AnSWErS to the StudEnt S Book ExErCiSES

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1 nswers to the StudEnt S ook EErCiSES Chapter Eercise. (page ) 9 Eercise. (page ) ; ; HCF ; LCM ; ; HCF ; LCM ; ; HCF ; LCM ; ; HCF ; LCM ; ; HCF ; LCM ; ; HCF 9; LCM 9 ; ; HCF ; LCM ; ; HCF ; LCM 9 ; ; HCF ; LCM ; 9 ; HCF ; LCM 9 Eercise. (page ) Eercise. (page ) a) 9 c) d) e) f) g) h) cm a) c) d) e). a). c).9 d) e). a).9 c). d). e) a). c) d). e). and. is also a possible answer since Eercise. (page ) a) c) a) c) d) e) a) c) d) e) a) c) d) a) c) d) Eercise. (page ) a) c) 9 d) e) a) 9 c) d) e) a) c) _ d) e) _ a). c). d). e). Mied eercise (page ) a) c) a),, HCF, LCM,, HCF, LCM c),, HCF, LCM a) c) d) a),, c), a) a) a)., 9., 9 c).,.9 a) 9.,..,.99 c)., 9.9 Higher WJEC GCSE Mathematics, Hodder Education nswers to the Student s ook eercises 9

2 9 a) c) d) e) a) c) d) e). or _ Chapter Eercise. (page ) a) 9, _, c), 9 a) _ 9 c) _ d) e) _ f) _ g) _ h) _ i) _ j) _ k) _ 9 l) _ a) 9 c) d) _ e) f) g) h) _ i) j) k) l) 9 a) c) d) e) _ f) g) h) i) j) k) l) _ Eercise. (page 9) a) d) g) a) _ d) 9 c) e) f) h) _ c) e) f) 9 a) c) d) _ e) _ f) g) h) _ i) j) _ 9 k) _ l) a) c) _ d) e) _ f) 9 g) h) _ i) _ j) _ k) _ l) 9 Eercise. (page ) a) a) c) e) f) h) 9 c) e) _ 9 d) g) _ d) a) c) d) _ e) a) _ cm _ cm Eercise. (page ) a).. c). d). e). a) Terminating, is a factor of Recurring, is not a factor of c) Recurring, 9 is not a factor of d) Terminating, has onl factors which are factors of e) Recurring, is not a factor of a). Si Eercise. (page ) Eercise. (page 9) a).. c). d). e). f). g) h) i). j). k).9 l).9 a) c) d) 9 e) f) g) h) i) j) k). l) a).. c).99 d) 9. e). f). g) 9. h). i). j). k). l) 9.9 a) 9 c) d) e) f) g). h).9 i).9 j). k). l). Eercise. (page ) a)..() c). d). e). f). g) (.) h).() a)..() c). d).9 e).9 f). g). h) Mied eercise (page ) a), _, _ c), a) c) d) _ e) f) g) h) _ i) j) k) _ l) m) n) o) 9 p) _ q) r) _ s) t) 9 _ a).. c). d). a) 9.. c). d). a). c). d). e) 9. f). a) c) d) e) 9 f). a) c) _ d) _ nswers to the Student s ook eercises Higher WJEC GCSE Mathematics, Hodder Education

3 Chapter Eercise. (page ) a) : : c) : d) : : e) : : a) : : c) : d) : e) : : : : : : Eercise. (page ) a) : : c) :. d) :. e) :. f) : g) :. h) : : : Eercise. (page ) a) cm. cm a) babies 9 helpers a) litres litres mm or cm a) miles inches a) ml teaspoons a) ml ml a) g g 9 a) g g Eercise. (page ) Dave, Sam a) litres litres kg sand a) ml ml mit, ree, Chris 9 a) g g Eercise. (page ) In all these questions either cost per unit or number of units per penn can be used. oth are given in each answer. Where necessar, answers are rounded to decimal places, unless otherwise indicated. Cost per gram: g bag.p, g bag.p Grams per penn: g bag. g, g bag.9 g g bag is better value Cost per litre: litre bottle.p, litre bottle.p Millilitres per penn: litre bottle. ml, litre bottle.9 ml litre bottle is better value Cost per gram: g pack.p,. kg pack.9p Grams per penn: g pack. g,. kg pack.9 g. kg pack is better value Cost per nail: pack.p, pack.p Nails per penn: pack. nails, pack. nails pack is better value Cost per roll: pack.9p, pack.p Rolls per penn: pack. rolls, pack.9 rolls (answers rounded to decimal places) pack is better value Cost per ml: ml tube.9p, ml tube.p Millilitres per penn: ml tube.9 ml, ml tube. ml ml tube is better value Cost per litre: litres.p, litres.p, litre p Litres per pound: litres. litres, litres. litres, litre. litres litre bottle is the best value Cost per gram: g.9p,. kg.9p, kg.p (answers rounded to decimal places) Grams per penn: g.9 g,. kg. g, kg.9 g. kg packet is the best value Mied eercise (page ) a) : : c) : d) 9 : e) : a) : :. c) : d) : e) :. a) cm cm g a) g g a) ml ml In questions and either cost per unit or number of units per penn can be used. oth are given in each answer. Where necessar, answers are rounded to decimal places, unless otherwise indicated. Cost per litre: litres., litres. Litres per pound: litres. litres, litres. litres litres is better value Cost per millilitre: pint.p, litre.p (answers rounded to decimal places) Millilitres per penn: pint. ml, litre. ml Litres are better value Chapter Eercise. (page ) a). c) d) e). f). g) h). i) j) Higher WJEC GCSE Mathematics, Hodder Education nswers to the Student s ook eercises 9

4 a).9 c) d) e) 9. f) g) 9 h) i). j) 99 a) c). d) e) f) g) h) i) j) a) c) d) e) f) g). h) i) j) a) c) d) e) f) g) h) i) j) a) c) d) e) f) g) h) i) j) a) c) d) e) 9 f) g) 9 h). i).9 j).9 a) c) d) e) 9 a) c) d) e). 9. cm. ml a) cm cm and Eercise. (page ) a) c) d) e) f) g) h). i). j) k) l) a) c) d) e) f). g). h). i) j) k). l) a) c) d) 9 e) f). g).9 h). i). j).99 a). 9. c) d) e) f). g).9 h). i). j). or cm or cm cm or cm 9 or cm or cm mph a) 9 c) or d) 9 or e) or f). g). or. h) or i) or j) k). or or l) or Eercise. (page ) a) p p c) p d) p e) p f) p a) p p c) p d) p e) f) p : p cm p cm Eercise. (page 9) a) 9. c). d). e). f) g) h) i) j) 9 k). l). a). c). d) e). f) 9 g) h) i) j) k). l) a). c) d). e) f) a) 9. c) d) e). f) a). c) d). e). f) Mied eercise (page 9) a) 9. c).9 d). e) f). g) h). i) j).9 a). c) d) e) f) g). h). i) 9 j) a) c) d) 9 e) f) g) h) 9 i) j) a) 9. c) d) e) 9. a) 9 c) d) e) f) g) h). i). j) cm or cm mph 9 a) c) d) or e) or f). g) h) or i) j) or a) 9.. c). d) e) a). c).9 d). e). a) p 9p c) p d) 9p e) p f) p a) c) d).9 e) 9 f) g). h) i) j) a). c) 9 d). e) 9 c). a). c) d). e). f). 9 nswers to the Student s ook eercises Higher WJEC GCSE Mathematics, Hodder Education

5 Chapter Eercise. (page ) Eercise. (page ) Check students answers. Possible answers include the following. a) positive negative negative Multipling b number less than should make answer smaller c) and answer should be more than this d) and answer should be less than this Check students answers. Possible answers include the following. a) nswer is too large, since.9 is near negative negative positive c) and answer should be less than this d) so last digit should be a)... c) a) 9 or c) a)... or c)... d).9. 9., or a).. a). 9. a).. 9 a) (i) (ii). (iii) 9 < (iv)... (i). (ii).9 (iii).9 (to d.p.) (iv) (to nearest whole number) Eercise. (page ) a) hours and minutes 9 minutes a). hours.9 hours hours and minutes hour and minutes. and. ml or. litre mph 9 9. or 9.. (to d.p.). g/cm. cm Mied eercise (page ) a).. (to d.p.) a) The answer should be more than, which is 9. Multipling. b a number less than should give an answer less than.. c) 9 <, not nearl (or equivalent argument). d) The answer should be negative. a) 9.. c) or < a).. a) (i) (ii). 9 (iii) < (iv).. (i) 9. (ii). (iii).9 (to d.p.) (iv) (to nearest integer) a) hours minutes hours minutes c) minutes d) minutes 9. mph (to d.p.) people 9.9 or cm (to d.p.) Chapter Eercise. (page ) a) 9.. c). a) c).. rabbits Eercise. (page 9) a) 9 c) 9. d). a) 9 c). d) or or.9 or 9 or 9. Higher WJEC GCSE Mathematics, Hodder Education nswers to the Student s ook eercises 9

6 votes 9 a) 9p. a). Mied eercise (page 9) 9 bacteria people a).. c). d) 9. e). 9 copies seats a).. c). a).. 9 a).. miles per gallon Chapter Eercise. (page 99) a) _ c) _ a) _ c) d) e) f) g) h) _ 9 i) j) k) l) _ m) n) o) _ a) c) _ d) e) f) g) h) Eercise. (page ) a).. c).9 d).9 e) f). g).9 h) a). 9. c).9 d). e).9 f). g). h) Eercise. (page ) a) c) _ d) e) n f) 9n g) n a) c) d) e) Cannot be simplified f) n a) c) d) e) a) c) d) Eercise. (page ) a). c). d). e). f). g) h).9 a). c). d). e). f). a) c). d) 9 e). f) g) 9 h). i). j) 99 k). l) Eercise. (page ) a). c). d) e). f) g). h). a).. c). d). e). f).9 g).9 h). Mied eercise (page ) a) 9 c) _ 9 d) _ e) a) c) 9 d) _ or _ a).. c).9 d).9 e). a).9. 9 c). d). a) c) d) _ e) _ a) c) d) e) a)..9 c). d). a). c) d). 9 a). c). d). 9 e) f). g). h). i).9 j). a).. c). d). e). f). Chapter Eercise. (page ) a)..9 c). a) 9.. c).9 a)..9 c). 9 nswers to the Student s ook eercises Higher WJEC GCSE Mathematics, Hodder Education

7 a).. c).9 a).. c) 9. a).. c). a).. c).9 a).. c).9 9 a).. c). a).. c). Eercise. (page ) a) a. t (i). (ii) 9. a) v 9. t (i). (ii). c) ears a) (i) (ii) c) hours a) % c) Number of ears invested d) (i) 9. (ii). a) P. t (i) 9 (ii) c). ears a) m.9 t (i). g (ii). g c). ears Eercise. (page ) a) U. m, L. m U. kg, L. kg c) U.9 m, L.9 m d) U. seconds, L. seconds e) U. ml, L 9. ml.99 m < length,. m No. U for card. cm, L for envelope. cm a) U g, L g U m, L 9 m c) U seconds, L seconds Eercise. (page 9) U. cm, L. cm U. cm, L 9. cm U kg, L. kg U cm, L cm a) U., L. U., L. U. m/s, L. m/s U 9 people/square mile, L 9 people/square mile U., L. 9 U. L. a) Least. kg, Greatest. kg (i) Least kg, Greatest kg (ii)... 9 blocks is too man.., 9 blocks is under kg. t most 9 blocks. Mied eercise (page ) a). c). a).. c). a).9.9 c). a).. a) % c) Number of ears d) (i). (ii). a) v. t (i) 9. (ii) 9. c) ears a) U. kg, L. kg U kg, L kg U. m, L. m 9 U. km/h, L. km/h Chapter 9 Eercise 9. (page ) a) and c)... a).. c). d). e). a) _,, c) and e) a)... c). d). e). a) a) a) a) c) _ d) _ 9 _ 9 c) 9 d) 9 99 c) d) 99 c) 99 d) Eercise 9. (page ) a) 9 c) d) e) f) a) c) d) e) f) a) c) d) e) f) a) c) d) a) 9 c) d) e) f) a) c) 9 d) 99 Higher WJEC GCSE Mathematics, Hodder Education nswers to the Student s ook eercises 99

8 a) 9 c) d) e) 9 f) 9 9 a) c) d) e) f) a) c) d) Mied eercise 9 (page ) a) _, c) and e).. a).. c).. d). e). a) c) _ d) a) _ c) d) a) c) d) e) f) a) c) d) e) f) a) c) d) 9 a) c) d) e) f) 9 a) c) d) e) a) d) Chapter Eercise. (page ) f) c) e) f) a b c d e f g h u v w z v 9 w a g b i j k m n p r s t Eercise. (page ) a) a b c) c d) a a) s t v 9w c) d) v w a) c) z d) a) n 9p q r c) d e d) f g e) h j f) k m Eercise. (page ) a) ( ) ( ) c) ( ) d) ( ) a) ( ) ( ) c) ( ) d) ( ) a) ( ) ( ) c) ( ) d) ( ) Eercise. (page 9) a) a a b b c) c c a) 9d d e e c) f f a) g g h h 9 c) j j a) k k m m c) n n a) p p r r c) s s Eercise. (page ) a) c) a) c) z a) m n f g c) p r a) k c) d Mied eercise (page ) a) a b a b c) a b d) 9a b e) f) g) h) i) f g j) j k k) r s l) v w a) c) d) e) f) g) a h) m i) p j) t k) j l) a) ( ) ( ) c) ( ) d) ( ) e) ( ) f) ( ) g) ( ) h) ( ) i) ( ) j) ( ) k) ( ) l) ( ) m) ( ) n) ( ) o) z(z ) a) a 9a a a c) a a d) e) f) g) h) i) p p j) p p k) t t l) a a a) c) d) a e) j f) t g) v w h) d e i) j) p nswers to the Student s ook eercises Higher WJEC GCSE Mathematics, Hodder Education

9 Chapter Eercise. (page ) ( ) ( ) Eercise. (page ) ( ) ( ) ( ) ( ) ( ) a) ( )( ) ( )( ) c) ( )( ) d) ( )( ) e) ( )( 9) f) ( )( ) g) ( )( ) h) ( )( ) a) ( )( ) ( )( ) c) ( )( ) d) ( )( ) e) ( )( ) f) ( )( ) g) ( )( ) h) ( )( ) a) ( )( ) ( )( ) c) ( )( ) d) ( )( ) e) ( )( ) f) ( )( ) g) ( )( ) h) ( )( ) Eercise. (page ) a) ( )( ) ( )( ) c) ( )( ) d) ( 9)( 9) e) ( )( ) f) ( )( ) a) ( )( ) ( )( ) c) ( )( ) d) ( )( ) e) ( )( ) f) ( )( ) Eercise. (page 9) a c b a b c a d bc e z 9t w v z tv 9 e f g a 9 a b c e g f a c 9b d 9 a b Eercise. (page ) a) ( )( ) ( )( ) c) ( )( ) d) ( )( ) e) ( )( ) f) ( )( ) g) ( )( ) h) ( )( ) i) ( )( ) a) ( )( ) ( )( ) c) ( )( ) d) ( )( ) e) ( )( ) f) ( )( ) g) ( )( ) h) ( )( ) i) ( )( ) a) ( )( ) ( )( ) c) ( )( ) d) ( )( ) e) ( )( ) f) ( )( ) g) ( )( ) h) ( )( ) i) ( )( ) Eercise. (page ) ( )( ) ( )( ) (9 )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) 9 ( )( ) ( )( ) Eercise. (page ) ( ) 9 Mied eercise (page ) a) d) g) e) h) ( ) ( ) ( ) ( ) c) f) ( ) ( ) a) ( )( ) ( )( ) c) ( )( ) d) ( )( ) e) ( )( ) f) ( )( ) g) ( )( ) h) ( )( ) a) ( 9)( 9) ( )( ) c) ( )( ) d) ( )( ) e) ( )( ) f) ( )( ) g) ( )( ) h) ( )( ) a) d) g) a bc v tw e) h) c) z z f) a q s r ten a) ( )( ) ( )( ) c) ( )( ) d) ( )( ) e) ( )( ) f) ( )( ) g) ( )( ) h) ( )( ) i) ( )( ) j) ( )( ) k) ( )( ) l) ( )( ) a) d) g) ( ) e) h) ( ) ( ) ( ) c) f) Higher WJEC GCSE Mathematics, Hodder Education nswers to the Student s ook eercises

10 Chapter Eercise. (page ). 9 m 9 m 9 Eercise. (page 9) p 9 a _ 9. Eercise. (page ) 9. 9 Eercise. (page ) a p m 9 Eercise. (page ).,, < > >, > 9, 9.. < 9 <..,.. > 9 <, Mied eercise (page ) m 9 p p or or p or 9 or a or 9 a < >, 9.. Chapter Eercise. (page 9) 9 _ Eercise. (page ) _. _ Eercise. (page ). <.... <. < 9 < <. Eercise. (page ) R nswers to the Student s ook eercises Higher WJEC GCSE Mathematics, Hodder Education

11 R R R R Mied eercise (page ) _. _ 9..9., > _.. 9 R Chapter Eercise. (page 9) Three points plotted, e.g. (, ), (, ), (, ), straight line drawn through them. Three points plotted, e.g. (, ), (, ), (, ), straight line drawn through them. Three points plotted, e.g. (, ), (, ), (, ), straight line drawn through them. Three points plotted, e.g. (, ), (, ), (, ), straight line drawn through them. Three points plotted, e.g. (, ), (, ), (, ), straight line drawn through them. Eercise. (page ) Three points plotted, e.g. (, ), (, ), (, ), straight line drawn through them. Points (, ) and (., ) plotted, straight line drawn through them. Points (, ) and (, ) plotted, straight line drawn through them. Three points plotted, e.g. (, ), (, _ ), (, 9), straight line drawn through them. Points (, ) and (., ) plotted, straight line drawn through them. Eercise. (page ) a) She walked at km/h for minutes (distance km), waited for minutes, travelled in a bus (or car) at km/h for minutes (distance 9 km). pproimatel minutes c) (i). km/minute (ii) km/h d) (i) pproimatel. km/minute (ii) pproimatel km/h Higher WJEC GCSE Mathematics, Hodder Education nswers to the Student s ook eercises

12 Description to include: winning, second, C third ran at a stead speed, started off quickl but graduall slowed down, C ran in a series of sprints and rests. Ma also mention approimatel when overtaking took place. a) p c) Distance (km) d) e) 9p (to nearest penn) a) D H c) F d) C a) 9.. c) a) Charge ( ) Cost ( ) Charge ( ) d) 9 Number of boes 9 Water used (cubic metres) Less than 9 cubic metres Eercise. (page 9) nswers read from graphs ma be approimate. a) 9 9 c) (i). (ii). to. or. to. a) 9 c) (i). to.9 (ii). or. a) c) (i). (ii). or. nswers to the Student s ook eercises Higher WJEC GCSE Mathematics, Hodder Education

13 a) c) (i). (ii). or. a) c) (i). (ii). to. or. to. a) 9 9 c) (i). or. (ii). or. a) 9 c) (i). or. (ii). or. a) 9 c) (i). (ii). to. Mied eercise (page 9) Higher WJEC GCSE Mathematics, Hodder Education nswers to the Student s ook eercises

14 a) 9 c) p a) a) 9 9 Cost ( ) Gas b a) d d Gas used (kwh) t c) (i). (ii). or. 9 a) ( ) ( ) ( )( ) t a) She stopped (e.g. waited for bus) minutes c) km/h d) (i) km (ii) km a) Quadratic, Not quadratic c) Quadratic, d) Quadratic, e) Not quadratic f) Not quadratic g) Quadratic, c) (i). (ii). to. or. to. nswers to the Student s ook eercises Higher WJEC GCSE Mathematics, Hodder Education

15 a) 9 c) (i). or. (ii). to. or. to. a) 9 c) (i). or. (ii). Chapter Eercise. (page ) a). c) a) c) d) e)., C., C a). c). a) Line drawn through (, ) and (, 9), gradient Line drawn through (, ) and (, ), gradient c) Line drawn through (, ) and (, ), gradient d) Line drawn through (, ) and (, ), gradient e) Line drawn through (, ) and (, ), gradient. a) km/h. m/s Eercise. (page ) a) c) a) _ or c) a) gradient, -intercept gradient, -intercept c) gradient, -intercept d) gradient, -intercept e) gradient., -intercept a) gradient, -intercept gradient, -intercept. c) gradient., -intercept. d) gradient., -intercept e) gradient., -intercept a) c). or Eercise. (page ) Graph of drawn through (, ), (, ) and (, ) Graph of drawn through (, ), (, ) and (, ), Graph of drawn through (, ), (, ) and (, ) Graph of drawn through (, ), (, ) and (, ), Graph of drawn through (, ), (, ) and (, ) Graph of drawn through (, ), (, ) and (, ), Graph of drawn through (, 9), (, ) and (, ) Graph of drawn through (, ), (, ) and (, ), Graph of drawn through (,.), (,.) and (,.) Graph of drawn through (,.), (, ) and (, ),. Higher WJEC GCSE Mathematics, Hodder Education nswers to the Student s ook eercises

16 Eercise. (page ),,,,,,,, 9,, Eercise. (page 9),,,,,,,, 9.,., Mied eercise (page ) a). a). a) Gradient, -intercept Gradient., -intercept c) Gradient., -intercept d) Gradient, -intercept a) or a) 9, 9, a),, c), d), e), f), g), h), Chapter Eercise. (page ) a) Velocit (m/s). m/s a) Velocit (m/s). m/s Time (seconds) Time (seconds) nswers to the Student s ook eercises Higher WJEC GCSE Mathematics, Hodder Education

17 The velocit increases from m/s to m/s in seconds (acceleration m/s ). The velocit is constant at m/s for seconds. The velocit decreases from m/s to m/s in seconds (acceleration m/s ). Velocit (m/s) a) a) Time (seconds) Gradient is approimatel c)..... square units of area c) The answer in is slightl greater than the actual area as all the trapeziums are formed b going above the curve. a) pproimate acceleration is. m/s pproimate total distance in the first seconds is 9 metres. Velocit approimatel km/h Eercise. (page 9) a) 9 c), and, d).,. a), c), and, d).,. a), c), and, 9 a), c).,. and., Eercise. (page ) nswers are given to decimal place. a) (i) or (ii). or. (iii). or. (iv). or. a) (i). or. (ii). or. (iii). or. Higher WJEC GCSE Mathematics, Hodder Education nswers to the Student s ook eercises 9

18 a) 9 (i).9 or. (ii). or.9 a) (i). or. (ii). or. (iii). or. Eercise. (page ) a), or c) a) Year Number of birds (n) n n Year c) n. where is the number of ears from the start (9) a) The table of values is shown... (i). (ii). a) n The missing values for n are and. a) (i) 9. (ii). a) The table of values is shown nswers to the Student s ook eercises Higher WJEC GCSE Mathematics, Hodder Education

19 a) 9 a., b Mied eercise (page 9) a b Velocit m/s at start, slowing down. Stops at t. (Negative acceleration until t, then positive acceleration.) Then moves in opposite direction. Stops again when t 9. a), a) (i). and. (ii). and. a) a). and. 9 c) (, 9) and (.,.) a). and. (i). (ii). Higher WJEC GCSE Mathematics, Hodder Education nswers to the Student s ook eercises

20 a) c) (i). (ii). Gradient at should be around, gradient at should be around. 9 () square units, the negative indicates that the area is below the -ais.. km/hr. m pproimatel Chapter Eercise. (page ) a) _ metres a) or _ 9 miles 9 a) or $ a) _ rungs a) or 9 g 9 a) _. hours a) or hours a). 9 a) or 9.9 a). kg or 9. Eercise. (page ) a) or minutes a) or weeks a) _ hours a) or _ minutes a) or 9 das a) _ 9 hours a) _ kilometres per hour a) 9 a) a) or 9 _ or _ or 9 Eercise. (page ) weeks. hours das a) Direct a) Direct c) a) Direct _ a) Direct _ c) a) Direct a) Inverse a) Inverse a) Inverse 9 a) Inverse a) Inverse Eercise. (page ) c) c). c). a) ~ a) ~ c) a) ~ _ a) ~. c) 9 a) ~. a) ~ c) a) ~ a) ~ c). 9 a) ~ a) ~ c) Mied eercise (page ) a) revolutions 9 metres c) miles d) grams e) 9. litres a) hours. hours c) 9 das d) 9 das e) das a) (i) ~ (ii) (i) ~ (ii) (iii) c) (i) ~ (ii) _ d) (i) ~ (ii) _ (iii) e) (i) ~ f) (i) ~ a) h. s. m c) 9. m/s (ii) (ii) (iii). nswers to the Student s ook eercises Higher WJEC GCSE Mathematics, Hodder Education

21 a) a) d s (i). m (ii). m/s Chapter Eercise. (page ) Eercise. (page ) c) _ a) Check students answers. Check students graphs. a) _ 9 a) and and 9 a) c) (, ) Mied eercise (page ) a) 9 a) _ or or c) _ or a) or c) _ or a) _ c) _ d) a) _ or or c) 9 : C: C: a) c) a) c) 9 (i) a) (ii) (ii) (., ) c) (ii) a) (, ) Chapter 9 Eercise 9. (page ) or or or or or or _ or 9 or or or or Eercise 9. (page ) or or or or or or or or 9 or or or or or 9 _ or or _ or 9 or or or or _ or or or _ or _ or _ or _ 9 (repeated) _ or _ or _ or or _ Higher WJEC GCSE Mathematics, Hodder Education nswers to the Student s ook eercises

22 Eercise 9. (page ) or or or or or or or or _ 9 or or Eercise 9. (page ) a) (i) ( ) (ii) ( ) (iii) ( ) (iv) (.). (i) ( ) 9 (ii) ( ) (iii) ( ) (iv) (.). a) ( ) ( ) c) ( ) d) ( ) e) ( ) f) ( ) g) ( ) h) (.). i) (.). Eercise 9. (page ) a). or.. or. c). or.9 d). or. a) ( ),. or. ( ),. or. c) ( ),. or. d) ( ),. or. e) ( ), 9. or. f) ( ),. or. g) ( ),. or. h) ( ),.9 or. i) (.).,. or. Eercise 9. (page ). or.. or.. or.. or.. or. No real solutions. or.. or. 9. or.. or.. or.. or.. or.9 No real solutions.9 or.. or.. or 9.. or. 9 No real solutions.9 or.9. or. Mied eercise 9 (page ) a) or or c) _ or d) _ or _ a) or 9 or c) or d) or e) or a) or _ or _ c) _ or d) _ or e) _ or a) or or c) or d) or e) _ or _ a) ( ) ( ) c) ( ) d) (.). a). or.. or 9. c). or. d). or. a). or.9.9 or. c). or. d). or. and c) have no solutions. For both, b ac is negative ( in each case). 9 ( )( ), or (reject), dimensions are cm and cm. ( ),. or a) ( ) ( ) ( )( ) Students assuming the cuboid is solid rather than open will end up with.,. c).,.,. cm a) h ( ) _ ( ). 9.. cm Chapter Eercise. (page ),,,,, _,,, 9,,, _, _,, _,, _,, 9,, _, _ Eercise. (page 9),,,,,, Mied eercise (page ) a), _, c), d), a),, a), Pen p, eercise book p. nswers to the Student s ook eercises Higher WJEC GCSE Mathematics, Hodder Education

23 Chapter Eercise. (page ) a) Multipl the pattern number b a) Pattern number Number of matchsticks The go up b each time; the are the times table plus. c) a) 9 a),, 9,, (i) Each term is more than the equivalent term in the sequence of square numbers. (ii) n c) a) Each term is times the equivalent term in the sequence of square numbers. n c) Mied eercise (page 9) a) T n n a) You add more each time, so T, T, T, T, T a),,, a),,,, 9,, c),,, a),, 9,,,,,, c),,,,,,,,,,, 9 For eample. This is the sequence of square numbers; the th pattern has stars. a) T,,, a),,,,,, c),,,,,,, a) T n n T n n c) T n n a) Linear:, 9 Not linear c) Not linear d) Linear:, a), 9,,, Powers of 9 suitable answer is as follows. and so on. For eample and so on. Eercise. (page ) a) n n c) n a) n n c) n a) Linear:, Not linear c) Linear:, d) Not linear a),,,, n a) Number of tickets Cost in n c),,,,,,,,, a),,,, Powers of a),, 9,, T n n Chapter Eercise. (page 9) a) 9 minutes minutes C a) s d t km/h 9 m a) a) 9 a) hours minutes. kg miles a) Number of posts, P Number of chains, C 9 c) C P or C (P ) d) a) cm. cm Higher WJEC GCSE Mathematics, Hodder Education nswers to the Student s ook eercises

24 a) cm cm a) miles Eercise. (page 9) a) b a c a w c) t v u a d) t p c e) q pr or q p p r f) g p f g) n Ft m u sbn v h a b R I PT a) h V. cm pr a) F C (F ) _ 9 r V ph a) a v u u v s as Eercise. (page 9). a). a). a) a). (or.) a) ( ), i.e., (or, ). Mied eercise (page ) a) F F c) F 9p a) cm. cm a) minutes. minutes a) q p r r s c) r ms pq d) t or t t a) w T w. kg a) cm cm a) words words 9 a). a). a). Chapter Eercise. (page ) r pq P s t ( ) r pq p q s t u a sv 9 u v s g e f Eercise. (page ) a) RT p rq r q q q p b a a b fu v u f c(a ) b a l gt p c) h ( pr) r e) r V f) t s ph a a) 9 cm r V ph c). cm a).9. m c) d z d). m d) u v as Mied eercise (page ) a) a rb g lp r t c) u fv v f e) a b b g) a bc b i) d) b ac c f) h) j) n p r p nswers to the Student s ook eercises Higher WJEC GCSE Mathematics, Hodder Education

25 ( np) k) q m) ns a) units (to s.f.) r V p c) 9. m (to s.f.) Chapter Eercise. (page ) l) F np F n) b a am m a) a) c) a) (i) 9 (ii) a) (i) 9 (ii) a) _ (i) (ii) a) (i) (ii) a) (i) (ii) a) or (i) (ii) Eercise. (page ) a) a) ( ) translation of ( ) translation of ( ) a) ( ) ( ) translation of ( ) a) 9 θ sin θ sin a) ( ) f( ) f() g( ) f() g() ( ) 9 cos a) ( ) ( ) Eercise. (page ) a) g() sin θ 9 reflection in the -ais a) sin θ sin θ 9 sin θ θ θ Higher WJEC GCSE Mathematics, Hodder Education nswers to the Student s ook eercises

26 one-wa stretch of scale factor, parallel to the -ais a) reflection in the -ais reflection in the -ais c) one-wa stretch of scale factor parallel to the -ais cos a) a) a) translation of ( ) one-wa stretch parallel to the -ais of scale factor c) one-wa stretch parallel to the -ais of scale factor. d) one-wa stretch parallel to the -ais of scale factor and a one-wa stretch parallel to the -ais of scale factor _ a) c) ( ) ( ) or 9 a) _ (, ) c) k Mied eercise (page 9) _ d) (, _ ) a) _ (i) 9 (ii) a) ± (i) (ii) a) (i) (ii) a) Translation b ( ) a) 9 a) Translation b ( ) θ sin θ One-wa stretch with scale factor _, parallel to the -ais c) One-wa stretch with scale factor, parallel to the -ais d) Reflection in the -ais a) cos cos 9 a) a) [( ) ] or (, ) (, ) Chapter Eercise. (page ) ( ) ( ) 9 ( ) Eercise. (page ) 9 ( )( ) ( ) ( )( ) ( )( ) ( )( ) ( )( ) ( ) ( ) f() ( )( ) Eercise. (page ) ( ) 9 ( ) ( ) ( ) ( )( ) ( )( ) 9 ( )( ) ( ) ( )( ) ( ) ( )( ) or or. or.. or.. or. 9. or.9 nswers to the Student s ook eercises Higher WJEC GCSE Mathematics, Hodder Education

27 Mied eercise (page ) a) c) a) c) ( ) ( )( ) ( ) ( ) d) d) 9 ( )( ) ( ) 9 ( )( ) a) c) d) or a). or.. or. Chapter Eercise. (page ) cm cm m mm cm. cm cm cm 9 m m Eercise. (page ) cm cm m cm cm cm cm m 9 cm cm Eercise. (page ) a (lternate angles) b (llied angles) c (Corresponding angles) d (lternate angles) e (Corresponding or verticall opposite angles) f (lternate angles) g (Corresponding or verticall opposite angles) h (llied angles) i (Corresponding angles) j (lternate or verticall opposite angles) k (Corresponding angles) l (lternate or verticall opposite angles) m (llied angles) n (Verticall opposite angles) o (Corresponding angles) p (Corresponding angles) q (lternate angles) 9 r 9 (llied angles) s (Corresponding angles) t 9 (ngles in a triangle add up to ) u (lternate angles) v (Corresponding angles) w (ngles on a straight line add up to ) Eercise. (page ) a (ngles in a triangle add up to ) b (ngles in a triangle add up to ) c (ngles in a triangle add up to ) d (ngles in an isosceles triangle) e (ngles in an equilateral triangle) f (The eterior angle of a triangle is equal to the sum of the opposite interior angles) g (The eterior angle of a triangle is equal to the sum of the opposite interior angles) h 9 (ngles on a straight line add up to ) i (ngles in a quadrilateral add up to or angle sum of a triangle ) 9 j (ngles in a quadrilateral add up to ) k (ngles on a straight line add up to ) l (ngles on a straight line add up to ) m (ngles in a quadrilateral add up to ) Eercise. (page ) : trapezium : rhombus C: square D: kite E: rectangle F: square G: arrowhead H: parallelogram I: isosceles trapezium J: rhombus K: parallelogram a) Square, rhombus Rectangle, parallelogram, kite, arrowhead c) Rectangle, parallelogram d) Trapezium e) Square, rhombus, kite a) Rhombus Higher WJEC GCSE Mathematics, Hodder Education nswers to the Student s ook eercises 9

28 c) d) Trapezium Parallelogram Kite ll the angles are 9 and the diagonals are equal length. Isosceles trapezium, parallelogram or rhombus Isosceles trapezium Parallelogram Rhombus Eercise. (page ) a),, 9, 9 a) 9,,,, e ; i e. ; i. Mied eercise (page 9) a) 9 cm cm c) cm a) cm cm c) cm a) a Corresponding angles. b llied angles or ngles on a straight line. c lternate angles. d Corresponding angles or Opposite angles. c) e lternate angles. f ngles on a straight line. g Corresponding angles or angles in a triangle. a) a 9 ngles in a triangle add up to. b ase angles in an isosceles triangle are equal. c) c Eterior angle of a triangle is equal to the sum of the opposite, interior angles. d ngles on a straight line add up to or ngles in a triangle add up to. a) a ngles in a quadrilateral add up to. b 9 ngles on a straight line add up to. c ngles in a quadrilateral add up to. a) Rectangle, parallelogram, kite, arrowhead Rhombus, isosceles trapezium, parallelogram c) Square, rectangle, isosceles trapezium a) 9 Eterior angle, interior angle c) Chapter Eercise. (page ) cm cm cm cm Eercise. (page ) a) cm. m c). cm d) cm e). cm f). cm g). m h) 9. m i). cm. m. inches Eercise. (page ) Yes (This is the,, triangle) No? No? Yes. 9. (This is. the,, triangle) Yes.. (This is. the,, triangle) No? No. 9? Yes.. (This is. the,, triangle) Eercise. (page ) a) (., ) (, ) c) (., ) d) (., ) e) (., ) f) (.,.) a) (, ) (, ) c) (,.) d) (.,.) e) (, ) f) (, ) nswers to the Student s ook eercises Higher WJEC GCSE Mathematics, Hodder Education

29 Eercise. (page ) a) (,, ) (,, ) c) (,, ) d) (,, ) a) (,, ) (,, ) c) (,, ) d) (,, ) a) (,, ) (,, ) c) (,, ) d) (,, ) Mied eercise (page ) a) cm cm a). cm. cm c). cm d).99 cm a) No? 9 Yes 9 (This is the,, triangle) c) Yes.. (This is. the,, triangle) d) No..? 9. a) (, ) (, _ ) c) ( _, _ ).9 m. cm. m a) (i) (,, ) (ii) (,, ) (iii) (,, ) (,, ) Chapter Eercise. (page ) C a) C a) reflection in the line reflection in the line c) reflection in the line a) reflection in the line reflection in the line c) reflection in the line Eercise. (page ) C C C 9 D C D O 9 c) C Higher WJEC GCSE Mathematics, Hodder Education nswers to the Student s ook eercises

30 a) rotation of 9 anticlockwise about the origin rotation of about (, ) c) rotation of 9 clockwise about (, ) a) rotation of 9 clockwise about the origin rotation of about (, ) c) rotation of 9 anticlockwise about (, ) 9 rotation of clockwise about O a) reflection in the line rotation of 9 anticlockwise about (, ) c) reflection in the line d) rotation of 9 anticlockwise about the origin e) reflection in the line Eercise. (page ) C D C D a) translation b vector ( ) translation b vector ( ) c) translation b vector ( ) d) translation b vector ( ) a) translation b vector ( ) rotation of 9 anticlockwise about the origin c) rotation of 9 clockwise about (, ) d) translation b vector ( ) e) reflection in the line f) reflection in the line g) translation b vector ( ) h) rotation of about (, ) Eercise. (page ) a), c) n enlargement with scale factor, centre the origin a), C c) n enlargement with scale factor, centre (, ) a), c) n enlargement with scale factor _, centre the origin a), C c) n enlargement with scale factor _, centre (, ) a) n enlargement with scale factor, centre (, ) n enlargement with scale factor _, centre (, ) c) n enlargement with scale factor _, centre the origin d) n enlargement with scale factor _, centre the origin nswers to the Student s ook eercises Higher WJEC GCSE Mathematics, Hodder Education

31 a) reflection in the line n enlargement with scale factor, centre (, ) c) translation b vector ( ) d) n enlargement with scale factor _, centre the origin e) translation b vector ( ) f) n enlargement with scale factor _, centre (, ) a) reflection in the line n enlargement with scale factor, centre (, ) c) rotation of 9 anticlockwise about the origin d) reflection in the line e) n enlargement with scale factor _, centre the origin f) translation b vector ( ) a) reflection in the line rotation of 9 clockwise or about the origin c) translation b vector ( ) d) reflection in the line e) n enlargement with scale factor _, centre (, ) f) n enlargement with scale factor _, centre (, ) g) n enlargement with scale factor, centre (, ) Mied eercise (page ) a) C C C D Higher WJEC GCSE Mathematics, Hodder Education nswers to the Student s ook eercises

32 a) reflection in the line rotation of 9 clockwise about the origin c) n enlargement with scale factor, centre (, ) d) translation b vector ( ) e) n enlargement with scale factor _, centre the origin f) translation b vector ( ) g) reflection in the line a) reflection in the line translation b vector ( ) c) n enlargement with scale factor, centre (, ) d) rotation of 9 anticlockwise about (, ) e) n enlargement with scale factor _, centre the origin f) rotation of about the origin g) translation b vector ( ) Chapter 9 Eercise 9. (page ) a) cm mm c) cm d) mm a) cm mm c) 9 cm d). mm a) 9 cm. cm c) m d) 9. m a) cm. m c). m d) cm a) cm 9. litres c) ml d).9 litre ll the units need to be the same; change cm to. m.. m cm Eercise 9. (page 9) a). m and. m. ml and. ml c).9 seconds and.9 seconds a). g and. g. ml and. ml c). m and. m a) to m cans (.) a).9 mm.9 mm No; 9. mm is greater than 9. cm. a).9 cm and. cm.9 cm and. cm c).9 cm and. cm Maimum d: longest rod minus least depth. 9. mm Minimum d: shortest rod minus greatest depth.. mm (..) cm and (. 9.) cm Eercise 9. (page 9) a). minutes weeks c) kg d) m a). m c) km d). cm Eercise 9. (page 9). m/s mph. miles hours cm mph 9 g/cm km/h 9. g/cm a).9 g/cm. g 9. kg a). kg (i).9 m (ii) 9. m a) km/h. km/h. g/cm. people per square kilometre Mied eercise 9 (page 9) a) cm mm c) cm d) mm a) mm. m c) 9 cm d) cm a) cm. litres c) ml d).9 litres a). cm and. cm. cm and. cm c). m and. m Greatest speed: greatest distance least time...9 m/s a). mm and. mm Greatest perimeter: greatest length.. mm a) hour minutes km/h a) mph 9 miles 9 9 m Chapter Eercise. (page ) Diagrams are not full size. The measurements given are correct for the suggested scale. cm Scale cm m. cm cm nswers to the Student s ook eercises Higher WJEC GCSE Mathematics, Hodder Education

33 Scale cm m Hedge Scale cm km cm cm P Q Tree cm cm C cm cm cm cm Scale cm m cm D cm cm cm cm cm D C Scale cm m H cm G N NW NE T cm cm W E E C F SW SE cm 9 cm S cm cm cm Locus cm Scale cm m 9 C cm cm cm cm cm cm Scale cm m Note: You could have used a different scale. cm m. cm Locus cm cm Castle cm cm Eercise. (page ) Diagrams are not full size. The measurements given are correct for the suggested scale. cm cm Scale cm km C cm 9. cm cm cm cm Higher WJEC GCSE Mathematics, Hodder Education nswers to the Student s ook eercises

34 9 Scale cm m cm Scale cm km cm House. cm cm. cm cm cm Scale cm miles cm cm H cm K Scale cm m D C cm cm Mied eercise (page ) Diagrams are not full size. Measurements given are correct for the suggested scale. G cm cm cm E cm 9 Scale cm m cm F cm cm cm cm cm cm Scale cm m C cm cm. cm 9 cm rea. cm S cm R P cm cm Q cm cm cm cm cm Chapter cm cm cm Eercise. (page 9) These answers have been calculated using the p button on a calculator.. cm ( d.p.). cm ( d.p.). cm ( d.p.). mm ( d.p.) mm (nearest whole number). cm ( d.p.) nswers to the Student s ook eercises Higher WJEC GCSE Mathematics, Hodder Education

35 . cm ( d.p.). cm ( d.p.) 9.9 cm ( d.p.).9 m ( d.p.) 9. m ( d.p.). m ( d.p.) Eercise. (page ) These answers have been calculated using the p button on a calculator. a) cm (nearest whole number) cm (nearest whole number) c) cm (nearest whole number) d) mm (nearest whole number) e) mm (nearest whole number) f) 9 cm (nearest whole number) g) 9 cm (nearest whole number) h). cm ( d.p.) i) 9. cm ( d.p.) j). m ( d.p.) k). m ( d.p.) l).9 m ( d.p.) a) cm (nearest whole number) cm (nearest whole number) c) cm (nearest whole number) d) mm (nearest whole number) e) mm (nearest whole number) f) cm (nearest whole number) g) 9 cm (nearest whole number) h). cm ( d.p.) i). cm ( d.p.) j). m ( d.p.) k). m ( d.p.) l). m ( d.p.) Eercise. (page ) cm cm cm cm cm cm Eercise. (page ) a) cm cm c) 9. cm d). cm e) 9 cm f) cm cm Eercise. (page ) a) cm cm c) 9. cm d) 9. cm e). cm f). cm 9 mm Eercise. (page ) These answers have been calculated using the p button on a calculator. a) cm (nearest whole number) cm (nearest whole number) c) 9 cm (nearest whole number) d) mm (nearest whole number) e) mm (nearest whole number) f) mm (nearest whole number) g) m (nearest whole number) h) m (nearest whole number) cm (nearest whole number) Eercise. (page ) These answers have been calculated using the p button on a calculator. a) cm (nearest whole number) cm (nearest whole number) c) cm (nearest whole number) d) 9 mm (nearest whole number) e) mm (nearest whole number) f). mm ( d.p.) g).9 m ( d.p.) h). m ( d.p.) cm (nearest whole number) a) cm (nearest whole number) 99 cm (nearest whole number) c) cm (nearest whole number) d) mm (nearest whole number) e) 9 mm (nearest whole number) f). mm ( d.p.) g) 9. m ( d.p.) h) 9. m ( d.p.) Eercise. (page ) Plan Front elevation Side elevation Plan Front elevation Side elevation Higher WJEC GCSE Mathematics, Hodder Education nswers to the Student s ook eercises

36 Plan Front elevation Side elevation Plan Front elevation Side elevation a). cm ( d.p.). mm ( d.p.) c). cm ( d.p.) d). m ( d.p.) a) mm (nearest whole number). mm ( d.p.) c) cm (nearest whole number) d) cm (nearest whole number) e) 9 m (nearest whole number) f). m ( d.p.) a) 9 m (nearest whole number) cm (nearest whole number) c). cm ( d.p.) d) mm (nearest whole number) 9 a) mm (nearest whole number) m (nearest whole number) c) cm (nearest whole number) d) cm (nearest whole number) a) Plan Plan Plan Plan Side elevation Side elevation Front elevation Front elevation Front elevation Front elevation Side elevation Side elevation c) Plan d) Plan Mied eercise (page ) Where necessar, the p button on a calculator has been used to work out these answers, which are given to s.f. (unless stated otherwise). a). cm 9. cm c) cm d) mm a) cm. m c) mm d) 9. mm e) cm f). m Check students diagrams. a) 9. cm ( d.p.) cm c). cm ( d.p.) d). cm ( d.p.) a) cm cm c) 9. cm ( d.p.) d) 9 cm e). cm ( d.p.) f). cm ( d.p.) Side elevation Front elevation Side elevation Front elevation nswers to the Student s ook eercises Higher WJEC GCSE Mathematics, Hodder Education

37 Chapter ll answers are given correct to significant figures. Eercise. (page ) a. cm b. cm c. cm d. cm e. cm f. cm g. m h. m. m a). cm. cm Eercise. (page ) a 9. cm b. cm c. cm d. m e. cm f. cm g. m h. m 9. km a).9 m. m Eercise. (page ) a. b 9. c. d 9. e. f. g 9. h Mied eercise (page ) a 9. cm b.9 m c 9.9 m d. cm e. m f. m a. b 9. a).9 m. a)., safe.9 m c).9 m a) N a) c) a). cm 9. cm Eercise. (page ) a) a. cm angle C c) angle 9 d) r. cm e) p. cm f) angle Y a) angle R, angle P, QR. cm angle Y, angle X, YZ. cm c) angle,.9 cm, C. cm ( d.p) d) angle C, 9. cm, C. cm ( d.p) e) angle 9, angle 9, C. cm ( d.p) f) angle Q, PQ. cm, QR. cm ( d.p) Eercise. (page ) a) a. cm angle c) b. cm d) angle C a) angle, angle,. cm ( d.p) angle, angle, angle C c) angle, angle C, C. cm ( d.p) d) angle, angle 9, angle C e) angle P 9, angle R, PR. cm ( d.p) f) angle P, angle Q, angle R g) angle P, angle Q, angle R h) angle X, angle Y, XY. cm ( d.p) i) angle X 9, angle Y, angle Z 9 j) angle X, angle Y, XY.9 cm ( d.p) a) 9. cm a) c) Eercise. (page ) a). sin θ 9 θ km (i) km (ii). km.. cm a). 9. cm 9. m. m Chapter Eercise. (page ) ll lengths and areas are given correct to s.f. and all angles to the nearest degree. a). cm. cm c). cm d). cm e). cm f). cm g) 9. cm h). cm,, 9 and a) cos θ 9 9., and θ Higher WJEC GCSE Mathematics, Hodder Education nswers to the Student s ook eercises 9

38 a) sin θ 9 9 θ and approimatel a) cos θ 9 θ, and approimatel ( ),, and a) sin θ 9 θ 9 θ tan θ cos θ and approimatel Eercise. (page ) 9 θ a),, c), 9 d), e), f), cos θ. sin θ 9 θ 9 θ nswers to the Student s ook eercises Higher WJEC GCSE Mathematics, Hodder Education

39 d) (i) cos θ 9 The solutions of cos. are, and Mied eercise (page ) a). cm.9 cm c). cm d). cm a) c) a).9 cm. cm a). cm 9 c) d).9 cm a) PR Q, QP R, QR. cm XY Z, ZX Y 9, YZ 9. cm c) C 9, C. cm,. cm d) PQ R, QR. cm, PR 9. cm Side XY is longest at. cm a). cm 9. cm c) d) a) C, C,. cm C, C, C c) QP R, PQ R, PQ. cm d) YX Z, XY Z, XZ Y 9 9,, a) a) (i) sin θ θ tan θ θ (ii) pproimatel and e) (i), (ii), (iii), 9 (iv), (v), (vi), (vii), (viii), f) (i) sin θ (ii) 9 θ cos θ θ θ (iii) cos θ (ii) pproimatel and (i) cos θ θ θ (ii) pproimatel and c),, 9 Higher WJEC GCSE Mathematics, Hodder Education nswers to the Student s ook eercises

40 g) (iv). sin θ θ sin θ Values of are approimatel 9,,,,,,,, 9 and Chapter Unless stated otherwise, lengths are given correct to d.p. and areas and volumes to s.f. Eercise. (page 9) a) and a) and c) and c) a) Length Volume c) rea a) Volume rea c) Nonsense d) Length Eercise. (page ) a). cm.9 cm c). cm a). cm. cm c) cm a) c) 9 d) a) 9. cm. cm c). cm a).9 cm. cm c) 9. cm d). cm,. cm cm (to s.f.) Eercise. (page ) a). cm cm c). cm a). cm cm c) 9. cm a) cm cm c) cm cm cm a). cm. cm c). cm a). cm. cm c) 9.9 cm a) cm cm c) cm 9 a) cm cm c) 9 cm a). cm. cm c). cm d). cm θ Eercise. (page 9) a).9 cm. cm c). cm 9 m a) cm. cm c) cm 99 cm a). cm, cm. cm,. cm c). cm, cm a) 9 cm. cm, cm a) Check students answers.. litres cm 9. cm, cm cm Mied eercise (page ) a) a, bc and d) pa d a) Length Volume c) None d) rea a) rc length. cm, area. cm rc length.9 cm, area cm a) 9. cm. cm cm (to s.f.).(9 ) cm Chapter Eercise. (page ), and C are similar. D and E are similar. XY cm, YZ 9 cm C. cm, X. cm, X. cm m. cm, cm. cm, cm cm a) ngle C ngle CDE (lternate angles) ngle C ngle DCE (Verticall opposite angles) ngle C ngle CED (lternate angles) Corresponding angles are equal so triangle C is similar to triangle CDE. C. cm, C cm Eercise. (page ) C D D C nswers to the Student s ook eercises Higher WJEC GCSE Mathematics, Hodder Education

41 a) (, ) C D D C a) (, ) a) (, ). Eercise. (page 9) a).. cm c) cm d). cm e) The ratio of the areas is the square of the ratio of the lengths. a),, c), d).,. a),, c).,. d).,. ml a). m. litres a) c). m. cm. m or cm 9. :. :.. cm Mied eercise (page 9) a cm b. cm c cm d. cm e. cm a) 9 cm cm D C 9 9(,.) 9(.,.) C9(., ) D9(, ) a) (, ) cm a) m. litre or ml a). :. or. :.9 cm C D Chapter ll answers which are not eact are given correct to decimal place. Eercise. (page 9) 9.9 cm 9. cm. cm. cm. cm a). cm (i). (ii). a). cm. a).9 m.9 c). m Mied eercise (page 9) 9. cm 9.9 cm a).. cm a). m 9. m c). a). cm c). cm d). a). m 9. a). cm. a). cm. Chapter Eercise. (page ) CX CY (Given.) ngle C is common C C (Given.) Therefore triangle CX is congruent to triangle CY (SS). DZ DV VZ VC VZ ZC DV ZC (Given.) So DZ VC Triangle DXC is isosceles. DX XC (Given.) So angle DZ angle CV ngle X angle CV (lternate angles.) ngle X angle DZ (lternate angles.) So triangle X is isosceles. So X X So D C Therefore triangle DZ is congruent to triangle CV (SS). a) a cm, b cm, Higher WJEC GCSE Mathematics, Hodder Education nswers to the Student s ook eercises

42 a) (i) ngle QPX angle XRS (lternate angles.) ngle PQX angle RSX (lternate angles.) PQ SR (Given.) So triangle PQX is congruent to triangle RSX (S). (ii) ngle QRX angle SPX (lternate angles.) ngle RQX angle PSX (lternate angles.) QR SP (Given.) So triangle RQX is congruent to triangle SPX (S). SX XQ - (Since triangles PQX and RSX are congruent.) PX XR (Since triangles RQX and SPX are congruent.) So X is the midpoint of SQ and PR. SR RQ (PQRS is a rhombus.) ngle RSX angle RQX (Triangle QSR is isosceles.) XR is common to both triangle SXR and triangle QXR. So triangle SXR is congruent to triangle QXR (SS). So angle SXR angle QXR. ngle SXR angle QXR 9 (Since SQ is a straight line.) and P P Q QC CR RD DS S (ecause P, Q, R and S are the midpoints of the sides of the square CD) So all the triangles are isosceles and congruent and all the marked angles are. S P Q D R C So the interior angles of the quadrilateral PQRS are 9 (ngles on a straight line.) ll the sides, PS, SR, RQ and QP, are equal. So PQRS is a square. ngle DC angle DC (CD bisects angle C.) ngle DC angle CE (lternate angles.) ngle DC angle EC (Corresponding angles.) So angle EC angle CE So triangle CE is isosceles and C CE. ngle C angle C (ase angles of an isosceles triangle are equal.) ngle CD (lternate angles.) So angle CD So angle DC angle DC (ase angles of an isosceles triangle are equal.) 9 ngle CD (lternate angles.) ngle DCE (ngles on a straight line add up to.) ngle CY (Verticall opposite angles are equal.) ngle C (ngles on a straight line add up to.) ngle D 9 (ngle sum of triangle E.) ngle DC (ase angles of an isosceles triangle are equal.) So angle DC (ngles in a triangle add up to.) So angle C (D bisects angle C.) So angle C (ngle sum of triangle C.) ngle RQ (ngles in a quadrilateral add up to.) ngle RP (ngles on straight line add up to.) So a (Eterior angle of triangle is equal to the sum of the opposite, interior angles.) Mied eercise (page ) (lternate angles.) (ase angles of an isosceles triangle (PRS) are equal and ngles in a triangle add up to.) z (lternate angles.) (ngles in a triangle add up to.) (lternate angles.) z (Verticall opposite angles.) ngle DC (ngles in a quadrilateral add up to.) So angle C angle CD (Given that C bisects angle DC.) ngle DC (ngles in a triangle add up to.) So angle C (.) Since C C, triangle C is isosceles. a (llied angles.) b (lternate angles.) (ngles in a quadrilateral add up to.) nswers to the Student s ook eercises Higher WJEC GCSE Mathematics, Hodder Education

43 D C E D, DE D and E is common to triangles DE and E. So triangles DE and E are congruent (SSS). So angle DE angle E ngle DE angle E 9. (Since D is a straight line.) CD C, DE E and CE is common to triangles CDE and CE. So triangles CDE and CE are congruent (SSS). So angle CED angle CE ngle CED angle CE 9 (Since D is a straight line.) This proves that the diagonals of a kite cross at right angles. C E CE ED, angle CE angle DE and E is common to triangles EC and ED. So triangles EC and ED are congruent (SS). So C D CE ED, angle CE angle DE and E is common to triangles CE and DE. So triangles CE and DE are congruent (SS). So C D E E, angle ED angle ED and ED is common to triangles ED and ED. So triangles ED and ED are congruent (SS). So D D So C C D D Chapter Eercise. (page ) a b c d e f g D h i j k m 9 n p q r cm 9 s t u v 9 w z a b c d 9 e f g h cm 9 i 9 j k Eercise. (page ) a b c d e f 9 g h i j k m n p q r 9 s t u v w Mied eercise (page 9) a b 9 c d e 9 f g h i j 9 k. cm m.9 n p q r 9 s t u v w Chapter 9 Eercise 9. (page ) Frequenc ge (ears) Higher WJEC GCSE Mathematics, Hodder Education nswers to the Student s ook eercises

44 a) Frequenc 9 Rainfall (cm) < r, 9 c) 9 < r, a) Frequenc 9 Weight (kg) < w, 9 c) < w, 9 Lifetime of lightbulb (h hours) Frequenc < h, < h, 9 < h, < h, < h, < h, < h, < h, < h, Eercise 9. (page ) Frequenc Frequenc Weight (kg) 9 Time (minutes) Frequenc a) 9 Frequenc Height (cm) ook ook No. of words Possible answers include: ook has a wider variet of sentence lengths. ook has more shorter sentences. Eercise 9. (page 9) a), e) Number of bad peaches d) Deliver time (hours) Strong positive correlation c). hours f) bout a), e) d) Paper Strong positive correlation c) 9. f) bout a), e) Paper Petrol consumption (mpg) d) Engine size (litres) Strong negative correlation c).9 mpg f) bout mpg nswers to the Student s ook eercises Higher WJEC GCSE Mathematics, Hodder Education

45 a) Mark Circumference of head (mm) No correlation c) No d) Don t know the ages of the people involved. Mied eercise 9 (page ) a) Time < t, < t, < t, < t, (t mins) Frequenc a) Frequenc Time (minutes) c) < t, d) < t, Frequenc 9 Marks Suitable comments include the following. The marks range from to 9. There are few low and high marks. Most of the marks are around to. c) < m, d) e) _ a), c) verage weight (g) 9 ge of rabbit (months) Strong positive correlation d) (i) bout g (ii) bout g e) No. rabbit s weight cannot keep increasing. Chapter Eercise. (page ) a) (i) (ii) (iii) (iv). (i) (ii) (iii) (iv) 9. c) (i) (ii) (iii) (iv). d) (i) (ii) (iii) (iv). a).9. c).9 d). a).. c). d)... Eercise. (page ) a) (i) (ii). (i) (ii). c) (i) (ii). d) (i) (ii). a) (i) (ii) (iii).9 (i) 9 (ii) (iii). c) (i) 99 (ii) (iii). d) (i) (ii) (iii). a) (i) (ii). (i) (ii). c) (i) 9 (ii). d) (i) 99 (ii). 9. Eercise. (page ) a) (i) cm (ii). cm (i) g (ii). g c) (i) cm (ii). cm d) (i) mm (ii). mm a) (i) <, (ii) 9. das (i) <, (ii). g c) (i) <, (ii). cm d) (i) <, (ii). miniutes a) <, <, c).. g. pence Mied eercise (page ) a) (i) (ii) (iii). (i) (ii) (iii). c) (i) (ii) (iii). d) (i) (ii) (iii). e) (i) (ii) (iii). f) (i) (ii) (iii)... ( d.p.) a) (i) cm (ii).9 cm (i) km/h (ii). km/h c) (i) seconds (ii) 9. seconds d) (i) kg (ii). kg a) <, <, c) 9. minutes.9 (or.9 thousand) Higher WJEC GCSE Mathematics, Hodder Education nswers to the Student s ook eercises

46 Chapter Eercise. (page ).9.. Eercise. (page )... Eercise. (page ) 9 a) ellow, blue, green Eercise. (page ) a) Score Relative frequenc _ or. (to d.p.) c) Yes, the dice is biased. The relative frequenc for seems too low and the relative frequencies for and seem too high. Small number of trials. Cannot be predicted from these past events. a) Part Relative frequenc Labour. Conservative. Lib. Dem.. Other.. a). which is the probabilit of tossing a coin and getting a head.. which is ver different from.. c) Emma. More trials give a more reliable indication. a) Score Relative frequenc.... Yes. ll values are approimatel equal to.. c) Either,,, (if the spinner is fair) or Score Relative frequenc 9 a) is a large number of trials. Travel b us Car ike Walk Estimate of probabilit.... Mied eercise (page 9) _ 9.. a) red, white, blue das a), which is the probabilit of getting heads with a fair coin. She is not necessaril correct. She should carr out more trials. a) bout 9 (i) (ii) 9 (iii) Chapter Eercise. (page ) a) a).. a).. c). d). e). The events are not mutuall eclusive: _.. a).. a) 9 c) 9 a) 9 c) a).. c). nswers to the Student s ook eercises Higher WJEC GCSE Mathematics, Hodder Education

47 Eercise. (page ) a) First dice Second dice Outcome Probabilit Si SS Si Not a si SN Not a si Si NS Not a si NN a) (i) (ii) First da Second da Outcome Probabilit. Late LL... Late.. Not late LN.... Not late. Late NL.... Not late (i). (ii). a) First disc Second disc NN Outcome... Probabilit lack 9 lack White W White lack W White WW 9 a) (i) 9 (ii) First match 9 (iii) Second match Outcome Probabilit. W W.. D. L. W.. D. D L.. W L.. D L (i). (ii). (iii). WW WD WL DW DD DL LW LD LL Higher WJEC GCSE Mathematics, Hodder Education nswers to the Student s ook eercises 9

48 a) First toss Second toss Third toss Outcome Probabilit H T H T H H T H T H T HHH HHT HTH HTT THH THT (i) _ H T (ii) _ Eercise. (page ) a) First ball T (iii) Second ball TTH TTT Outcome Probabilit Yellow YY Yellow Red YR Red Yellow RY (i) 99 a) 9 a) First game (ii) Red 99 9 Second game RR Outcome Probabilit. Judith wins JJ...9 Judith wins.. Suki wins JS.... Suki wins. Judith wins SJ... Mied eercise (page ) a).. a) _ a)..9 a) c) a). c) Suki wins (i).9 (ii). (iii). a).. a) 9 c) _ SS... nswers to the Student s ook eercises Higher WJEC GCSE Mathematics, Hodder Education

49 a) First disc Second disc Outcome Probabilit lack lack White W White lack W White WW 9 (i) a) (ii) First plant (iii) Second plant Outcome Probabilit. Red RR.9 Red.. Not red RN.. Not red. Red NR.. Not red (i).9 (ii). 9 a) 9 9 a).. NN.9 Chapter Eercise. (page 9) a) Primar Secondar c) Primar d) Secondar Possible answers include the following. a) Those not in the phone book have no chance of being included. Those working on Saturda would not be included. Possible answers include the following. Make the categories eclusive (in Paul s first draft, for eample, hour could go in two categories); have more categories, for eample, split the groups into classes of minutes rather than hour. Possible faults include the following. a) The person s favourite sport might be one that isn t listed. This question is vague: it needs categories, such as hours spent. c) This is a leading question. Check students new questions. a) Possible answers include the following. Q is too vague. Q is an open question and the answers would be ver difficult to analse. Check students rewrites of Q. It should have better categories. Check students questions. Mied eercise (page ) Secondar. Jan did not collect the data herself. a) Possible answers included the following. sk people to draw a angle without a protractor. Show people three drawn angles and ask them to estimate what size the angles are. Possible answers include the following. Choose students from Year, from Year 9 and from Year. Choose a random sample of students from a mied-age group. c) Check students data collection sheets. The sheets should include the age or ear-group of the student as well as data on the angle(s) drawn/estimated. Check students answers. Higher WJEC GCSE Mathematics, Hodder Education nswers to the Student s ook eercises