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Collins CSEC Maths Workbook answers

Section 1 Computation1. a) 1

8 = 0.125 [2]

b) 23 = 0.667 [2]

c) 15 = 0.2 [2]

2. a) 0.375 = 3751000

= 38 [2]

b) 0.75 = 75100

= 34 [2]

c) 0.02 = 2100

= 150

[2]

3. a) 58 = 5

8 100

1 = 62.5% [2]

b) 0.135 = 0.135 100 = 13.5 % [2] c) 5

7 = 5

7 100

1 = 71.4% [2]

4. a) 3770 [1] b) 1.07 [1] c) 1.2 [1] d) 25 000 [1]5. a) 2 500 000 = 2.5 106 [1] b) 0.003 251 = 3.251 103 [1] c) 362 000 = 3.62 105 [1] d) 0.000 009 = 9.0 106 [1]6. a) Angle A = 2

6 180 = 60 [1]

Angle B = 36 180 = 90 [1]

Angle C = 16 180 = 30 [1]

b) Length of longest piece = 510

40 = 20 m [2]

c) Melissa receives 45

Kerry receives 15

Let x represent the total sum shared Kerry received 1

5 of x which is $45

Then, x = $45 (5) = $225. [2]7. a) Duration = 9 hr 30 min 7 hr 25 min = 2 hr 5 min [2] b) Time taken (hours) = 2 hr + ( 560) hr = 2.08 hours Average speed = distance

time = 92 km

2.08 = 44.2 km/hr [2]

8. a) 2 1

2 3

512

15

= 52

35

310

= 15103

10

= 1510

310

= 1510

103

= 5 [4]

b) 14.25 (1.24)2 = 14.25 1.5376 = 12.7124 = 12.7 (to 3 significant figures) [3]9. a) 2.14(3 1.26) = 6.42 2.6964 = 3.7236 = 3.72 (to 3 significant figures) [2] b) 2.15

0.82 0.22 = 2.15

0.64 0.22 = 2.15

0.42 = 5.119 = 5.12

(to 3 significant figures) [3]

10. 1 cm = 10 000 000 cm (from scale given) 1 cm = 100 km 4.2 cm = 420 km [2]11. a) 20 000 cm [1] b) 0.2 km [1] c) 0.9 km [1]12. a) 0.125 80 = 10 [1] b) 20% = 25 1% = 2520 Therefore, 100% = 2520 100 = 125 [1]

c) 1260 100 = 20% [1]

d) 1050 = 15 [1]

13. a) 2.5 1000 = 2500 m [1] b) 3000 cm = 30 m 30 m = 301000 = 0.03 km [1] c) 1 litre = 1000 ml 2 litres = 2000 ml [1]

Section 2 Number theory1. a) Whole numbers B [1] b) Integers C [1] c) Natural numbers A [1]2. a) Factors of 12 1, 2, 3, 4, 6, 12 [2] b) Factors of 10 1, 2, 5, 10 [2] c) Factors of 21 1, 3, 7, 21 [2]3. a) Factors of 12 1, 2, 3, 4, 6, 12 [2]

Factors of 18 1, 2, 3, 6, 9, 18 [2]HCF 6 [1]

b) Factors of 30 1, 2, 3, 5, 6, 10, 15, 30 [2]Factors of 15 1, 3, 5, 15 [2]HCF 15 [1]

c) Factors of 15 1, 3, 5, 15 [2] Factors of 25 1, 5, 25 [2] Factors of 40 1, 2, 4, 5, 8, 10, 20, 40 [2] HCF 5 [1]4. a) The first four multiples of 5 5, 10, 15, 20 [2] b) The first four multiples of 6 6, 12, 18, 24 [2] c) The first four multiples of 12 12, 24, 36, 48 [2]5. a) Multiples of 9 9, 18, 27, 36 [2]

Multiples of 12 12, 24, 36 [2]LCM 36 [1]

b) Multiples of 5 5, 10, 15, 20, 25, 30, 35, 40 [2]Multiples of 8 8, 16, 24, 32, 40 [2]LCM 40 [1]

c) Multiples of 6 6, 12, 18, 24, 30, 36, 42 [2] Multiples of 7 7, 14, 21, 28, 35, 42 [2] LCM 42 [1]6. a) 8, 13, 21 [2] b) 22, 26, 30 [2] c) 25, 36, 49 [2]

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4

7. a) Distributive law [1] b) Associative law [1] c) Commutative law [1]8. a) 110112 = (1 24) + (1 23) + (0 22) + (1 21) + (1 20)

= 16 + 8 + 0 + 2 + 1= 27 [2]

b) 2324 = (2 42) + (3 41) + (2 40)= 32 + 12 + 2= 46 [2]

c) 12425 = (1 53) + (2 52) + (4 51) + (2 50)= 125 + 50 + 20 + 2= 197 [2]

9. a) 2 157 R 1

1 R 1

0 R 1

3 R 1

2

2

2

11112 [2] b) 5 27

5 R 2

0 R 1

1 R 0

5

5

1025 [2] c) 8 90

11 R 2

0 R 1

1 R 3

8

8

1328 [2]10. a) 1101102 +

1100121001111

Answer 10011112 [3] b) 11112

100120110

Answer 1102 [3]

Section 3 Consumer arithmetic1. a) Total hire purchase price = 800 + (300 10)

= 800 + 3000 = $3800 [2] b) Money that would be saved = 3800 3000 = $800 [1]2. a) Amount received by the grocer = 120 32 = $3840 [1] b) Profit = 3840 3360 = $480 [1] c) Percentage profit = 4803360 100 = 14.3% [2]

3. a) Hourly rate = 60040 = $15 per hour [1] b) Overtime rate = 1.5 $15 = $22.50 Overtime wage = 8 $22.50 = $180 [2] c) Wage for 40 hours = 40 $15 = $600 Wage for 10 hours overtime = 10 $22.50 = $225 Total wage = $600 + $225 = $825 [3]

4. a) TT $6.30 = US $1.00 TT $5000 = US $ (5000 1.006.30 ) = US $793.65 [2] b) Amount left = US $793.65 US $650 = US $143.65 US $1.00 = TT $6.30 US $143.65 = TT $(143.65 6.30) = TT $905 [3]5. a) Percentage profit = selling price cost pricecost price 100%

= 420 000 350 000350 000 100 = 20% [2] b) Loss = $75 000 $40 000 = $35 000 Percentage loss = losscost price 100% =

35 00075 000 100 = 46.7%

[2] c) i) Depreciation after 1 year = 0.10 $180 000

= $18 000 Value of car after 1 year = $180 000 $18 000

= $162 000 [2] ii) Depreciation after 2 years = 0.10 $162 000

= $16 200 Value of car after 2 years = $162 000 $16 200

= $145 800 [2]6. a) i) Total interest repaid = P R T100 =

120 000 10 5100

= $60 000 [2] ii) Total amount of money repaid = $60 000 + $120 000

= $180 000 [2] iii) Monthly instalment = 180 0005 12 = $3000 per month

[2] b) Amount = P(1 + R100)

n

= 10 000(1 + 2.5100)5

= $11 314.08 Compound interest = $11 314.08 $10 000 = $1314.08 [2]7. a) Discount = 10% $6500 = $ 650 Amount paid = $6500 $650 = $5850 [2] b) Tax = 15% $3000 = $450 Amount paid = $3000 + $450 = $3450 [2]

Section 4 Sets1. a) n(U) = 19 [1] b) A = {6, 9, 12, 15, 18, 21} [2] c) B = {5, 7, 9, 11, 13, 15, 17, 19, 21} [2] d)

9

15

21

54

8

10

14

16 20 22

11

17

7

13

19

6

12

18

A B

U

[3]

2. a) n(A) = 8 [1] b) n(B) = 5 [1] c) A B = {9, 11, 15} [1] d) A B = {2, 3, 4, 5, 7, 9, 11, 13, 15, 17} [1]

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3. a) A B

U

[1]

b) UBA

[1]

c) UBA

[1]

d) UBA

[1]

4. a) Number of subsets = 23 = 8 [1] b) { }, {2}, {4}, {6}, {2, 4}, {2, 6}, {4, 6}, {2, 4, 6} [2]5. a) Infinite [1] b) Finite [1] c) Finite [1] d) Infinite [1]6. a) B and E [1] b) D is a subset of B [1] c) B and C OR C and D [1] d) A [1] e) B, D OR E [1] f) C [1] g) 4 [1] h) Number of subsets = 24 = 16 [1]

7. a)

25 x 18 xx

2

n(u) = 36

n(B) = 25 n(C) = 18

[3]

b) 25 x + x + 18 x + 2 = 36 45 x = 36 x = 45 36 x = 9 [2]8. a)

4 + x8 + x

9 x 5 x

6 x

4 + x

n(P) = 18

x

2

n(u) = 40

n(B) = 23 n(C) = 15

[6] b) 8 + x + 6 x + x + 9 x + 4 + x + 5 x + 4 + x + 2 = 40 x + 38 = 40 [2] c) x + 38 = 40 x = 40 38 x = 2 [2] d) n(Biology only) = 8 + x = 8 + 2 = 10 [1] e) n(Chemistry and Biology only) = 6 x = 6 2 = 4 [1]

Section 5 Measurement1. a) C = 2r = 2 3.14 6 = 37.68 cm [2] b) A = r2 = 3.14 62 = 113 cm2 [2] c) Area of minor sector = 360 A =

120360 113 = 37.7 cm

2 [2]

d) Area of triangle AOB = 12 ab sin C = 12 6 6 sin 120

= 15.6 cm2 [2] e) Area of shaded region = 37.7 15.6 = 22.1 cm2 [2] f) Length of minor arc = 360 C =

120360 37.68 = 12.56 cm [2]

g) Length of major arc = 360 C = 240360 37.68 = 25.12 cm [2]

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h) 120

6cm6cm

30A BX

AX = 6 cos 30 = 5.2 cm AB = 2 5.2 = 10.4 cm Perimeter of shaded region = length of minor arc + AB

= 12.56 + 10.4 = 22.96 cm [2]2. a) A = l b = 6 8.2 = 49.2 cm2 [2] b) V = A h = 49.2 12 = 590 cm3 [2] c) Total surface area = 2 (12 6) + 2 (12 8.2)

+ 2 (6 8.1) = 144 + 196.8 + 98.4 = 439.2 cm2 [4]3. a) Total area = Area of triangle + Area of square

+ Area of semi-circle = (12 2 4) + (4 4) + ( (2)

2

2 ) = 4 + 16 + 6.28 = 26.28 cm2 [3] b) Total area = Area of

rectangle ABCD Area of semi-circle = (8 6) ( (4)22 ) = 48 25.12 = 22.88 m2 [4]4. a) Area of shaded cross-section = r 2 = 3.14 22

= 12.56 cm2 [2] b) Volume of cylinder = r 2h = 12.56 8 = 100.48 cm3 [2] c) Area of curved part of cylinder = h 2r

= 8 2 3.14 2 = 100.48 cm2 [2]

5. a) i) Length of one side of square = 196 = 14 cm [2] ii) Perimeter of square = 4 14 = 56 cm [1] b) i) Circumference = 56 cm [1] ii) 2r = 56 r = 56

2(227 ) = 8.91 cm [2]

iii) Area of circle = r 2 = 227

(8.91)2 = 249.5 cm2 [2]6. a) Curved surface area of the cylinder = 2rh

= 2 3.14 2 6 = 75.36 cm2 [2] b) TOTAL surface areas of the two hemispheres

(or one sphere) = 4r 2 = 4 3.14 22 = 50.24 cm2 [2]

c) TOTAL surface area of perfume bottle = 75.36 + 50.24 = 125.6 cm2 [1]

d) Volume of cylinder = r 2h = 3.14 22 6 = 75.36 cm3 [2] e) TOTAL volume of the two hemispheres (or one sphere)

= 43 r 3 = 4

3 (2)3

= 33.49 cm3 [2] f) TOTAL volume of perfume bottle = 75.36 + 33.49

= 108.85 cm3 [1]7. a) BDC = 30 (BDC is an isosceles triangle) [2] b) DBC = 180 (30 + 30) = 180 60 = 120 ABD = 150 120 = 30 [2] c) ADB = 180 30

2 = 75 [2]

8. a) Area of trapezium = 12(8 + 10) 6 = 54 cm2 [2]

b) 110 + x + 120 + 60 = 360 x + 290 = 360 x = 360 290 x = 70 [1]

Section 6 Statistics1. a) Score (x) Tally Frequency (f ) x f

1 ||| 3 32 |||| 4 83 |||| 4 124 |||| 4 165 || 2 106 |||| ||| 8 487 | 1 78 ||| 3 249 | 1 9

[5] b) Mode = 6 [1] c) Median = 4 + 52 = 4.5 [1]