Answers Ace Form 5 Math/Answers.pdf · Penjelmaan S ialah satu putaran 90 ... Penjelmaan R ialah satu translasi 1 52 3. 6. (a) (i) ... Penjelmaan X ialah satu pembesaran pada titik

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Mathematics Form 5 Answers

Question Bank

Form 4

Chapter 1 Standard Form

1. 4 800 000 2. 11 3. (a) 0.0001003 (b) 0.5 4. (a) 29 000 000 (b) 18 5. (a) 1.54 × 108 (b) 6.92 × 10–4

6. 1.6 × 10–1

7. 6.56 × 108

8. (a) 1.23 × 10–5 (b) 2.4 × 104

Chapter 2 Quadratic Expressions and Equations

1. (a) 10x 2 – 17x – 20 (b) 13x 2 – 19x 2. (a) 7x(1 – 8x) (b) (3y – 4x)(3y + 4x) 3. (a) (2x – 5)2 (b) 3(1 + x)(5 – 3x)

4. (a) x = –4 or x = 2 (b) p = 32

or p = –4

x = –4 atau x = 2 p = 32

atau p = –4

5. (a) y = – 56

(b) q = –3 or q = 2 q = –3 atau q = 2 6. (a) 3(4 – 3x)(4 + 3x)

(b) m = – 72

or m = 3

m = – 72

atau m = 3

Chapter 3 Set

1. (a) A

B

C

(b) A

B

C

2. (a)

P QR

(b)

P Q R

3. (a) (i) N = {c, d, e, f, g}(ii) M 9 N = {c, f, g}

(b) (i) 4 (ii) 5 4. (a) x = 6, y = 8 (b) 17 5. (a)

AC

B

17

3

59

28

10

(b)

AC

B

6. (a) H = {10, 15, 20, 25}; J = {18, 19, 24, 25}(b) I J = {19, 25}(c) 6

Chapter 4 Mathematical Reasoning

1. (a) Yes. It is a true statement.Ya. Ia adalah pernyataan benar.

(b) Yes. It is a false statement.Ya. Ia adalah pernyataan palsu.

(c) No. It cannot be determined either true or false.Tidak. Ia tidak dapat ditentukan sama ada benar atau palsu.

2. (a) Some (b) AllSebilangan Semua

3. (a) Antecedent: A BAntejadian: A B

Consequence: A B = AAkibat: A B = A

(b) Implication I : If (3 m) = (3 5), then m = 5.Implikasi I : Jika (3 m) = (3 5), maka m = 5.

Implication II : If m = 5, then (3 m) = (3 5).Implikasi II : Jika m = 5, maka (3 m) = (3 5).

4. (a) (i) = (ii) ≠(b) (i) 52 = 25 or 102 = 20

52 = 25 atau 102 = 20(ii) 52 = 25 and 102 = 20 52 = 25 dan 102 = 20

5. (a) (i) True (ii) False Benar Palsu

(b) m can be divided by 2. m boleh dibahagi dengan 2.

6. (a) If a – b 0, then a b; true Jika a – b 0, maka a b; benar(b) cos 100° 0 Kos 100° 0

Answers

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7. (a) (i) Line AB and line CD are not parallel. Garis AB dan garis CD tidak selari.(ii) All prime numbers which are greater than

2 are odd numbers. Semua nombor perdana yang lebih besar daripada

2 adalah nombor ganjil.(b) 6 + 3n, n = 1, 2, 3, 4, …

8. (a) If p is a multiple of 10, then p is a multiple of 5.Jika p ialah gandaan 10, maka p ialah gandaan 5.

(b) nn + 3, n = 1, 2, 3, …(c) Set A has 24 subsets.

Set A mempunyai 24 subset.

Chapter 5 The Straight Line

5 1. (a) — (b) –5 2 1 1 38 2. (a) — (b) y = —x + — 7 7 7 5 3. (a) P(4, 0) (b) y = – —x + 8 4 4. (a) L(0, 6) (b) 2

(c) –2; y = –2x – 2

5 6 5. (a) y = —x – 3 (b) S1—, 02 2 5 25(c) — 12

1 9 6. (a) J1—, 02, I(0, – 4) (b) – — 2 2

8(c) – — 9

Chapter 6 Statistics III

1. (a) 50 – 59 kg (b) 53.5 kg(c)

0

2

4

6

8

10

12

29.5 39.5 49.5 59.5 69.5 79.5

Fre

quen

cy /

Kek

erap

an

Weight / Jisim (kg)

2. (a) ScoreSkor

20 – 29 30 – 39 40 – 49 50 – 59 60 – 69

FrequencyKekerapan

6 12 3 8 3

(b) 41.375

(c)

0

2

14.5 24.5 34.5 44.5 54.5 64.5 74.5

4

6

8

10

12

Score / Skor

Fre

quen

cy /

Kek

erap

an

3. (a) LengthPanjang(cm)

Upper boundarySempadan

atas

FrequencyKekerapan

Cumulative frequencyKekerapan longgokan

45 – 49 49.5 0 0

50 – 54 54.5 4 4

55 – 59 59.5 10 14

60 – 64 64.5 14 28

65 – 69 69.5 18 46

70 – 74 74.5 8 54

75 – 79 79.5 5 59

80 – 84 84.5 1 60



(b)

0

5

10

15

20

25

30

35

40

45

50

55

60

54.549.5 59.5

60 65 69

64.5 69.5 74.5 79.5 84.5

Length / Panjang (cm)

Cum

ulat

ive

freq

uenc

y / K

eker

apan

long

goka

n

(c) (i) 65 cm (ii) 9

4. (a) Height (cm)Tinggi (cm)

FrequencyKekerapan

151 – 155 4

156 – 160 2

161 – 165 8

166 – 170 14

171 – 175 10

176 – 180 8

181 – 185 6

(b) Height Tinggi(cm)


atas

FrequencyKekerapan


146 – 150 150.5 0 0

151 – 155 155.5 4 4

156 – 160 160.5 2 6

161 – 165 165.5 8 14

166 – 170 170.5 14 28

171 – 175 175.5 10 38

176 – 180 180.5 8 46

181 – 185 185.5 6 52

(c)

0

5

150.5 155.5 160.5 165.5 170.5 175.5 180.5

10

15

20

25

30

35

40

45

185.5

50

55

Height / Tinggi (cm)

Cum

ulat

ive

freq

uenc

y / K

eker

apan

long

goka

n

(d) 28.85%

5. (a) ScoreSkor(%)

MidpointTitik

tengah


atas

FrequencyKekerapan


0 – 9 4.5 9.5 0 0

10 – 19 14.5 19.5 13 13

20 – 29 24.5 29.5 20 33

30 – 39 34.5 39.5 28 61

40 – 49 44.5 49.5 37 98

50 – 59 54.5 59.5 25 123

60 – 69 64.5 69.5 15 138

70 – 79 74.5 79.5 10 148

80 – 89 84.5 89.5 2 150

90 – 99 94.5 99.5 0 150

(b) (i) (40 – 49)%(ii) 43.57%



2. (a) Graph I: y = cos x Graf I: y = kos x

Graph II: y = sin x Graf II: y = sin x

(b) P(225°, –0.7071)(c) 90°

4 4 3. (a) 8 cm (b) — (c) – — 3 5

4. (a) 315° (b) 0.7071 (c) 0.7071 2 5. (a) 14.42 cm (b) 0.5547 (c) – — 3 6. (a) 28 cm (b) 1 (c) –1

Chapter 10 Angles of Elevation and Depression

1. (a) 17.02 m (b) 10.72 m 2. (a) 48.80 m (b) 23°99

3. (a) 38°409 (b) 58° 4. (a) 33.2 m (b) 4°359

5. (a) 11.71 (b) 44°179

6. (a) 12.59 (b) 30°479

Chapter 11 Lines and Planes in Three Dimensions

1. (a) ∠HBD (b) ∠FCG(c) ∠GBF (d) ∠DGC

2. (a) ∠PXS(b) (i) 9.43 cm (ii) 58°

3. (a) 15.26 cm (b) 51°509 (c) ∠KGJ 4. (a) ∠CEB (b) 3.45 cm (c) 34°369

5. (a) 4.20 cm (b) 43°139 (c) 83°379

6. (a) ∠QTR (b) 36°529 (c) 56°199

Form 5

Chapter 1 Number Bases

1. 8210 2. 2105

3. 110112 4. 1068

5. 4810 6. 3718

7. 25 8. 3 9. 668 10. 11010012

Chapter 2 Graphs of Functions II

1.

x

y

1

1–20

y = 1 – 2x

2. m = 2, n = –2 3. b = 3, c = –1 1 4. x 0, x + y 4, y —x + 1 2

(c)

0

20

9.5 19.5

40

60

80

100

120

140

160

29.5 39.5

43.5

49.5 59.5 69.5 79.5 89.5Score / Skor (%)

Cum

ulat

ive

freq

uenc

y / K

eker

apan

long

goka

n

(d) 43.5%

Chapter 7 Probability I

7 17 11 1. (a) — (b) — (c) — 60 60 20 5 9 2. (a) 50 (b) — (c) — 24 22

3. (a) 200 000 (b) 0.375 (c) 375 000 1 4. (a) 21 (b) 15 (c) — 6 13 23 5. (a) 80 (b) — (c) — 40 39 4 6. (a) 60 (b) — (c) 108 5

Chapter 8 Circles III

1. (a) 55° (b) 55° (c) 70° 2. (a) 36° (b) 144° (c) 85° 3. (a) 33° (b) 66° (c) 90° 4. (a) 34° (b) 28° (c) 96° 5. (a) 22° (b) 112° (c) 34° 6. (a) 50° (b) 260° (c) 11.34 cm

Chapter 9 Trigonometry II

1. (a) (i) –0.8910 (ii) –0.9304(iii) –1.025

(b) 290°119

(c) 128°409, 308°409



5. (a) a = 7, b = 12(b)

x

y

0–1

–5

5

1 2 3 4

10

15

20

25

–2–3

y = 2x 2 – x – 3

3.653

(c) (i) 3.65 (ii) 3

6. (a) p = –2, q = 8(b)

x

y

2

4

6

8

–2

0–2–3 –1 211.2

1.6–1.7 –0.65

3

–4

–6

–8

y = 2x + 1

4xy = –

(c) (i) 1.6 (ii) –0.65(d) –1.7, 1.2

Chapter 3 Transformations III

1. A9(1, 2)

2. P9(2, 2)

3. Q9(2, 3)

4. R(–3, 1)

5. (a) (i) (–2, 0) (ii) (–2, 1)(b) Transformation S is a rotation of 90° anticlockwise

about the origin. Penjelmaan S ialah satu putaran 90° lawan arah jam

pada asalan. 5 Transformation R is a translation 1 2. 3 Penjelmaan R ialah satu translasi 1 5 23

.

6. (a) (i) (4, 4) (ii) (–4, 2)(b) (i) Transformation Y is a reflection in the y-axis.

Penjelmaan Y ialah satu pantulan pada paksi-y.

Transformation X is an enlargement at point (–5, 2) with a scale factor of 2.

Penjelmaan X ialah satu pembesaran pada titik (–5, 2) dengan faktor skala 2.

(ii) 150 unit2

7. (a) (i) (7, 2) (ii) (5, 5)(b) (i) Transformation Q is a rotation of 90°

clockwise about (5, 4). Penjelmaan Q ialah satu putaran 90° ikut arah jam

pada (5, 4). Transformation P is an enlargement at point

(1, 6) with a scale factor of 2. Penjelmaan P ialah satu pembesaran pada titik

(1, 6) dengan faktor skala 2.(ii) 30 m2

Chapter 4 Matrices

1. p = –2, q = –8

12 4 2. 1 2 6 2

3. –2

1 1 – — 2 4. 1 2 3 –2 — 2

2 1 — — 5 5 5. (a) 1 2 1 1 – — — 10 5

1(b) x = 4, y = — 2

6. (a) k = 2, m = –2 17 9(b) x = — , y = — 2 2

–1 –2 7. (a) 1 2 3 5 – — – — 2 2

3(b) x = –2, y = – — 2

Chapter 5 Variations

25 1. — 2

2. 25 3. 2



2 4. – — 5 5. 1000 6. 1 7. ±2 5m 8. F = ——— n

Chapter 6 Gradient and Area under a Graph

1. (a) 25 m (b) 0.5 m s–1

2. (a) 35 (b) 100 m

3. (a) –0.5 m s–2 (b) 30 m

(c) 69 m

4. (a) 80 km h–2 (b) 3 80 km j–2

(c) 280 km

5. (a) 30 (b) 30 m

Chapter 7 Probability II

3 1. — 5 2. 16 3 3. — 7 4. 36 1 5. — 4 7 7 6. (a) — (b) — 40 20 9 1 7. (a) — (b) — 35 4

8. (a) S = {(R, B), (R, G), (P, B), (P, G), (Y, B), (Y, G)}S = {(M, H), (M, K), (U, H), (U, K), (K, H), (K, K)}

1(b) — 2

9. (a) S = { (S, A), (S, L), (S, T), (A, S), (A, L), (A, T), (L, S), (L, A), (L, T), (T, S), (T, A), (T, L)}

1(b) — 2

Chapter 8 Bearing

1. 255°

2. 155°

3. 325°

4. 100°

5. 230°

6. 252°

7. (a) 200° (b) 050°

Chapter 9 Earth as a Sphere

1. Q(45°N, 75°W)Q(45°U, 75°B)

2. 35°W35°B

3. 30°N30°U

4. Q(0°, 65°E)Q(0°, 65°T)

5. (a) B(72°N, 120°W)B(72°U, 120°B)

(b) C(72°S, 120°W)C(72°S, 120°B)

(c) 1080 nautical miles1080 batu nautika

(d) (i) 11 977.38 nautical miles 11 977.38 batu nautika(ii) 665.41 knots 665.41 knot

6. (a) B(55°S, 26.1°E)B(55°S, 26.1°T)

(b) C(35°S, 26.1°E)C(35°S, 26.1°T)

(c) (i) 5394.63 nautical miles 5394.63 batu nautika(ii) 770.67 knots 770.67 knot

Chapter 10 Plans and Elevations

1. (a)

N/K

M/JL/O H/G

I/DE/F

A/B C

2 cm

2 cm

2 cm 3 cm

5 cm

(b)

N /M

I /H

B /F /O C /D /GK /J

A /E /L

4 cm

2 cm

2 cm

2 cm 3 cm

(c)

A

I H

N/E

C/B

M/L

G/J/OD/K/F

2 cm 2 cm2 cm

2 cm



4. (a)

J/F

H/G

E/A

C/B

I D

2 cm1 cm

3 cm

(b) (i)

L/I/H

K/M

F/G

D/C A/B3 cm1 cm

2 cm

2 cm

2 cm

N

O

E

J

(ii)

C/H/M

D/I

L/K E/J A/F

B/GO/N

4 cm

1 cm

3 cm

2 cm1 cm 2 cm

Specimen Paper

Paper 1

1. B 2. C 3. A 4. D 5. C 6. A 7. B 8. C 9. C 10. C 11. B 12. D 13. C 14. A 15. B 16. D 17. D 18. C 19. A 20. A 21. C 22. D 23. A 24. A 25. B 26. D 27. C 28. A 29. B 30. C 31. C 32. D 33. A 34. B 35. C 36. A 37. C 38. A 39. D 40. C

Paper 2

1. (a)

R

QP

(b)

R

QP

2. (a)

F/J

A/E

G/H

B/C

I

D2 cm 2 cm

3 cm

(b)

A/F

E/J

B/G

D/I

C/H1 cm

2 cm1.5 cm

4 cm

4 cm

(c)

B /A

D /E I /J

G /F

C H1 cm

3 cm

3 cm

3. (a)

A/D B/C

H

E F

G

2 cm

1 cm

3 cm

(b) (i)

E /A

J /M Q /K /N P /O

S /TH /R /D

F /I /B G /L /C

2 cm

2 cm

4 cm

4 cm

6 cm

(ii)

G /H

Q /R

N /C /DM /B /A

K /LJ /I

F /E

P /S

O /T4 cm

2 cm2 cm

2 cm

2 cm

1 cm



2. x = –2, y = 15 3. x = 1, 4 4. 39.23° 5. (a) x = 3

(b) 222 4—7

cm3

6. (a) True statementPernyataan benar

(b) The product of gradient of line PQ and gradient of line RS is –1.Hasil darab kecerunan garis PQ dan kecerunan garis RS ialah –1.

(c) (i) Statement Pernyataan(ii) Not a statement Bukan satu pernyataan

7. (a) 25 8—9

cm (b) 38.33 cm2

8. (a) 4—9

(b) 2—9

9. (a) 4y = 3x + 4 (b) k = 13—–4

10. (a) 1 2 1 22.5 1.5

(b) 1 3 –22–5 4 1 x 2y = 1 6 24

; x = 16, y = 21

11. (a) 16 m s–1

(b) k = 15(c) 10.4 m s–1

12. (a) (i) (3, 3) (ii) (1, 0) (iii) (–1, 5)(b) (i) P is an enlargement at centre (0, –1) with

scale factor 1—3

;

P ialah satu pembesaran pada pusat (0, –1) dengan

faktor skala 13

;

Q is a reflection in the line y = x + 2. Q ialah satu pantulan pada garis y = x + 2.

(ii) 56 m2

13. (a)

Class intervalSelang kelas

MidpointTitik tengah

FrequencyKekerapan

140 – 144 142 5

145 – 149 147 6

150 – 154 152 7

155 – 159 157 9

160 – 164 162 10

165 – 169 167 8

170 – 174 172 5

(b) (160 – 164) cm(c) 157.7 cm

(d)

0

1

2

3

4

5

6

7

8

9

10

139.5 144.5 149.5 154.5 159.5Height / Tinggi (cm)

164.5 169.5 174.5

FrequencyKekerapan

14. (a)

HD

A E

G/F3 cm

4 cm

1 cm

C/I/B



(b) (i)

C/G

D/H

4 cm

5 cm

4 cm

B/F

A/E

(ii)

A/B CD/I

E/F GH

2 cm 1 cm 1 cm

3 cm

15. (a) h = –3.2, k = 5(b)

0

2

4

6

8

–8

–6

–4

–2

y

y = x

y = –

1

8x

2 3

2.85

6.7

–1.6–2.85

4–4 –3 –2 –1x

(c) (i) 6.7(ii) –1.6

(d) x = –2.85, 2.85

16. (a) B(60°S, 60°E) B(60°S, 60°T)

(b) 10°N 10°U

(c) 6600 nautical miles 6600 batu nautika

(d) 646.15 knots 646.15 knot

Documents

Answers Ace Form 5 Math/Answers.pdf · Penjelmaan S ialah satu putaran 90 ... Penjelmaan R ialah satu translasi 1 52 3. 6. (a) (i) ... Penjelmaan X ialah satu pembesaran pada titik