Cambridge IGCSE IGCSE MathematicsMathematics .Cambridge IGCSE IGCSE MathematicsMathematics Study

  • View
    324

  • Download
    16

Embed Size (px)

Text of Cambridge IGCSE IGCSE MathematicsMathematics .Cambridge IGCSE IGCSE MathematicsMathematics Study

  • Cambridge IGCSECambridge IGCSECambridge IGCSECambridgeCambridgeCambridge IGCSE IGCSE IGCSECambridge IGCSE

    MathematicsMathematicsCambridgeCambridgeCambridgeCambridgeCambridgeCambridgeCambridgeCambridgeCambridgeCambridge IGCSE IGCSE IGCSE IGCSE IGCSE IGCSE IGCSE IGCSE IGCSE IGCSE

    MathematicsMathematicsMathematicsMathematicsMathematicsMathematicsMathematicsMathematicsMathematicsMathematicsStudy GuideStudy GuideStudy GuideStudy GuideStudy GuideStudy GuideStudy GuideStudy GuideStudy Guide

    CambridgeInternationalExaminations

    Answer key and markscheme

  • CONTENTSAnswer Key

    Chapter 1 Numbers 1Chapter 2 Algebra 9Chapter 3 Geometry 21Chapter 4 Mensuration 27Chapter 5 Coordinate Geometry 28Chapter 6 Trigonometry and Pythagoras Theorem 30Chapter 7 Vectors and Matrices 33Chapter 8 Probability 38Chapter 9 Statistics 41

    Practice test markscheme

    Practice Test (Paper 2) 47

    Practice Test (Paper 4) 51

  • 1

    Answer Key

    2017 NTK Publishing Limited

    Chapter 1 NumbersExercise 1.1

    1 (a) 7, 2, 111, 25, 0

    (b) 7, 2, 34

    , 111, 2.4, 25, 0, 512

    (c) , 3

    (d) 25, 0

    2 (a) 71, 81

    (b) 4, 3

    (c) 6.2, 4, 89

    , 3, 71, 81, 3.1

    (d) 81

    3 (a) 3, 7, 13 (b) 2, 17

    (c) 23, 29, 31 (d) 5, 37, 43

    (e) 41, 43, 47 (f) 53, 61, 79

    4 (a) 1, 3, 25 (b) 5

    (c) 2, 2.1, 1, 3, 5, 4.62, 43

    , 25

    (d) 3, 25

    5 7, 14, 56, 63, 70

    6 (a) 1, 2, 3, 6 (b) 1, 2, 3, 4, 6, 12

    (c) 1, 5, 25 (d) 1, 13

    (e) 1, 2, 3, 5, 6, 10, 15, 30

    (f) 1, 2, 4, 8, 16, 32, 64

    7 (a) 4 (b) 8

    8 (a) 24 (b) 60

    9 (a) 32 5 (b) 32 23

    (c) 7 3 22 (d) 23 3 5

    (e) 2 7 9 (f) 5 33

    (g) 2 3 5 7 (h) 32 5 7

    10 (a) H.C.F = 6 L.C.M = 1560

    (b) H.C.F = 45 L.C.M = 1350

    (c) H.C.F = 15 L.C.M = 4725

    (d) H.C.F = 12 L.C.M = 11880

    (e) H.C.F = 36 L.C.M = 2592

    (f) H.C.F = 90 L.C.M = 1080

    Exercise 1.2A

    1 A 11,13,17,19{ }=

    2 (a) P

    Q

    4, 8,12,16

    3, 6, 9,12,15,18

    { }{ }

    =

    = (b)

    P

    Q

    4, 8,12,16

    3, 6, 9,12,15,18

    { }{ }

    =

    =

    3 B 1, 3, 9,13{ }=

    4 (a) All elements in A are in B

    (b) Yes, it is because 26 is not in B

    5 (a) 3, 7, 9{ } (b) 2, 3, 5, 7, 8, 9,11{ }

    6 (a) 4 (b) 4

    (c) 0 (d) 2 , 2, 4 , 42 2{ } { }{ }7 (a) 9 is a multiple of 3

    (b) 12{ } (c) 11

    8 (a) 2, 3, 5, 7{ } (b) 4

    (c) True, since 6.5 is not a member of set A.

    9 (a) A 7, 6, 5, 4, 2, 1, 2, 3, 4, 6{ } = (b) 3, 5{ } (c) 8, 5, 3, 0,1, 2, 5, 7, 8{ }

  • 2

    Cambridge IGCSE Mathematics Study Guide

    2017 NTK Publishing Limited

    10 (a) 8, 7, 6, 5, 2, 1, 0{ } (b) 4, 2{ } (c) 8, 7, 6, 5, 3, 2, 1, 0,1, 3{ }

    Exercise 1.2B

    1 (a) 5,10,15{ } (b)

    (c) 5, 7, 8, 9,10,15{ }

    2 (a) 1, 2,13,15,17{ } (b) 5, 8,10,13,15,17, 30, 33{ } (c) 30, 33{ }

    3 (a) 5, 9{ } (b) 22, 24{ } (c)

    4 (a) 4, 5, 6{ } (b) 4, 5{ } (c) 3, 8, 20, 22{ }

    5 (a)

    A

    ab

    ef

    d

    c

    B

    (b) c{ }

    6 (a)

    A

    B C

    3

    248

    9

    10 5

    1 7

    (b) A B CA B C 10

    ( ) { } = =

    7

    A

    B C

    2

    4.2

    933

    15

    5

    107

    8 (a)

    A B

    (b) A B

    (c) A B

    (d) A

    B C

    9 (a) 7 (b) 8

    10 (a) 0 (b) 2

    (c) 5 (d) 7

    (e) 18 (f) 1

    11 (a) 1 (b) 0

    (c) 13

  • 3

    Answer Key

    2017 NTK Publishing Limited

    12 A

    1 2 3

    5

    B

    Exercise 1.2C

    1 14

    2 (a)

    C

    50 50 100

    T

    (b) 50

    3 (a) 28 (b) 5

    (c) 5

    4 (a)

    M

    5 5

    5

    10

    S

    (b) 15 (c) 5

    (d) 5

    5 (a)

    G

    5 5

    5

    15

    S

    (b) 5 (c) 15

    6 (a)

    B

    7 8

    20

    15

    F

    (b) 8 (c) 20

    (d) 7

    7 (a)

    x

    Sandwich

    Chocolate Coffee

    20

    15

    8 x

    7 x

    9

    10

    (b) 4

    8 (a) 15 (b) 10

    Exercise 1.3

    1 (a) 121 (b) 6.25

    (c) 49 (d) 3

    10

    (e) 2710

    (f) 16

    2 (a) 125 (b) 64

    (c) 1 (d) 0.2

    (e) 1.5 (f) 25

    3 13

    4 4.913

    5 62.9

    6 4 9 2 3 5

    4 9 13 5

    + = + =

    + =

    7 41 or 41

    Exercise 1.4

    1 (a) 17C (b) 30C

    (c) Moscow

    2 8084

    3 (a) 4C (b) 0.5C

  • 4

    Cambridge IGCSE Mathematics Study Guide

    2017 NTK Publishing Limited

    Exercise 1.5

    1 (a) 2330

    (b) 2328

    (c) 528

    (d) 59

    (e) 2924

    (f) 8135

    (g) 192

    (h) 12152

    2 (a) 113

    (b) 34

    (c) 12

    (d) 3

    3 (a) 2.4 (b) 2400 mL

    4 (a) 0.34, 1.5, 2.4, 3.7, 6.45

    (b) 1.4, 7.85, 7.94, 9.3, 10.7

    5 (a) Terminating decimals: 0.35, 0.6, 4.7

    Recurring decimals: 2.6, 2.87

    (b) Terminating decimals: 1.3, 3.56, 2.43, 4.7

    Recurring decimals: 3.8

    6 (a) 45

    (b) 2750

    (c) 3325

    (d) 7625

    (e) 23

    (f) 4599

    (g) 2753999

    (h) 21

    18

    7 (a) 1

    250 (b)

    1425

    (c) 2310

    (d) 131

    5000

    8 Fractions Decimals Percentages

    (a)25

    0.4 40%

    (b)123100

    1.23 123%

    (c)625

    0.24 24%

    (d)29

    0.2 22.2%

    (e)51750

    10.34 1034%

    (f)115

    2.2 220%

    Exercise 1.6

    1 (a) 7 > 2 (b) 1 < 0

    (c) 0.23 < 0.32 (d) 0.1 > 1

    (e) >312

    3 (f)

  • 5

    Answer Key

    2017 NTK Publishing Limited

    3 (a) 254

    (b) 19

    (c) 13 (d) 4

    (e) 1

    32 (f) 8

    (g) 1

    16 (h)

    58

    4 (a) 4.98 109 (b) 9.999 1010

    5 (a) 124 000 000 (b) 0.000 000 62

    6 (a) 1.512 (b) 1.6 104

    (c) 4.2 108 (d) 9.72 102

    (e) 3.33 1010 (f) 2.30 106

    (g) 2.32 1010 (h) 3.06 101

    7 723, by 40 353 607 times.

    8 500 s

    9

    1

    22 10, 4.2 10 , 2 10 , 23

    4 223

    Exercise 1.8

    1 (a) 1 (b) 6

    (c) 0.6 (d) 0.2

    (e) 16 (f) 21

    (g) 64 (h) 43.47

    (i) 8 (j) 12

    (k) 4 (l) 16

    2 (a) 1 (b) 25

    (c) 20 (d) 33

    (e) 6 (f) 3

    3 (a) 32

    (b) 56

    (c)

    3258

    125

    = (d)

    10332

    209

    =

    Exercise 1.9

    1 (a) 232.12 (b) 0.01

    (c) 132.13 (d) 0.54

    2 (a) 3 720 000 (b) 0

    (c) 6000 (d) 93 000

    3 (a) 70 000 (b) 0.2

    (c) 10 (d) 0.7

    4 (a) 1030 (b) 1 500 000

    (c) 737 000 000 (d) 93.8

    5 (a) 8009.21 (b) 8010

    (c) 8000 (d) 8009.2

    (e) 8009.206

    6 (a) 7 8

    4

    (b) 14

    7 14.02

    8 (a) 4 26

    43

    = (b)

    2 22

    82( )+=

    (c) 48

    13

    =

    Exercise 1.10

    1 upper bound: 9.80.12

    9.85+ = ; lower bound

    9.8 0.12

    9.75 =

  • 6

    Cambridge IGCSE Mathematics Study Guide

    2017 NTK Publishing Limited

    2 (a) lower bound: 512

    8 12

    = 33.75

    (b) upper bound: 8+ 1

    2

    5 12

    = 179

    3 number of small tanks: 900+ 10

    2

    3.5 0.12

    = 262 2269

    4 (a) upper bound: 4 6.81+ 0.012

    = 27.26

    (b) lower bound: 4 6.81 0.012

    = 27.22

    5 (a) lowest possible: 2612

    25.5 kg =

    (b) upper bound: 5 26+ 12

    = 132.5 kg

    6 (a) upper bound: 65+ 12

    58 12

    = 8 kg

    (b) lower bound: 65 12

    58+ 12

    = 6 kg

    7 (a) lower bound:

    2 3.14 0.012

    3.56 0.012

    9.81+ 0.012

    = 3.77

    (b) upper bound:

    2 3.14+ 0.012

    3.56+ 0.012

    9.81 0.012

    = 3.79

    8 upper bound: 6 7.4+ 0.12

    2

    = 333.015

    lower bound: 6 7.4 0.12

    2

    = 324.135

    Warm up 1.11

    1 (a) 1:3 (b) 3:5

    (c) 8:11 (d) 1:2:8

    (e) 15:48:20

    2 (a) a:b:c = 1:2:6

    (b) a:b:c = 5:4:8

    (c) a:b:c = 40:15:50 = 8:3:10

    (d) a:b:c = 9:12:8

    Exercise 1.11

    1 (a) =P w14

    3 (b) 7294

    (c) 36 m/s

    2 (a) = d L3 10 5 (b) 125 000 mm

    3 35 km

    4 6

    5 78 kg

    6 (a) 743.04 (b) 639.6

    7 (a) =tn

    80 (b) 16

    (c) decrease by 1 hour

    8 (a) =xf

    3.6 105 (b) f = 1440

    (c) 240

    9 40 minutes

    10 1 day

    11 7 days

    12 4

  • 7

    Answer Key

    2017 NTK Publishing Limited

    13 (a) (i) C = 4500N (ii) =tN

    192

    (b) (i) C = 4500 192t

    C = 864000t

    (ii) Inverse proportion

    (c) (i) Decrease, it is because the salary budget is inversely proportional to the time required to finish the project.

    (ii) =

    =t

    t

    108000 864000

    8 4 months

    14 (a) 8:12 (b) 36:9

    (c) 115:92 (d) 144:192

    (e) 4104:912

    15 (a) 8:12 (b) 36:9

    (c) 115:92 (d) 144:192

    (e) 4104:912

    16 (a) 280 (b) $2240

    17 (a) 5.5 kg (b) 22

    (c) 12.8

    18 (a) 3 km (b) 3.6 km/h

    Warm up 1.12

    1 (a) $2 (b) 13.176

    (c) 4.2 kg (d) 6.4 g

    (e) 9 (f) 464.4

    2 (a) 10.2 (b) 105.176

    (c) 64.5 (d) 4185.44

    (e) 12.84 (f) 773.85

    3 (a) 11.76 (b) 173.4

    (c) 595.92 (d) 56.55

    (e) 62.328 (f) 8.75

    4 (a) 10% increase (b) 10% decrease

    (c) 1.18% increase (d) 1.83% decrease

    (e) 7.24% decrease (f) 13% decrease

    Exercise 1.12

    1 15.9%

    2 (a) 85% (b) 3:17

    3 60

    4 750

    5 4.62%

    6 96

    7 11%

    8 5.6%

    9 403.2