given that the universal set
ξ = {x : 1 ≤ x ≤ 10, x is an integer},
It is given that the universal set
ξ = T ∪U ∪V and n(T′) = n(T ∩ V). set A = {4, 5, 6, 8}, set B = {x : x is a multiple of 2}
Find the value of x.
Diberi bahawa set semesta ξ = T ∪U ∪V dan and set C = {x : x is a prime number}.
n(T′) = n(T ∩ V). What are the elements of the set (P ∪Q)′ ∩ R?
Cari nilai x.
A4 C6 Diberi bahawa set semesta
B5 D7 ξ = {x : 1 ≤ x ≤ 10, x ialah integer},

18. The Venn diagram shows all the elements in set A = {4, 5, 6, 8},
set Q and some of the elements in set P and set R.
Gambar rajah Venn menunjukkan semua unsur set B = {x : x ialah gandaan 2}dan
dalam set Q dan beberapa unsur dalam set P dan
set R. set C = {x : x ialah nombor perdana}.
Apakah unsur-unsur set (P ∪Q)′ ∩ R?

A 3, 7 C 1, 3, 5, 7

B 1, 3, 7 D 2, 3, 5, 7

21. Diagram is a Venn diagram which shows the
number of elements in set P, set Q and setR.
Rajah ialah gambar rajah Venn yang menunjukkan
bilangan unsur dalam set P, set Q dan set R.

Diagram/Rajah Diagram/Rajah

It is given that the universal set It is given that the universal set,
ξ = P ∪Q ∪R and n(ξ) = 18.
ξ = P ∪Q ∪R, n(P′) = 12 and n(P ∪Q) = 15. Find the value of n(R′).
Find n(P ∪R′). Diberi bahawa set semesta, ξ = P ∪Q ∪R dan
n(ξ) = 18. Cari nilai n(R′).
Diberi bahawa set semesta A5 C9
ξ = P ∪Q ∪R, n(P′) = 12 dan n(P ∪Q) = 15. B 7 D 11
Cari n(P ∪R′).
84
A 10 C 12

B 11 D 13

SMK BUKIT JALIL PANITIA MATEMATIK

22. Given the universal set ξ = P ∪ Q and P' ∩ Q = Q. 24. Given the universal
Which of the following Venn diagrams represents set ξ = {x : 1 ≤ x ≤ 15, x is an integer},
the relations? set P = {x : 2x – 5 > 17},
Diberi set semesta ξ = P ∪ Q dan P' ∩ Q = Q.
Antara gambar rajah Venn berikut, yang mewakili set Q = {x : x is a prime number with one digit} and
hubungan itu? set R = {x : x is a multiple of 3}.
List the elements of set set P ∪ Q ∩ R'.
23. Given Diberi set semesta
set P = {multiples of 2 which are less than 10}, ξ = {x : 1 ≤ x ≤ 15, x ialah integer},
set Q = {multiples of 3 which are less than 10}, set P = {x : 2x – 5 > 17},
set R = {factors of 10} and the universal set set Q = {x : x ialah nombor perdana satu digit} dan
ξ = P ∪ Q ∪ R. set R = {x : x ialah gandaan 3}.
Which of the following Venn diagrams shows the Senaraikan unsur-unsur bagi set P ∪ Q ∩ R'.
relation between sets P, Q and R? A {2, 3, 5, 7, 13}
Diberi B {2, 5, 7, 13, 14}
set P = {gandaan 2 yang kurang daripada 10}, C {2, 3, 5, 7, 11, 13}
set Q = {gandaan 3 yang kurang daripada 10}, D {2, 5, 7, 11, 13, 14}
set R = {faktor bagi 10} dan set semesta
ξ = P ∪ Q ∪ R. 25. Given the universal
Antara gambar rajah Venn berikut, yang manakah set ξ = {x : 10 ≤ x ≤ 20, x is an integer),
menunjukkan hubungan antara set P, Q, dan R? set P = {x : x is a prime number} and
set Q = {x : x is such that when divided by 5, the
remainder is 3}.
Find the elements of set (P ∪ Q)'.
Diberi set semesta
ξ = {x : 10 ≤ x ≤ 20, x ialah integer},
set P = {x : x ialah nombor perdana} dan
set Q = {x : x dibahagi dengan 5, bakinya ialah 3}.
Cari unsur bagi set (P ∪ Q)'.
A {10, 11, 12, 14, 20}
B {11, 13, 17, 18, 19}
C {10, 12, 14, 15, 16, 20}
D {12, 13, 17, 18, 19, 20}

SMK BUKIT JALIL PANITIA MATEMATIK 85

Chapter 4 : Mathematical Reasonings C EFGH is a trapezium.
Bab 4 : Penaklukan Matematik EFGH ialah sebuah trapezium

Easy / Senang D EFGH has two parallel lines.
1. Which of the following is a statement? EFGH mempunyai dua garis selari.

Antara berikut, yang manakah satu pernyataan? 6. Premise 1: If m > 2, then 3m > 7
A 6 < –4 Premis 1: Jika m > 2, maka 3m > 7
B 3x = 9
C 2+3–1 Premise 2: .............................................................
D (3y)2 Premis 2:

2. Which of the following is a true statement? Conclusion: 3 × 3 > 7
Antara berikut, yang manakah satu pernyataan Kesimpulan:
benar?
A All integers are positive. Premise 2 in the above argument is
Semua integer adalah nombor positif. Premis 2 dalam hujah di atas ialah
B All odd numbers are prime numbers. A 3>2
Semua nombor ganjil adalah nombor perdana. B 4>2
C Some perfect squares are even numbers. C 3×3>2
Sebilangan kuasa dua sempurna ialah nombor D 3×4>7
genap.
D All multiples of 2 are multiples of 8. 7. Given the number sequence –8, –7, –4, 1, …, the
Semua gandaan 2 adalah gandaan 8. general conclusion by induction for the number
sequence is
3. “If x = 3, then 3x – 2 = 7”. Diberi senarai nombor berpola –8, –7, –4, 1,
…, kesimpulan umum secara aruhan bagi senarai
The consequent in the above implication is nombor berpola di atas ialah
“Jika x = 3, maka 3x – 2 = 7.” A n2, n = 0, 1, 2, 3,…
B n2 – 8, n = 0, 1, 2, 3,…
Dalam implikasi di atas, akibat ialah C 2n2 – 1, n = 0, 1, 2, 3,…
D 2n2 + 1, n = 1, 2, 3,…
A 3x = 7 C 3x – 2 = 7
8. Given a numerical sequence is 1, 13, 33, 61, ...
B x=3 D x=7 Diberi senarai nombor berpola adalah 1, 13, 33,
61, ...
4. State the antecedent in the implication „if y = –4, and/dan 1 = 4(1)2 – 3
then y 2 = 16‟. 13 = 4(2)2 – 3
Nyatakan antejadian dalam implikasi „jika y = – 33 = 4(3)2 – 3
4, maka y2 = 16‟. 61 = 4(4)2 – 3
A y = –4
Which of the following is the general conclusion by
B y=4 induction for the numerical sequence?
C y2 = 16 Antara berikut, yang manakah ialah kesimpulan
D y3 = –16 secara aruhan bagi senarai nombor berpola itu?
A 4n – 2, n = 0, 1, 2, ...
5. Premise 1: All trapeziums have two parallel lines. B 4n – 3, n = 0, 1, 2, ...
Premis 1: Semua trapezium mempunyai dua garis C 4n – 3, n = 1, 2, 3, ...
selari. D 4n2 – 3, n = 1, 2, 3, ...
Premise 2: EFGH is a trapezium.
Premis 2: EFGH ialah sebuah trapezium.
Conclusion: ...........................................................
Kesimpulan:
The conclusion in the argument is
Dalam hujah di atas, kesimpulan ialah
A A trapezium has two parallel lines.
Sebuah trapezium mempunyai dua garis selari.
B A trapezium has two equal sides.
Sebuah trapezium mempunyai 2 sisi yang sama
panjang.

SMK BUKIT JALIL PANITIA MATEMATIK 86

9. Complete the premise in the following argument: 14. Which of the statements can be generalised to cover
all cases using the quantifier „all‟?
Lengkapkan premis dalam hujah berikut: Antara pernyataan berikut, yang manakah boleh
diperluaskan untuk meliputi semua kes dengan
Premise 1: If p < 0, then 2p < 0. menggunakan pengkuantiti „semua‟?
A
Premis 1: Jika p < 0, maka 2p < 0.
is a proper fraction.
Premise 2: ..............................................

Premis 2 : .................................................

Conclusion : p > 0

Kesimpulan : p > 0

A p>0 C p <0 ialah pecahan wajar.
B A pyramid has five flat faces.
B 2p > 0 D 2p <0
Sebuah piramid mempunyai lima permukaan
10. The following sentences are statements except rata.
C Triangle ABC has three acute angles.
Ayat-ayat yang berikut ialah pernyataan kecuali Segi tiga ABC mempunyai tiga sudut tirus.
A C 7−2 × 75 D A regular octagon has an interior angle of
135°.
B −12 > −11 D {e, u}⊂{a, e, i, o, u} Sebuah oktagon sekata mempunyai sudut
pedalaman sebanyak 135°.
11. Which of the following statements is not true?

Antara pernyataan berikut, yang

manakah tidak benar? 15. Which of the following statements which uses the
A 0.0038 ≠ 3.8 × 10−3 C {5, 9} ⊄ {2, 5, 7} word „and‟ is true?

B 4−3 = 1 D 12 ∈ {3, 6, 9, 12} Antara pernyataan berikut, yang manakah
64 menggunakan perkataan „dan‟ ialah benar?

12. Which of the following statements is true? A
Antara pernyataan berikut, yang manakah benar?
A Some equilateral triangles have three equal > and < .
sides.
Sebilangan segi tiga sama sisi mempunyai tiga > dan <.
sisi yang sama. B 3−2 = 9 and = 7.
B Some pyramids have a square base.
Sebilangan piramid mempunyai tapak yang 3−2 = 9 dan = 7.
berbentuk segi empat sama.
C Some regular nonagons have an interior angle C {0} is a empty set and (S ∪ T) ⊂ T.
of 140°
Sebilangan nonagon sekata mempunyai sudut {0} ialah set kosong dan (S ∪T) ⊂ T.
pedalaman sebanyak 140°. D 49 ∈ {perfect squares} and g ∉ {vowels}.
D Some regular pentagons have an exterior angle 49 ∈ {kuasa dua sempurna} dan g ∉{huruf
of 72°.
Sebilangan pentagon sekata mempunyai sudut vokal}.
peluaran sebanyak 72°.
16. Which of the following statements which uses the
13. Which of the following statements is true? word „or‟ is true?
Antara pernyataan berikut, yang manakah benar?
A All decagons have 10 sides. Antara pernyataan berikut, yang manakah
Semua dekagon mempunyai 10 sisi. menggunakan perkataan „atau‟ ialah benar?
B All factors of 20 are factors of 8. A (−6)2 = 36 or 62 = 36.
Semua faktor bagi 20 ialah faktor bagi 8.
C All multiples of 10 are multiples of 20. (−6)2 = 36 atau 62 = 36.
Semua gandaan 10 ialah gandaan 20.
D All prime numbers are odd numbers. B A reflex angle or an obtuse angle is less than
Semua nombor perdana ialah nombor ganjil. 90°.

Sudut refleks atau sudut cakah adalah kurang

daripada 90°.

C The apple or the grape is a local fruit of
Malaysia.

Epal atau anggur ialah buah-buahan tempatan

Malaysia.

D 8 is a factor of 36 or 1 is a prime number.
8 ialah faktor bagi 36 atau 1 ialah nombor

perdana.

SMK BUKIT JALIL PANITIA MATEMATIK 87

17. All the statements below are true except 3. Which of the following is a statement?
Semua pernyataan berikut ialah benar kecuali
A Set M is a subset of M ∪N. Antara berikut, yang manakah ialah suatu
Set M ialah subset M ∪N.
B sin 30° is not equal to cos 60°. pernyataan? C sin 60˚ – cos 30˚
sin 30° tidak sama dengan kos 60°. A 3+5 D 63 < 12
C Not all even numbers are divisible by 4. B x+3=5
Bukan semua nombor genap boleh dibahagi
tepat dengan 4. 4. Which of the following statements can be
D x = 3 is not a root of the quadratic equation (x − generalised to cover all cases using the quantifier
5)(x + 3) = 0. „all‟?
x = 3 bukan satu punca bagi persamaan Antara pernyataan berikut, yang manakah boleh
kuadratik (x − 5)(x + 3) = 0. diperluaskan untuk meliputi semua kes dengan
menggunakan pengkuantiti „semua‟?
18. If (X ∩ Y) = X, then X ⊂ Y. A Factors of 6 are factors of 9.
“X ⊂ Y” is known as Faktor bagi 6 ialah faktor bagi 9.
Jika (X ∩ Y) = X, maka X ⊂ Y. B Factors of 6 are factors of 24.
“X ⊂ Y” disebut sebagai Faktor bagi 6 ialah faktor bagi 24.
C Multiples of 6 are multiples of 8.
A an implication C an antecedent Gandaan 6 ialah gandaan 8.
implikasi hantejadian D Prime numbers are odd numbers.
Nombor perdana ialah nombor ganjil.
B a consequence D a premise
akibat premis 5. Which of the following are implications for the
sentence “l > m if and only if l + 3 > m + 3”?
19. If set W has 16 subsets, then n(W ) = 4.
The statement “set W has 16 subsets” is known as Antara berikut, yang manakah implikasi untuk
pernyataan “l > m jika dan hanya jika l + 3 > m +
Jika set W mempunyai 16 subset, maka n(W) = 4. 3”?
Pernyataan “set W mempunyai 16 subset” disebut
I If l > m, then l + 3 > m + 3.
sebagai
Jika l > m, maka l + 3 > m + 3.
A an implication C an antecedent
II If l < m, then 5l > 5m.
implikasi antejadian
Jika l > m, maka 5l > 5m.
B a conclusion D a consequence
III If l + 3 > m + 3, then l > m.

Jika l + 3 > m + 3, maka l > m.

kesimpulan akibat

Moderate / Sederhana A I only C I and III only
I sahaja I dan III sahaja
1. Which of the following is a true statement?
B III only D II and III only
Antara berikut, yang manakah satu pernyataan III sahaja II dan III sahaja

benar? 6. It is given that x is an acute angle if and only if 0˚
A (–4)2 = –16 or –2(–4) = –8 < x < 90˚.

(–4)2 = –16 atau –2(–4) = –8 Which of the following is a possible value of x?
B (p2)3 = p5 or p2 + p3 = p5
Diberi bahawa x ialah sudut tirus jika dan hanya
(p2)3 = p5 atau p2 + p3 = p5 jika 0˚ < x < 90˚.
C 7 > 4 and –5 > –8
Antara berikut, yang manakah mungkin nilai x?
7 > 4 dan –5 > –8
A 60˚ C 120˚
D 25 is a perfect square and 6 is a multiple of 4.
B 90˚ D 280˚
25 ialah kuasa dua sempurna dan 6 ialah

gandaan 4.

2. Which of the following is a statement? 7. If m < 0, then

Antara berikut, yang manakah ialah suatu Jika m < 0, maka C m2 < 0
A −m < 0 D 2m > 0
pernyataan? B −m > 0
A 6 < −4
C 2+3−1
B 3x = 9 D (3y)2

SMK BUKIT JALIL PANITIA MATEMATIK 88

8. “If m = −5, then m2 = 25”. 11.Premise 1/Premis 1 : ………………………………………

The antecedent in the above implication is Premise 2 : tan θ ≠ 1.
“Jika m = −5, maka m2 = 25”. Premis 2 : tan θ ≠ 1.

Antejadian bagi implikasi itu ialah Conclusion : θ ≠ 45˚.
Kesimpulan : θ ≠ 45˚.
A m = −5 C m2 = −25
D m2 = 2
B m=5

9. Premise 1 : All negative integers are less than 0.

Premis 1 : Semua integer negatif adalah kurang

daripada 0. Premise 1 for the above argument is

Premise 2 : −17 is a negative integer. Premis 1 bagi hujah di atas ialah
Premis 2 : −17 ialah integer negatif.
A If θ ≠ 45˚, then tan θ ≠ 1.
Conclusion/Kesimpulan : Jika θ ≠ 45˚, maka tan θ ≠ 1.
……………………………………………….
B If tan θ = 1, then θ = 45°.
The conclusion for the premises given above is Jika tan θ = 1, maka θ = 45°.

C If θ = 45˚, then tan θ = 1
Jika θ = 45˚, maka tan θ = 1

D If tan θ ≠ 1, then θ ≠ 45°.
Jika tan θ ≠ 1, maka θ ≠ 45°.

Kesimpulan bagi premis yang diberi di atas ialah 12. Premise 1: If x < 0, then x3 < 0.
A −17 is less than 0. Premis 1: Jika x < 0, maka x3 < 0.

−17 adalah kurang daripada 0.

B A negative integer is less than 0.

Suatu integer negatif adalah kurang daripada 0. Premise 2/Premis 2 : x < 0.
Conclusion/Kesimpulan : …………………………………
C Negative integer −17 is less than 0.
Integer negatif −17adalah kurang daripada 0.

D −17, a negative integer is less than 0.
−17, suatu integer negatif adalah kurang

daripada 0. What is the conclusion for the above argument?

Apakah kesimpulan bagi hujah di atas?

10. A x<0 C x3 < 0
Premise 1 : If p is positive, then > 0. D x3 > 0
Premis 1 : Jika p ialah positif, maka > 0. B x>0

Premise 2/Premis 2 : 13. Premise 1 : If x > 10, then x2 > 100.
..…………………………………….. Premis 1 : Jika x > 10, maka x2 > 100.

Conclusion : > 0. Premise 2/Premis 2 : 11 > 10.
Kesimpulan : > 0. Conclusion/Kesimpulan : …………………………………

Premise 2 for the above argument is What is the conclusion for the above argument?
Premis 2 bagi hujah di atas ialah
A p is positive. Apakah kesimpulan bagi hujah di atas?

p adalah positif. A 112 > 10 C 121 > 10
B 8 is positive. B 112 > 100
D 121 < 100
8 adalah positif.
C is positive.

adalah positif.
D 8 and are positive.

8 dan adalah positif.
P

SMK BUKIT JALIL PANITIA MATEMATIK 89

14. 17. Given the sequence of numbers, 6, 15, 30, 51, …
Premise 1 : If 3x < 21, then x < 7.
Premis 1 : Jika 3x < 21, maka x < 7. and
Diberi urutan nombor 6, 15, 30, 51, … dan

Premise 2/Premis 2 : …………………………………………… 6 = 3(1)2 + 3
Conclusion/Kesimpulan : 3x > 21. 15 = 3(2)2 + 3
Premise 2 for the above argument is 30 = 3(3)2 + 3
51 = 3(4)2 + 3

……………..

Premis 2 bagi hujah di atas ialah

A x<7 C x < 21 Find the 10th term of the sequence.

B x>7 D x > 21 Cari sebutan ke-10 bagi urutan itu.

A 283 C 303

15. B 293 D 313

The sum of the first p positive integers is . 18. Given the sequence of numbers, 1, 5, 9, 13, … and
Find the sum of the first 21 positive integers. Diberi urutan nombor 1, 5, 9, 13, … dan
Hasil tambah p integer positif yang pertama

ialah . 1=4×1–3
5=4×2–3
Cari hasil tambah 21 integer positif yang pertama. 9=4×3–3
13 = 4 × 4 – 3
A 210 C 242 ……………..

B 231 D 253

16. Diagram shows a right prism with Find the 9th term of the sequence.
trapezium QRWV as its uniform cross section.
Rajah menunjukkan sebuah prisma tegak dengan Cari sebutan ke-9 bagi urutan itu.
trapezium QRWV sebagai keratan rentas
seragamnya. A 30 C 36

B 33 D 39

19. It is given that (ab)c = abc, where a,b and c are
numbers.

Find the value of .

Diberi bahawa (ab)c = abc, dengan keadaan a, b dan

c ialah nombor.

Cari nilai .
A 10
Diagram/Rajah B 103
C

D

It is given that the volume of the right prism is 20. The sum of the interior angles of a polygon
(a + b)cd and a = 3, b = 6, c = 10 and d = 9. with n sides is (n – 2) × 180˚.
Make a conclusion by deduction for the volume of
the prism. Find the sum of the interior angles of a regular

Diberi bawawa isipadu prisma tegak itu ialah octagon.

(a + b)cd dan a = 3, b = 6, c = 10 dan d = 9. Hasil tambah sudut pedalaman sebuah poligon
dengan n sisi ialah (n – 2) × 180˚.
Buat satu kesimpulan secara deduksi bagi isi padu
Cari hasil tambah sudut pedalaman sebuah
prisma tegak itu.
A 40.5 cm3 C 405 cm3 oktagon sekata. C 1 440˚
D 1 800˚
B 45 cm3 D 810 cm3 A 720˚
B 1 080˚

SMK BUKIT JALIL PANITIA MATEMATIK 90

Difficult / Sukar C 10 is a perfect square or 2 is a multiple of 10.
1. It is given that the statement a is “0.07 = 7%” and 10 ialah kuasa dua sempurna atau 2 ialah
gandaan 10.
statement b is “5.3 × 10 = 53”.
D 10 is a perfect square and 2 is a multiple of 10.
Which of the following is true? 10 ialah kuasa dua sempurna dan 2 ialah
Diberi bahawa pernyataan a ialah “0.07 = gandaan 10.
7%” dan pernyataan b ialah “5.3 × 10 = 53”.
6. Which converse of the implication is true?
Antara berikut, yang manakah benar? Akas bagi implikasi manakah adalah benar?
A Implication: If x > 10, then x > 8.
A ~a and ~b C ~a and b Converse: If x > 8, then x > 10.
Implikasi: Jika x > 10, maka x > 8.
~a dan ~b ~a dan b Akas: Jika x > 8, maka x > 10.
B Implication: If y < 15, then y < 13.
B a and ~b D a and b Converse: If y < 13, then y < 15.
Implikasi: Jika y < 15, maka y < 13.
a dan ~b a dan b Akas: Jika y < 13, maka y < 15.
C Implication: If m > −11, then m > −13.
2. Which of the following statements is true? Converse: If m > −13, then m > -11.
Implikasi: Jika m > −11, maka m > −13.
Antara pernyataan berikut, yang manakah benar? Akas: Jika m > −13, maka m > −11.
A x > 3 or x2 > 9. D Implication: If n < −9, then n < −7.
Converse: If n < −7, then n < −9.
x > 3 atau x2 > 9. Implikasi: Jika n < −9, maka n < −7.
B If x2 = 25, then x = 5. Akas: Jika n < −7, maka n < −9.

Jika x2 = 25, maka x = 5. 7. Which of the following converses is not true?
C (52)3 = 55 or 5.6 × 10−1 = 0.56. Antara akas berikut, yang manakah tidak benar?
A If x < 0, then x2 > 0.
(52)3 = 55 atau 5.6 × 10−1 = 0.56. Jika x < 0, maka x2 > 0.
D 2∈{2, 4} and {4}∈{2, 4}. B
If x > y, then .
2∈{2, 4} dan {4}∈{2, 4}.
Jika x > y, maka .
3. Which of the following statements is not true? C If x > 3, then x > 6.

Antara pernyataan berikut, yang Jika x > 3, maka x > 6.
D If x < −3, then x < 0.
manakah tidak benar?
A 4 < 8 and −6 > −3. Jika x < −3, maka x < 0.

4 < 8 dan −6 > −3. 8. Which converse of the implication is not true?
B (p2)3 = p5 or p2 + p3 ≠ p5. Akas bagi implikasi manakah adalah tidak benar?
A If y = 4, then y3 = 64.
(p2)3 = p5 atau p2 + p3 ≠ p5. Jika y = 4, maka y3 = 64.
C (−4)2 = 16 or −2(−4) = −8. B If x = 5, then x + 3 = 8.
Jika x = 5, maka x + 3 = 8.
(−4)2 = 16 atau −2(−4) = −8 C If x and y are odd numbers, then x + y is an odd
number.
D 25 is a perfect square and 6 is a multiple of 3. Jika x dan y ialah nombor ganjil, maka x + y
ialah nombor ganjil.
25 ialah kuasa dua sempurna dan 6 ialah D If EFG is an equilateral triangle,
then EF = FG = EG.
gandaan 3. Jika EFG ialah sebuah segi tiga sama sisi,
maka EF = FG = EG.
4. Which of the following statements is true?

Antara pernyataan berikut, yang manakah benar?
A 7 > 3 and −3 < −7.

7 > 3 dan −3 < −7.
B (x2)−3 = x−6 and x2 + x3 = x5.

(x2)−3 = x−6 dan x2 + x3 = x5.
C (−5)2 = 25 or 2 × (−5) = −10.

(−5)2 = 25 atau 2 × (−5) = −10.

D 4 cm = 400 mm or 4 kg = 400 g.

4 cm = 400 mm atau 4 kg = 400 g.

5. Which of the following statements is true?
Antara pernyataan berikut, yang manakah benar?
A 9 is a perfect square or 3 is a multiple of 9.
9 ialah kuasa dua sempurna atau 3 ialah
gandaan 9.
B 9 is a perfect square and 3 is a multiple of 9.
9 ialah kuasa dua sempurna dan 3 ialah
gandaan 3.

SMK BUKIT JALIL PANITIA MATEMATIK 91

9. Premise 1 : If p > 5, then 2p > 10. 14. Given the sequence of numbers, −8, −7, −4, 1, … ,
Premis 1 : Jika p > 5, maka 2p > 10. what is the general conclusion?
Diberi urutan nombor −8, −7, −4, 1, … , apakah
Premise 2/Premis 2 : kesimpulan umumnya?
…………………………………………… A n2, n = 0, 1, 2, 3, …
B n2 – 8, n = 0, 1, 2, 3, …
Conclusion/Kesimpulan : 12 > 10. C 2n2 – 1, n = 0, 1, 2, 3, …
D 2n2 + 1, n = 1, 2, 3, …
Premise 2 for the above argument is
15. What is the general conclusion for the sequence of
Premis 2 bagi hujah di atas ialah numbers, 1, 5, 9, 13, … ?
Apakah kesimpulan umum untuk urutan nombor 1,
A 6>5 C 2(12) > 5 5, 9, 13, … ?
A 2n2 – 1, n = 1, 2, 3, …
B 12 > 5 D 2(12) > 10 B 2n2 + 1, n = 1, 2, 3, …
C 4n – 3, n = 1, 2, 3, …
10. D 4n + 3, n = 1, 2, 3, …
Premise 1 : If c > 2, then 3c > 7.
Premis 1 : Jika c > 2, maka 3c > 7.

Premise 2/Premis 2 : …………………………………1…6.…W…h…at is the general conclusion for the sequence of

numbers, 1, 7, 17, 31, … ?

Conclusion/Kesimpulan : 3 × 3 > 7. Apakah kesimpulan umum untuk urutan nombor 1,

7, 17, 31, … ?

Premise 2 for the above argument is A 2n2 – 1, n = 1, 2, 3, …
B 3n2 – 2, n = 1, 2, 3, …
Premis 2 bagi hujah di atas ialah C 2n – 3, n = 2, 3, 4, …
D −n + 2, n = 1, 2, 3, …
A 3>2 C 4>2

B 3×3>2 D 3×4>7

11. Make a generalization by induction based on the 17. What is the general conclusion for the sequence of
following pattern of numerical sequence 1, 15, 53, numbers, 5, 11, 17, 23, … ?
127, … Apakah kesimpulan umum untuk urutan nombor 5,
Buat satu kesimpulan umum secara aruhan 11, 17, 23, …?
berdasarkan pola urutan nombor 1, 15, 53, 127, … A 4n + 1, n = 1, 2, 3, …
A 2n2 −1, n = 1, 2, 3 C 2n2 − 1, n = 1, 2, 3, … B 3n + 2, n = 1, 2, 3, …
B 2n3 − 1, n = 1, 2, 3 D 2n3 − 1, n = 1, 2, 3, … C 5n + 5, n = 1, 2, 3, …
D 6n + 5, n = 0, 1, 2, 3, …
12. What is the general conclusion for the sequence of
numbers, 2, 5, 10, 17, … ? 18. What is the general conclusion for the sequence
Apakah kesimpulan umum untuk urutan nombor 2, of numbers, 0, 5, 12, 21, … ?
5, 10, 17, … ? Apakah kesimpulan umum untuk urutan nombor 0,
A 1 – n2, n = 0, 1, 2, … 5, 12, 21, …?
B 1 + n2, n = 1, 2, 3, … A 4n – 4, n = 1, 2, 3, …
C 1 + (n + 1)2, n = 1, 2, 3, … B n2 – 3, n = 3, 4, 5, …
D 1 + (n – 1)2, n = 1, 2, 3, … C 3n – 3, n = 1, 2, 3, …
D n2 – 4, n = 2, 3, 4, …
13. Given the sequence of numbers, −3, 3, 13, … ,
what is the general conclusion? 19. What is the general conclusion for the sequence of
Diberi urutan nombor −3, 3, 13, … , apakah numbers, −5, 1, 11, 25, … ?
kesimpulan umumnya? Apakah kesimpulan umum untuk urutan
A n2, n 1, 2, 3, … nombor −5, 1, 11, 25, … ?
B 2n2, n = 1, 2, 3, … A −n + 4, n = 1, 2, 3, …
C 2n2 – 5, n = 1, 2, 3, … B n2 – 4, n = 1, 2, 3, …
D 2n2 – 9, n = 1, 2, 3, … C 4n – 5, n = 0, 1, 2, 3, …
D 2n2 – 7, n = 1, 2, 3, …

SMK BUKIT JALIL PANITIA MATEMATIK 92

Chapter 5 : The Straight Line A –2 C 1
Bab 5 : Garis Lurus 2

Easy / Senang B – 1 D2
1. 2

The diagram shows a straight line PQ. 5. Find the gradient of the straight line 5x + 3y = 3.
Cari kecerunan bagi garis lurus 5x + 3y = 3.
Calculate the gradient of PQ.
A –5
Rajah di sebelah menunjukkan garis lurus PQ. 3

Hitung kecerunan PQ. B1
5

C3
5

D
5

A − 1 C 2 6. Determine the x-intercept of the straight line 3x +
2 3
2y + 7 = 0.
1
B 2 D2 Tentukan pintasan-x bagi garis lurus 3x + 2y + 7 =

0.

2. A – 7
3

B – 2
3

C3

D9

The diagram shows a straight line EFG. Given that 7.
the equation of EFG is 2x + 3y = 6, determine the
value of k. The diagram shows a straight line RS. Find the
Rajah di atas menunjukkan garis lurus EFG.
Diberi persamaan bagi EFG ialah 2x + 3y =
6, tentukan nilai k.
A2 C4
B3 D6

3. Find the gradient of the straight line 3x – 9y = 10. gradient of RS.
Cari kecerunan untuk garis lurus 3x – 9y = 10.
Rajah di atas menunjukkan garis lurus RS. Cari

A − 1 C3 kecerunan RS.
3 A –2

B 1 D9 B – 2
3 3

C 3
4
4.
D2

In the diagram,MN is a straight line. 8. State the y-intercept of the straight line 5x – 2y + 10
What is the gradient of MN?
Dalam rajah di atas, MN ialah garis lurus. = 0.
Apakah kecerunan bagi MN? Nyatakan pintasan-y bagi garis lurus 5x – 2y + 10

= 0.
A –5
B –2

C2

D5

SMK BUKIT JALIL PANITIA MATEMATIK 93

9. Diagram shows a straight line PQ on a Cartesian 12. Diagram below shows a straight line PQ on a

plane. Cartesian plane.

Rajah menunjukkan satu garis lurus PQ pada suatu Rajah dibawah menunjukkan garis lurus PQ pada

satah Cartesan. satah Cartesan.

Find the gradient of PQ. The gradient of PQ is
Cari kecerunan PQ.
Kecerunan bagi PQ ialah

A –2 C1

B –1 D2

13. .
Find the x-intercept of the straight line
10. Find the x-intercept of the straight line 4y – 5x = – .
Cari pintasan-x bagi garis lurus
20. A2
B3
Cari pintasan-x bagi garis lurus 4y – 5x = –20. C5
D6
A –5 C4

B –4 D5

11. Diagram shows a straight line PQ on a Cartesian 14. Diagram below shows two straight
plane. lines, TU and UV,on a Cartesian plane.
Rajah menunjukkan garis lurus PQ pada satah Rajah di bawah menunjukkan dua garis lurus, TU
Cartesan. dan UV, pada satah Cartesan.

What is the gradient of PQ? Given TU = UV, find the gradient of the straight
line UV.
Apakah kecerunan bagi PQ? Diberi TU = UV, cari kecerunan bagi garis lurus
UV.

A −9 A − 3
4 5

B −3 B − 5
2 3

C 3 C 3
2 5

D 9 D 5
4 3

SMK BUKIT JALIL PANITIA MATEMATIK 94

15. In Diagram below, the gradient of the straight 18. The y-intercept of the straight line 3x + 4y = –7 is
Pintasan-y bagi garis lurus 3x + 4y = –7 ialah
line PQ is – .
Dalam Rajah di bawah, kecerunan bagi garis lurus A4

PQ ialah – . B – 3
4

C – 7
4

D –7

19. In Diagram below, POQ is a straight line and O is
the origin.
Dalam Rajah di bawah, POQ ialah garis lurus dan
O ialah asalan.

Diagram /Rajah

Find the y-intercept of the straight line PQ. Diagram /Rajah
Cari pintasan-y bagi garis lurus PQ.
A3 Find the gradient of the straight line POQ.
B6
C 12 Cari kecerunan bagi garis lurus POQ.
D 24
A − 4
16. In Diagram below, PQ is a straight line with a 3

gradient of . 3
Dalam Rajah di bawah, PQ ialah garis lurus 4

dengan kecerunan .

B −

C 4
3

D 3
4

Diagram /Rajah 20. In Diagram below, the straight line GH is parallel
to the straight line PR.
Dalam Rajah di bawah, garis lurus GH adalah
selari dengan garis lurus PR.

Find the y-intercept of the straight line PQ.

Cari pintasan-y bagi garis lurus PQ.

A 3 C3
4

B 4 D4
3

17. Find the x-intercept of the straight line 8y = –4x + Diagram / Rajah

12.

Cari pintasan-x bagi garis lurus 8y = –4x + 12. Find the value of k.
Cari nilai k.
A –3 C3 A2
B3
B – 3 D4 C4
2 D6

SMK BUKIT JALIL PANITIA MATEMATIK 95

21. Diagram shows a straight line PQ. 23. Diagram shows a straight line ST.
Rajah menunjukkan satu garis lurus PQ. Rajah menunjukkan satu garis lurus ST.

Find the vertical distance and horizontal distances Diagram/Rajah
between points P and Q on the straight line.
Cari jarak mencancang dan jarak mengufuk di Find the gradient of the straight line ST.
antara titik P dengan titik Q pada garis lurus itu.
A vertical distance = 5 Cari kecerunan garis lurus ST.

jarak mencancang = 5 A 1 C2
horizontal distance = 2 2
jarak mengufuk = 2
B vertical distance = 2 B 3 D3
jarak mencancang = 2 5
horizontal distance = 5
jarak mengufuk = 5 24. In Diagram, PQ is a straight line.
C vertical distance = 4 Dalam Rajah, PQ ialah satu garis lurus.
jarak mencancang = 4
horizontal distance = 2
jarak mengufuk = 2
D vertical distance = 2
jarak mencancang = 2
horizontal distance = 4
jarak mengufuk = 4

22. Diagram shows a straight line MN.
Rajah menunjukkan satu garis lurus MN.

Diagram/Rajah

Find the ratio of the vertical distance to the The gradient of PQ is

horizontal distance between point M and point N. Kecerunan PQ ialah

Cari nisbah jarak mencancang kepada jarak A 1 C2
3 D3
mengufuk di antara titik M dengan titik N.
1
A 3 C 4 B 2
5 3

B 3 D 5
4 3

SMK BUKIT JALIL PANITIA MATEMATIK 96

25. In Diagram, PQRS is a quadrilateral. 3.
Dalam Rajah, PQRS ialah sebuah sisi empat.

The diagram shows a straight line EF with a

gradient of . Find the equation of EF.
Rajah di atas menunjukkan garis lurus EF dengan

kecerunan . Cari persamaan bagi EF.

A C 3y = x + 21
y= x+3

B y=x+7 D 3y = 3x + 1

Diagram/Rajah 4.

Which of the straight lines has a negative gradient?

Garis lurus manakah yang mempunyai kecerunan

negatif?

A PQ C RS

B QR D PS

Moderate / Sederhana In the diagram, PQ is a straight line with a gradient
1.
of .
Find the y-intercept of PQ.
Dalam rajah di atas, PQ ialah garis lurus dengan

kecerunan .

Cari pintasan-y bagi PQ.

A –12 C3

The diagram shows a straight line RS. B –3 D 12

Given that the gradient of RS is , find the 5. The coordinates of point M are (4, 7) and the
coordinates of point S. gradient of the straight line MN is 3. Which of the
Rajah di atas menunjukkan garis lurus RS. following are the coordinates of point N?

Diberi kecerunan RS ialah , cari koordinat bagi Koordinat titik M ialah (4, 7) dan kecerunan garis
lurus MN ialah 3. Antara berikut, yang manakah

titik S. ialah koordinat bagi titik N?

A (–3, 0) C (0, –3) A (0, 3)
B (–1, 0) D (0, –1) B (0, –5)
C (0, –1)

2. Given the gradient of the straight line that joins two D (0, 4)

points (3, 2) and (h, 1) is –1. Find the value of h. 6. Given that the two straight lines y = x – 4 and x +

Diberi kecerunan untuk satu garis lurus yang

menyambungkan titik (3, 2) dan (h, 1) ialah – 2y = 10 intersect at point (p, 2), find the value of p.

1. Cari nilai h. Diberi dua garis lurus y = x – 4 dan x + 2y =

A2 C4 10 bersilang pada titik (p, 2). Cari nilai p.
B3 D5 A2 C6
B 4 D 10

SMK BUKIT JALIL PANITIA MATEMATIK 97

7. In Diagram below, KL is a straight line. 10. Find the gradient of the straight line which has a y-
Dalam Rajah di bawah, KL ialah garis lurus. intercept of –5 and passes through point P(–3, 4).

Cari kecerunan suatu garis lurus yang mempunyai
pintasan-y –5 dan melalui titik P(–3, 4).
A −3

B − 4
3

Diagram /Rajah C 4
3

D3

Find the equation of KL.

Cari persamaan bagi KL. 11.
In Diagram, GH is a straight line with gradient .
A y=x+5 C y = 2x + 5 Dalam Rajah, GH ialah garis lurus yang
B y=x+3 D y = 2x – 5

8. In Diagram below, the equation of the straight mempunyai kecerunan .
line PQ is 2y + x = 6. The two straight
lines, PQ and RS intersect at point T on the y-axis.
Dalam Rajah di bawah, persamaan garis lurus PQ
ialah 2y + x = 6. Dua garis lurus, PQ dan RS
bersilang pada titik T di atas paksi-y.

Diagram /Rajah Find the x-intercept of the straight line.
Cari pintasan-x bagi garis lurus itu.
If the gradient of the straight line RTS is , find A −9
the equation of RTS. B −4
C4
Jika kecerunan garis lurus RTS ialah , cari D6

persamaan bagi RTS. 12. In Diagram below, the straight lines PQ and QR are
drawn on a Cartesian plane.
A y=x+3 C y= 1 x+3 Dalam Rajah di bawah, garis lurus PQ dan QR
2 dilukis pada satah Cartesan.

B y=x+6 D y=– 1 x+5
2

9. State the y-intercept of the straight line:
Nyatakan pintasan-y bagi garis lurus:

A2 C7 Given the gradient of QR is 0.5 , find the equation
B3 D8
of the straight line PQ.
SMK BUKIT JALIL PANITIA MATEMATIK
Diberi kecerunan bagi QR ialah 0.5, cari

persamaan garis lurus PQ.

A y = –2x + 8 C y=x+8

B y = –x +8 D y = 2x + 8

98

13. Given the straight line y = kx + 8 is parallel to the A −27 C3
straight line 9x – 3y = 3. Find the value of k. B −3 D 27

Diberi garis lurus y = kx + 8 adalah selari dengan 18. Diagram below shows a straight line PQ with
garis lurus 9x – 3y = 3. Cari nilai k. equation 2y − kx + 18 = 0, where k is a constant.

A1 C6 Rajah di bawah menunjukkan garis lurus PQ yang
B3 D9 mempunyai persamaan 2y − kx + 18 = 0, dengan

14. The coordinates of point M are (2, –3) and the keadaan kialah pemalar.
gradient of the straight line MN is –2.

The coordinates of point N could be
Koordinat bagi titik M ialah (2, –3) dan kecerunan
garis lurus MN ialah –2.

Koordinat bagi titik N yang mungkin ialah
A (–2, –5)
B (–2, 5)
C (2, –5)
D (2, 5)

15. Which graph represents y = –2x – 4? Diagram / Rajah
Graf manakah yang mewakili y = –2x – 4?

It is given that OP : OQ = 2 : 3.

Find the value of k.

Diberi bahawa OP : OQ = 2 : 3.

Cari nilai k. C
A −3

B D3

19. In Diagram below, PQ is a straight line.
Dalam Rajah di bawah, PQ ialah garis lurus.

16. Diagram / Rajah

The gradient of a straight line is . The straight
line passes through the points (–2, 4) and (k, –2).

Find the value of k.

Kecerunan bagi satu garis lurus ialah . Garis Find the x-intercept of the straight line PQ.
lurus itu melalui titik-titik (–2, 4) dan (k, –2).
Cari pintasan-x bagi garis lurus PQ.

Cari nilai k. A −6 C −2

A –8 C7 B −3 D −1
B –6 D 11
20. Calculate the gradient of the straight line which
17. passes through point M(3, 5) and point N(7, −9).
A straight line has a gradient − and passes
through the point (0, −9). Hitung kecerunan garis lurus yang melalui titik
M(3, 5) dan titik N(7, −9).
The x-intercept of the straight line is
A −7 C 2
2 7

Satu garis lurus mempunyai kecerunan − dan B − 2 D 7
melalui titik (0, −9). 7 2

Pintasan-x bagi garis lurus itu ialah

SMK BUKIT JALIL PANITIA MATEMATIK 99

21. Calculate the gradient of the straight line which 23. Diagram shows four straight lines, l1, l2, l3 and l4.
passes through point P(−2, −6) and point Q(1, 3). Rajah menunjukkan empat garis lurus, l1, l2, l3 dan
l4.
Hitung kecerunan garis lurus yang melalui titik
P(−2, −6) dan titik Q(1, 3).

A −3 C 1
3

B − 1 D3
3

22. Diagram shows four straight
lines OP, OQ, OR and OS.
Rajah menunjukkan empat garis lurus OP, OQ, OR
dan OS.

Diagram/Rajah

The gradient of the straight line l4 is

Kecerunan garis lurus l4 ialah

A −1 C 1
3 3

B −3 D3

24. Find the equation of a straight line which passes
through point P(2, −3) and has a gradient of −4.

Cari persamaan garis lurus yang melalui titik P(2,

−3) dan mempunyai kecerunan −4.

Diagram/Rajah A y = −4x − 11 C y = −4x + 5

Which of the following statements is not true? B y = −4x − 10 D y = −4x + 14
Antara pernyataan berikut, yang
manakah tidak benar? 25. Find the equation of the straight line which passes
A OR has a value of gradient which is greater through point W(−2, 4) and is parallel to the

than OQ. straight line y = − x + 3.
OR mempunyai nilai kecerunan yang lebih Cari persamaan garis lurus yang melalui titik
besar daripada OQ.
B OP has the largest value of gradient and the W(−2, 4) dan selari dengan garis lurus y = − x+
steepest slope .
OP mempunyai nilai kecerunan yang terbesar 3.
dan cerun yang tercuram.
C OS has the smallest value of gradient and the A y = − 1 x − 7 C y = − 1 x − 1
gentlest slope. 4 2 4
OS mempunyai nilai kecerunan yang terkecil
dan cerun yang terlandai. B y = − 1 x + 7 D y = − 1 x + 1
D 4 2 4
OQ has a gradient of which is lower than OP.

OQ mempunyai kecerunan sebanyak iaitu
lebih rendah daripada OP.

SMK BUKIT JALIL PANITIA MATEMATIK 100