1202 Question Bank Mathematics Form 5

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Contents






Must Know iii - x


Chapter 1 Variation 1 – 11
NOTES 1
Paper 1 3
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Paper 2 7


Chapter 2 Matrices 12 – 22
NOTES 12
Paper 1 14
Paper 2 18


Chapter 3 Consumer Mathematics: Insurance 23 – 30
NOTES 23
Paper 1 25
Paper 2 27


Chapter 4 Consumer Mathematics: Taxation 31 – 40
NOTES 31
Paper 1 33
Paper 2 36



Chapter 5 Congruency, Enlargement and Combined Transformations 41 – 56
NOTES 41
Paper 1 44
Paper 2 49


Chapter 6 Ratios and Graphs of Trigonometric Functions 57 – 73
NOTES 57
Paper 1 59
Paper 2 67


Chapter 7 Measures of Dispersion for Grouped Data 74 – 94
NOTES 74
Paper 1 76
Paper 2 82



Chapter 8 Mathematical Modeling 95 – 104
NOTES 95
Paper 1 97
Paper 2 99


SPM Assessment 105 – 117




Answers 118 – 134

ii




Contents 1202BS Maths F5.indd 2 07/01/2022 3:35 PM

MUST


KNOW Important Definitions







Congruency and Enlargement Class Interval and Cumulative Frequency
• The pairs of objects are congruent when the two objects have the • Class interval is the range of a division of data.
same size and shape even though their position or arrangement is
different. • The cumulative frequency of a class interval is the sum
of the frequency of the class and the total frequency of the
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• Enlargement is a transformation in which all the points of an classes before it.
object move from a fixed point with a constant ratio is known as
the scale factor.












Important Definitions (Chapter 5) 13 @ Pan Asia Publications Sdn. Bhd. Important Definitions (Chapter 7) 19 @ Pan Asia Publications Sdn. Bhd.


Combined Transformation and Tessellation Quartile, Interquartile Range and Percentile
• Combined transformation AB means transformation B • Quartiles are values that divide a set of data into four equal
followed by transformation A. parts.

• A tessellation is a pattern of recurring shapes that fills a • Interquartile range is the difference between the value of
plane without leaving empty spaces or overlapping. third quartile and the value of first quartile.
• A percentile is a value that divides a set of data into 100
equal parts.











Important Definitions (Chapter 5) 15 @ Pan Asia Publications Sdn. Bhd. Important Definitions (Chapter 7) 21 @ Pan Asia Publications Sdn. Bhd.


Unit Circle and Corresponding Reference Angle Mathematical Model, Variables, Optimum and
Simple Interest
• A unit circle is a circle that has a radius of 1 unit and is
centred on the origin. • A mathematical model is a representation of a system or
scenario that is used to gain qualitative and/or quantitative
• The corresponding reference angle, a is always less than understanding of some real-world problems and to predict
90°. future behaviour.

• The process of constructing mathematical model is called
mathematical modeling.
• A variable is a quantity with an unknown value.
• Optimum means the best or the most profitable.
• Simple interest is a reward given to the depositor at a
certain rate on the principal amount for a certain period of
time.




Important Definitions (Chapter 6) 17 @ Pan Asia Publications Sdn. Bhd. Important Definitions (Chapter 8) 23 @ Pan Asia Publications Sdn. Bhd.



Must Know 1202BS Maths F5.indd 3 21/01/2022 4:16 PM

MUST


KNOW Important Facts







Formula for Size of Class Interval, Midpoint, Upper Scale Factor and The Image of The Enlargement of
Boundary and Lower Boundary Object
• Size of class interval = Upper boundary – Lower boundary • Scale factor can be obtained by dividing the distance of the
image with the distance of object and represented by letter k.
upper limit + lower limit
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• Midpoint = Triangle A′B′C′ is the image of
2
C' triangle ABC.
• Lower boundary Scale factor, k = PB′ = PC′
Upper limit of the class before it + Lower limit of the class C A' PB PC
= B' A′B′ A′C′
2 A B = AB = AC
6
• Upper boundary P k = = 2
3
Upper limit of the class + Lower limit of the class after it
=
2


Important Facts (Chapter 7) 20 @ Pan Asia Publications Sdn. Bhd. Important Facts (Chapter 5) 14 @ Pan Asia Publications Sdn. Bhd.


Formula for Mean, Variance and Standard Deviation Formula of the Area of Image and Type of
Transformation
–
• Mean, x = ∑ fx
f • The area of the image of an enlargement can be obtained
with the following formula:
∑ fx 2
2
• Variance, s  = – x –2 Area of the image = k × Area of the object
2
∑ f
!
• Standard Deviation, s = ∑ fx 2 – x –2 • In addition to enlargement, other transformation include
reflection, translation and rotation.
∑ f









Important Facts (Chapter 7) 22 @ Pan Asia Publications Sdn. Bhd. Important Facts (Chapter 5) 16 @ Pan Asia Publications Sdn. Bhd.

Mathematical Modeling Values of Sine, Cosine and Tangent of Special
Angles and Four Different Quadrants
• There are a few important components in mathematical
modeling such as identifying and defining the problems, • Values of sine, cosine and tangent of special angles.
making assumptions and identifying the variables, q 0° 30° 45° 60° 90° 180° 270° 360°
applying mathematics to solve problems, verifying and 1 1
interpreting solutions in the context of problem, refining the sin q 0 2 ! 2 ! 3 1 0 –1 0
2
mathematical model and reporting the findings. 1
cos q 1 ! 3 1 0 –1 0 1
• Real-life problems can be solved through mathematical 2 ! 2 2
modeling involving linear, quadratic and exponential 0 1 1 ! 3 ∞ 0 ∞ 0
functions. tan q ! 3
• Values of sin q, cos q and tan q in the four different quadrants.
Quadrant I Quadrant II Quadrant III Quadrant IV
sin q positive positive negative negative
cos q positive negative negative positive
tan q positive negative positive negative


Important Facts (Chapter 8) 24 @ Pan Asia Publications Sdn. Bhd. Important Facts (Chapter 6) 18 @ Pan Asia Publications Sdn. Bhd.



Must Know 1202BS Maths F5.indd 4 21/01/2022 4:16 PM

MUST


KNOW Common Mistakes







Combined Transformation Size of Class Interval
Correct Wrong Correct Wrong

The combined transformation The combined transformation If the class interval is If the class interval is
©PAN ASIA PUBLICATIONS
PQ indicate that performing PQ indicate that performing 6 – 10, the size of the class 6 – 10, then size class interval
the transformation Q first, then the transformation P interval is the upper boundary is 10 – 6 = 4.
followed by transformation P. first, then followed by – the lower boundary, thus
transformation Q. 10.5 – 5.5 = 5












Common Mistakes (Chapter 5) 37 @ Pan Asia Publications Sdn. Bhd. Common Mistakes (Chapter 7) 43 @ Pan Asia Publications Sdn. Bhd.


The value of sin x The correct way to get the value of fx 2

Correct Wrong Correct Wrong
sin x is 0.5. sin x is 0.5. Most students The value of fx is calculate as The value of fx is calculate
2
2
The correct value of x are will only give the value of f multiplied by the value of x . as f x.
2
2
x = 30° and 150°. x = 30°.












Common Mistakes (Chapter 6) 39 @ Pan Asia Publications Sdn. Bhd. Common Mistakes (Chapter 7) 45 @ Pan Asia Publications Sdn. Bhd.

Enlargement and Scale Factor Mathematical Modeling

Correct Wrong Correct Wrong
State the transformation of State the transformation of The mathematical equation The assumption that the
enlargement with scale factor. enlargement without mention which is used to solve mathematical equation which
the scale factor. problem can be changed is used to some problem is
based on the change in the fixed and not influenced by
relationship between the the change in the relationship
relevant variables. between the relevant
variables.










Common Mistakes (Chapter 5) 41 @ Pan Asia Publications Sdn. Bhd. Common Mistakes (Chapter 8) 47 @ Pan Asia Publications Sdn. Bhd.



Must Know 1202BS Maths F5.indd 7 21/01/2022 4:16 PM

MUST


KNOW Important Diagrams







Histogram and Frequency Polygon Image under Translation and Enlargement
• Histogram ∆STU is the image of ∆PQR under transformation M
(translation)
Frequency
10 y
F
8
8
6 7
N
4 6 E
5
2 T
4 G
0 44.5 49.5 54.5 59.5 64.5 69.5 74.5 Mark 3 S U
• Frequency polygon 2 Q
1 P
Number of participant R
M
O x
6 1 2 3 4 5 6 7
∆EFG is the image of ∆STU under transformation N
4
(enlargement)
2
0
47 52 57 62 67 72 77
Time (s)
Important Diagrams (Chapter 7) 44 @ Pan Asia Publications Sdn. Bhd. Important Diagrams (Chapter 5) 38 @ Pan Asia Publications Sdn. Bhd.
Ogive Graph of Sine and Cosine
• Ogive • y = sin x
Cumulative frequency y
Maximum point
1
40 y = sin x
Amplitude
x
35 ©PAN ASIA PUBLICATIONS
0 90° 180° 270°360°
30
–1 Period
25 Minimum point

20
• y = cos x
15
y
10 Maximum point
5 1 y = cos x
Amplitude
0
10 20 30 40 50 60 0 x
Time (minute) 90° 180° 270°360°
–1
Period Minimum point

Important Diagrams (Chapter 7) 46 @ Pan Asia Publications Sdn. Bhd. Important Diagrams (Chapter 6) 40 @ Pan Asia Publications Sdn. Bhd.
Processes in Mathematical Modeling Graph of Tangent
Real-world Reporting • y = tan x
problem the findings y
2 y = tan x
1
Identifying and defining Refining the x
the problems mathematical model –1 0 90° 180° 270°360°
–2
Period
Verifying and interpreting
Making assumption and
identifying the variables solutions in the context of the
problem


Applying mathematics to solve problems


Important Diagrams (Chapter 8) 48 @ Pan Asia Publications Sdn. Bhd. Important Diagrams (Chapter 6) 42 @ Pan Asia Publications Sdn. Bhd.



Must Know 1202BS Maths F5.indd 8 21/01/2022 4:16 PM

Chapter 1 Variation




NOTes



1.1 Direct Variation Hence, E 1 = E 2
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1. If y varies directly as x, then ! F 1 ! F 2
y fi x When 9 = E 2
y ! 36 ! 16
y = kx or = k
x E = 9 × ! 16
2
where k is the constant of variation. ! 36
Example: = 9 × 4
Given that y varies directly as x and y = 20 when 6
x = 5. = 6
Then, y fi x
y = kx 1.2 Inverse Variation
20 = k(5) 1. If y varies inversely as x, then
20
k = = 4 1
5 y fi x
Therefore, y = 4x
1
that is y = k ( )
x
2
3
2. Other cases of direct variation are y fi x , y fi x ,
k
1 y = or xy = k
2
2
y fi x or y fi ! x which can be written as y = kx , x
1
3
2
y = kx , y = kx or y = k! x . where k is the constant of variation.
Example:
Example:
Given that E varies directly as the square root of F Given that y varies inversely as x and y = 9 when
and E = 9 when F = 36. Calculate the value of E x = 6. 1
when F = 16. Then, y fi
x
METHOD 1 (Find the value of k) y = k
x
k = xy
E fi ! F
k = 6 × 9 = 54
E = k! F 54
Therefore, y =
9 = k! 36 x
9 = k(6) 1 1
9 3 2. Other cases of inverse variation are y fi , y fi ,
3
2
k = = x x
6 2 1 k k
3 y = which can be written as y = x 2 , y = x 3 ,
Hence, E = ! F ! x
2
When F = 16 y = k .
! x
3
E = × ! 16
2 Example:
3
= × 4 Given that w varies inversely as the square of v and
2 w = 5 when v = 3.
= 6
Then, w fi 1 2
METHOD 2 (Make k as the subject of equation) v
w = k 2
E fi ! F v k
E = k! F 5 = 3 2
2
E k = 5 × 3 = 45
k =
! F Therefore, w = 45
v 2
1
C01 1202BS Maths F5.indd 1 26/01/2022 3:43 PM

1.3 Combined Variation Therefore, p = 9! r
s
1. Joint variation is a relation between three or more When p = 18 and s = 2
variables. The relation can be
(a) two direct variation 18 = 9! r
Example: 2
p varies directly as s and t. ! r = 18 × 2
p fi s and p fi t 9
that is, ! r = 4

2
p fi st (! r ) = 4 2
p = ©PAN ASIA PUBLICATIONS
p = kst r = 16
where k is a constant.
(b) two inverse variation METHOD 2
Example:
y varies inversely as the cube of x and the square p = 9! r
of z. s
1 1 ps
y fi and y fi k =
x 3 x 2 ! r
that is,
p s p s
Hence, 1 1 = 2 2
1
y fi ! r ! r
x x 1 2
3 2
k 6(3) 18(2)
y = =
3 2
x x ! 4 ! r
2
where k is a constant. 36 × ! 4
(c) One direct variation and one inverse variation ! r = 18
2
Example:
! r = 4
2
u varies directly as m and inversely as the square r = 4 = 16
2
root of n. 2
1
u fi m and u fi 3. Distance, s travelled by a bike is varies
! n
that is, directly as the square of the speed, v, and
varies inversely as acceleration, a. Given that
m
u fi s = 120 m, v = 6 m s , and a = 0.5 m s . Calculate the
–1
–2
! n –1
value of a when s = 360 m and v = 9 m s .
km
u = Solution:
! n 2
s fi v
where k is a constant. a 2
s = kv
2. Solving problem in joint variation a
Example: 120 = k(6) 2
Given that p varies directly as ! r and inversely as s. 0.5
p = 6 when r = 4 and s = 3. Find the value of r when k = 120 × 0.5
p = 18 and s = 2. 5 36
=
3
METHOD 1 5
( ) (9) 2
! r 360 = 3
p fi 36
s
135
k! r a = 360
s
= 0.375 m s −2
k! 4
6 =
3
6 × 3
k = = 9
! 4
2




C01 1202BS Maths F5.indd 2 26/01/2022 3:43 PM

PAPER 1


Every question has 4 answer options A, B, C and D. Choose one answer for every question.


1. Given that t varies directly as the square root of s and 6. If h varies directly as the square root of k, the relation
t = 24 when s = 9. Express t in terms of s. between h and k is
2
A t = 8! s A h fi k C h fi k
B t = 3s 1 1
2
B h fi k D h fi
C t = 24 2 ! k
C p = 5q ©PAN ASIA PUBLICATIONS
s
9
D t = 24s 7. P varies inversely as the square of Q and Q = 2 when
P = 2. Find the value of P when Q = 4.
1 1
2. Given that p fi and p = 3 when q = 2. Find the A –5 C
q 2
value of p when q = –5. B 1 D 1
A –5 32 8
B –6 1
C 5 8. Given that m fi 1 and m = 12 when n = , calculate
4
6 SPM ! n
D – CLONE
5 the value of m when n = 4.
1
3. The table shows some values of the variables E and F A 3 C 12
where E varies directly as the cube of F. B 3 D 24
E 24 y
F 2 3 9. R varies inversely as the cube of S and R = 32 when
1 1
Calculate the value of y. S = . Calculate the value of S when R = .
4 2
A 27 1
A R =
B 81 2
C 9 B 1
D 1 4
C 1
D R = 2S 2
4. The table shows the relation between the variables H
and K as direct variation.
3
10. Given that h fi k and h = 64 when k = 2. Determine
H 30 42 the constant of variation.
K 5 7 A 1 C 32
8
Which of the following is true?
C 16 D 8
A H = K
2
B H = 6! K
11. The table shows some values of the variables p and q
C H = 6K where q varies inversely as the square root of p.
K
D H =
6 p 4 64
q 8 2
2
5. Given that p is directly proportional to q and p = 20
when q = 2, express p in terms of q.
Find the relation between p and q.
A p = 10q 16
2
A q = C q = 16! p
2
B p = q
! p
2 4
2
B q = 4p D q =
q
D p = ! p
6
3
Question 3: Question 9:
The relation is varies directly, E fi F . E = kF , find the value of The relation is varies inversely, R fi 1 . R = k , find the value of
3
3
constant k. constant k. S 3 S 3 SOS TIP


C01 1202BS Maths F5.indd 3 26/01/2022 3:43 PM

12. The table shows some values of the variable H and K 17. Given that H fi 1 and H fi ! F. If H = 12 when G =
such that H varies inversely as the square root of K. G
Find the value of x. 4 and F = 36, calculate the value of G when H = 12
and F = 81.
H 2 3
A 54
K 36 x B 18
A 3 C 6
B 4 D 2
C 16
D 12 18. The table shows some values of the variables p, q and
©PAN ASIA PUBLICATIONS
SPM q
CLONE r which satisfy the relation p fi .
13. Given that w varies directly as ! v and inversely as ! r
3
u . v = 16 when u = 2 and w = 3. Express w in terms p 24 18
of v and u.
q 8 6
6! v
A r x 16
u 3
8! v Calculate the value of x.
B
3 ! u A 6
B 2
C 6! v u
3
C 16
! 16v 3
D D 8
u
14. x varies directly as the square root of y and inversely 19. The table shows the relation between the variables k,
as the square of z. The relation between x, y and z is SPM m and n.
CLONE
y 2
A x fi k m n
! z
3 y 9
B x fi ! y z 5 20 4
2
z 2
C x fi
! y Given that k fi m , find the value of y.
! n
! y 9
D x fi A 18 C
z 2 2
3
15. Given that s varies inversely as t and u. The table B 54 D 2
shows some values of the variables.
20. P varies directly as the square root of Q and inversely
s t u
as the square root of R. Given that P = 3 when Q = 32
3 2 x and R = 2. Calculate the value of R when P = 6 and
5 4 3 Q = 192.
A 6 C 9
Find the value of x.
B 4 D 3
A 6 C 15
B 10 D 20
21. The table shows some values of the variables E
and F.
16. It is given that E varies directly as m and inversely as
3
n . Given E = 15 when m = 20 and n = 2. Calculate E 2 4 6 8
the value of E when m = 9 and n = 3. F 12 6 4 3
A 6 Find the relation between E and F.
B 2 1
A F fi E C F fi
C 1 E
1 B F fi 1 D F fi E
2
D
2 ! E
4 Question 16:
SOS TIP The relation involved both directly and inversely relationship, find the value of constant k.
After substitute, the given value of k, m and n into the equation, then find the value of E.








C01 1202BS Maths F5.indd 4 26/01/2022 3:43 PM

PAPER 2


Section A

1. Table below shows some values of the variables p 3. L varies directly as the square root of m and inversely
4
and q. as the square of n. Given that L = when m = 64 and
5
1 q = 5.
p 1 x
5 (a) Express L in terms of m and n. [2 marks]
(b) Find the value of L when m = 81 and n = 3
q 4 108 y
©PAN ASIA PUBLICATIONS
[1 mark]
It is given that q varies inversely as the cube of p. (c) Find the value of m when L = 15 and n = 4.
(a) Write an equation which relates p and q. 8 [1 mark]
[2 marks]
(b) Find the values of p and of q. [2 marks] Answer:
(a)
Answer:
(a)


(b)

(b)


(c)






2. It is given that w varies directly as the cube of x and 4. The volume of a cone, V with base radius r and height
inversely as the square root of y. Given that w = 27 h is V = r h.
1 2
when x = 3 and y = 4. 3
(a) Write an equation which relates w, x and y. (a) What is the relation between h and r?
[2 marks] (Using symbol fi and h as the subject.)
(b) Find the value of w when x = 4 and y = 16. [1 mark]
[2 marks] (b) Given that the height is 5 cm when its base radius
is 4 cm. Calculate its height when the base radius
Answer: is 2 cm. [2 marks]
(a)
Answer:
(a)




(b)
(b)











7
Question 4:
Change the subject of the relation to h.
Based on the new relation, substitute all the given values of unknowns to find the value of h. SOS TIP








C01 1202BS Maths F5.indd 7 26/01/2022 3:43 PM

Section B

9. Given m varies inversely as y in which y = 3x – 1. 11. Table shows some of the values of three variables X,
1
Given x = 5 when m = 2. Y and Z such that X fi and X fi Z .
2
(a) Express m in terms of y. [2 marks] Y
(b) Express m in terms of x. [1 mark] X 8 25
(c) Calculate the value of x when m = 4. [1 mark] Y 3 h
Answer: Z 4 10
(a)
(a) Express X in terms of Y and Z. [2 marks]
©PAN ASIA PUBLICATIONS
(b) Calculate the value of h. [1 mark]
Answer:
(a)
(b)




(b)

(c)










3
10. It is given p varies directly as q and r . Given p = 108 12. It is given that M varies directly as ! N and inversely
when q = 2 and r = 3. as G . Given N = 4 when G = 2 and M = 1 .
1
3
(a) Express p in terms of q and r. [2 marks] 2
3 (a) Express M in terms of N and G. [2 marks]
(b) Calculate the value of p when q = and r = 4.
4 (b) Calculate the value of M when N = 9 and G = 3.
[1 mark]
[1 mark]
1
(c) Find the value of q when p = 6 and r = . 3
3 (c) Calculate the value of N when M = 4 and
[1 mark] G = 4. [1 mark]
Answer: Answer:
(a) (a)



(b)
(b)



(c)

(c)






9
Question 9:
Find the value of constant which relates the m and y.
Replace y with 3x – 1 and form a new equation of the relationship between m and x. SOS TIP
Enter the given value of y and find the value of m.







C01 1202BS Maths F5.indd 9 26/01/2022 3:43 PM

Section C

15. Encik Aman wants to install rectangular tiles for 16. Amran needs some money to expand his business.
his new house floor. The number of tiles needed, T, He decided to borrow money from a bank. It is given
varies inversely as the length, L m and width, W m, that the interest charge on the loan, C, varies directly
of the tiles used. Encik Aman needs 580 pieces of as the amount of loan, L, and the period in year, T
tiles if the tile is 0.5 m in length and 0.3 m in width. for repaying the loan. Amran has to pay total interest
(a) Calculate the number of tiles needed if the RM4 800 to settle his loan of RM20 000 over three
length is 0.4 m and the width is 0.3 m. [2 marks] years.
(b) If the tiles he ordered are in square shape and (a) Calculate the period for Amran to repay the
©PAN ASIA PUBLICATIONS
the length of the square tile is 0.5 m. The price of loan of RM30 000 if he has to pay total interest
one unit of the tile is RM1.90. How much Encik RM7 200 to the bank. [3 marks]
Aman has to pay for the tiles installation? (b) Amran pay total interest RM7 200 to repay the
[2 marks] loan. If Amran able to repay the loan within
(c) If the area of the tile decreases, what is the 5 year’s time. Find the amount of money that he
change in the number of tiles needed for the borrowed from the bank.
installation? HOTS Analysing [1 mark] Does he increase or decrease the amount of
money he borrowed from the bank? Explain
Answer: your answer. HOTS Analysing [4 marks]
(a)
Answer:
(a)







(b)








(b)


(c)

























11
Question 15:
Form an equation to relates T, L and W.
T = k , substitute the value of T, L and W then find the value of constant k. SOS TIP
LW
Substitute the new values of L and W, then find the number of tiles, T.





C01 1202BS Maths F5.indd 11 26/01/2022 3:43 PM

SPM Assessment





PAPER 1

Time: 1 hour 30 minutes
This paper has 40 questions. Answer all questions.
©PAN ASIA PUBLICATIONS
1. Diagram 1 shows a triangle PQR. 4. It is given that
Q ξ = {x : 27 , x , 38},
M = {x : x is a multiple of 4},
N = {x : x is a whole number and the remainder is 1
h after divided by 3}
State the members of (M  N).
P R A {28, 32, 36} C {29, 30, 33, 35}
2x + 6
B {28, 31, 34, 37} D {28, 31, 32, 34, 36, 37}
Diagram 1
It is given that the area of the triangle is 5. Table 1 shows the equivalent value of the number in
2
(4x – 36) cm . Express h in terms of x. base eight and base five.
2
A x – 3 C 4x – 12
Base 8 Base 5
B 2x – 9 D 3x + 12
001 1
2. Which of the following graph represents the 011 K
quadratic equation of y = (2 – x) (3 + x)?
100 124
A y C y
101 G
Table 1
6 6 Find the value of K + G as a number in base 5.
A 1001 C 74
5 5
B 144 D 244
5 5
x x
3
0
–3 2 –2 3 6. Given that x = 8 + (2 × 8) + (4 × 8 ), find the value
8
of x.
B y D y A 324 C 6 464
B 1 201 D 1 024
x
6 –2 3 7. Diagram 3 shows an archery target board consists
of five concentric circles with the same width The
radius of the target board is 100 cm.
–6
x
–3 2 V
IV
III
3. Diagram 2 shows a piece of land PQRS which is a II
trapezium belong to Encik Tan. I
W (3k + 4) m X


13 m
2k m
Diagram 3
An arrow is released to hit the archery target board.
Z (4k + 3) m Y
Find the probability of the arrow hit the region III.
Diagram 2 A 1 C 3
Find the value of k. 5 25
A k = 3 C k = 5 B 1 D 7
B k = 6 D k = 12 25 25
105




MPaper 1202BS Maths F5.indd 105 25/01/2022 11:49 AM

8. A total of 270 candidates pass the interview for C D
the job of medical assistant, nurse, and pharmacy
assistant. A total of 72 candidates are appointed as
medical assistants. The probability to choose a nurse
3
from the group of candidates is . Calculate the
5
number of pharmacy assistants.
13. Diagram 7 shows a graph with loops and multiple
A 54 B 36 C 216 D 198 edges.

9. Given that W = 343 , find the value of W.
8 7
©PAN ASIA PUBLICATIONS
A 250 B 110 C 262 D 178
10. Diagram 4 shows the Venn diagram that shows the
relation between set P, set Q and set R.
ξ
Q
P
● 7 Diagram 7
● 3 Based on the graph above, which of the following is
● 8 R
● 5 ● 6 true?
● 4
● 2 A n(V) = 4, n(E) = 8, ∑d(v) = 18
● 1
● 9 B n(V) = 5, n(E) = 7, ∑d(v) = 14
C n(V) = 4, n(E) = 8, ∑d(v) = 16
Diagram 4 D n(V) = 6, n(E) = 6, ∑d(v) = 16
Which of the following is true?
A (P  Q)´ = {2, 4, 9} 14. Diagram 8 shows a graph of the relation between
B P  R = {2, 4, 5, 8} three linear inequalities.
C P  Q  R = {6} y
D (Q  R)  P = {2, 4, 5, 6, 8}
y = x + 3
11. Diagram 5 shows a graph with multiple edges and
loops. C y = 3x – 9
3
P Q
A B
x
–3 O 3
D x + y = 3
R S

T –9

Diagram 5 Diagram 8
Which of the following is true? Which of the region A, B, C or D, satisfied the linear
inequalities system of y < x + 3, y > 3x – 9 and
A d(P) = 2 C d(Q) = 4
x + y > 3?
A d(R) = 3 D ∑d(v) = 18
15. Diagram below shows a straight line graph of
12. Diagram 6 shows a graph. y = 3x – 5.
y
y = 3x – 5



x
Diagram 6
Which of the following is not the tree drawn from the
–5
graph above?
A B
Diagram 9
Which of the following point satisfied the inequality
of y . 3x – 5?
A (3, –2) C (–1, 3)

B (0, –5) D (5, 0)
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MPaper 1202BS Maths F5.indd 106 25/01/2022 11:49 AM

PAPER 2


Time: 2 hours 30 minutes
Section A
[40 marks]
Answer all questions in this section.
1. (a) Determine whether the statement is true or false. Answer:
11 = 5.5 or 2 = 6 (a)
3
2
[1 mark]
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(b) State whether the statement below is a statement
or not a statement.
x + 3 – p (b)
[1 mark]
(c) Make a general conclusion by induction for the
sequence of numbers 9, 27, 57, 99 which follows
the following pattern:
9 = 6 (1) + 3 (c)
27 = 6 (4) + 3
57 = 6 (9) + 3
99 = 6 (16) + 3 [2 marks]

Answer:
(a) 3. Table 1 shows the name of three male students and
two female students in a school. They are assigned to
clean the class during recess.
Male Female
(b) Ahmad Devi
Borhan Eliana
Chong
Table 1
(c) Three students are chosen at random to clean the
class.
(a) List all the possible outcomes of the event for
this sample space. You may use the capital letter
such as A for Ahmad and so on. [2 marks]
(b) Find the probability that
2. Diagram 1 shows a distance-time graph for the (i) The two students chosen are female.
journey of a train from Seremban to Kajang. (ii) Borhan and Chong are not assigned
together. [2 marks]
Distance (km)
Answer:
(Kajang) 70
(a)



(Mantin) 25
(b) (i)

(Seremban) 0 Time (min)
20 25 t
Diagram 1
(a) It is given that the speed of the train travel from (ii)
–1
Mantin to Kajang is 1.5 km min . Find the value
of t. [2 marks]
(b) How long, in minutes, the time taken by the train
reached Mantin from Seremban? [1 mark]
–1
(c) Calculate the average speed, in km h , for the
whole journey. [1 mark]
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MPaper 1202BS Maths F5.indd 110 25/01/2022 11:49 AM

Section B
[45 marks]
Answer all questions in this section.

11. A furniture shop sells two types of chairs, type A and 12. Table 3 shows the individual income tax assessment
type B. The profit from the sale of a unit of chair of form for Encik Yusof.
type A is RM8 and a unit of chair of type B is RM5. Tax
The shop sells x unit of type A chair and y unit of Item assessment
type B chair. The maximum number of chairs sold (RM)
is 160. The number of chair of type B sold is at least
(d) ©PAN ASIA PUBLICATIONS
2 of the number of chair of type A. The total profit Employment income RM95 560
3
from the selling of chairs is at least RM400. RELIEF
(a) Based on the given situation, state three linear Individual 9 000
inequalities, other than x > 0 and y > 0.
[3 marks] Lifestyle (limited to 2 500)
(b) Using a scale of 2 cm to 20 chairs on both axes,
Child whose age is below 18 years old 2 000
draw and shade the region which satisfies the
system of linear inequalities in (a). [3 marks] Life insurance and EPF (limited to 7 000)
(c) From the graph in (b), determine the minimum
Education and Medical insurance
number of chair of type A if 40 of the chair of
(limited to 3 000)
type B are sold. [1 mark]
(d) It is given that the shop managed to sell 80 chairs TAX SUMMARY
of type A. Calculate the maximum total profit
obtained by the company from the sales of the Total income RM95 560
two types of chairs. [2 marks] Total tax relief W
Answer:
CHARGEABLE INCOME X
(a)
Tax on the first (50 000 or 70 000) Y
Tax on the next balance (× 14% or × 21%) Z

Table 3
In the assessment year, Encik Yusof spent RM2 890
for lifestyle, RM5 680 for life insurance and RM3
150 for medical insurance. Encik Yusof also paid
(b)
zakat amounting to RM500.
Table 4 shows the income tax rate:

Chargeable Calculation Rate Tax
Income (RM) (RM) (%) (RM)

50 001 – 70 000 On the first 50 000 1 800
Next 20 000 14 2 800
(c)
70 001 – 100 000 On the first 70 000 4 600
Next 30 000 21 6 300

Table 4
You are advised to complete the space for the tax
assessment related to tax relief in the table above
before answer the following questions.
(a) Find the value of W, X, Y and Z. [4 marks]
(b) Calculate the income tax payable imposed on
Encik Yusof for the assessment year. [2 marks]
(c) If Encik Yusof join the Monthly Tax Deduction
(PCB) system and RM250 is deducted from his
salary every month. Does Encik Aman need to
pay any more income tax to the Inland Revenue
Board (IRB)? [3 marks]

113




MPaper 1202BS Maths F5.indd 113 25/01/2022 11:49 AM

15. Cik Rita wants to buy a house worth RM350 000. Answer:
She needs to pay the preliminary money amounting (a)
to 15% of the original price of the house. But she
only has money amounting to M. She decided to save
her money M in the bank as fix deposits account. The
bank offered interest rate of r% per annum for the
fix deposits account and compounded every year. (b)
She will receive the new total saving, S, after t years
of saving which followed the mathematical model
S(t) = 28 000(1.06) .
t
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(a) What is the saving principal, M of Cik Rita and
the annual interest rate offered by the bank?
[2 marks]
(b) Calculate the total saving in the fix deposits (c)
account of Cik Rita after 6 years of saving.
[2 marks]
(c) How many year does Cik Rita needs to save
her money M in fix deposits account to enable
her to pay for the preliminary money to buy the
house? [3 marks]
(d) Refining the mathematical model if the interest (d)
rate for the fix deposits account offered by the
bank is compounded every three months.
[2 marks]












Section C
[15 marks]
Answer any one of the question from this section.
16. Diagram 6 shows a histogram which represents (a) Based on the information in the histogram,
the mark obtained by a group of students in a complete the table in the answer space provided.
mathematics test. [3 marks]
Frequency (b) Based on the data in the table,
(i) State the modal class, [1 mark]
11 (ii) Find the mean mark of the mathematics
test. [3 marks]
10
(iii) Calculate the standard deviation for the
9
mark of the mathematics test. [3 marks]
8 (c) Using a scale of 2 cm to 5 marks on the horizontal
axis and 2 cm to 5 students on the vertical axis,
7
draw an ogive for the data. [3 marks]
6 (d) Based on the ogive drawn in (c), calculate the
5 interquartile range of the data. [2 marks]
4

3
2
1
0 Marks
19.5 24.5 29.5 34.5 39.5 44.5 49.5 54.5
Diagram 6
115




MPaper 1202BS Maths F5.indd 115 25/01/2022 11:49 AM

Answer: 17. (a) Diagram 7 shows point W on a Cartesian plane.
Class interval Frequency, Midpoint, y
(Mark) f x
6
20 – 24 5
4
3
2
1
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x
–4 –3 –2 –1 O 1 2 3 4 5 6
–1
–2
–3
W
(b) (i) –4

Diagram 7
( )
4
Transformation G is a translation .
2
Transformation H is a rotation of 90°
(ii)
anticlockwise about the centre (1, 1).
State the coordinates of the image of point W
under each of the following transformations:
(i) H 2
(ii) HG [4 marks]
(b) Diagram 8 shows three pentagons ABCDE,
(iii)
FGHIJ and FGRSJ, drawn on a Cartesian plane.
y
B
12
R
10 C E
(c) A
8
6
D
4
H 2 S
x
–10 –8 –6 –4 –2 O 2 4 6 8 10
G F –2
I
–4
J
–6
–8
–10

Diagram 8
(i) Pentagon FGRSJ is the image of ABCDE
under the combined transformation XY.
Describe, in full, the transformation:
(a) Y,
(b) X [4 marks]
(d) (ii) It is given that pentagon FGRSJ represents
2
a region of area 315 m . Calculate the area,
in m , of the shaded region. [5 marks]
2
(iii) Draw the image of FGHIJ under a reflection
at the line y = 4 on the Cartesian plane.
[2 marks]


116




MPaper 1202BS Maths F5.indd 116 25/01/2022 11:49 AM

Answers Complete Answers (Paper 1)

https://bit.ly/3JQiyOg


CHAPTER 1 ! m = 12 (c) when h = 16
m = 144 Q = 6h + 4
Paper 1 1 Q = 6(16) + 4
2
4. (a) V = πr h
1. A 2. D 3. B 4. C 5. C 3 Q = 100
3V
6. B 7. C 8. B 9. C 10. D h = πr 2 P = ! 100
11. A 12. C 13. A 14. D 15. B 2
1
16. B 17. C 18. C 19. A 20. D h fi P = 10
2
21. C 22. A 23. D 24. B 25. B r 2
L = ©PAN ASIA PUBLICATIONS
26. C 27. D 28. B 29. C 30. A (b) h = 5 when r = 4 = 5
k
31. C 32. D 33. B 34. B 35. C h = r 2 8. (a) q fi p
36. D 37. B 38. A k ! r
5 =
4 2 kp
Paper 2 q =
h = 5 × 16 = 80 ! r
1. (a) q fi 1 h = 80 k(3)
p 3 4 2 9 =
k when r = 2 ! 16
q =
p 3 80 9 × 4 = 3k
h = = 20
k 2 2 36
4 = k =
1 3 5. (a) k = pm 2 3
k = 4 n 3 k = 12
2
4 8(2 ) q = 12p
q = (b) k =
p 3 4 3 ! r
4 k = 32 12(6)
(b) 108 = 64 (b) 8 =
p 3 1 ! r
4 k =
3
p = 2 8! r = 72
108 n 3
1 (c) p = 2m n 2 3 2 ! r = 72
p =
3
CHAPTER 1 2. (a) w fi ! y 3 3 3 6. (a) p = kq n = ! 216 9. (a) m fi k 1 y 2
8
27

12 =
1
! r = 9
2(3 )
p =
r = 9
3

12 × 18 = n
q = 500
r = 81
3
x
n = 6
kx
m =
w =
y
1
k =
k
6
k3
27 = ! y 3 2 = k(12) m = 3x – 1
q
! 4 (b) p = k
6 2 =
k(27) 72 3(5) – 1
27 = x = k
2 6 2 =
k = 2 x = 12 14
y k = 28
2x 3 3 = 28
w = 6 hence, m =
! y y = 3 × 6 y
2(4) 3 (b) m = 28
(b) w = y = 18 3x – 1
! 16 (c) when m = 4
2(64) 7. (a) P fi ! Q 28
w = P = k! Q 4 =
2 y
w = 32 P = k! 6h + 4 28
y =
k! m P = k! (6 × 10) + 4 4
3. (a) L =
n 2 y = 7
4 = k! 64 3x – 1 = 7
4 = k! 64 4 = 8k
5 5 2 k = 4 3x = 8 8
25 × 4 8 x =
k = 3
8 × 5 k = 1 x = 2 2
5 2 3
k =
2 P = ! Q 10. (a) p fi qr 3
5! m 2 p = kqr 3
2n 2 (b) when P = 2 108 = k(2)(3) 3
! Q 108 = 54k
5! 81 2 =
(b) L = 2 108
2(3 ) ! Q = 2 × 2 k = 54
2
5
L = ! Q = 4 = 3
2 3
15 5! m Q = 4 2 p = 2qr
(c) = (b) p = 2qr 3
8 2(4 ) Q = 16
2
3
15 × 32 6h + 4 = 16 p = 2 ( ) (4 ) 3
! m = 6h = 12 4
8 × 5 = 96
h = 2
118
Answers 1202BS Maths F5.indd 118 25/01/2022 11:47 AM

(b) The possible assumptions: RM6 500P = RM520 000
ξ
(i) The speed of the river water and W Z 520 000
the speed of the motorboat are Y P = 6 500
constant all the time. = 80
(ii) The friction between the 10. The balance of red balls
motorboat and the surface of = 131 – 45 6
6
river water, the friction with the 5. (a) x + 3y = 8 = 42
6
air are ignored. When x = 2, 2 + 3h = 8, = 4 × 6 + 2
3h = 8 – 2, = 26
10
SPM ASSESSMENT 3h = 6 The balance of blue balls
h = 2
Paper 1 = 54 – 35 6
6
1. C 2. A 3. B 4. C 5. D (b) Point on x-axis, y = 0 = 15 6
x + 3(0) = 8
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6. D 7. A 8. B 9. C 10. D x = 8 = 1 × 6 + 5
11. D 12. C 13. C 14. C 15. B Coordinate of the point = (8, 0) = 11
10
16. B 17. D 18. A 19. C 20. B Section B
21. B 22. D 23. C 24. A 25. B Gradient of two points = 12 – 0 = 3
26. B 27. C 28. A 29. D 30. C 12 – 8 11. (a) x + y < 160
2
31. D 32. C 33. A 34. C 35. B y = mx + c y > x
36. C 37. B 38. C 39. A 40. B 0 = 3(8) + c 3
c = –24 8x + 5y > 400
Paper 2 hence, the equation of the straight (b) y
Section A line is y = 3x – 24 180
The three inequalities that satisfy the
1. (a) True shaded region: 160
(b) Not a statement x + 3y > 8, y , x, y > 3x – 24 140 x + y = 160
(c) y = 6x + 3 120
2
6. The nearest road that travelled by Ahmad
2. (a) The distance from Mantin to Kajang = 4 + 3 + 8 + 8 = 23 km 100 2
= 70 – 25 = 45 km The nearest road that travelled by Muthu 80 y = –x
3
Time taken from Mantin to Kajang = 11 + 5 + 12 = 28 km 60
= t – 25 Ahmad will reach the library first. 40
Distance
Speed = = 1.5 km min With the the same average speed, it will 20 8x + 5y = 400
–1
Time 0 x
45 = 1.5 take less time for Ahmad to travel. 20 40 60 80 100120140160
t – 25 7. (a) Income = RM3 500, (c) 25 chairs of type A.
45 = 1.5(t – 25) Total expenses (d) When 80 chairs of type A are sold,
45 = 1.5t – 37.5 = 500 + 300 + 1 500 the maximum number of chair of
45 + 37.5 = 1.5t = RM2 300 type B is 80. CHAPTER 8 – SPM Assessment
1.5t = 82.5 Cash flow = RM3 500 – RM2 300 Profit = 8x + 5y
82.5 = RM1 000
t = = 8(80) + 5(800)
1.5 (c) Monthly surplus = RM1 000 + RM600 = 640 + 400
= 55 minutes = RM1600 = RM1 040
(b) Time taken = t – 25 Extra expenses = RM2 500
= 55 – 25 Cash flow = RM1 600 – RM2 500 12. (a) Total income = RM95 560
= 30 min = –RM900 Total tax relief, W
(c) Total distance = 70 km, Total time The cash flow of Encik Faizal = RM9 000 + RM2 500 + RM2 000
taken = 55 min become negative and has a deficit of + RM5 680 + RM3 000
70 km RM900. The cash deficit occurred = RM22 180
Average speed =
55 min because the expenses of Encik Faizal Chargeable income, X
70 km is more than the total income earned. = RM95 560 – RM22 180
= = RM73 380
( ) hour 8. (a) L fi j fi s Tax on the first 70 000, Y
55
60
L = kjs
70 × 60 = RM4 600
= km j 120 = k(2.5)(8)
–1
55 120 Tax on the next balance, Z
= 76.36 km j k = 2.5 × 8 = 6 = (RM73 380 – RM70 000) × 21%
–1
3. (a) A = Ahmad, B = Borhan, C = Chong, L = 6js, = RM3 380 × 21
D = Devi, E = Eliana L = 6(3)(9) 100
= RM709.80
S = {ABC, ABD, ABE, ACD, ACE, = 162 cm 2 (b) Income tax payable
ADE, BCD, BCE, CDE} (b) The curved surface area will
(b) (i) Consist of two female = {ADE, decrease. = Tax on the first 70 000 + tax on the
next balance (3380 × 21%) – Zakat
BDE, CDE} 9. Amount of required insurance = RM4 600 + RM709.80 – RM500
3 1 P
Probability = = = × RM6 500 = RM6 500P = RM4 809.80
9 3 100
(ii) Borhan and Chong together = Amount of compensation (c) Income tax payable in the assessment
{ABC, BCD, BCE} year = RM4 809.80
Probability of Borhan and = Amount of required insurance × Total deduction of PCB
1 Amount of required insurance = RM328 × 12
Chong not together = 1 – 3 RM299 885
2 = RM3 936
= RM450 000 Total of PCB deduction < total
3 = × RM350 000 – RM3 000
4. (a) (i) ξ = P  Q  R RM6 500P income tax payable
(ii) R  Q (set R is the subset for set Amount of required insurance, The balance of the income tax
Q) RM450 000 × RM350 000 payable
(b) W = {3, 6, 9, 12, 15, 18} RM6 500P = RM299 885 + RM3 000 = RM4 809.80 – RM3 936
Y = {1, 2, 4} = RM520 000 = RM873.80
Z = {1, 2, 4, 8}
133
Answers 1202BS Maths F5.indd 133 25/01/2022 11:47 AM

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