Praktis Hebat 2021 - Additional Mathematics F4

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CVR_PraktisHebat_2021_AddMaths_F4&5.indd 1-2 4/8/21 4:40 PM

CONTENTS







Functions 1
PRACTICE
1 Fungsi
HOTS Practices

Quadratic Functions 8
PRACTICE
2 Fungsi Kuadratik
HOTS Practices


Systems of Equations 18
PRACTICE
3 Sistem Persamaan
HOTS Practices

Indices, Surds and Logarithms 21
PRACTICE
4 Indeks, Surd dan Logaritma
HOTS Practices

Progressions 28
PRACTICE
5 Janjang
HOTS Practices

Linear Law 38
PRACTICE
6 Hukum Linear
HOTS Practices

Coordinate Geometry 50
PRACTICE
7 Geometri Koordinat
HOTS Practices

Vectors 61
PRACTICE
8 Vektor
HOTS Practices

Solution of Triangles 72
PRACTICE
9 Penyelesaian Segi Tiga
HOTS Practices

Index Numbers 79
PRACTICE
10 Nombor Indeks
HOTS Practices


Assessment Paper –––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– 92

Answers ––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––––– A1 – A16










CONTENT HEBAT ADD MATH F4 1P.indd 1 09/04/2021 5:25 PM

Additional Mathematics Form 4 Practice 1 Functions
PRACTICE Functions
1 Fungsi





FORMULAE

–1
1. fg(x) = f[g(x)] 2. If f(x) = y then f (y) = x
Jika f(x) = y maka f (y) = x
–1
PAPER 1

Berdasarkan ujian yang dinyatakan di (a),
1.1 Functions TEXTBOOK tentukan sama ada graf ini adalah fungsi
Fungsi pg. 2 – 11
dan berikan satu sebab.
[3 marks / markah]
1. The diagram below shows the arrow diagram
that maps an element in set P to another 3.
element in set Q. PL 2 f
Rajah di bawah menunjukkan gambar rajah
anak panah yang memetakan satu unsur dalam –1 –1
set P kepada unsur lain dalam set Q. 0 0
P Q 1 1
2 8
1 1
3 27 Based on the diagram above, write the
relationship for function f using function
4 64
notation. PL 3
Berdasarkan rajah di atas, tulis hubungan bagi
Is the relationship above a function? Give one fungsi f menggunakan tatanda fungsi.
reason. [2 marks / markah]
Adakah hubungan di atas ialah suatu fungsi?
Berikan satu sebab. 4. Determine the domain, codomain and range for
[2 marks / markah]
each of the following function g. PL 3
Tentukan domain, kodomain dan julat bagi
2. The diagram below shows a graph. PL 3 setiap fungsi g yang berikut.
Rajah di bawah menunjukkan suatu graf.
(a) g
y x y
1
a
2
b
5
x c
0 7
d
8
(a) State a test can be used to determine
whether this graph is a function. (b) f(x)
Nyatakan satu ujian yang boleh 5
digunakan untuk menentukan sama ada 4
graf ini adalah fungsi. 3
(b) Based on the test stated in (a), determine 2 1
whether this graph is a function and give x
one reason. –1 0 1 2 [4 marks / markah]


1 © Penerbitan Pelangi Sdn. Bhd.






01 HEBAT ADD MATH F4 1P.indd 1 09/04/2021 5:28 PM

Additional Mathematics Form 4 Practice 1 Functions
5. The function f is defined by f : x → 2x – 9. 11. Determine the corresponding range of f for the
2
Find PL 3 domain given. PL 3
Fungsi f ditakrifkan oleh f : x → 2x – 9. Cari Tentukan julat nilai f yang sepadan untuk
2
(a) f(3) domain yang diberikan.
(b) f(–1) (a) f : x → |x – 1|, –1 < x < 7
(c) the value of x when f(x) = 3x (b) f : x → |3x – 2|, –2 < x < 5
nilai x apabila f(x) = 3x [2 marks / markah]
[3 marks / markah]
12. Sketch the graph f based on the domain given.
6. Find image for the object given. PL 3 Lakarkan graf f berdasarkan domain yang
Cari imej bagi objek yang diberikan. diberikan. PL 3
(a) f(x) = 5 – 6x, x = 2 (a) f : x → |2x – 3|, –3 < x < 3
x (b) f : x → |5x – 5|, –2 < x < 3
(b) f(x) = 4 + 7, x = –8
[2 marks / markah] [4 marks / markah]
13. Find the values of x for each of the following
7. Find object for the image given. PL 3
Cari objek bagi imej yang diberikan. based on the value of f(x) given. PL 4
Cari nilai-nilai x bagi setiap yang berikut
(a) f(x) = 4x – 1 [Image/Imej = 11] berdasarkan nilai f(x) yang diberikan.
(b) f(x) = x – 6 [Image/Imej = x] (a) f : x → |6x + 1|, f(x) = 7
2
[2 marks / markah]
(b) f : x → |5x – 3|, f(x) = 2
8. Given the function f(x) = 3x – 8. Find PL 3 [2 marks / markah]
Diberi fungsi f(x) = 3x – 8. Cari 14. Find the values of x for each of the following
(a) f(–1) when mapping onto itself. PL 4
(b) the value of x when its image is 4x. Cari nilai-nilai x bagi setiap yang berikut
nilai x apabila imejnya ialah 4x. apabila memetakan kepada diri sendiri.
[2 marks / markah] (a) f : x → |4x – 3|
(b) f : x → |5x + 4|
9. Given the function f(x) = px + 3. PL 3
Diberi fungsi f(x) = px + 3. [2 marks / markah]
(a) Find the value of p if f(–2) = – 3. 15. A ball is thrown to the air. The path passed
Cari nilai p apabila f(–2) = – 3. through by the ball is represented by the
(b) Using the value of p in (a), find the value function h(t)= 64t – 8t , such that h is the
2
of x if f(x) = 0. height, in metres and t is the time, in seconds.
Menggunakan nilai p di (a), cari nilai x Sebiji bola dibaling ke udara. Laluan yang
apabila f(x) = 0. dilalui oleh bola itu diwakili oleh fungsi
2
[3 marks / markah] h(t)= 64t – 8t , dengan keadaan h ialah
ketinggian, dalam meter dan t ialah masa,
2
10. Given the function f : x → 4x + 10x. Find PL 4 dalam saat.
Diberi fungsi f : x → 4x + 10x. Cari (a) State the height reached by the ball when
2
(a) f (–1) Nyatakan ketinggian yang dicapai oleh
(b) the values of x which map onto itself by bola itu apabila PL 5
f(x). (i) t = 3
nilai-nilai x yang memetakan kepada diri (ii) t = 6
sendiri oleh f(x). (b) When the ball will reach the ground?
[2 marks / markah]
Bilakah bola itu akan mencecah
permukaan tanah?
[4 marks / markah]




© Penerbitan Pelangi Sdn. Bhd. 2






01 HEBAT ADD MATH F4 1P.indd 2 09/04/2021 5:28 PM

Additional Mathematics Form 4 Practice 1 Functions
(a) f(x) = 4x – 3, fg(x) = 20x – 3
1.2 Composite Functions TEXTBOOK (b) f(x) = 7x + 1, fg(x) = 7x + 1
2
Fungsi Gubahan pg. 12 –19
[4 marks / markah]
16. Function f and function g are defined by f : x 22. Find function g based on the function f and
→ 2x – 3 and g : x → 4x – 1 respectively. Find composite function gf given. PL 3
the expression for PL 3 Cari fungsi g berdasarkan fungsi f and fungsi
Fungsi f dan fungsi g adalah masing-masing gubahan gf yang diberikan.
ditakrifkan oleh f : x → 2x – 3 dan g : x → 4x (a) f(x) = 2x, gf(x) = 18x – 2
– 1. Cari ungkapan bagi (b) f(x) = 4x, gf(x) = 16x – 1
2
(a) fg [4 marks / markah]
(b) gf
[4 marks / markah] 23. Given f(x) = 5x – 3 and fg(x) = 17 – 5x, find
PL 4
17. Given that f : x → 4x + 1 and g : x → 2x – 7. Diberi f(x) = 5x – 3 dan fg(x) = 17 – 5x, cari
Find the expression for PL 3 (a) g(x)
Diberi f : x → 4x + 1 dan g : x → 2x – 7. Cari (b) g(–3)
ungkapan bagi (c) the value of x when f(x) = g(x)
(a) f 2 nilai x apabila f(x) = g(x).
(b) g 2 [4 marks / markah]
[4 marks / markah]
24. Given that g(x) = 7x – 2 and fg(x) = 7 x. Find
18. Given that f : x → px + q and f : x → 25x – 6 2
2
such that p and q are constants. Find the value Diberi bahawa g(x) = 7x – 2 and fg(x) = 7 x.
of both constants. PL 3 Cari PL 4 2
Diberi f : x → px + q dan f : x → 25x – 6 (a) f(x)
2
dengan keadaan p dan q ialah pemalar. Cari (b) the value of x when f(x) = fg(x).
nilai bagi kedua-dua pemalar tersebut. nilai x apabila f(x) = fg(x).
[3 marks / markah] [3 marks / markah]

19. Two functions g and h are defined by g : x → 25. Given that h(x) = mx + n, m . 0 and h (x) =
2
3x + 5 and h : x → 5x – 2. Find the value of x 25x + 12. Find the value of m and n. PL 4
when PL 4 Diberi bahawa h(x) = mx + n, m . 0 dan h (x)
2
Dua fungsi g dan h ditakrifkan oleh g : x → 3x = 25x + 12. Cari nilai m dan n.
+ 5 dan h : x → 5x – 2. Cari nilai x apabila [4 marks / markah]
(a) gh(x) = g(x)
(b) g (x) = h (x) 26. Given that f(x) = x + 8, g(x) = 8 – 3x and gf(x)
2
2
2
[4 marks / markah] = (p – 1) x – q . Find PL 4
Diberi bahawa f(x) = x + 8, g(x) = 8 – 3x dan
2
20. Given g(x) = 2 – x and h(x) = 5x – 1. Find gf(x) = (p – 1) x – q . Cari
3
the value of x if gh(x) = g(x). PL 4 (a) the value of p.

nilai p.
Diberi g(x) = 2 – 3 x dan h(x) = 5x – 1. Cari (b) the possible values of q.
nilai x apabila gh(x) = g(x). nilai-nilai q yang mungkin.
[3 marks / markah] [4 marks / markah]
21. Find function g based on the function f and 27. Given the function h(x) = px + q and h (x) =
2
composite function fg given. PL 3 9x – 4. Find the possible values of p and q.
Cari fungsi g berdasarkan fungsi f dan fungsi Diberi fungsi h(x) = px + q dan h (x) = 9x – 4.
2
gubahan fg yang diberikan. Cari nilai-nilai p dan q yang mungkin. PL 3
[3 marks / markah]


3 © Penerbitan Pelangi Sdn. Bhd.






01 HEBAT ADD MATH F4 1P.indd 3 09/04/2021 5:28 PM

Additional Mathematics Form 4 Practice 1 Functions
28. Function f is defined by f : x → 2x – 3. Find (a) f
the function g if PL 3 x y
Fungsi f ditakrifkan oleh f : x → 2x – 3. Cari 1 –5
fungsi g jika 2 –3
(a) fg : x → 5x – 1 3 –1
2
(b) gf : x → 5x – 1 4 1
2
[4 marks / markah] 5 3
7 (b) f : x → 9 – x 2
29. Given the function h(x) = x , x ≠ 0 and gh(x) [4 marks / markah]
= 14 + x . Find PL 4
x
Diberi fungsi h(x) = 7 , x ≠ 0 dan gh(x) = 32. Verify the truth that each of the following
14 + x . Cari x function f(x) has the inverse function g(x).
x
PL 3
(a) g(x) Sahkan kebenaran bahawa setiap fungsi f(x)
(b) the possible values of x when hg(x) = yang berikut mempunyai fungsi songsang g(x).
gh(x) – 14 x + 4
3
nilai-nilai yang mungkin bagi x apabila (a) f(x) = 2x – 4, g(x) = 2
x
hg(x) = gh(x) – 14 (b) f(x) = + 2, g(x) = 3x – 6
3
3
[4 marks / markah] [4 marks / markah]
33. Find the inverse function for each of the
1.3 Inverse Functions TEXTBOOK following function. PL 3
Cari fungsi songsang bagi setiap fungsi yang
Fungsi Songsang pg. 20 –29
berikut.
30. In the arrow diagram below, the function f (a) f(x) = 7x – 2
maps x onto y. PL 3 (a) f(x) = 3x + 11
Dalam gambar rajah anak panah di bawah, [4 marks / markah]
fungsi f memetakan x kepada y.
34. Find the inverse function for each function
f
x y given. PL 3
Cari fungsi songsang bagi setiap fungsi yang
1 2 diberikan.
x
2 5 (a) f(x) = + 1
5
4
3 10 (b) f(x) = x + 2 , x ≠ – 2
[4 marks / markah]
Determine the value of 35. Find the inverse function for the function
Tentukan nilai bagi x – 1
(a) f (2) f(x) = x + 1 , x ≠ –1. Hence, find the value of
–1
–1
(b) f (5) f (–4). PL 3
–1
(c) f (10) Cari fungsi songsang bagi fungsi f(x) = x – 1 ,
–1
x + 1
[ 3 marks / markah] x ≠ –1. Seterusnya, cari nilai bagi f (–4).
–1
31. Determine whether each of the following [3 marks / markah]
function f has the inverse function. Give your 36. Find the function f(x) for each of the following
reason. PL 2
Tentukan sama ada setiap fungsi f yang berikut inverse function. PL 3
Cari fungsi f(x) bagi setiap fungsi songsang
mempunyai fungsi songsangan. Berikan sebab yang berikut.
anda. x – 1
(a) f (x) =
–1
2

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01 HEBAT ADD MATH F4 1P.indd 4 09/04/2021 5:28 PM

Additional Mathematics Form 4 Practice 1 Functions

(b) f (x) = 2x + 5 39. Given that f : x → x – 8 , x ≠ 4. Find PL 3
–1
–1
3 x – 4
[4 marks / markah] x – 8
Diberi bahawa f : x → x – 4 , x ≠ 4. Cari
–1
37. Given the inverse function f is defined by (a) f(3)
–1
f : x → 2 – x . Find PL 3 (b) the possible values of m such that
–1
5
m
–1
Diberi fungsi songsang f ditakrifkan oleh f (m) = 24 .
–1
f : x → 2 – x . Cari nilai-nilai yang mungkin bagi m dengan
–1
5
(a) f(x) keadaan f (m) = m .
–1
(b) the value of x such that f(x) = –2 24 [4 marks / markah]
nilai x dengan keadaan f(x) = –2
[4 marks / markah] 40. Function f and g are defined by f : x → 3x – 5
and g : x → 7 , x ≠ 4 . Solve the
38. Solve each of the following such that 4 – 3x 3
–1
–1
–1
h(x) = h (x). PL 3 equation f (x) = x[g (x)]. PL 4
Selesaikan setiap yang berikut dengan keadaan Fungsi f dan g ditakrifkan oleh f : x → 3x – 5
h(x) = h (x). dan g : x → 7 , x ≠ 4 . Selesaikan
–1
(a) h : x → 3x – 6 4 – 3x 3
–1
–1
(b) h : x → 7x + 1 persamaan f (x) = x[g (x)].
[4 marks / markah] [5 marks / markah]
PAPER 2
1. The function f is defined by f : x → |3x - 4|. PL3 Subtopic 1.1
Fungsi f ditakrifkan oleh f : x → |3x - 4|.
TEXTBOOK
pg. 2 – 19
(a) Sketch the graph of f for the domain –2 < x < 3.
Lakarkan graf bagi f untuk domain –2 < x < 3. [3 marks / markah]
(b) State the corresponding range of f for the domain.
Nyatakan julat f yang sepadan untuk domain tersebut. [2 marks / markah]
(c) Solve the equation f(x) = 11.
Selesaikan persamaan f (x) = 11. [2 marks / markah]
2. The function g is defined by g : x → 5x + 4 , x ≠ 0. Find PL3 Subtopic 1.1

x
TEXTBOOK 4

pg. 2 – 11 Fungsi g ditakrifkan oleh g : x → 5x + x , x ≠ 0. Cari
(a) g(–4) [2 marks / markah]
(b) the image for –2 under g.
imej bagi –2 di bawah g. [2 marks / markah]
(c) the possible values of x when its image is 12.
nilai-nilai x yang mungkin apabila imejnya ialah 12. [2 marks / markah]

3. The function h is defined by h : x → px – q. Given that h(–3) = –13 and h(2) = –3. Find PL3 Subtopic 1.1
Fungsi h ditakrifkan oleh h : x → px – q. Diberi bahawa h(–3) = –13 dan h(2) = –3. Cari
TEXTBOOK
pg. 2 – 11
(a) the value of p and q.
nilai p dan q. [4 marks / markah]
(b) the image for 5 under h.
imej bagi 5 di bawah h. [2 marks / markah]
(c) the value of x which maps onto itself.
nilai x yang memetakan kepada diri sendiri. [2 marks / markah]


5 © Penerbitan Pelangi Sdn. Bhd.






01 HEBAT ADD MATH F4 1P.indd 5 09/04/2021 5:28 PM

Additional Mathematics Form 4 Practice 1 Functions
2
4. Two functions are defined by f : x → 4x and g : x → 3x – x + 20. PL4 Subtopic 1.2
2
TEXTBOOK Dua fungsi ditakrifkan oleh f : x → 4x dan g : x → 3x – x + 20.
pg. 12 – 19
(a) Find the composite function fg(x) and gf(x). Is fg(x) equal to gf(x)?
Cari fungsi gubahan fg(x) dan gf(x). Adakah fg(x) sama dengan gf(x)? [4 marks / markah]
(b) Find the possible values of x to satisfy the equation f (x) = g(x).
2
Cari nilai-nilai x yang mungkin untuk memuaskan persamaan f (x) = g(x). [3 marks / markah]
2
1
5. The function g and h are defined by g: x → x – 1 , x ≠ 1 and h : x → 2x + 3 respectively. PL4 Subtopic 1.2

TEXTBOOK Fungsi g dan h masing-masing ditakrifkan oleh g : x → 1 , x ≠ 1 dan h : x → 2x + 3.

pg. 12 – 19 x – 1
(a) Find the expression for gh(x), hg(x) g (x) and h (x).
2
2
Cari ungkapan bagi gh(x), hg(x) g (x) dan h (x). [8 marks / markah]
2
2
(b) Find the value of x when gh(x) = hg(x) – 31 .
8
31
Cari nilai x apabila gh(x) = hg(x) – 8 . [2 marks / markah]
6. Given that the inverse function g (x) = x – 4 . PL4 Subtopic 1.3
–1
TEXTBOOK Diberi fungsi songsang g (x) = x – 4 . 11
–1
pg. 20 – 29 11
(a) Find the function g(x).
Cari fungsi g(x). [2 marks / markah]
(b) Solve the following equations.
Selesaikan persamaan yang berikut.
(i) g(x) = g (x) (ii) g(x) = gg (x) [4 marks / markah]
–1
–1
kx – 9 mx + n
–1
7. Given that f : x → x + 4 , x ≠ –4 and f : x → 5 – x , x ≠ 5. PL4 Subtopic 1.3
TEXTBOOK
pg. 20 – 29 Diberi bahawa f : x → kx – 9 , x ≠ –4 dan f : x → mx + n , x ≠ 5.
–1
x + 4 5 – x
(a) Find the values of k, m and n.
Cari nilai k, m dan n. [3 marks / markah]
(b) Find the value of x when f(x) + 11 = f (x).
–1
2
Cari nilai x apabila f(x) + 11 = f (x). [2 marks / markah]
–1
2
(c) Determine whether ff (x) = x. Hence, determine whether each equation given is true or false. Give
–1
your reason.
Tentukan sama ada ff (x) = x. Seterusnya, tentukan sama ada setiap persamaan yang diberikan
–1
adalah benar atau palsu. Berikan alasan anda.
(i) ff (–2) = –2 (ii) ff (3) = –3 [5 marks / markah]
–1
–1
8. Given that f : x → 3x – 7 and g : x → 10 – 9x. PL3 Subtopic 1.1 & 1.2
TEXTBOOK Diberi bahawa f : x → 3x – 7 dan g : x → 10 – 9x.
pg. 2 – 19
(a) Find / Cari
(i) f (–3) [2 marks / markah]
(ii) the value of m if f(m – 4) = 1 f(–3)
4
nilai m jika f(m – 4) = 1 f(–3) [2 marks / markah]
4
(iii) gf(x) [3 marks / markah]
(b) Hence, sketch the graph of y = |gf(x)| for –2 < x < 4. State the range of y.
Seterusnya, lakar graf y = |gf(x)| untuk –2 < x < 4. Nyatakan julat y. [3 marks / markah]




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01 HEBAT ADD MATH F4 1P.indd 6 09/04/2021 5:28 PM

Additional Mathematics Form 4 Practice 1 Functions
9. Given that f(x) = 7x – 1 and gf(x) = 14x + 1. Find PL3 Subtopic 1.2 & 1.3
Diberi bahawa f(x) = 7x – 1 dan gf(x) = 14x + 1. Cari
TEXTBOOK
pg. 12 – 19 (a) gf(x) [3 marks / markah]
(b) g f(x) [4 marks / markah]
–1
(c) the value of x when fg(x) = g f(x).
–1
nilai x apabila fg(x) = g f(x). [3 marks / markah]
–1
2
10. Function f is defined by f : x → x – 7 for the domain 0 < x < 6. PL4 Subtopic 1.3
2
TEXTBOOK Fungsi f ditakrifkan oleh f : x → x – 7 untuk domain 0 < x < 6.
pg. 20 – 29
(a) On the same plane, sketch the graph of f and f .
–1
Pada satah yang sama, lakar graf bagi f dan f . [4 marks / markah]
–1
(b) Hence, state the domain and range of f .
–1
Seterusnya, nyatakan domain dan julat bagi f . [2 marks / markah]
–1
x
(
f
(c) Find the possible values of x such that ) + 2 = f (x).
–1
f
(
Cari nilai-nilai yang mungkin bagi x dengan keadaan ) + 2 = f (x). [4 marks / markah]
x
–1
HOTS Practices
HO
HO
TS
TS
Practices
1. Diagram below shows a graph.
Rajah di bawah menunjukkan suatu graf.
y
Determine whether this graph is a function. Why?
Tentukan sama ada graf ini adalah suatu fungsi. Mengapa?
x
0


2. The function g, h, gh and hg are defined as shown below.
Fungsi g, h, gh dan hg adalah ditunjukkan seperti di bawah.
g(x) = px – 3, h(x) = (x – q) , gh(x) = px – 4px + 12q + 1
2
2
(a) Find the value of p and of q.
Cari nilai p dan nilai q.
2 2
(b) Using the value of p and q obtained in (a), find the expression for hg(x) if hg(x) = p x – 35qx + 4p
– 3.
Menggunakan nilai p dan q yang diperoleh di (a), cari ungkapan bagi hg(x) jika hg(x) = p x – 35qx
2 2
+ 4p – 3
(c) Find the possible values of x when gh(x) = hg(x).
Cari nilai-nilai yang mungkin bagi x apabila gh(x) = hg(x).
(d) Find the value of x when g (x) = g (x)
2
–1
Cari nilai x apabila g (x) = g (x)
–1
2





7 © Penerbitan Pelangi Sdn. Bhd.






01 HEBAT ADD MATH F4 1P.indd 7 09/04/2021 5:28 PM

Additional Mathematics Form 4 Answers
ANSWERS






f(x)
PRACTICE Functions 16
1 Fungsi 14
12
10
PAPER 1
8
1. (a) The relation is a function because each object 6
has only one image. 4
Hubungan ini ialah fungsi kerana setiap objek 2
mempunyai satu imej sahaja. x
2. (a) Vertical line test –2 –1 0 1 2 3
Ujian garis mencancang 4 1
(b) This graph is not a function because when tested 13. (a) x = 1, x = – — (b) x = 1, x = —
5
3
with the vertical line test, the line cuts two points
3
2
on the graph. 14. (a) x = 1, x = — (b) x = –1, x = – —
Graf ini bukan fungsi kerana apabila diuji dengan 5 3
ujian garis mencancang, garis itu memotong dua
titik pada graf. 15. (a) (i) h(3)= 120 (ii) h(6)= 96
3. f : x → x 3 (b) (t = 0, t = 8)
4. (a) Domain = {a, b, c, d} 16. (a) fg(x) = 8x – 5 (b) gf(x) = 8x – 13
Codomain / Kodomain = {1, 2, 5, 7, 8} 17. (a) f (x) = 16x + 5 (b) g (x) = 4x – 21
2
2
Range / Julat = {1, 5, 7, 8} 18. p = 5, q = –1
(b) Domain = {–1, 0, 1, 2} 1
Codomain / Kodomain = {0, 1, 2, 3, 4, 5} 19. (a) x = — (b) x = 32
2
1
Range / Julat = {0,1,2,3,4} 20. x = —
5. (a) f(3) = 9 4
(b) f(–1) = –7 21. (a) g(x) = 5x (b) g(x) = x 2
3
(c) x = 3, x = – — 22. (a) 9x – 2 (b) x – 1
2
2
23. (a) g(x) = 4 – x (b) g(–3) = 7
6. (a) f(2) = –7 (b) f(–8) = 5
7
7. (a) x = 3 (b) x = 3, x = –2 (c) x = —
6
8. (a) f(–1) = –11 (b) x = –8 1 1
9. (a) p = 3 (b) x = –1 24. (a) f(x) = —x + 1 (b) x = —
2
3
9
10. (a) f(–1) = –6 (b) x = 0, x = – — 25. (m = 5, n = 2)
4
11. (a) 0 < f(x) < 6 (b) 0 < f(x) < 13 26. (a) p = –2 (b) q = 4, q = –4
12. (a) f : x → |2x – 3|, –3 < x < 3 27. p = 3, q = –1
5
2
x –3 0 1.5 3 28. (a) g(x) = —x + 1 (b) g(x) = 5x + 30x + 41
2
2 4
f(x) 9 3 0 3 7
29. (a) g(x) = 2x + 1 (b) x = 3, x = –
f(x) 30. (a) f (2) = 1 (b) f (5) = 2 11
–1
–1
10 (c) f (10) = 3
–1
9
8 31. (a) f is a function because the type of function for the
7 arrow diagram above is a one - to - one function.
6 Each element in the domain is mapped to only
5 one element in the codomain. Therefore, the
4 function f has an inverse function.
3 f ialah suatu fungsi kerana jenis fungsi bagi
2 gambar rajah anak panah di atas ialah fungsi
1 satu dengan satu. Setiap unsur dalam domain
x dipetakan kepada hanya satu unsur dalam
–3 –2 –1 0 1 2 3
kodomain. Oleh itu, fungsi f mempunyai fungsi
(b) f : x → |5x – 5|, –2 < x < 3 songsang.
(b) f is not a one - to - one function because two
x -2 0 1 3
different objects have the same image. Therefore,
f(x) 15 5 0 10 the function f has no inverse function.
A1 © Penerbitan Pelangi Sdn. Bhd.
ANS HEBAT ADD MATH F4 1P.indd 1 09/04/2021 3:49 PM

Additional Mathematics Form 4 Answers
f bukan suatu fungsi satu dengan satu kerana 5. (a) gh(x) = 1
dua objek yang berlainan mempunyai satu imej 2(x + 1)
yang sama. Oleh itu, fungsi f tidak mempunyai 3x – 1
fungsi songsang. hg(x) = x – 1
x + 4
32. (a) Since fg(x) = gf(x) = x, hence g(x) = 2 is an g (x) = – x – 1
2
inverse function fg(x) = 2x – 4. x – 2
x + 4 h (x) = 4x + 9
2
Oleh sebab fg(x) = gf(x) = x, maka g(x) =
ialah fungsi songsang bagi fg(x) = 2x – 4. 2 9
(b) Since fg(x) = gf(x) = x, hence g(x) = 3x – 6 is an (b) x = 3, x = – 7
inverse function of fg(x) = x + 2. 6. (a) g(x) = 4 + 11x
3
Oleh sebab fg(x) = gf(x) = x, maka g(x) = 3x – 6 (b) (i) x = – 11
ialah fungsi songsang bagi fg(x) = x + 2. 15
3 (ii) gg (x) = x, x = – 2
–1
x + 2 x – 11 5
33. (a) f (x) = (b) f (x) =
–1
–1
7 3 7. (a) k = 5, m = 4, n = 9
4 (b) x = 2, x = –1
–1
34. (a) f (x) = 5x – 5 (b) f (x) = – 2 –1
–1
x (c) Yes/ Ya, ff (x) = x
x + 1 3 (i) True because when / Benar kerana apabila
35. (a) f (x) = (b) f (–4) = – x = –2, ff (–2) = –2
–1
–1
–1
1 – x 5 (ii) False because when / Palsu kerana apabila
3x – 5
36. (a) f(x) = 2x + 1 (b) f(x) = x = 3, ff (3) = 3
–1
2
4 8. (a) (i) f(–3) = –16
37. (a) f(x) = –5x + 2 (b) x = (ii) m = 5
5
1 (iii) gf(x) = –27x + 73
38. (a) x = 3 (b) x = –
6 (b) 73
39. (a) f(3) = 2 (b) m = 12, m = 16 x –2 0 27 4
x + 5
40. f (x) = 3 y 127 73 0 35
–1
4x – 7
g (x) =
–1
3x y
x = 4 140
120
PAPER 2 100
1. (a) x –2 0 4 3 80
3 60
f(x) 10 4 0 5 40
20
f(x) x
–2 –1 0 1 2 3 4
12
10
8 9. (a) g(x) = 2x + 3
6 –1 7x – 4
(b) g f(x) =
4 44 2
2 (c) x = – 21
x
0
–2 –1 1 2 3 10. (a) f(x)
7 35 y = f(x)
(b) 0 < f(x) < 10 (c) x = 5, x = – 30
3 25
2. (a) g(–4) = –21 (b) g(–2) = –12 20
(c) x =2, x = 2 15
5 10
3. (a) p = 2, q = 7 5 y = f –1 (x)
(b) h(5) = 3 –10 –5 0 5 10 15 20 25 30 35 x
(c) x = 7 –5
4. (a) fg(x) = 12x – 4x + 80
2
gf(x) = 48x – 4x + 20 (b) Domain: –7 < x < 29
2
–1
fg(x) ≠ gf(x) Range / Julat: 0 < f (x) < 6
5 (c) x = 4, x = –3
(b) x = 4, x =
3
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ANS HEBAT ADD MATH F4 1P.indd 2 09/04/2021 3:50 PM

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