Model Paper Spm

7/30/2019 Model Paper Spm

1/9

1 Penerbitan Pelangi Sdn. Bhd.

1. 0.005429 = 0.00543 (3 signicant gures)The two zeros are not counted as signicant gures.

Answer: C

2. 0.000248 = 2.48 104

Answer: C

3. The number o small bottles o shampoo

=4500 103 ml

15 ml

= 3 105

Answer: D

4. 3.7 106 0.00000012

= 3.7 106 0.12 106

= (3.7 0.12) 106

= 3.58 106

Answer: B

5. 1011112

5 7

Hence, 1011112 = 578

Answer: C

6. 10112

+ 11112

110102

Answer: B

7.

115

108

36

72yF

E

L K

JHG

x

y = 72

x= 180 115

= 65

Hence, x+y = 72 + 65

= 137

Answer: C

8. FJH= 40

FOJ= 180 40 40= 100

Answer: D

9.

A

D

C

B

II

I

III

R

Triangles A, B and C are images oR under refection

in lines I, II and III respectively.

Answer: D

10.P

L M

K J

G H

E

N

Scale actor =EPEK

= 2

Centre o enlargement isE.

Answer: A

11.T

R Q

13 cm12 cm

5 cm

x

P


2/9

Mathematics SPM Model Paper

2Penerbitan Pelangi Sdn. Bhd.

RQ =102

= 5 cm

TR = 132 52

= 12 cm

sinx = sin TQR

= 1213

Answer: B

12. R

Q

10 cmx

O

QO =QS

2=

162

= 8 cm

OR = 102 82

= 6 cm

tanx =86

= 43

Answer: D

13. sin 0 = 0

sin 90 = 1

sin 180 = 0

sin 270 = 1

Answer: B

14.

SV

T W

R

QP

U

Answer: B

15. E

F

G R

T

Answer: C

16.

Y

X

Q31

50 m

tan 31 =XY

50XY= 50 tan 31

= 30.0 m

Answer: B

17.

G

H

60

North

Answer: D

18. Latitude oR = (60 40)S

= 20S

Longitude oR = (180 130)W

= 50W

Hence, the position oR = (20S, 50W)

Answer: A

19. 5xx(2 3x) = 5x (2x 3x2)= 5x 2x+ 3x2

= 3x2 + 3x

Answer: D


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20. (4p2 2pq) p

q2(2p q)

= 2p(2p q) p

q2(2p q)

=2p2

q2

Answer: C

21. ef+ 1 =4e 3f

3

3(ef+ 1) = 4e 3f

3ef+ 3 = 4e 3f

3ef+ 3f= 4e 3

f(3e + 3) = 4e 3

f=4e 3

3e + 3

Answer: D

22. 72

+ 2m = 4(1 m)

72

+ 2m = 4 + 4m

72

+ 4 = 4m 2m

72

+ 82

= 2m

2m =152

m =154

Answer: D

23.213

712 34

2

=73 33

712 34

2

=76 3671 38

= 76 1 36 8

= 75 32

Answer: A

24. x+ 1 12x , x 1

4(x+ 6)

2x+ 2 x , 4x x+ 6

2xx 2 , 4xx 6

x 2 , 3x 6

x 2

Hence, x= 2, 1, 0, 1

Answer: C

25. Median =20 + 1

2th observation

= 10.5th observation

Median = 2 + 32

= 2.5

Answer: B

26. The number o can drinks sold in 3rd and 4th week

= 4050 (12 150)

= 2250

Let the number o can drinks sold in the 4th week

bex.

2x+x = 2250

3x = 2250

x = 750

Hence, the number o can drinks sold in the 3rd

week

= 750 2= 1500

Answer: B

27. 5, 5, 5, k, k, 10

Median = 6

5 + k

2= 6

k= 7

Mean =

5 + 5 + 5 + 7 + 7 + 10 + 3 + 4

8

= 468

= 5.75

Answer: C

28. y = 8 2x2 is a quadratic unction with a maximum

point andy-intercept = 8.

Answer: A

29. Element 0 is not in the set F.

Answer: B


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30.E

F'

FE

E'

F

=

E

E' F'

F

Answer: A

31. n(P Q) = n(R)4 + 2k= 8 + 4 + 7 k

4 + 2k= 19 k

2k+ k= 19 43k= 15

k= 5

Answer: A

32. 2y + 3x 5 = 0

2y = 3x+ 5

y = 32x+ 5

2

Hence, y-intercept =52

Answer: A

33. 4y + mx 28 = 0

Substitute (8, 1) into the equation.

4(1) + m(8) 28 = 0

8m 24 = 0

8m = 24

m = 3

Answer: B

34. Total number = 13

The number divisible by 2 are 4, 6, 8, 10, 14, 16.The probability that the number is divisible by 2

= 613

Answer: B

35. Total number o pens

= 6 + 4 +x

= 10 +x

P(choosing a red pen) =4

10 + x

16

=4

10 + x

10 + x= 24

x= 14

Answer: D

36. y1

t2

y =k

t2

4 =k

32

k= 32 4

= 36

Hence, y =36

t2

Wheny = 9, 9 = 36t2

t2 = 4

t= 2

Answer: A

37. Hx3

H= kx3

3 = k12

3

k= 24

Hence, H= 24x3

Answer: D

38. wp

q

w = kp

q

13

= k8

4

k=1

12

Hence, w = 112

pq

14

=1

12

x

25

14

=1

12

x5

x= 15

Answer: D


5/9

Draw the line

Shade correctly

Correct equation

Factorise correctly

Correct

answers

Correct working

Correct answer

Correct

method

Correct answer

Correct answers

Equation with one

unknown

Correct answers

Correct

method

Identiy angle correctly



39.4

2+ 3

1

2

5

8

=4

2+

3

6

5

8

= 4 3 + 5

2 + 6 8

= 6

4

Answer: A

40. EF = (2 4)1

3

= (2 1 + 4 (3))= (14)

Answer: A

Important step

1.

y= 5

0

y

x

3

2y= x 4

x+ y= 5

2. 2x(x 6) =x+ 7

2x2 12x =x+ 7

2x2 12xx 7 = 0

2x2 13x 7 = 0

(2x+ 1)(x 7) = 0

2x+ 1 = 0 or x 7 = 0

x= 12

or x= 7

3.

F

E

C

ND

AM

B8 cm

6cm

12 cm

The angle between line EB and the base ABCD is

EBN.BN2 =BC 2 + CN2

= 82 + 62

BN= 100

= 10 cm

tan EBN=EN

BN

= 910

EBN= 41.99

4. Volume o the remaining solid = 489

12

(8 + 12) 9 8 r2 6 = 489

720 227

r2 6 = 489

720 1327

r2 = 489

132

7 r

2

= 720 489r2 = 231 7

132

r= 12.25= 3.5 cm

5. (a) (i) 2 is a prime number or 32 = 6.

(ii) (4)(2) = 8 and 4 2.

(b) Numberp is an even number.

(c) 2n3 + 1, n = 1, 2, 3,

6. x+ 4y = 12 .........................1

34xy = 11............................2

2 4, 3x 4y = 44 ..............31 +3, 4x= 32

x= 8

Substitutex= 8 into1.8 + 4y = 12

4y = 12 8

y = 204

y = 5

7. (a) P(choosing a boy) =n(boys)

n(S)

=45


6/9

Correct answers

Correct method

Add all the edges

Subtract to nd the area o

the shaded region

Substitute correctly

Correct method

Correct method

Correct answers

Correct answers

Correct method

Correct answers



(b) LetB be boy and G be girl.

1st pupil 2nd pupil Outcomes

B1

B2

B1B

2

B3

B1B

3

G B1G

B2

B1

B2B

1

B3 B2B3G B

2G

B3

B1

B3B

1

B2

B3B

2

G B3G

G

B1

GB1

B2

GB2

B3

GB3

n(S) = 12

P(the two other pupils are o dierent gender)

=6

12

=12

8. (a) QT= 7 cm

Length o arcPQR

=120

360

2 22

7

21

= 44 cm

Hence, the perimeter o the sectorOPQR

= 44 + 21 + 21

= 86 cm

(b) Area o the sectorOPQR

=120

360

22

7

212

= 462 cm2

Area o the circle

=22

7

72

= 154 cm2

Hence, the area o the shaded region

= 462 154

= 308 cm2

9. (a) 5x+ 2y 12 = 0

2y = 5x+ 12

y = 52

x+ 6

Using m = 52

xand G(2, 4),

y = mx+ c

4 = 52

(2) + c

4 = 5 + c

c = 4 + 5

= 1

Hence, the equation o the straight line passes

through G and parallel toEF isy = 52x+ 1.

(b) Wheny = 0, 0 = 52x+ 1

52x = 1

x =25

Hence, thex-intercept =25

10. (a) Length o time which the car is stationary

= 55 30

= 25 minutes

(b) Speed o the car in the rst 30 minutes

=40

30

=43

km per minute

(c) (i) Average speed o the motorcycle

=60

80= 0.75 km per minute

(ii) Distance travelled by the motorcycle in

30 minutes

= 0.75 30

= 22.5 km

Distance travelled by the car in 30 minutes

= 40 km

Hence, the distance between the car and the

motorcycle

= 40 22.5

= 17.5 km

11. (a) E = 4 1

3 t

WhenE has no inverse,

4t (1)(3) = 0

4t = 3

t = 34


7/9

Correct matrix

equation

Correct

method

Correct answers

Correct method

Correct

inversematrix

Correct answers



(b) E = 4 1

3 2

(i) E1 =1

(4)(2) (1)(3)

2 1

3 4

=1

11

2 1

3 4

(ii) 4xy = 17

3x+ 2y = 1

4 1

3 2

x

y=

17

1

x

y=

111

2 1

3 4

17

1

=1

11

34 1

51 4

=

111

33

111

(55)

=3

5

Hence,x= 3, y = 5

12. (a)

40

2

2

2 8

(8, 2)

(3, 1)

(6, 2)

(1, 5)

6

4

y

x

(i) (1, 5) T

(3, 1)

(ii) (1, 5) R

(6, 2)

(i) (1, 5) R

(6, 2) T

(8, 2)

(b) y

x

AJ K

LM

H

E F

G

D

CB

4

2

2

2 4 6 8 100

(i) (I) W is a relection in the line y = 0

(or thex-axis).

(II) V is an enlargement about the centre

(5, 2) with scale actor o 3.

Correct transormations

Correct descriptions

(ii) Area oJKLM

= 32 area oADCB

= 9 15.4

= 138.6 m2

Area o the shaded region

= 138.6 15.4

= 123.2 m2

13. (a)x 1 2

y 10 11

(b)

5

7

1.75 2.3

2.45

5

1 10

2 3

2 cm

2 cm

x

y

y= 4 2x

y= 9 4x 3x2

23

10

15

20

25

30

35

40

10

Correct axes and uniorm scale

All points correctly plotted

Smooth curve

(c) From the graph,

(i) whenx= 1.7,y = 7

(ii) wheny = 16,x= 2.3

Correct readings


8/9

Correct method

Correct answers



(d) y = 9 4x3x2........................10 = 13 + 2x+ 3x2 ..................2

1 +2, y = 4 2x

Draw the correct straight line

\x= 2.45 or 1.75

Correct answers

14. (a)Savings

(RM)Midpoint

Upper

boundary

Cumulative

frequency

6 10 8 10.5 3

11 15 13 15.5 9

16 20 18 20.5 17

21 25 23 25.5 28

26 30 28 30.5 36

31 35 33 35.5 40

(b) Estimated mean savings

=

(3 8) + (6 13) + (8 18) + (11 23)+ (8 28) + (4 33)

3 + 6 + 8 + 11 + 8 + 4

=855

40

= RM21.38

(c)

0

5

10

15

20

25

30

35

40

26.5

5.5 10.5 15.5 20.5 25.5 30.5 35.5

Cumulative frequency

Savings (RM)

2 cm

2 cm

Extend curve to zero

(d) (i) The third quartile = RM26.50.

(ii) There are 10 pupils who saved more than

RM26.50 per month.

15. (a)G/H

F/E

A/D B/C

L/KM/J

3 cm

3 cm

6 cm

4 cm

4 cm

(b) (i)F/A

2 cm

G/M

4 cm

L/B

4 cm

U/H/J/P

E/D

T/S

K/C

3 cm

3 cmQ R


9/9

Correct method

Correct method



(ii)TU

K/J

R/SB/A

L/M

F

G

Q/C/P/D

H

E 8 cm

3 cm

3 cm

1 cm

2 cm

4 cm

Correct orms

Correct measurements

Angles at corner are 90

16. (a) Longitude oB

= (60 38)E

= 22E

(b)

0

D

B

O

N

S

q =3420

60

= 57Latitude oD

= (57 52)S

= 5S

Hence, the position oD = (5S, 22E)

(c) (i) Distance travelled by aeroplaneX

= 180 60 cos 52

= 6649 nautical miles

(ii) Distance travelled by aeroplane Y

= [180 2(52)] 60

= 4560 nautical miles

Time o fight o aeroplaneX

=6649

600

= 11.08 hours

Time o fight o aeroplane Y

=4560

600

= 7.6 hours

Hence, the dierence in arrival time

= 11.08 7.6

= 3.48 hours

Correct answers

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Model Paper Spm