F4 Answer

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Panitia Matematik Daerah Seremban 2006

ANSWERS CHAPTER 1 : STANDARD FORM EXERCISE 1 1. (a) 43000 (b) 1800 2. (a) 68.7 (b) 70 3. (a) 0.00305 (b) 0.0030 (c) 0.003 4. (a) 1106.5 × (b) 210241.7 × (c) 1103.9 −× (d) 31081.2 −× 5. (a) 346000 (b) 0.00297 6. (a) 31068.5 −× (b) 71006.4 × 7. (a) 41061.5 −× (b) 81079.4 × 8. (a) 810667.8 −× (b) 12101598.3 × 9. (a) 7109× (b) 5106×

EXERCISE 2 1. (a) 2960 (b) 51900 2. (a) 771⋅ (b) 70 3. (a) 06050 ⋅ (b) 0610 ⋅ (c) 060 ⋅ 4. (a) 41084 ×⋅ (b) 310200059 ×⋅ (c) 21062 −×⋅ (d) 71083 −×⋅ 5. (a) 2190 (b) 000820 ⋅ 6. (a) 710851 ×⋅ (b) 11011411 ×⋅ 7. (a) 510338 ×⋅ (b) 2102054 −×⋅ 8. (a) 310363 ×⋅ (b) 4108851 −×⋅ 9. (a) 0104581 ×⋅ (b) 31042 −×⋅

DIAGNOSTIC TEST

1. D 6. D 2. C 7. D 3. A 8. A 4. A 9. D 5. C 10.D

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CHAPTER 2 : QUADRATIC EXPRESSIONS EXERCISE 1

1. x2 – 5x – 24 2. x2 – 9 3. mx + my – x – y 4. 2x2 + 5x – 3 5. – x2 – x – 8 6. 2x2 – 18x 7. 2x2 – 11x – 40 8. 3u2 – 5us + 2s2 9. 5x – 5x2 10. –u2 + u + 15

EXERCISE 2

1. 3p2 – 3pq + q2 2. 2q2 – 2pq 3. 6f2 – fg – 2g2 4. 3hk – 17h2 5. 6x2 + 2x + 1 6. – 3p2 – q2 7. – 16x + 16 8. 9x2 – 11x – 4 9. a2 – 56a + 16 10. 3m2 + 5k2 – 4mk

DIAGNOSTIC TEST

1. B 2. D 3. B 4. A 5. B 6. A 7. C 8. D 9. C 10. B

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CHAPTER 2 : QUADRATIC EXPRESSIONS AND EQUATIONS

EXERCISE 1 1. p(p – 2) 2. (2x-9)(2x+9) 3. (r – 6)(r + 2) 4. k= 2 , 10 5. Area = 12x2 + 3x EXERCISE 2

1. b = 34− ,

21

2. ( 3 + 2x ) ( 2 – 7x )

3. w = - 21 , w = 3

4. m = 4 , m = - 2 5. Johan’s age is 6 years old DIAGNOSTIC TEST

1. y = 0 , 31

2. y = - 32 , y = 1

3. y = -1 , 23

4. x = 2,35

5. (a) (2x)2 + 92 = (x + 9)2 (b) AC = 12 cm

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CHAPTER 3 : SETS

EXERCISE 1 1. 5 2. { E , R , N } 3. 9 4. { 3 , 7 , 9 , 12 } 5. 18 6. { 11 , 13 , 14 , 16 , 17 , 19 } 7. K L M 8. 10 9. IV 10. 25

DIAGNOSTIC TEST 1. D 2. C 3. A 4. C 5. B

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CHAPTER 3: SETS EXERCISE 1. 1. . a. A B∪ b. A DIAGRAM 1 DIAGRAM 2 2. a. . P ∩ Q ∩ R’ b. 'RQP ∩∪ DIAGRAM 3 DIAGRAM 4 3. a b.

DIAGRAM 5 DIAGRAM 6 c. DIAGRAM 7 c.

E

G F

B C

A

BC

P Q R

R

Q P

E

G F

E

G F

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4. a) i. 3 ii. 2 b) i. 5 ii. 6 EXERCISE 2 1. (a) B = {20, 30} C = {20, 21, 30, 31, 32}

(b) 4 (c) 2

2. (a) T S •7 •3 •8 •12 •1 R •2 •4 •6 •0

(b) {2, 3, 4, 5, 6} (c) 7

3.

(a) P∩Q (b) P'∩Q∩R P Q P Q

R R

DIAGRAM 1 DIAGRAM 2 4. (a) P = {21, 24, 27, 30}

(b) Q= {20, 25} (c) 2

5. a) 11 b) 3 c) 13

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5. (a) P R DIAGRAM 3 DIAGRAM 4 DIAGNOSTICS TEST 1. (a) (b) DIAGRAM 1 2. (a) (b) DIAGRAM 3 DIAGRAM 4 3. (a) (b) DIAGRAM 5 DIAGRAM 6

ξ

P Q R

ξ

P Q

R

J K L J K L

P

S

RP

S

R

DIAGRAM 2

Q R

P

R

Q

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4. (a) (b) DIAGRAM 7 DIAGRAM 8 (c)

DIAGRAM 9 5. DIAGRAM 10

J K

A B C

AB C

A B C

ξ

L

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CHAPTER 4 : MATHEMATICAL REASONING EXERCISE 1 1(a) true (b) Implication 1: If x is a multiple of 3 , then it is divisible by 3. Implication 2: If x is divisible by 3 , then it is a multiple of 3. (c) Premise 2 : y is less than zero. 2 (a) Statement. (b) Conclusion: The side of cube p is not 4 cm. (c) 10 m x 10 n = 10 m+n 3 (a) 52 = 10 or 1 = 0.25 4 (b) Premise 2 : x is an angle in a semicircle. (c) some 4 (a) Some even numbers are divisible by 4. (b) (i) false (ii) true (c) Conclusion : m > 0 5 (a) statement . It’s a false statement. (b) ‘2 is multiple of 4…or...... x + 2x = 3x’ (C) Premise 1 : All quadrilaterals have 4 sides.

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EXERCISE 2 1(a) Implication 1: If x – g > y – g , then x > y

Implication 2: If x > y, then x – g > y – g

(b) i) Some ii) All

2 (a) i) k < 3 ii) 2 is a factor of 4 (b) or 3 (a) The numerical sequence is represented by 1n2 − where n = 1, 2, 3, 4,…

(b) All angles less than 90º are acute angles 4 (a) If tan α =1, then α = 45º

If α = 45º, then tan α = 1 (b) If –1 x a > 0, then a < 0.

(c) True 5 (a) n is not an even integer (b) All isosceles triangles have two sides of equal length. (c) It is a statement because it can be determined as a true statement.

DIAGNOSTIC TEST 1(a) (i) non statement (ii) statement (b) (i) > (ii) > (c) All (d) 5 has only two factors. 2(a) (i) true (ii) false (b) Implication 1: If mn = 0 , then m = 0 or n = 0 Implication 2: If m = 0 or n = 0, then mn = 0 (c) Premise 2: The circumference of circle P is not 10п

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3 (a) Some odd numbers are prime numbers. (b) 3 + (- 2) = 5 or 16 is a perfect square. (c) Premise 1 : If the sum of interior angles of a polygon is 540° , then it is a pentagon. 4(a) Antecedent : a triangle has two equal sides. Consequent : it is an isosceles triangle. (b) (i) If x < 6, then x < 4 , false (ii) If A ⊂ B , then A ∩ B = A , true (c) 2 + 7 n where n = 0,1,2,3,……. (d) Premise 1 : If M is a subset of N then M ∩ N = M 5.(a) (i) true (ii) false (b) some (c) Premise 1 : All natural numbers are grater than zero . (d) n2 is an odd number if and only if n is an odd number

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CHAPTER 5 : THE STRAIGHT INE EXERCISE 1 1 a) 1 b) -2 2 a) 3 b) y =3x +3

3 -41

4 6

5 - 21

6 31

−

7 3

8 41

−

9 y = x + 4 10 a) M(0 ,4 ) b) x = 6

DIAGNOSTIC TEST 1. C 2. C 3. D 4. D 5. A 6. C 7. B 8. D 9. A 10. B

EXERCISE 2 1 6

2 a) k = -1 b) - 61

3 a) 2 b) y = 2x -11 4 a) y = -3 x + 6 b) R(0,-6) 5 a )k = 6 b) y = -x + 6

6 a) -6 b) -32

7 a) 4 b)2

19

8 a) (6,9) b) 3

9 a) 35

− b) y = 3x -1

10 ( 6,0)

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CHAPTER 5 : THE STRAIGHT LINE

EXERCISE 1 1 a) 2 b) y = 2x-3 c) 1.5 2 a) -3 b) y = -3x + 15 c) 15 3 a) 10 b) y = 2x – 4 c) (0,4) 4 a) (5,0) b) -20 c) y = 4x - 20 5 a) 6 b) 2 c) 2y = -x + 4 EXERCISE 2

1 a) 10=y b) -8 c) 1045

+= xy

2. a) -21 b) 8

21

+−= xy c) 16

3. a) -7 b ) 24 c ) y = -4x + 24

4. a ) ( 0 , 5 ) b ) y = 23 x + 5

5. a ) 3 b ) y = 3x – 9 c ) -9 DIAGNOSTIC TEST

1. a)-21 b) (0, 3) c) y = -

21 x + 8

2. a) 9 b) y =5

12 x – 5 c) y=5

12 x + 9

3. a) (0, 8) b) 32 c) y =

32 x + 8

4. a) k = 5 b) y = -x + 2 c) (2, 0) 5. a) h = 8, k = 6 b) 7y = -3x + 33

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CHAPTER 6 : STATISTICS Exercise 1

1. 13.5 2. 5 3. 15.65 4. 1 – 5 5. 6.5 6. 6 7. 2.59 8. 24 9 29-34 10 31.5

Exercise 2: 1(a) 4 (b) 8 2(a) 3 (b) 3 (c) 3.433 3(a) 2, 5,8,11,14 (b) 8.107 4(a) 11 (b) 17 5(a)14 (b)11 6(a) 13 (b) 19 7 (a) 40 (b) 140 (c ) 190 8(a) 680 (b)1400 9(a) 19.75 (b) 18 10(a) 20-29 (b) 24.5 DIAGNOSTIC TEST: 1. A 2. C 3. C 4 B 5 B 6. B 7 C 8 B 9 B 10C

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CHAPTER 6 : STATISTICS

EXERCISE 1 1.

Mark Frequency 10 – 16 5 17 – 23 6 24 – 30 6 31 – 37 11 38 – 44 2

2.

Class Lower limit

Upper limit

Lower boundary

Upper boundary Class size

55 – 60 55 60 54.5 60.5 6 61 – 66 61 66 60.5 66.5 6 67 – 72 67 72 66.5 72.5 6 73 - 78 73 78 72.5 78.5 6

TABLE 1

3. a) Mass of

fruits (kg) Frequency Class midpoint

36 – 43 3 39.5 44 – 51 7 47.5 52 – 59 8 55.5 60 – 67 4 63.5 68 – 75 5 71.5 76 – 83 3 79.5

(b) (52 – 59) kg

(c) Mean = 354873

)35.79()55.71()45.63()85.55()75.47()35.39(+++++

×+×+×+×+×+×

= 58.17 kg

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4. (a) Based on the data in Diagram 3 and by using a class interval of 5, complete Table

2.

Class interval Frequency Midpoint 20 – 24 4 22 25 – 29 8 27 30 – 34 10 32 35 – 39 5 37 40 – 44 2 42 45 – 49 1 47

(b) Mean = 1251084

)147()242()537()1032()827()422(+++++

×+×+×+×+×+×

= 31.33

5. (a) 30 cm (b)

Height (cm) Frequency Midpoint Upper boundary

10 – 16 5 13 16.5 17 – 23 6 20 23.5 24 – 30 7 27 30.5 31 – 37 10 34 37.5 38 – 44 2 41 44.5

TABLE 3

(c) i) (31 – 37) cm

ii) Mean = 210765

)241()1034()727()620()513(++++

×+×+×+×+×

= 26.53 cm

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CHAPTER 7 : PROBABILITY 1 Exercise 1 1. (a) {1,3,5} (b) {3, 6} 2. (a) P = { N, E, R}

(b) Q = { N, R, 3, 9 } 3. 11 4. (a) HH, TT (b) HT, TH 5. 28 6. 146

7. (a)61

(b) 32

8. 90

9. 31

10. (a) 135 (b) 30 Exercise 2 1. 9 2. O, A, I, I 3. HHT , HTH , THH

4. 31

5. 7 6. 110 7. 6 8. 30 9. 80

10. 307

Diagnostic Test

1. A 2. B 3. A 4. D

5. B

6. A 7. C 8. B 9. C

10. B

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CHAPTER 8: CIRCLES III EXERCISE 1 Answers: 1. a) 35˚ b) 35˚ 2. a) 70˚ b) 70˚ 3. a) 80˚ b) 30˚ 4. a) 115˚ b) 30˚ 5. a) 56˚ b) 24˚ 6. 65˚ 7. 41˚ 8. 6˚ 9. 64˚ 10. 70˚ EXERCISE 2 1a) 60˚ b) 60˚ c) 30˚ 2a) 24˚ b) 24˚ c) 156˚ 3a) 66˚ b) 33˚ c) 57˚ 4a) 40˚ b) 70˚ c) 20˚ 5a) 56˚ b) 22˚ 6. 40˚ 7. 28˚ 8. 14˚ 9. 105˚ 10. 130˚

DIAGNOSTIC TEST 1. B 70˚ 6. A 76˚ 2. D 70˚ 7. B 132˚ 3. A 30˚ 8. D 40˚ 4. A 40˚ 9. B 80˚ 5. C 30˚ 10 C 96˚

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CHAPTER 9: TRIGONOMETRY II

EXERCISE 1:

1. sin x = 53

2. cos y = 1312−

3. 5 4. y = sin x 5. 20o

6. 0.4743 7. 0.8944 8. BC = 15 cm 9. BC = 16 cm 10. AB = 12 cm

EXERCISE 2:

(1) 178

(2) 4.8 cm (3) '26216o or o4.216 (4) – 0.75

(5) 135

−

(6) o240

(7) 178

−

(8) 9 cm

(9) 1715

−

(10) 54

DIAGNOSTIC TEST: (1) C (2) B (3) A (4) D (5) C (6) A (7) A (8) D (9) B (10) B

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CHAPTER 10 : ANGLES OF ELEVATION AND DEPRESSION EXERCISE 1 1. ∠RPQ 2. 61.44m 3. 5.2m 4. 14.69m 5. 12.29m 6. 20o 7. 7.4m 8. 58o 9. 50o 54’ 10. 30o EXERCISE 2 1. 14m 2. 84m 3. 15m 4. 69.28m 5. 23m 6. 58.32 m 7. a) 458 m b) 56° 46’ 8. a) 40° b) 22° c) 43.07m 9. a) 6.882 m b) 16° 12’ 10. a) CD- 14.66 EF- 0.671 b) 7.1° 4’

DIAGNOSTIC TEST 1. D 2. A 3. C 4. C 5. B 6. C 7. D 8. B 9. B 10. A

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CHAPTER 11 : LINES AND PLANES IN 3-DIMENSION EXERCISE 1 (paper 1) 1. a) ∠DBH b) ∠AHB c) ∠EBA 2. a) ∠CHG b) ∠AGE 3. a) ∠QRP b) ∠VRU 4. a) ∠GRF b) ∠CED c) ∠GQP 5. a) ∠AZM b) ∠AYM c) ∠NBX EXERCISE 2 1. a) ∠EDH b) ∠CHG c) ∠GDH 2. ∠PEM = 33° 41 ' 3. ∠TRS = 28° 18 ' 4. a) ∠DXS b) i) 9.17 cm b) ii) 23° 35 ' 5. a) 60° b) 26° 34 ' c) ∠SAT DIAGNOSTIC TEST 1. a) ∠EDF or ∠ACB

b) 19° 26 ' or 19.44° 2. a) ∠PRQ b) 49° 41 ' or 49.68° 3. 32° 4. 24° 47 ' or 24.8° 5. 36° 52 ' or 36.9°

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CHAPTER 11 : LINES AND PLANES IN 3-DIMENSION EXERCISE 1 1. (a) LN = 4 cm

(b) ∠ MLN (c) ∠ KNL = 36º 52´

2. ∠ VCN = 617 ′o 3. (a) EG = 10 cm

(b) ∠ DGE = 16º 42´

4. (a) ∠ VPT = 45º (b) ∠ VQT = 51° 20´ 5. (a) BT = 17 cm (b) ∠ ACT = 56° 19´

6. ∠ MQS = 38° 40´ 7. ∠ DQC = 29º 7´ 8. (a) ∠ DAM (b) ∠ MBN = 24.78º 9. (a) ∠ BGF = 53.13º (b) ∠ HBD = 25.09º 10. (a) ∠ RTS (b ∠ RPT = 35.75º EXERCISE 2 1.. (a) 13 cm. (b) ∠ ACB (c) 31º 36´ 2. (a) ∠ PRM = 26.57º (b) ∠ POM 3. (a) ∠ BGF (b) ∠ BHC = 35.26º 4. (a) ∠ TSN = 33.56º (b) ∠ MTN

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5. ∠ QTU = 26º 34´ 6. ∠ HUS = 36º 52´ 7. ∠ PZQ 8. ∠ WHT 9. ∠ VSM = 24º 47´ 10. ∠ LRQ = 32°

DIAGNOSTIC TEST 1. B 2. B 3. C 4. C 5. D 6. B 7. B 8. C 9. D

10. C

Health & Medicine

F4 Answer