1

PERATURAN PEMARKAHAN PEPERIKSAAN PERCUBAAN SPM 2019

MODUL PINTAS

MATEMATIK TAMBAHAN KERTAS 2

NO SOLUTIONS MARKS

1 (a)

0

9

)9( dyy

y

y

92

2

81

2

810

2

81

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K1

K1

N1

4

6

(b) (7 × 8) − 211

3

342

3

K1

N1

2

2 (a) 23(1) − 4(1) ∙ 21 + 21 − 2

0

K1

N1

2

(b) log𝑎 𝑁 =1

2(log𝑎 24 − log𝑎 0.375 − log𝑎 729)

log𝑎 𝑁 =1

2(log𝑎

24

(0.375)(729))

log𝑎 𝑁 = log𝑎(64

729)1

2

log𝑎 𝑁 = log𝑎8

27

𝑁 =8

27

log𝑎 𝑁 = 3

K1

K1

K1

K1

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N1

6

10

SET 1

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2

3 (a) (i) 3a

(ii) -a + b

(iii) PA = 1

3 PQ

- 1

3 +

1

3 𝐛 (accept answer without working)

N1

N1

K1

N1

4

6

(b) 𝑂𝐵 ⃗⃗⃗⃗ ⃗⃗ ⃗⃗ = 9

5 (𝑂𝑃⃗⃗⃗⃗ ⃗ + 𝑃𝐴⃗⃗⃗⃗ ⃗)

6

5 a +

3

5𝐛

K1

NI

2

4 (30.2 𝑥 20.4) − 𝑥𝑦 = 500

2𝑥 + 2𝑦 = 43.2

𝑥 = 21.6 − 𝑦

(21.6 − 𝑦)(𝑦) = 116.08

𝑦2 − 21.6𝑦 + 116.08 = 0

𝑦 =−(−21.6)±√(−21.6)2−4(1)(116.08)

2(1)

05.10,55.11 xy or 55.11,05.10 xy

Perimeter of the ungrazed field =101.2

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P1

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K1

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7

7

5 (a) (62 × 18) + (88 × 23) + (16 × 28) + (13 × 33) +(11 × 38) + (10 × 43)

(62 × 18) + (88 × 23) + (16 × 28) + (13 × 33) + (11 × 38) + (10 × 43)

200

24. 33

(62 × 182) + (88 × 232) + (16 × 282) + (13 × 33) + (11 × 382) + (10 × 432)

√(62 × 182) + (88 × 232) + (16 × 282) + (13 × 332) + (11 × 382) + (10 × 432)

200− (24.33 )2

6.828

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K1

N1

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N1

6

(b) Mean will reduce 5 and standard deviation unchanged N1 1 7

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3

6 (a)

t

tt

ttt

sin2

sincos

)sin(cossin2

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N1

3

6

(b)

P1

P1

P1

3

7 (a)

275.52 104.48

8cos COP or or

1.823

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N1

2

(b) 10

37.76kos

or

228 2

37.7612.65 3.142

180

8.338PB or

2.65BC or PD = 12.65

8.338 2.65 7.746

18.73

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K1

K1

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N1

5

(c) 2

1(12.65) 0.6591

2 or

1(10) 7.746

2

21

(12.65) 0.65912

- 1

(10) 7.7462

14.01

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K1

N1

3

10

Use identity:

sin 2t = 2 sin t cos t

or cos 2t = 1- 2 sin2t

Shape: sin t or cos t

Amplitude=2

Cycle = 1 20 t

v

2

-2

t

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4

8

( 2) 3( )

7 3 2

ka

k = 4

K1

N1

2

10

7 3 4 ( 2)( ) ,

2 2b

51

18

m

)1(4

78 xy

4

39

4

7 xy

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N1

4

(c) )1)(2()3(4)7(8)8(3)2(7)8(1

2

1

or

)5(3)2(6)4(1)1(2)3(4)6(52

1

26 or 6.5

5.6

26

4 : 1

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N1

4

9 a) p =

2

5 or q =

3

5

(i) 1- P (X=0) – P (X=1) – P (X=2) or

1- 0.0467 – 0.1866 – 0.31104

0.4557

(ii) 1308

𝜎 = 28.01

b)(i) 13−10

4 @ 0.75 𝑠𝑒𝑒𝑛

0.7734

(ii) P ( 𝑋 > 136 ) or P ( X < 9.6)

0.1841 x 145 or 0.4602 x 145

13: 33

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N1

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N1

K1

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N1

5

5

10

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5

10 (a) All values of x and log10y correct

x 1 2 3 4 5 6

log 10 y 0.26 0.43 0.61 0.78 0.96 1.05 (b) refer graph

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K1N1

4

(c) (i) y incorrect =11.22 and yactual valu e= 13.49

(ii) pkxy logloglog 1010

175.0log k (0.17 - 0.175)

50.1k (1.48 - 1.50)

85.0log p

p = 7.079

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6

10

11 (a)A = πr2 + 2πrh + 2 πr2

A = 3πr2 + 2πrh

V = πr2h + 2

3πr3

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N1

3

10

(b) 3πr2 + 2πrh = 20π

220 3

2

rh

r

V = πr2220 3

2

r

r

+ 2

3πr3

V = 10πr - 5

6 πr3

K1

K1

K1

N1

4

(c)

2

2

510

2

510 (1.5) 0.4

2

1.75

dvr

dr

K1

K1

N1

3

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6

12 (a)(i) 2t – 6 = 0

v = (3)2 – 6(3) + 8

v = -1

(ii) (t – 2)(t – 4) = 0

𝑡3

3− 3𝑡2 + 8𝑡

(43

3− 3(4)2 + 8(4)) - (

23

3− 3(2)2 + 8(2))

4

3

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NI

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7

10

(b)

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3

13

(a) 𝑥

3.50x100 = 125 or

6

𝑦x100 = 110 or

5.50

4.00x100 = 𝑧

𝑥 = 4.38

𝑦 = 5.45

𝑧 = 137.5

K1

N1

N1

N1

4

10

(b) (120x5) + (125x3) + (110x4) + (137.5x1)

(120x5) + (125x3) + (110x4) + (137.5x1)

13

119.42

K1

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N1

3

(c) 119.42x115

100

𝑝

40x100 = 137.33

RM 54.93

K1

K1

N1

3

Shape graph ∪

Graph intersect x-axis at 2 and 4

3 < 𝑡 ≤ 7

v

t

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7

14

(a) (i) 4.72 = 6.52 + 52 – 2(6.5)(5) cos A

45.99

(ii) 02.88sin

5

99.45sin

BD

3.598

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N1

4

10

P1

K1

N1

N1

4

1( ) (6.5)(4.7)(sin 38.09)

2c

9.423

K1

N1

2

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8

15 (a) 𝑥 ≥ 50

𝑦 ≥ 180

24 𝑥 + 8 𝑦 ≤ 8000 or 3 𝑥 + 𝑦 ≤ 1000

𝑥 + 𝑦 ≤ 800

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4

10

(b) Refer to graph paper

One *straight line drawn correctly

All * straight line drawn correctly

Correct region

K1

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N1

3

(c) (i) 180 ≤ x ≤ 390

(ii) Pmax = 30 x + 10 y

30 ( 100 ) + 10 (700 )

1000

N1

K1

N1

3

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9

QUESTION 10

Plot log10 y against x with correct axes,

uniform scales and at least one point K1

6 points plotted correctly K1

Line of best fit N1

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10

QUESTION 15

1000

900

0 100 200 300 400 500 600 700

100

200

300

400

500

600

700

800

800

R

100 200 300 400 500 600 700

100

200

300

400

500

600

700

800

800

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