- 1 -

PEPERIKSAAN PERCUBAAN PMR 2011

MATHEMATICS PAPER 2

ANSWER

No Solution and Mark Scheme Sub

Mark

Full

Mark

1

3 × (– 18 + 20 4 )

= 3 × ( –18 + 5 )

= 3 × ( – 13 )

= – 39

1

1

2

2

(4− 0.22) × 12

1

= 3.78 × 2

3

= 5.67

1

1

2

3

. a. 4

16

= 4

25

= 2

5 OR 2

2

1

b. . (64

81 − 1 )

3

= ( 8

9 − 1 )

3

= (8

1)3

= 512

1

1

1

1

3

Note:

Award 1 mark for – 13 seen

Note:

Award 1 mark for 3.78 seen

Note:

Award 1 mark for 8

9 or

8

1 seen

- 2 -

4

a. 4 − x = 1

− x = 1 − 4

− x = − 3

x = 3

b. 4

x − 3 = x + 3

. 4

x − x = 3 + 3

. 4

3x = 6

−3x = 24

x = − 8

1

1

1

3

5

Complete diagram drawn

2

6

(a) (4,3)

(b) 3

1

1

2

P

Q R

S

R′

S′ M

N

Q′ P′

- 3 -

7 (a) PN

Note: Award 1 mark for PN drawn on the diagram.

(b)

Locus Y drawn correctly

Locus Z drawn correctly

marked correctly

2

1

1

1

5

8

Uniform scale marked correctly on vertical axis

All the five points marked correctly

All the points joined with straight line

Note: If scale is not written or different scale used, but all

the points plotted correctly, award 1 mark.

If scale is not written or different scale used, but line

graph drawn correctly, award 2 marks.

1

1

1

3

Number of

students

Bilangan pelajar

2006 2007 2008 2009 Year

Tahun

2010

25

20

15

10

5

P Q

S R N

M

Locus Z

Locus Y

- 4 -

9

a) 4t + 5

b) mmm 101525102

= 102 m

1

1

1

3

10 (a) 2g( 5 – k)

(b) 12 – 27p2

= 3 ( 4 – 9p2)

= 3 ( 2 + 3p ) ( 2 – 3p)

1

1

1

3

11

Complete diagram drawn

Note: Any 2 sides drawn correctly, award 1 mark

Any 3 sides drawn correctly, award 2 marks

3

- 5 -

12 (a) (i), (ii)

Correct construction of 60°.

Line SR = 4 cm correctly drawn.

Complete quadrilateral drawn.

Correct construction of perpendicular line from point S to QR.

(b) 3.5 cm ± 0.1

1

1

1

1

1

5

13

22 )3()2( ddc

2

92 ddc OR 2

232 ddc

ddc 2

92

2

92 dd

c

OR 2

19 )(

ddc

1

1

1

3

14 a) 235 p

= 0p

= 1

b) 4)3(2 33 xx

4)3(2 xx

462 xx

642 xx

10x

1

1

1

3

Q R

P

S

- 6 -

15 a)

Grades

Gred A B C D E

Frequency

Kekerapan 2 8 5 4 1

Note: 3 or 4 answers in the frequency table correctly

filled, award 1 mark.

b) Grade B

2

1

3

16

26

65

2

3

p

p

p

2

6

659

p

pp

2

6

64

p

p

2

6

322

p

p )(

2

3

32

p

p

1

1

1

3

17

a. 3 + q ≤ 7

q ≤ 7 − 3

q ≤ 4

b. 6x − 2 ≥ 2(3 + x )

6x − 2 ≥ 6 + 2 x

6x − 2x ≥ 6 + 2

4 x ≥ 8

x ≥ 2

1

1

1

3

18

ST

PQ =

SR

QR

ST

2 =

8

3

ST = 3

82

= 3

16 OR 5

3

1 cm

1

1

2

- 7 -

19 (a) cos x

o =

10

6 =

5

3

(b) PS = 22 817 = 15 OR PR = 22 810 = 6

RS = PS – PR

=15 – 6

= 9 cm

Note : If 15 or 6 is marked correctly in the diagram, award 1 mark

1

1

1

3

20

x

y

5

х

х

х

х

х

х

х

10

15

20

1 2 3 O – 1 – 2 – 3

– 5

– 10

- 8 -

1. Uniform scale on y-axis marked correctly in the

range 2010 y

2. All 7 points correctly plotted.

Note:

5 or 6 points marked correctly or curve passes through 5

or 6 points, award 1 mark.

3. Smooth curve passes through all the 7 points.

Note:

If scale is not written but all the points plotted correctly,

award 2 marks.

For other scale on the y-axis, deduct 1 mark from the

total marks obtained.

1

2

1

4