soalan topikal spm

8/12/2019 soalan topikal spm

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PART A

SETS

1. The Venn diagram in the answer space shows setsX, YandZsuch that the universal set,.X Y Z

On the diagrams in the answer space, shade

(a) the set Y Z (b) the set ( ) .X Y Z

[3 marks]

Answer:

(a)

(b)

2. The Venn diagram in the answer space shows sets P, Q and R with = PQR.

On the diagram provided in answer space, shade

a) P Q'

b) Q ( P R )

[3 marks]

Answer :

a) P Q

R


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b)

P Q

R

3. On the diagrams provided in the answer space, shade the region which

represent the following operation of set.

(a)Set A B'(b)(b) A (B C)'

[3 marks]

Answer:

( a )

(b)

4 The Venn Diagram in the answer space shows sets A, B and C.On the diagram provided in the answer space, shade

a the set A B'

b the set A B C'

Answer:

(a) (b)

CBA

C

BA

A

B CA

B

C


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5 The Venn diagram in the answer space shows sets P,Q and R such that the universal set,

= P Q R.

On the diagram in the answer space, shade

a the set P/Q

b the set ( P Q /) R.

Answer:

(a)

(b)

P

P

Q

Q

R

R

P

P

Q

Q

R

R


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LINEAR INEQUALITIES

1. On the graph in the answer space, shade the region which satisfies the three

inequalities 3 12,y x 2 4y x and 2x .

[3 marks]

Answer :

2. On the graph provided, shade the region which satisfies the three inequalities

y 2x + 8, y x and y < 8.

[3 marks]

Answer :

y=

x

y=

2x

+8

x

y

O

2 4y x

3 12y x

O x

y


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3. On the graph in the answer space, shade the region which satisfies the three inequalitiesy 2x + 10, x < 5 and y 10.

[3 marks]

Answer :

x

y

O

y = 10

y=-2

x+10

5


y -2x + 5, y x and y < 5.[3 marks]

Answer :

y = -2x + 5

y = x

y

xO


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y x + 3, x > -3 and 3x + y 2.

[3 marks]

Answer:

y = x + 3

3x + y = 2

y

x- 3 OI


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SIMULTANEOUS LINEAR EQUATIONS

1. Calculate the values of mand nthat satisfy the following simultaneous

linear equations.

54

1332

nm

nm

[ 4 marks]

2. Calculate the values ofpand qthat satisfy the following simultaneous

linear equations.

243

1322

1

qp

qp [ 4 marks]

3. Calculate the values of randsthat satisfy the following simultaneous

linear equations.

72

3

62

sr

sr

[ 4 marks]


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4. Calculate the values ofgand hthat satisfy the following simultaneous

linear equations.

1834

12

hg

hg [ 4 marks]

5. Calculate the values ofxandythat satisfy the following simultaneous

linear equations.

164

32

3

yx

yx [ 4 marks]

6. Calculate the values of aand bthat satisfy the following simultaneous

linear equations.

93

53

12

ba

ba [ 4 marks]


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7. Calculate the values of dand ethat satisfy the following simultaneous

linear equations.

732

24

ed

ed

[ 4 marks]

8. Calculate the values of hand kthat satisfy the following simultaneous

linear equations.

42

1

434

kh

kh

[ 4 marks]

9. Calculate the values of m and n that satisfy the simultaneous linear

equations.

52

72

nm

nm

[ 4 marks]


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10. Calculate the values of u and v that satisfy the simultaneous linear equat

46

734

vu

vu

[ 4 marks]

.


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QUADRATIC EXPRESSIONS AND EQUATIONS

1. Solve the equation 21

522

x

xx [ 4 marks]

2. Solve the quadratic equation yy

33

522

[ 4 marks]

3. Solve the quadratic equation 62

)1(3

p

pp [ 4 marks]


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4. Using factorization, solve the following quadratic equation.

qq 17154 2 [ 4 marks]

5. Solve the quadratic equationr

rr

2

361

[ 4 marks]

6. Solve the quadratic equation2

562

w

w

[ 4 marks]


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7. Solve the quadratic equation 7)2)(12( aa [ 4 marks]

8. Solve the quadratic equation 12

32 p

p [ 4 marks]

9. Solve the following quadratic equation

)3(5)3)(1( eee [ 4 marks]


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10. Solve the equation 52)4( 2 yy [ 4 marks]


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SOLID GEOMETRY

1.

DIAGRAM 1

Diagram 1 shows a composite solid formed by the combination of a cuboid and a half-

cylinder. Using =7

22

calculate the volume, in cm3, of the solid. [4 marks]

21 cm8 cm

P Q

RS

T

UV

W7 cm


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2.

DIAGRAM 2

Diagram 2 shows a solid cylinder of height 15 cm and diameter 14 cm. A cone with height 6 cm is

taken out of the solid. Calculate the volume, in cm3, of the remaining solid. (Use =7

22).

` [4 marks]

15 cm


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3.

DIAGRAM 3

Diagram 3 shows a solid cuboid ABCDEFGH. A right pyramid with its base EFGH is

taken out of the solid. The volume of the remaining solid is 480 cm 3 . Calculate the heightof the solid, h.

(Use =7

22). [4 marks]


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4. The diagram 4 shows a composite solid, formed by the combination of a cylinder to a right

prism. Trapezium ABEFis the uniform cross-section of the prism.AB= BC= 10 cm.

The diameter of the cylinder is 7 cm and the volume of the composite solid is 1075.5 cm3.

Using7

22 , calculate

(a) the volume, in cm3, of the right prism

(b) the length h in cm, of the cylinder.

[5 marks]

DIAGRAM 4


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5. The diagram 5 below shows a combined solid of a right prism and a right pyramid which are

joined at the planePQRS. T is vertically above the basePQRS. Trapezium PQKJ is the uniform

cross section of the prism.

The height of the pyramid is 6 cm andPQ= 18 cm.

(a)Calculate the volume, in cm3, of the right pyramid.(b)It is given that the volume of the combined solid is 448 cm3. Calculate the length, in cm, of

PJ.

[5 marks]

DIAGRAM 5


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MATHEMATICAL REASONING

1. a) State whether the following statement is true or false

b) Write down two implications based on the following sentence

c) State the converse of the following statement and hence determine whether its

converse is true or false

if 2x >8, then x > 4

Answer :

(a)

(b) Implication 1 :

Implication 2 :

(c)

2. (a) Complete each statement in the answer space with the quantifier all or

some so that it will become a true statement.

(b) State the converse of the following statement and hence, determinewhether its converse is true or false.

(c) Write down Premise 2 to complete the following argument :Premise 1 : If mis less than zero, then mis a negative number.

Premise 2 : _________________________________________________

Conclusion : - 4 is a negative number. [5 marks]

Answer :

(a) (i) of the multiples of 5 are even numbers.

(ii) hexagons have six sides.

(b)

(c) Premise 2 :

Ifp > 7, thenp> 4

9 > 8 or 4 = 8

x = 64 if and only ifx= 4


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3. (a) State whether the sentence below a statement or non-statement ?

(b) Statement 1 : a 0 = 1 for any values of a except a = 0

Statement 2 : All prime numbers are odd numbers

Combine the above statement to form a new statement which is

(i) true

(ii) false

(c) Make a general conclusion by induction for the following number pattern:

5 = 3(2 )1

10 = 3(22)2

21 = 3(23)360 = 3(24)4

[5 marks]

Answer :

(a)

(b) Conclusion :

(c) Conclusion :

4. (a) State whether each of the following statement is true or false.

(i) 23= 6 or = 3.5

(ii) ( -4 ) x ( -5 ) = 20 and -4 > -2

(b) Complete the premise in the following argument:

Premise 1 : If the determinant of a matrix = 0, then the matrix does not

have an inverse.

Premise 2 : _______________________________________________

Conclusion :Matrix A does not have an inverse.

(c) Write down two implications based on the following sentence.

ABif and only if AB= A'

[5 marks]

Answer :

(a) (i)

(ii)

p+ q= 2

2

7


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(b) Premise 2 :

(c) Implication 1 :

Implication 2 :

5. (a) State whether the following statement is true or false.

(b) Write down two implications based on the following statement:

(c) State the converse of the following statement and hence determine whether

its converse is true or false

if x >9, then x > 5

[5 marks ]

Answer :

(a)

(b) Implication 1 :

Implication 2 :

(c)

6. (a) State whether each of the following statement is true or false.

(i) 42= 8 or = -2

(ii) a { a, b, c } and -3 > -7

(b) Write down premise 1 to complete the following argument.

Premise 1 :_________________________________________________

Premise 2 : 6 p 42

Conclusion :p7

(c) Form a general conclusion by induction for the number sequence

11, 23, 43, 71, which follow the pattern

11 = 4(1)2 + 7

23 = 4(2)2+ 7

43 = 4(3)2+ 7

71 = 4(4)2+ 7 [5 marks ]

-2 3 = 6 or -4 > -5

p = 8 if and only ifp= 2

3 8


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Answer :

(a) (i)

(ii)

(b) Premise 1 :

(c) Conclusion:

7. (a) Determine whether each of the following sentence is a statement.

(i) 9 is a prime number.

(ii) 2x(x2) = 0

(b) Fill in the suitable quantifier to make the following statement become true.

(c) Write down two implications based on the following sentence

3m >15 if and only if m >5 [5 marks]

Answer :

(a) (i)(ii)

(b)

(c)

8. (a) State whether the following statement is true or false.

(i) 8 + 2 = 10 and 2 < -3

(ii) All perfect square numbers are even numbers

.

(b) Complete the following argument.

Premise 1 : If 3t= 0, then t= 0.

Premise 2 : ________________________________________________

Conclusion :3t0

(c) State the converse of the following statement and hence, determine

whether its converse is true or false.

[5 marks]

. rime number are odd numbers

Ifx3= 27 then x= 3


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Answer :

(a) (i)(ii)

(b) Premise 2 :

(c)

9. (a) Is the sentence below a statement or non-statement?

(b) Write down two implications based on the following sentence:

(c) Make a general conclusion by induction for the following number pattern :

2 = (0)2+ 2

3 = (1)2+ 2

6 = (2)2+ 2

11 = (3)2+ 2

. = .. [5 marks]

Answer :(a)

(b) Implication 1 :Implication 2 :

(c)

10. (a) State whether each of the following statement is true or false

(i) (-2)2= 4 or ( -3 )3= -9

(ii)1 1

2 21

16 8 and 255

(b) Complete the following argument.

Premise 1 :_________________________________________________

Premise 2 :xn+xis not a quadratic expressions.

Conclusion : n 2.

(c) Write down two implications based on the following sentence.

[5 marks]

3 and 4 are factors of 8

mis an even number If and only if m can be divided by 2.

1q> 2 if and only if q< -1


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Answer :

(a) (i)(ii)

(b) Premise 1 :

(b) (c) Implication 1 :

Implication 2 :


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THE STRAIGHT LINE

1. In Diagram 1, O is the origin, point R lies on the x-axis and point P lies on the y-axis. Straightline PU is parallel to x-axis and the straight line PR is parallel to straight line ST. The equation

of straight line PR is x + 2y = 14.

R xO

T(2,-5)

S

U

x + 2y = 14

y

(a) State the equation of the straight line PU. [2 marks]

(b) Find the equation of the straight line ST and hence,

state its x-intercept. [3 marks]

Answer:

P

DIAGRAM 1


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2. The diagram below shows that the straight line EF and GH are parallel.

DIAGRAM 2

Find

(a) the equation of EF. [3 marks](b)the y - intercept and x - intercept of EF [2 marks]

Answer:


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4. In the diagram 4, the gradient of the straight line KLM is2

1 . Find

(a) the value of p.

(b) the x-intercept of the straight line MN.

Answer:

K(0, p)

0

y

x

N

M

L 2 4

DIAGRAM 4


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5. The diagram 5 below shows STUV is a trapezium

i) Given that gradient of TU is -3, find

a) the coordinates of point T. [2 marks]

b) the equation of straight line TU. [1 marks]

ii) The equation of straight line TV [2 marks]

Answer:

DIAGRAM 5


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PERIMETER AND AREA

1.

18 cm

Diagram 1

15 15

E

A

B

O F

C D

In Diagram 1, OAB, OCD and OFE are three sectors in a circle centre O. AOF, BCO and EDO are

straight lines. C and D are midpoints of OB and OE respectively.

Using22

7

, calculate

a) the perimeter , in cm, of the whole diagram,

b) the area, in cm2, of the shaded region. [6 marks]


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2.

Diagram 2

S

O

R

P Q120

Diagram 2 shows two sector ORS and OPQ with the same centre O. P and Q are midpoints of OR

and OS respectively and OS = 28 cm. Using22

7 , calculate

a) the perimeter, in cm, of the whole diagram



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3.

In Diagram 3, OFIE is a quadrant of a circle with centre O and GH is an arc of another circle with

centre O. OFG and OIH are straight lines.

OF = FG = 14 cm, and 35GOH .

Using22

7 , calculate



Diagram 3

H

E

GF

I

O


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4.

14 cmDiagram 4

OP

Q

R

T

U

S

Diagram 4 shows two semicircles RSO and RTU with centre Q and O respectively. OPQ is a

quadrant of a circle with centre O. RQ = QO. ROU is a straight line.

Using22

7 , calculate




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5.

H

GF

EI

Diagram 5

J

K

In diagram 5, two arcs of two equal circles, GFE and GIJ, with centres H and K respectively. It is

given that GH = 14 cm.

Using22

7 , calculate




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6.

.

Diagram 6

O S

Q

RP

150

Diagram 6 shows two sectors OPQ and OQR with centre O. OS = SR = 7 cm. POSR is a straight

line.

Using 227

, calculate




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MATRICES

1a) The inverse matrix of is4

5 3

pq

.Find the value ofpand of q.

b) Using matrices, calculate the values ofxandythat satisfy the following simultaneousequations :

3x2y= 6 [6 marks]

5x4y= 4

Answer:

1a) 1b)

2.a) Given that F = and the inverse matrix of F is find the value

of mand of n.

b) Hence, using matrices, calculate the value ofpand of qthat satisfies the followingequation

2

5

pF

q

[6 marks]

Answer:

2a) 2b)

45

23

n

m

2

3,

2

34

14

1

m


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5. Given the matrix K is ,

a) Find the matrix L so that KL =

b) Hence, calculate the values of h and k, which satisfy the matrix equation:

[6 marks]

Answer :

5a) 5b)

6. Given matrix M = 1 22 6

, find

a) the inverse matrix of M.

b) hence, using matrix, find the values ofxandythat satisfy the following

simultaneous equations :

x2y = 3

2x + 6y = 4 [6 marks]

Answer:

6a) 6b)

11

7

58

34

k

h

10

01

58

34


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7. It is given that matrix A =1

3 4

a

does not have an inverse matrix.

a) Find the value of a.

b) If a= 2, find the inverse matrix of A and hence, using matrices, find the values ofx andythat satisfy the following simultaneous linear equations.

x2y = 63x+ 4y = 2 [6 marks]

Answer :

7a) 7b)

8a) Find matrix Gsuch that 3 1 3 14 2 4 2

G

b) Using matrices, calculate the values of pand qthat satisfy the following matrix

equation.

2p+ 4q= 4

p+ 3q = 8 [5 marks]

Answer :

8 a) 8b)


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9 a) Find the inverse of matrix4 5

1 2

b) Hence, using matrices, calculate the values of mand nthat satisfy the following

simultaneous equations :4m+ 5n= 1

m+ 2n= 2 [6 marks]

Answer:

9a) 9b)


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10a) Given matrix S =6 3

4 m

, find the value of m if matrix S has no inverse.

b) Given the matrix equations

and

i) Find the value of h and k

ii) Hence, find the value ofxandy. [6 marks]

Answer:

10a) 10bi)

10bii)

11. It is given matrix U =1 2

3 2

and matrix V =2 2

3v u

such that UV =1 0

0 1

a) find the values of u and v.

b) using the matrix method, calculate the values ofxandythat satisfy the following

simultaneous equations

x 2y= 3

3x+ 2y = 5 [6 marks]

Answer:

11a)

11b)

1

4

85

67

y

x 8 41

5 7 1

x k

y h


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GRADIENT AND AREA UNDER GRAPH

1. Diagram 1 shows a distance-time graph for the journey of a car and lorry from town Q.

Diagram 1GraphABCDrepresents the journey of the car and graphACErepresents the journey of the

lorry. Both vehicles depart from town Qat the same time along the same road.

(a) State the length of time, in hours, during which the car is stationary.

(b) Calculate the average speed in km/h for the total distance of the car.

(c) At the certain time during the journey, both vehicles meet at the same location.

(i) Find the distance, in km, between that location and town Q.

(ii) State the time taken by the lorry to reach that location from town Q.

[ 5 marks ]

Answer:

(a)

(b)

(c) (i)

(ii)

70

142

195

Time (hour)

Distance (km)

0 3.21.41.0

A

E

D

B C


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2. The diagram shows a speed-time graph of the movement of a particle for a period of 35 s.

(a) State the uniform speed, in ms-1, of the particle.

(b) Given the distance travelled by the particle at a uniform speed is 250m,

calculate

(i) the value of t,

(ii) the average of speed, in ms-1, of the particle for the period of 35 seconds.

[ 6 marks ]

Answer:

(a)

(b) (i)

(ii)

Time (s)

Speed (m s- )

20

12

10 t 35


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3. Diagram 2 shows a distance-time graph for the journey of a bus and van.

Diagram 2

GraphAFBrepresents the journey of the van from townXto town Y. The graph CDEFG

represents the journey of the bus from town Yto townX. The van leaves townXand the

bus leaves town Yat 9.45 p.m. and they travel along the same road.

(a) (i) At what time do the vehicles meet ?

(ii) Find the distance, in km, from town Y when the vehicles meet.

(b) State the length of time, in minutes, during which the bus is stationary.

(c) Calculate the average speed, in km h-1, of the bus for the whole journey.

[ 5 marks ]

Answer:(a) (i)

(ii)

(b)

(c)

Time

(minutes)0

10 50 70 150

B

Distance (km)

65

100

A

C

G

DTown Y E

F

TownX


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4. Diagram 3 shows a speed-time graph for a particle, of 30 seconds.

Speed (m s-1)

(a) The distance travelled during the last seconds is 106 m, find the value of v.

(b) Calculate the acceleration, in m s-2, of the particle in the last 5 seconds.

(c) The total distance travelled before 10 seconds is 230 m. Calculate the average

speed for the whole journey.

[ 6 marks]Answer:

(a) (i)

(b)

(c)

10 25 30 Time (s)

21

0

Diagram 3

v

25


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5. The diagram 4 shows the speed-time graphs of two particlesMandNover a period of 100

seconds.ABCDis the speed-time graph of particle MandEFGis the speed-time graph of

particleN.

(a) State the length of time in seconds, during which the particle N is constant speed.

(b) Calculate the rate of change of speed, in ms-2, of the particleM in the first 20s,

(c) Given that the distance travelled by both particles over the 100 s period is the

same and the distance traveled by particles N is 8500 m. Calculate the value of v.

[ 6 marks ]

Answer:

(a)

(b) (i)

(ii)

Speed (ms-1)

20 40 60 10080Time s

0

v

80

145

G

D

F

E

BC

A

Diagram 4


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PROBABILITY

1.

StudentsProbability of choosing:

Biology Physics Chemistry

Ahmad4

3

8

1

Ling5

1

5

2

The table 1 shows the probability of how Ahmad and Ling might choose their subjects in

Form 6. The table is incomplete.

Calculate the probability that

(a) Ahmad will choose Chemistry and Ling will choose Biology,(b)Ahmad and Ling will choose the same subjects. [5 marks]

Answer:

(a)

(b)

2. In bagA, there are 4 blue balls and 3 yellow balls while in bagB, there are 5 blue balls and

6 yellow balls. A ball is drawn at random from bagA. After its colour is recorded, it is put

into begB. Then a ball is drawn at random from begB. Find the probability that

(a) the colour of the two balls are blue,(b) two different colour balls are drawn. [5 marks]

Answer:

(a)

(b)

Table 1


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3. A company van carries a group of workers consists of 6 males and 8 females. They are

dropped off at random at various houses along the route as shown in the diagram below to

serve customers.

(a) If two workers are dropped off at house A, calculate the probability that both are females,(b)Two male workers are dropped off at house A. If another two workers are then dropped

off at house B, calculate the probability that at least one of them is female.[5 marks]

Answer:

(a) (b)

4 In a lucky draw, there are three categories of gifts consisting of 4 hotel vouchers, 6 shopping

vouchers and 10 restaurant vouchers. All vouchers are placed inside similar envelopes and

put inside a box. The honored guests of the lucky draw are requested to draw at random two

envelopes from the box.

Calculate the probability that the first honored guest draw

(a) the first envelope with a hotel voucher and the second with a shopping voucher,

(b) two envelopes with vouchers of the same categories. [5 marks]

Answer:

(a)

(b)

Other houses

Company House A

House B


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5. The table below shows the number of participants in a quiz contest according to school and

gender.

School

Number of Participants

Male Female

SMK Ria 4 4

SMK ACS 5 2

SMK Puteri 3 6

(a) If two participants are chosen at random from SMK ACS, calculate the probability thatboth of them are males.

(b) If two participants are chosen from the male participants, calculate the probability that

both of them are from the same school. [5 marks]

Answer :

(a)

(b)

6. BottleAcontains three red marbles and two yellow marbles. BottleBcontains four red marbles

and three yellow marbles. A marble is chosen at random from each bottle.

Find the probability that

(a)both marbles are in yellow,

(b)both marbles are in different color. [5 marks]

Answer:

a)

b)

Table 2


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LINES AND PLANES IN 3-DIMENSIONS

1. Diagram 1 shows a pyramid with a horizontal rectangular base ABCD. M is the

mid-point of CD and apex V is 9 cm vertically above the point M

Identify and calculate the angle between the line VB and the base ABCD.

24 cm

14 cm

B

A

D

M

C

V

(4 marks)

Answer :

2. Diagram 2 shows a right prism. Right angled triangle PQR is the uniform cross-

section of the prism. Calculate the angle between the plane RTU and the plane

PQTU. (3 marks)

Answer :

DIAGRAM 1

T

P

5 cm

Q

DIAGRAM 2

R

S

U

18 cm

12 cm


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3. Diagram 3 shows a prism with a horizontal square base HJKL. Trapezium EFLK is

the uniform cross-section of the prism. The rectangular surface DEKJ is vertical while

the rectangular surface GFLH is inclined.

Calculate the angle between the line DL and the base HJKL (4 marks)

Answer :

4. Diagram 4 show s a right prism . Plan ABFE, ADHE and BCGF are rectangular

planes . Planes ABCD and EFGH are parallel trapezium. It also given BAD and

ADC = 90, FG = 5 cm, AB = 2 cm and CG = 12 cm. Identify and calculate the angle

between the plane ADG and AEHD.

5 cm

4 cm

HG

FE

D C

BA

[4 marks]

Answer :

8 cm

G

L

H

K

J

D

FE L

5 cm

6 cm DIAGRAM 3

DIAGRAM 4


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5. Diagram 5 shows a right prism with horizontal rectangle base. Right triangleRSW are the uniform cross section of the prism.

Calculate the angle between plane SRVand planeRSTU (3 marks)

Answer :

6. Diagram 6 shows a right prism. The base PQRS is a horizontal rectangle. Right angled

triangle QRU is the uniform cross section of the prism. V is the midpoint of PS.

Identify and calculate the angle between the line UV and the plane PQRS.

(4 marks)Answer :

DIAGRAM 5

5 cm

10 cm12 cm

T

U

W

S

R

VV

T

U

W

S

R

DIAGRAM 6

S

Q

U

T

P

10 cm

R

12 cm

5 cmV


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7. Diagram 7 shows a right prism. Right angled triangle PQR ia the uniform cross-

section of the prism. Calculate the angle between the line TR and the plane

PQTU. (4 marks)

Answer :

18 cm

12 cm

5 cm S

T

U

Q

P

R

DIAGRAM 7


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PART B

GRAPH OF FUNCTIONS

1 (a) Complete Table 1 in the answer space for the equation y =x

6by writing down

the values of y when x = -2 and x = 0.5 [2 marks](b)

(For this part of the questions, use a graph paper)

By using a scale 2 cm to 1 unit on the x-axis and 2 cm to 1 unit on the

y-axis, draw the graph of y =x

6 for -4 x 4. [4 marks]

(c) From your graph, find

i. the value of y when x = -2.7,ii. the value of x when y = 3.6. [2 marks]

(d) Draw a suitable straight line on the graph in (b) to find the values of x which

satisfy the equation 0236

x

x

for -4 x 4. [4 marks]

Answer:

(a)

X -4 -3 -2 -1 -0.5 0.5 0.8 1.5 2.5 4

Y -1.5 -2 -3 -6 -12 12 4 1.5

Table 1

(c) i) y =

ii) x =

(d) x =

2. (a) Complete Table 2 in the answer space for the equation y =x

72by writing

down the values of y when x = 2.4, x = 6 and x = 12.5 [3 marks]

(b) (For this part, use a graph paper)By using a scale 1 cm to 1 unit on the x-axis and 1 cm to 2 units on the y-axis, draw

the graph of y =x

72 for 2 x 1 4. [4 marks]

(c) From your graph, find

a. the value of y when x = 4.3,b. the value of x when y = 22. [2 marks]

(d) Draw a suitable straight line on your graph to find all the values of x which

satisfy the equation 0152

36

x

x

State these values of x. [3 marks]


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Answer:

(a)

X 2 2.4 3 4 6 8 10 11.6 12.5 14

Y 36 24 18 9 7.2 6.2 5.14

Table 2

(c) (i) y =

(ii) x =

(d) x =

3. a) Complete Table 3 in the answer space for the equation y = 2x2

5x3.[2 marks]

b) For this part, use a graph paper.By using a scale 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, draw

the graph ofy= 2x25x3 for -3 x 5. [4 marks]

c) From your graph, findi) the value ofy whenx= -2.4,ii) the value ofxwhen 2x25x3 = 0. [2 marks]

d) Draw a suitable straight line on your graph to find all the values of x which satisfy

the equation 2x28x= 7 for -3 x 5.State these values ofx. [4 marks]

Answer:

a)

c) i) y =

ii) x =

d) x =

x -3 -2 -1 0 0.5 1 2 3 4 5

y 30 4 -3 -6 -5 0 9 22

Table 3


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4. a) Complete Table 4 in the answer space for the equationy= -2x + 5x + 8 by writing

down the values ofywhenx= -2 andx= 3 [2 marks]

b) For this part of question , use the graph paper provided . You may use a flexible

curve ruler.

By using a scale 2 cm to 1 unit on the x axis and 2cm to 5 unit on they axis , draw

the graph of y= -2x + 5x+8 for -3.5 x 4 [4 marks]

c) From the graph, find

(i) the value ofywhenx= 3.3

(ii) the value ofxwheny= -16

[2 marks]

d) Find and draw a suitable straight line on your graph to determine the values of x

which satisfy the equation 2x2x = -10 for -3.5 x 4

State the values ofx [4 marks]

Answer :

a)

x -3.5 -3 -2 -1 0 1 2 3 4

y -34 -25 1 8 11 10 -4

c) i) y=

ii) x=

d) x=

5. a) Complete Table 5 in the answer space for the equation y = x313x + 18 .

[2 marks]

b) For this part, use a graph paper.By using a scale 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, draw the

graph of y = x313x + 18 for -4 x 4. [4 marks]

c) From your graph, findi. the value of y when x = -1.5,ii. the value of x when y = 25. [2 marks]

d) Draw a suitable straight line on your graph to find all the values of x which satisfy theequation x311x2 = 0 for -4 x 4. State these values of x. [4 marks]

Table 4


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Answer:

(a)

X -4 -3 -2 -1 0 1 2 3 4

Y 6 36 30 18 6 6 30

c) i) y =

ii)x =

d) x=

6. a) Complete Table 6 in the answer space for the equation y = x3+ x212x5.

[2 marks]

b) For this part, use a graph paper.By using a scale 2 cm to 1 unit on the x-axis and 2 cm to 5 units on the y-axis, draw

the graph of y = x3+ x212x5 for -4 x 4. [4 marks]

c) From your graph, findi. the value of y when x = 0.5,ii. the value of x when y =11.9. [2 marks]

d) Draw a suitable straight line on your graph to find all the values of x whichsatisfy the equation x3+ x210x = 0 for -4 x 4.

State these values of x. [4 marks]

Answer:

(a)

X -4 -3 -2 -1 0 1 2 3 4

Y -5 13 7 -5 -15 -17 27

c) i) y=

ii) x=

d ) x =

Table 5


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TRANSFORMATION

1. Diagram 3 shows three pentagons EFGHJ, EKLMN and KPQRS on a Cartesian

plane.

Diagram 3

(a)Transformation Tis the translation

2

3

Transformation Ris a reflection about the line KMN.

State the coordinates of the image of point J under the following

transformations:

(i) TR

(ii) RT[4 marks]

(b) EKLMN is the image of EFGHJ under transformation Vand EKLMN is the

image of KPQRS under transformation W.

Describe in full the transformation

(i) V

(ii) W

[5 marks]


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(c) Given that the area of EFGHJ is 26.8cm , calculate the area of shaded region

[3 marks]

Answer:

(a)

(i)

(ii)

(b)

(i) V =

(ii) W=

(c)

2 Diagram 5 shows quadrilateral ABCD, PQRS and KLRM drawn on a Cartesian

plane.

Diagram 5(a)

Transformation Tis the translation

2

4.

Transformation Vis a reflection in the line y = 1 .

State the coordinates of the image of point A under the following

transformations:

(i) Translation T,

(ii) Combined transformation VT

[3 marks]


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(b) (i) KLRM is the image of ABCD under the combined transformations WU.

Describe in full, the transformation Uand the transformation W.

(ii) Given that the shaded region KLQPSM represents a region of area 120 m .

Calculate the area, in m2, of the region represented by PQRS.

[9 marks]

Answer:

(a)

(i)

(ii)

(b)

(i) U =

V =

(ii)

3. (a) Diagram 3 shows the point Fon a Cartesian plane.

DIAGRAM 3

x

y

2 4 6 8 10 12 14 16

2

4

6

8

10

0

F


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Transformation Sis a translation

2

5.

Transformation Tis a reflection in the x = 9.

(i) State the coordinates of the image of point Funder transformation S.

(ii) State the coordinates of image of point F under transformation TS. [3 marks]

Answer:

(a) (i)

(ii)

(b) Diagram 4 shows three trianglePQR,ACG andEFGon a Cartesian

plane.

DIAGRAM 4

TriangleACG is the image of trianglePQR under transformation V.

TriangleEFG is the image of triangleACG under transformation W.

(i) Describe in full transformation :

(a) V

(b) W [6 marks]

(ii) Given that the area of triangleEFGrepresents a region of area 72 unit2.

x

y

E

2 4 6 8 10 12 14 16

2

4

6

8

10

O

F

C

A

GP

RQ


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PQRSis the image ofABCDunder transformation SandEFGHis the image ofPQRS

under transformation Q.

(i) Describe in full transformation :

(a)Transformation S

(b)Transformation Q [5 marks]

(ii) Given the area ofABCDis 64 unit2, calculate the area of shaded region.

[3 marks]

Answer:


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STATISTICS

1. The data in Diagram 1 shows the monthly pocket money, in RM, received by 40 students.

56 44 60 64 52 53 55 35

36 47 54 59 34 54 52 48

49 51 62 58 38 63 49 43

45 38 48 57 44 49 46 4032 41 46 56 42 48 51 39

Diagram 1

(a) Based on the data in Diagram 1 and using a class interval of RM5, complete

Table 1 in the answer space. [4 marks]

(b) From the table in a),

(i) state the modal class,

(ii) calculate the mean monthly pocket money of the students. [4 marks]

(c) By using a scale of 2 cm to RM5 on the x-axis and 2 cm to 1 student on the y-axis,draw a histogram based on the data.

[4 marks]

Answer:

(a)

Pocket money(RM) Frequency Midpoint

31-35

36-40

Table 1(b) (i)

(ii)

(c)


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2. The data in Diagram 2 shows the marks obtained by 42 students in a Mathematics finalexam.

51 20 45 31 26 40 30

48 32 37 41 25 36 38

46 38 28 37 39 23 3933 35 42 29 38 31 49

42 34 26 35 43 42 22

26 47 40 48 44 34 54

Diagram 2

(a) Based on the data in Diagram 2 and using a class interval 5 marks, complete

Table 2 in the answer space. [4 marks]

(b) From the table in a),

(i) state the modal class,(ii) calculate the mean mark for the Mathematics final exam and give your

answer correct to 2 decimal places. [4 marks]

(c) By using a scale of 2 cm to 5 marks on the horizontal axis and 2 cm to 1 student on

the vertical axis, draw a histogram based on the data. [4 marks]

Answer:

(a)

Marks Frequency Midpoint

20-24

25-29

Table 2

(b) (i)

(ii)

(c)


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3. The data below shows the height, in cm for a group of 40 students in a class.

132 141 146 156 142 148 151 139

136 147 154 159 134 154 152 148

140 153 162 155 138 163 149 143156 144 160 164 152 151 158 135

145 138 148 157 144 149 146 149

a) Based on the data, complete the Table 3in the answer space. [3 marks]

b) From the table in a),

i) State the modal class,ii) Calculate the mean height of the students. [4 marks]

c) By using a scale of 2 cm to 5cm on the x-axis and 2cm to 1 student on

the y-axis, draw a frequency polygon based on the data. [5 marks]

Answer:

a)

Height (cm) Midpoint Frequency

131-135136-140

Table 3

b i)

ii)

c)


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4. The data shows the time taken by 42 participants to complete a road race.

51 20 45 31 26 40 30

25 32 37 41 21 36 3846 38 28 37 39 23 39

33 35 42 29 38 31 23

42 34 26 35 43 28 22

25 47 31 48 44 34 54

a) Using the data above and a class interval of 5 minutes, complete Table 4 in the answer

space. [3marks]

Answer:

Minutes Midpoint Frequency

20-24

25 -29

Table 4

b) Based on your table in (a),

Calculate the mean for the time taken and give your answer correct to two decimal places.

c) By using a scale of 2 cm to 5 minutes on the horizontal axis and 2 cm to 1 participant on the

vertical axis, draw a frequency polygon based on the data. [5 marks]

d) Based on the polygon in (c), state one piece of information. [1 mark]


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5. The data shows the length, in cm, of 50 pieces of wood.

18 42 23 13 29 33 30 38 30 27

7 25 35 11 27 35 27 34 16 26

16 21 41 31 20 33 27 28 17 32

26 20 30 31 26 32 23 19 22 3721 24 25 28 35 12 29 32 33 31

a) Using the data and a class interval of 5 cm, complete Table 5 in the answer space.

[5 marks]

b) For this part of the question, use the graph paper.

By using a scale of 2 cm to 5 cm on the x-axis and 2 cm to 5 pieces of wood on the y-axis, draw

an ogive based on the data. [5 marks]

c) (i) From your ogive in (b), find the first quartile,

(ii) Hence, explain briefly the meaning of the first quartile. [2 marks]

Answer:

5a)

Length(cm) Upper

boundary

Frequency Cumulative Frequency

0 4

5 9

6. A donation drive for the School Building Fund accumulated a substantial amount of money from

400 people as shown in Table 6.

Collection

(RM)

1-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90

Frequency 10 20 40 60 85 90 50 35 10

Table 6

a) State the modal class for the above data. [1 mark]

b) Construct a cumulative frequency table. [2 marks]

c) By using a scale of 2 cm to RM10 on the x-axis and 2 cm to 40 people on the y-axis, plot an

ogive for the data. [5 marks]

d) From the ogive, find the

(i) median, [1 mark]

(ii) percentage of donors who donated less than RM30, [1 mark](iii) number of donors who donated at least RM65. [2 marks]

Table 5


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PLAN AND ELEVATION

1 (a) Diagram 1(i) shows a solid right prism. The base BCKJ is on horizontal plane.EFGM and CDLK are vertical planes whereas EDLM is a horizontal plane.The plane AFGH is inclined. Hexagon ABCDEF is the uniform cross section of the prism.The sides AB, FE and DC are vertical.

Draw in full scale, the plan of the solid . [3 marks]

(b) A half-cylinder is joined to in Diagram 1(i) at the vertical plane BCQP to form a combined solid asshown in Diagram 1(ii)The height of the half-cylinder is 2 cm

b ii)

Draw in full scale ,i. the elevation of the combined solid on a vertical plane parallel to BC as viewed from X [4 marks]ii. the elevation of the combined solid on a vertical plane parallel to CK as viewed from Y. [5 marks]

C

3 cm

K

L

M

ED

G

H

F

A

B

J

8 cm

3 cm

4 cm

6

6

DIAGRAM 1(i)

X C

K

L

M

ED

G

H

F

A

B

J

8 cm

3 cm

4 cm

DIAGRAM 1(ii)

P

Y

3 cm


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2. Diagram 2(i) shows a solid right prism with a rectangular baseABCD. ABMKGF is theuniform cross- section of the prism. Rectangle GHJK is an inclined plane.EFGH and

JKMN is a horizontal plane.

The edges AF, BM, CN and DE are verticals. BM = CN = 2cm, AF = DE = 4cm

AB =DC = 7cm, KM = JN = 5cm and FG = EH = 3cm.

S 2 cm

5 cm

6 cm

7 cm

3 cm

4 cm

J N

MK

H

G

E

F

D

C

BA

a) Draw full scale, the elevation of the solid on a vertical plane parallel toAB as

viewed from X. [3 marks]

b) A prism is joined to the solid in Diagram 2(i) at the vertical plane CDEHJN.Thecombined solid is as shown in Diagram 2(ii). Right angle triangle PQR and DSC is the

uniform cross-section of the prism.

QPR = SDC = 900, DP = CR = SQ = 6cm and PQ = 3 cm.

S

3 cm

R

Q

P

2 cm

5 cm

6 cm

7 cm

3 cm

4 cm

J N

MK

H

G

E

F

D

C

BA

Draw to full scale,

(i) The elevation of the combined solid on avertical plane parallel to BC as viewed

from Y. [4 marks]

(ii) The plan of the combined solid. [5 marks]

DIAGRAM 2(i)

DIAGRAM 2ii)

Y

X


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3. (a) Diagram 3(i) shows a solid prism.

Hexagon ABCDEF is the uniform cross section of the prism. The base ALGF is on the

horizontal plane. The sides BA, CD and EF are vertical whereas the sides BC and DE are

horizontal.

Draw in full scale, the plan of the solid prism. [3 marks]

(b) A solid prism with triangle AFM as its uniform cross section is joined at the vertical plane

ABCDEF to form a combined solid as shown in Diagram 3(ii).

Draw in full scale,

i. the elevation of the combined solid on a vertical plane parallel to GF as viewed from X.

[4 marks]

ii. the elevation of the combined solid on a vertical plane parallel to AF as viewed from Y.

[5 marks]

P

FG

H

E

DI

J

K B

C

AL

2 cm

4 cm

4 cm

4 cm

8 cm

5 cm

DIAGRAM 3(i)

DIAGRAM 2(ii)

6 cm

Y

M

FG

HE

DI

J

K B

C

A

L

2 cm

4 cm

4 cm

X

N

4 cm


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4. Diagram shows a solid right prism with rectangular base ABCD on a horizontal plane. The

surface BFGJKC is its uniform cross-section. The rectangle LKJI is an inclined plane and the

square EFGH is a horizontal plane. The edges GJ and HI are vertical and HI = GJ = 2 cm.

(a) Draw full scale, the elevation of the combined solid on a vertical plane parallel to JI asviewed from X. [3 marks]

(b) A half-cylinder of diameter 4 cm is joined to the prism in diagram 4(i) at the vertical planeLDPM. The combined solid is as shown in Diagram 4 (ii)

Draw full scale,

(i) the plan of the combined solid. [4 marks](ii) the elevation of the combined solid on a vertical plane parallel to AB as

viewed from Y.

[5marks]

C

B

E

A

DF

G

L

H

X

I J

K

4

8

86

DIAGRAM 4(i)

M

P

N

C

B

E

A

DF

G

L

H

Y

I J

K

4 cm

8 cm

8 cm6 cm

DIAGRAM 4(ii)


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5. Diagram 5(i) shows a solid right prism with square base ABCD on a horizontal plane.

ABKIGF is the uniform cross-section of the prism. AF, LC and BK are vertical edges.

Rectangle IJLK is a horizontal plane and rectangle EFGH is an inclined plane.

Answer :

(a) Draw full- scale, the plan of the solid. [3 marks]

(b) A prism with isosceles triangle as its uniform cross-section such that Q is 2 cm above the

midpoint of JL is joint to the prism at the plane MPLJ. The length of PL is 2 cm. The

combined solid is shown in the diagram 5(ii)

cm

Draw full-scale,

i. the elevation of the combined solid on a vertical plane parallel to AB as viewedfrom R [4 marks]

ii. the elevation of the combined solid on a vertical plane parallel to BC as viewedfrom S. [5 marks]

S

R

P

N

M

Q

2 cm

4 cm

5 cmL

K

J

I

H

G

F

E

D

C

B

A

DIAGRAM 5 (ii)

2 cm

2 cm

2 cm

4 cm

5 cmL

K

J

I

H

G

F

E

D

C

B

A

DIAGRAM 5 (i)


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EARTH AS A SPHERE

1. Table 1 shows the latitudes and longitudes of four pointsA,B, CandD, on the surface ofthe earth.

Point Latitude Longitude

A

BC

D

20 S

x0N200 S

300N

25 W

250 Wy0 E

y0 E

(a) Qis a point on the surface of the earth such that AQis the diameter of the earth.State the position of Q. [2 marks]

(b) Calculate(i) the value ofx, if the distance fromAtoBmeasured along the meridian is

4800 nautical mile,(ii) the value ofy, if the distance fromAdue east to Cmeasured along thecommon parallel of latitude is 3664.8 nautical mile. [7 marks]

(c) An aero plane took off fromAand flew due east to Calong the common parallel oflatitude and then due north toD.

If the average speed for the whole flight is 500 knots, calculate the time taken for the

whole flight. [3 marks]

2. P(600N, 600W), Q,Rand Sare four points on the surface of the earth.PQis the diameterof the parallel of latitude 600N. Slies 4800 nautical mile due to south ofPandRlies 450

due east ofP.(a) State the longitude of Q. [2 marks]

(b) Find the position ofR. [3 marks]

(c) Calculate the distance, in nautical mile, fromPto Qmeasured along the parallel

latitude. [3 marks]

(d) An aero plane took off from Qand flew towardsP using the shortest distance, as

measured along the surface of the earth, and then flew due south to S, with an average

speed of 600 knots.

Calculate the time, in hours, taken for the flight. [4 marks]

Table 1

soalan topikal spm

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