ppr maths nbk

SULIT 1449/1 1449/1 Matematik Kertas1 Peraturan Pemarkahan Ogos 2007

SEKTOR SEKOLAH BERASRAMA PENUH BAHAGIAN SEKOLAH

KEMENTERIAN PELAJARAN MALAYSIA

PERATURAN PEMARKAHAN PEPERIKSAAN PERCUBAAN SPM SELARAS SBP

TAHUN 2007

MATEMATIK

KERTAS 1 & 2

1449/1

2

QUESTION ANSWER QUESTION ANSWER

1 C 21 A

2 D 22 C

3 A 23 A

4 C 24 B

5 C 25 C

6 C 26 D

7 D 27 A

8 B 28 A

9 C 29 C

10 A 30 D

11 B 31 C

12 C 32 D

13 B 33 B

14 B 34 B

15 A 35 D

16 D 36 D

17 B 37 C

18 A 38 A

19 A 39 D

20 B 40 D

3

Section A [ 52 marks ]

No Marking Scheme Marks

1

8x2 – 14x + 3 = 0 ( 4x – 1 ) ( 2x – 3 ) = 0

x = 14

or x = 32

K1 K1 N1 N1

4

2 5x +

25

y = 25

211

y = 33

y = 6 x = 2

P1 K1 N1 N1

4

3

y = 1

2y = x - 4

y = 2x + 1

O

y

Draw the straight line y = 1 Region shaded correctly Notes :

1. Region that satisfies any two inequalities : P1

2. Deduct 1 mark from K1P2 if the straight line y = 1 drawn in solid line

K1

P2

3

4

No Marking Scheme Marks

4

Identify ∠ JSM or ∠MSJ or angle marked on the diagram correctly

tan ∠ JSM = 128

or equivalent

56⋅3o or 56o 19′

P1

K2

N1

4

5 (a)

(b)

y = 3

Gradient of JK = 12

or the gradient being used

( )12 32

c− = − + or ( )( )

2 13 2

yx− −

=− −

1 12 2

y x= + or equivalent

y−intercept = 12

P1

P1

K1

N1

P1

5

6

1 6 7 83× × ×

1 22 7 7 62 7 2 2⎛ ⎞× × ×⎜ ⎟⎝ ⎠

1 6 7 83× × × + 1 22 7 7 6

2 7 2 2⎛ ⎞× × ×⎜ ⎟⎝ ⎠

227.5

K1

K1

K1

N1

4

7(a)

(b)

5.37222

36060

××× or 77222

360180

×××

7 + 3.5 + 3.5 +22 + 113

2393

or 39.67

27

722

360180

×× or 27722

36060

×× or 25.3722

360180

×× or 25.3722

36060

××

27722

360180

×× - 27722

36060

×× - 25.3722

360180

×× + 25.3722

36060

××

= 3821 cm2 or 38.5 cm2

K1

K1

N1

K1

K1

N1

6

5

No Marking Scheme Marks

8(a)

(b)

(c)

Statement Implication 1: If P⊂ R then P ∩ R = P Implication 2 : If P ∩ R = P then P⊂ R Conclusion : 4n + n3 , where n = 1,2,3,4, ……..

P1 P1 P1 P1P1

5

9(a)

(b)

64200

825

60 59

120 119×

59238

K1

N1

K2

N1

5

10(a)

(b)

( )1 14 6 2 42 2

v v⎛ ⎞+ = × ×⎜ ⎟⎝ ⎠

v = 12 12 46 0−−

113

or 1.33

K2

N1

K2

N1

6

6

No Marking Scheme Marks

11 p =3 , k = 10

1 3 62 4 3

mn

− −⎛ ⎞⎛ ⎞ ⎛ ⎞=⎜ ⎟⎜ ⎟ ⎜ ⎟

⎝ ⎠⎝ ⎠ ⎝ ⎠

4 3 612 1 34 6

mn

−⎛ ⎞ ⎛ ⎞⎛ ⎞=⎜ ⎟ ⎜ ⎟⎜ ⎟−+⎝ ⎠ ⎝ ⎠⎝ ⎠

32

32

mn

⎛ ⎞−⎜ ⎟⎛ ⎞= ⎜ ⎟⎜ ⎟

⎝ ⎠ ⎜ ⎟⎜ ⎟⎝ ⎠

m = 32

− , n = 32

Notes:

1.

32

32

mn

⎛ ⎞−⎜ ⎟⎛ ⎞= ⎜ ⎟⎜ ⎟

⎝ ⎠ ⎜ ⎟⎜ ⎟⎝ ⎠

: N1

2. Solution without using matrices method cannot be accepted.

P1P1

P1

K1

N1,N1

6

7

Section B [48 marks]

No Marking Scheme Marks

12(a)

(b)

(c)

(d)

−7.6

– 2

Graph Axes are drawn in the correct direction, uniform scale for – 2.5 ≤ x ≤ 4 and – 2.5 ≤ y ≤ 46 6 points and 2 points* plotted accurately Smooth and continuous curve without straight line(s) and passes through all the 8 correct points for – 2.5 ≤ x ≤ 4 Notes : (1) 6 or 7 points plotted correctly, award K1

(2) Other scale being used, subtract 1 mark from the KN marks obtained.

2.5 < x < 2.7

20 < y < 22

Note : Do not accept the values of x and y obtained by calculation Identify the equation y = 6x – 5 or equivalent The straight line y = 6x – 5 drawn correctly

The values of x : 0 2 0 4x⋅ ≤ ≤ ⋅

2.9 3.1x≤ ≤ Notes : (1) Award N mark(s) if the value(s) of x shown on the graph

(2) Do not accept the value(s) of x obtained by calculation

K1

K1

K1

K2

N1

P1

P1

K1 K1

N1

N1

12

8

No Marking Scheme Marks 13 (a)

(b)

i) (5 , 6) ii) (10 , 3) Notes :

1. (6, 1) : P1

2. Accept answers without bracket. i) (a) Q : Rotation 90o anticlockwise about (0,6) (b) M : Enlargement with scale factor 3 centered at point (4, 9).

Notes:

1. Rotation 90o anticlockwise or Rotation about (0,6) : P2

2. Rotation only : P1

3. Enlargement, scale factor 3 or Enlargement, at point ( 4, 9) : P2

4. Enlargement only : P1

ii) 32 × 343 32 × 343 – 343 2744 Notes :

1. 343 283.5

× or equivalent : P2

2. Without calculation, K0N0

P1 P2 P3 P3 K1 K1 N1

12

14(a)

Number of

telephone calls Upper

Boundary FrequencyCumulative Frequency

6 - 10 10.5 0 0 11 - 15 15.5 1 1 16 - 20 20.5 3 4 21 - 25 25.5 6 10 26 - 30 30.5 10 20 31 - 35 35.5 11 31 36 - 40 40.5 7 38 41 - 45 45.5 2 40

9

No Marking Scheme Marks

(b)

(c)

Column I (all class interval correct)

Column II (all upper boundary correct)

Column III (all frequency correct)

Column IV(all cumulative frequency correct)

Note : Allow two mistakes in column III for P1 Ogive Axes are drawn in the correct direction, uniform scale for 10.5 ≤ x ≤ 45.5 and 0 ≤ y ≤ 40 The horizontal axis labeled with upper boundary or use the values of upper boundary for plotting Plot 7 points* Smooth and continuous curve without straight line(s) and passes through all the 8 correct points for 20.5 ≤ x ≤ 55.5.

Notes : (1) 5 or 6 points* plotted correctly, award K1

(2) Mark(s) for plotting can be given to a curve which passes through 7 points* and point (10.5, 0)

(3) Other scale being used, subtract 1 mark from the KN marks obtained.

First Quartile = 25.5 or Third Quartile = 35 ± 0.5 Interquartile range = 35 – 25.5 = 9.5 ± 0.5

P1

P1

P1

P1

K1

K1

K2

N1

K1

K1

N1

12

10

No Marking Scheme Marks 15 (a) (b)

The shape must be correct in quadrilateral form for RSTU and RSNM. R and S are linked by dotted lines UT = MN > UM = TN UR = TS < RM = SN The measurement is accurate to ± 0.2 cm. (one way ) and the angles at all verticals of the rectangle are 90° ± 1°

The shape must be correct in quadrilateral form for JKWG and GFNW . TSPN is a trapezium. All lines must be drawn in full. JK = GW = FN < JF = KN JG = KW > GF = WN KT < SP < TW The measurement is accurate to ± 0.2 cm. (one way ) and the angles at all verticals of the rectangle are 90° ± 1°

K1

K1

K1

N1

K1

K1

N2

SR

TU

M N

P

G

F N

W

S

T

KJ

11

No Marking Scheme Marks (c)

16.(a)

(b)

(c)

(d)

The shape must be correct in quadrilateral form for RSTL, LKJD and KTFJ. All lines must be drawn in full. RS = LT = DF < FD = SF RL = ST < LD = TF = KJ LK = KT = DJ = JF The measurement is accurate to ± 0.2 cm. (one way ) and the angles at all verticals of the rectangle are 90° ± 1° B(630N,550E) 630N or 550E : P1 C(630N,250E) 54 x 60 3240 n.m. 30x60xcos 630 : Award K1 for using cos 630 817.18 (63x2)x60 126 x 60 7560 817.18 + 7560 8377.18 8377.18

510

16.43

K1

K1

N2

P2

P1

K1K1N1

K1K1

N1

K1

K1

N1

12 12

K L

D J F

T

SR

12

Graph for number 12

13

Graph for number 14

0

5

10

15

20

25

30

35

40

15.5 20.5 25.5 30.5 35.5 40.5 45.5 10.5

×

×

×

×

×

×

× ×