12
Section A [ 52 marks ] No Marking Scheme Marks 1 (i) (ii) P1, P2 3 2. TJK seen 8 5 30 5 3 tan TJK TJK P1 K1 N1 4 3. 9x + 3x = x 2 9 2x 2 + 9x + 9 = 0 (2x + 3) (x + 3) = 0 x = 3 2 3 , K1 K1 N1, N1 4 4. 8u + v = -16 or equivalent 11u = -33 or equivalent u = -3 v = 8 K1 K1 K1 N1 4 5. ) 7 7 7 22 ( or ) 21 7 7 22 2 ( ) 7 10 7 7 22 ( 2 2 ) 7 7 7 22 ( + ) 21 7 7 22 2 ( + ) 7 10 7 7 22 ( 2 2 1346.54 K1 K1 K1 N1 6. (a) False (b) If 2m < 2 then m <4 If m < 2 then 2m < 4 (c) 2n 2 5 where n = 3, 4, 5, … P1 P1 P1 K1 N1 4

Peperiksaan Pertengahan Tahun Tingkatan 5 Matematik Sbp Skema

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Page 1: Peperiksaan Pertengahan Tahun Tingkatan 5 Matematik Sbp Skema

Section A [ 52 marks ]

No Marking Scheme Marks

1

(i) (ii)

P1, P2

3

2. TJK seen

8530

5

3tan

TJK

TJK

P1

K1

N1

4

3. 9x + 3x = x2 – 9

2x2 + 9x + 9 = 0

(2x + 3) (x + 3) = 0

x = 32

3 ,

K1

K1

N1, N1

4

4. 8u + v = -16 or equivalent

11u = -33 or equivalent

u = -3

v = 8

K1

K1

K1

N1

4

5. )77

7

22( or )217

7

222(

)71077

22( 22

)777

22( + )217

7

222( + )7107

7

22( 22

1346.54

K1

K1

K1

N1

6. (a) False

(b) If 2m < 2 then m <4

If m < 2 then 2m < 4

(c) 2n2 5 where n = 3, 4, 5, …

P1

P1

P1

K1 N1

4

Page 2: Peperiksaan Pertengahan Tahun Tingkatan 5 Matematik Sbp Skema

No Marking Scheme Marks

7. ( ) 4a y

( ) 5

105 10 5 7

7

5 25

5 25

5

LKb m

yor c

x

y x

x

x

P1

P1

K1

N1

K1

N1

6

8. (a) A and A or F and F or R and R

6

1

4

1

6

1

4

1

6

1

4

1

8

1

(b) 1 – 8

1

8

7

K1

K1

N1

K1

N1

6

9. (a) 7

7

222

360

120

21)77

222

360

1202(

50.33

(b)

277

22

360

90 or 77

2

1

77

2

17

7

22

360

90 2

14

K1

K1

N1

K1

K1

N1

6

10 (a) 50 km

(b) 3.15 pm

(c) 100

120

30

d or

060

20120

3060

20

d or equivalent

d = 36

(d) 100

60120

60

100120 or

72 kmh–1

P1

P1

K1

N1

K1

N1

6

Page 3: Peperiksaan Pertengahan Tahun Tingkatan 5 Matematik Sbp Skema

No Marking Scheme Marks

11

(a)

24

31

4312

1

)()(

24

31

14

1 or equivalent

(c)

1

10

14

32

y

x

1

10

24

31

14

1

y

x

=

32

1

x = 2

1, y = –3

K1

N1

K1

K1

N1, N1

5

Page 4: Peperiksaan Pertengahan Tahun Tingkatan 5 Matematik Sbp Skema

No Marking Scheme Marks

12

(a)

(b) Graph

Axes drawn in the correct direction , the uniform scale is in

the range given.

9 coordinates plotted correctly in the range given.

Smooth curve drawn continuously in the range without a

straight line at any part and passed through 9 correct

coordinates .

(c) (i) y = 18 0.5

(ii) x = 3.0, 0.9, 0.1

(d) Identify the equation y = 3x +2 or equivalent.

Draw the line y = 3x +2

x = 0.42 0.1 , 0.7 0.1

x 3 1

y 3 1

K1K1

K1

K2

N1

P1

P1

K1

K1

N1 N1

12

Page 5: Peperiksaan Pertengahan Tahun Tingkatan 5 Matematik Sbp Skema

13

(a)

(b) Graph

Axes drawn in the correct direction , the uniform scale is in

the range given.

9 coordinates plotted correctly in the range given.

Smooth curve drawn continuously in the range without a

straight line at any part and passed through 9 correct

coordinates .

(c) Identify the equation y = x + 4 or equivalent.

Draw the line y = x + 4

x = 2.58 0. 1 , -0.58 0.1

(d)

x 1.5 3

y 2 2

K1K1

K1

K2

N1

K1

K1

N1N1

P2

14 (a) (i) k = 3

(ii) (a) (2, 4)

(b) (–3, 2)

(c) (i) G is a rotation of 90° clockwise about centre (2, 0)

H is an enlargement with scale factor 2 at the centre

(–4, 6).

(ii) (2)2 × 20

80

P1

P1

P2

P3

P3

K1

N1

12

Page 6: Peperiksaan Pertengahan Tahun Tingkatan 5 Matematik Sbp Skema

15 (a)

Class interval

Selang kelas

Midpoint

Titik tengah

Frequency

Kekerapan

46 50 48 5

51 55 53 5

56 60 58 7

61 65 63 9

66 70 68 3

71 75 73 1

Column I

Column II

Column III

(b) (i) 61 65

(ii) 30

)73(1)68(3)63(9)58(7)53(5)48(5

58.5

(c) Axes drawn in the correct direction , the uniform scale is in

the range given.

6 points plotted correctly

Close polygon shape drawn through 6 points and point (43,0) and

(78,0)

P1

P1

P1

P1

K2

N1

K1

K2

N1

12

Page 7: Peperiksaan Pertengahan Tahun Tingkatan 5 Matematik Sbp Skema

16 (a) 42

(b)

Upper boundary

Sempadan atas

Cumulative frequency

Kekerapan

Longgokan

19.5 0

24.5 2

29.5 5

34.5 11

39.5 20

44.5 32

49.5 38

54.5 40

Column I

Column II

(c) Axes drawn in the correct direction , the uniform scale is in

the range given.

8 coordinates plotted correctly in the range given.

Smooth curve drawn continuously in the range without a

straight line at any part and passed through 8 correct

coordinates .

(d)(i) 7 orang

(ii) 43.5 34

9.5

P1

P1

P1

K1

K2

N1

N1

K1

N1

12

Page 8: Peperiksaan Pertengahan Tahun Tingkatan 5 Matematik Sbp Skema

-20

-15

-10

-5

y

x

5

10

15

20

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

25

30

No. 12

Page 9: Peperiksaan Pertengahan Tahun Tingkatan 5 Matematik Sbp Skema

Graph for Question 13

y

x

×

×

×

×

×

×

×

×

-3 -2 -1 1 2 3 4

8

6

4

2

O

2

4

6

8

10

12

14

×

×

×

R

Page 10: Peperiksaan Pertengahan Tahun Tingkatan 5 Matematik Sbp Skema

Question 15

10

9

8

7

6

5

4

3

2

1

43 48 53 58 63 68 73 78

Frequency

Time(s)

Page 11: Peperiksaan Pertengahan Tahun Tingkatan 5 Matematik Sbp Skema

Question 16

19.5 24.5 29.5 34.5 39.5 44.5 49.5 54.5 59.5

50

45

40

35

30

25

20

15

10

5

Page 12: Peperiksaan Pertengahan Tahun Tingkatan 5 Matematik Sbp Skema

SKEMA KERTAS 1

NO.

SOALAN

JAWAPAN NO.

SOALAN

JAWAPAN

1 D 21 D

2 B 22 C

3 B 23 A

4 C 24 A

5 B 25 C

6 A 26 C

7 A 27 D

8 C 28 A

9 B 29 B

10 B 30 B

11 C 31 B

12 A 32 C

13 D 33 B

14 D 34 B

15 D 35 B

16 C 36 D

17 A 37 A

18 C 38 B

19 A 39 B

20 D 40 C