CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Answers The questions and example answers that appear in this resource were written by the author. In examination, the way marks would be awarded to answers like these may be different. Chapter 1 Exercise 1.1 2 3 ____ 1 51 √512 = 8 3 ____ −57 0 1 51 10 270 √512 = 8 11 1 __ 2 (−0.2, 3.142 and 0 .3̇ can also be d − __ 7 expressed as fractions) 4 1 a b c 2 a 121, 144, 169, 196, … 1 , __ b __ 1 , __ 2 , __ 2 , etc. 4 6 7 9 c 83, 89, 97, 101, … d 2, 3, 5, 7 b 3 3 a 6.35 c 4 a b $2 847 379 794 and $2 797 501 328 $49 878 466 or forty-nine million, eight hundred and seventy-eight thousand, four hundred and sixty-six dollars 2.6 d 2 Exercise 1.2 1 39.55 a b c d e f g 2×2×3×3 5 × 13 2×2×2×2×2×2 2×2×3×7 2×2×2×2×5 2×2×2×5×5×5 2 × 5 × 127 h 13 × 151 a b c d e f LCM = 378, HCF = 1 LCM = 255, HCF = 5 LCM = 864, HCF = 3 LCM = 848, HCF = 1 LCM = 24 264, HCF = 2 LCM = 2970, HCF = 6 Exercise 1.4 1 −3 °C 2 a −2 °C b −9 °C c −12 °C 1 a d 18 24 b e 36 36 c f 90 24 3 a d 4 −2 b e 7 −3 c −1 2 a d 6 3 b e 18 10 c f 9 1 4 a d −3 0 b −26 c −14 3 18 metres 5 −5 −9 b e 41 16 −78 120 shoppers a d c 4 5 20 students 6 6 a a b 80.34 rupees : 1 euro −5.5 1024 cm2 b 210 tiles Exercise 1.3 Exercise 1.5 1 1 a b c 2, 3, 5, 7 53, 59 97, 101, 103 square: 121, 144, 169, 196, 225, 256, 289 cube: 125, 216 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK 2 a d 7 10 3 g __ 4 j 5 b e 5 3 c f 14 25 h 5 i 2 k l 12 m −5 n 3 1 __ 4 5 __ 6 o 6 3 a d g 1954 4096 3130 b e 155 1250 c f 1028 1875 4 a 23 cm b 529 cm2 5 1 a __ 4 ___ d 12 5 ___ g 14 3 ____ j 1 4 12 5 ___ e 13 3 ___ h 16 8 8 ___ f 15 2 ____ i 1 3 23 a d g j 2−1 2−3 11−2 3−1 b e h 6−1 3−3 4−3 c f i 3−2 2−4 5−1 7 a d g j m p 38 32 4−1 412 109 46 b e h k n 102 2−7 103 36 10−4 c f i l o 33 31 1 42 21 _ b√ 4 d (√ 4 ) e(√ 6 ) 8 9 _ 3 a √ 3 _ 3 _ 4 9 _1 b6 3 _3 e5 6 a7 2 d9 4 _1 _5 c8 3 b d 65 −163 a d g j m p s v 26 15.66 3.83 2.79 8.04 304.82 4.03 3.90 b e h k n q 66 3.39 2.15 7.82 1.09 94.78 6.87 −19.10 t w c f i l o r u x 23.2 2.44 1.76 0.21 8.78 0.63 6.61 20.19 Exercise 1.7 1 a b c d e f g h i i i i i i i i ii ii ii ii ii ii ii ii 2 a c 53 200 17.4 b d 713 000 0.00728 3 a c e g 36 12 000 430 000 0.0046 b d f h 5.2 0.0088 120 10 4 a c 4 × 5 = 20 1000 × 7 = 7000 b d 70 × 5 = 350 42 ÷ 6 = 7 5 a 20 b c 12 5.65 9.88 12.87 0.01 10.10 45.44 14.00 26.00 3 iii iii iii iii iii iii iii iii 5.7 9.9 12.9 0.0 10.1 45.4 14.0 26.0 d 6 10 13 0 10 45 14 26 243 _5 10 a d g j 0.04 0.273 27 0.111 b e h 9 0.16 0.8 11 a 1296 b −1 d 2 1 e __ 4 g 32 h 3 j __ 2 1 _ 9 c√ 5 17 15 Exercise 1.6 1 c __ 6 8 2 1 b __ 12 a c 4 c f i 1.5 2 18 8 c __ 3 1 f ____ 625 3 i __ 2 Review exercise 1 natural: 24, 17 3 1 , 0, 0.66, 17 rational: − __ , 24, 0.65, −12, 3 __ 4 2 integer: 24, −12, 0, 17 prime: 17 2 a b c d e 1, 2, 3, 4, 6, 9, 12, 18, 36 two are prime: 2 and 3 2×2×3×3 Any two from: 1, 2, 3, 4, 6, 9, 12, 18, 36 36 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK 3 9 2×2×7×7 3 × 3 × 5 × 41 2×2×3×3×5×7×7 4 14th and 26th March 5 a c true false b d true false a d g 5 145 5 b e h 5 48 10 c f 64 112 7 a d 16.07 11.01 b e 9.79 0.12 c f 13.51 −7.74 8 a 30 6 3 a b c b 33 c 3−2 d 3−1 e3 2 _3 f 32 g 30 h 3−2 i 38 j 3−4 a 37 b 26 c 2−1 10 a c x = −3 x = −2 b d x = −3 x=6 11 a c 1240 0.0238 b d 0.765 31.5 12 a b 92.16 cm2 19.78 cm2 d 40 _ 13 Yes, table sides are √ 1.4 = 1.18 metres or 118 cm long. Alternatively, area of cloth = 1.44 m2 and this is greater than the table area. 14 1.5 metres 15 a 40 b 6 c 22 d 72 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Chapter 2 Exercise 2.1 1 a 3(x + 2) b 6(x − 1) or 6(1 − x) c 2(11 + x) d 18x f x2 + 8 x + __ 1 3 12 − 5x or 5x − 12 e 3x2 + 4 1 − x g __ 5 i 4 + 3x h j p−4 c b 2x x 2x $ __ , $ ___ , and $ ___ 3 9 9 3 c d 3 x a $ __ 3 4 a b 3(x + 7) = 3x + 21 2x(4 + x) = 2x2 + 8x c 3x(6x) = 18x2 Exercise 2.4 d 2(x + __ 1 ) = 2x + 1 2 1 4p 4 x ___ s 6y Rectangle, P = 20x − 4 Right angled isosceles triangle, P = 13x − 1 Square, P = 8x − 16 Kite, P = 6x − 14 a Working shown to give the answers: a −3x3 + x2 + 9x b −7x2 − 3x + 11 c 2x2 − 3x + 5 d 3xy − 4xy2 + 2 a 2x2 − 4x b xy − 3x c −2x − 2 d −3x + 2 Exercise 2.2 e −2x2 + 6x f 3x + 1 1 g x3 h x2 + x + 2 x a x 2 + __ 2 3 c −8x + 4x2 + 2x b e 3x2 − 6x f x2 + xy x 3y __ + ___ 2 2 2 −5x − 6x g −5x2 − 6x a 2(5x + 4) − 3(x − 7) = 10x + 8 − 3x + 21 = 7x + 29 x3(x + 2y) − 2(x4 − y) = x4 + 2x3y − 2x4 + 2y = −x4 + 2x3y + 2y a c b d 54 cm2 110.25 cm2 2 −104 3 17 4 17.75 5 a 6 b 1.875 m2 8 cm2 91 2 3 Exercise 2.3 1 a b c 2 C is correct A cannot be simplified as there are no like terms B can be simplified, the correct answer is 4xy a c e 3x2 − 2x + 3 5ab − 4ac −30mn f h −4x3y k 3b 3 x 2 n ____ y 4 a b 2 p+5 b − 14y r _____ 5 15 a 2 _____ q 4 27 x 2 t _____ 10 b d 6x2y 4x2y − 2xy 4x2 + 5x − y − 5 g 6xy 3 1 i 4b j ___ 4y 20y 9m l ___ m ____ 4 3x 2 2 y y 2 ___ o ____ p 2 2 x b − 2x 2 −x d Exercise 2.5 1 x 6 a ___2 y 2 x 2 c ____ 3y 5x 9 e ____3 2y 50x 3 g _____ 27y i x7y x 16 k ____ y 16 b 3x4y d xy10 f x7y3 h 49 _______ 25x 3y j 8x 10y 3 _______ 3 l 3125x y __________ 4 2 16 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK 2 x 8 a ___2 y 8 c _____ x 5y 7 b d y 16 e ____ x 22 3 f 4 y 22 ____4 2x bx 15 cx 6 _1 dx 9 e f 2x 3y 3 i _1 x 3 h x 3y −1 or ___ y _ 1 2 y 4 _2 b x2 _7 d x2 ax 3 _1 e a 9a + b b c −4a4b + 6a2b3 d 6 5x 5 a ____ 6 b d 64x 9 e _____ y 15 11x − 3 −2x2 + 5x + 12 16x4y8 a 2 b 2 c e −4 f 2 3 g __ 2 1 d __ 4 3 h __ 4 4 a x + 12 b c 5x d e 4x f g 12 − x h x−4 x __ 3 x __ 4 x3 − x or x − x3 a −6 b 24 c a _1 5xy 3 y 9 c x −9yor ___ x h 5 x2 + 3x − 2 b d 29 __ Review exercise 5 7 c a c 7 fx − 4 y − 16 or _____ _11 __29 x 4 y 16 _3 ex 4 y 2 2 d 27x 4 g ____ 4y 3 cy 3 1 b 5 j x −2y −4 or _____ 21 4 x y x3 −2 4x e ___ y _1 8x3 2 __ 3 −2 a −7x + 4 5y f5x − ___ 2 8 __ 12 k y −2 or ___ y 5 3 _1 ax 2 gx 4 x 5 ___4 y ___ 19 x 6x2 + 15x − 8 −x3 + 3x2 − x + 5 1 c ___ x 4 15 f x9y8 xy 6 ____ 2 _1 bx 2 _5 2y 3 _1 _5 _1 d 2x − 3 y 3 or ____ x 3 8 Since n is even, we can replace n with 2x where x is some unknown number. Since m is even, we can replace it with 2y. Therefore, nm = 2x × 2y = 4xy. 4xy is a multiple of 4 and must be divisible by 4. 9 a b 1.86 mg 3.79 mg (Note that you have to work out four-hour dose then add that to next dose before applying formula for one hour to get the amount after five hours.) 10 44% ____ − 14 9 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Chapter 3 Exercise 3.1 Exercise 3.2 1 a b c d i 150° ii 180° 45° i 810° ii 72° quarter to one or 12 45 2 No. If the acute angle is < 45° it will produce an acute or right angle. a b c d e f 3 Yes. The smallest obtuse angle is 91° and the largest is 179°. Half of those will range from 45.5° to 89.5°, all of which are acute. g 4 a b c 45° (90 − x)° x° 5 a c e 135° (180 − x)° (90 + x)° iii i b d f 90° x° (90 − x)° angle QON = 48°, so a = 48° (vertically opposite) 7 a 8 a b c d 9 a b c d e f 1 h 6 b 135° angle EOD = 41 ° (angles on line), so x = 41° (vertically opposite) x = 20° (angles round point) x = 85° (co-int angles); y = 72° (alt angles) x = 99° (co-int angles); y = 123° (angle ABF = 123°, co-int angles then vertically opposite) x = 72° (angle BFE = 72°, then alt angles); y = 43° (angles in triangle BCJ ) x = 45° (angles round a point); y = 90° (co-int angles ) x = 112° (angle AFG = 112°, vertically opposite, then co-int angles) x = 45° (angle STQ corr angles then vertically opposite) x = 90° (angle ECD and angle ACD co-int angles then angles round a point) x = 18° (angle DFE co-int with angle CDF then angle BFE co-int with angle ABF ) x = 85° (angles ADC and EDF vertically opposite, then co-int with angles BAD) BCF = 98° (alt angles), so DCF = 98° − 43° = 55°; x = 125° (co-int angles) 2 a b c d 3 103° (angles in triangle) 51° (ext angle equals sum int opps) 68° (ext angle equals sum int opps) 53° (base angles isosceles) 60° (equilateral triangle) x = 58° (base angles isosceles and angles in triangle); y = 26° (ext angles equals sum int opps) x = 33° (base angles isosceles then ext angles equals sum int opps) x = 45° (co-int angles, angles on aline, then angles in triangle) x = 45° (base angles isosceles); y = 75° (base angles isosceles) x = 36°; so angle BAC = 36° and angle ABC = 72° x = 40°; so angle BAC = 80°; angle ABC = 40° and angle ACD = 120° x = 60° x = 72° angle ABC = 34°; angle ACB = 68° Exercise 3.3 1 a b c d e f g h i 2 square, rhombus rectangle, square square, rectangle square, rectangle, rhombus, parallelogram square, rectangle square, rectangle, parallelogram, rhombus square, rhombus, kite rhombus, square, (kite: one diagonal bisects one pair of angles) rhombus, square, kite a a f b e d g f a=b=c=d=e=f = 45° c a = d = e = 63° b = c = f = 27° 63° a e 6 b d b c Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK 3 a c e f x = 69° b x = 64° x = 52° d x = 115° x = 30°; 2x = 60°; 3x = 90° a = 44°; b = 68°; c = 44°; d = e = 68° a b c angle Q + angle R = 210° angle R = 140° angle Q = 70° 5 a b c angle MNP = 42° angle MNO = 104° angle PON = 56° 6 A − Kite B − Trapezium C − Rhombus D − Parallelogram E − Square F − Rectangle 4 Exercise 3.5 1 2 (b) chord i i i 1080° 1440° 2340° sector 50° (a) O diameter (e) major arc E N (c) P Exercise 3.6 1, 2 student’s own diagrams ii ii ii 3 student’s own diagram; scalene 4 If you only have the length of two sides, you need to know the size of the angle at A or B or the length of the third side to make sure you draw the given triangle. This diagram shows that AC could be any 5 cm length and that would mean that BC could be a number of different lengths, so Jay’s reasoning is faulty. 135° 144° 156° 5 cm arc C C AC = 5 cm, so point C can be anywhere on the arc: C 900 ____ = 128.57° 3 7 20 sides 4 a 165.6° 5 a b c x = 156° x = 85°; x − 50° = 35°, x − 10° = 75° x = 113°; y = 104° 6 Divide 360 by the number of angles to find the size of one exterior angle. Then use the fact that the exterior and interior angles form a straight line (180°) to work out the size of the interior angle. 7 7 a b c (d) tangent D Exercise 3.4 1 M C b 360 _____ = 25sides 14.4 Yes. If internal angle is 170°, then external angle = 10°. Sum of external angles is 360°, and 360° ÷ 10° = 36, so this would be a 36-sided regular polygon. A 5 7 cm B For example: Start by marking vertex A. Draw two 5 cm long lines from A to vertices B and C. Use compasses to mark 5 cm arcs from B and C. The arcs will intersect at vertex D. Join the vertices to form a rhombus. Review exercise 1 a b c d e f g h x = 113° x = 41° x = 66° x = 74°; y = 106°; z = 37° x = 46°; y = 104° x = 110°; y = 124° x = 40°; y = 70°; z = 70° x = 35°; y = 55° Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK 2 a b c x = 60 + 60 + 120 = 240° x = 90 + 90 + 135 = 315° x = 80° 3 a i radius ii chord iii diameter b OA, OB, OC, OD c 24.8 cm d Student’s own diagram 8 4 Student’s own diagram 5 Students should construct a triangle with sides 3 cm, 12 cm and 13 cm. Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Chapter 4 Exercise 4.1 f Stem 1 eye colour, hair colour 2 6 2 grade, height, shoe size, mass, number of brothers/sisters 3 8 4 0245689 3 shoe size, number of brothers/sisters 5 1234444555566777899 4 height, mass 6 013335577799 5 possible answers include: eye colour, hair colour – collected by observation; height, mass – collected by measuring; grade, shoe size, number of siblings – collected by survey, questionnaire 7 013688 8 028 9 1 Key: 2 | 6 represents 26 per cent The actual data values are given, so you can calculate exact mode, median and range. You can also see the shape of the distribution of the data quite clearly. Exercise 4.2 1 2 Text messages a b 3 a Tally | 1 2 || 2 3 || 2 4 | | | | 5 5 | | | | | | | | 9 6 | | | | | | 7 7 | | | | | 6 8 ||| 3 9 ||| 3 10 || 2 4 a Eye colour Brown Blue Green Blonde 0 0 1 Brown 3 0 0 Black 3 1 2 Hair colour b c 5 a Answers may vary. For example: All the students with brown hair have brown eyes. There are no blonde students with brown eyes. Most students have black hair. And so on, based on the data. Student’s own answer with a reason. Stem Leaf No. of 0 mosquitoes 1 2 3 4 5 6 0 1257 Frequency 6 9 7 8 7 6 1 22689 2 0349 3 1113579 4 138 5 1 7 It is impossible to say; frequency is very similar for all numbers of mosquitoes. Score Score Frequency b e Frequency 1 Frequency 9 Leaf 0–29 30–39 40–49 50–59 1 1 7 19 Key: 0 | 1 represents 1 car, 1 | 2 represents 12 cars 60–69 70–79 80–100 12 6 4 10 c 2 d 26 There are very few marks at the low and high end of the scale. 6 b 51 cars a b 74 34 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK c d e It does not show the games against each other, it simply shows the points scored in 12 games by the home team and their opponents. There is no link between the scores as there would be in a table or double bar graph showing points per game. Their lowest score of 34 is higher than the lowest opponent team score, so the home team could not have lost the game where the opponents scored 28 points. 8 games. Four of the opponents scores (74, 63, 64, 64) are higher than the highest home team score of 59. This means they could not win these four games. This does not mean that they won eight games, just that this is the most games they could have won. 4 Charts can be drawn vertically or horizontally. a Breakfast food chosen Bread Hot porridge Cereal 0 4 8 12 16 20 24 28 32 Frequency b Breakfast food chosen Bread Key Grade 10 Exercise 4.3 1 a b c d e f g pictogram number of students in each year group in a school 30 students half a stick figure 225 Year 11; 285 rounded; unlikely the year groups will all be multiples of 15 2 student’s own pictogram 3 a e The number of students in Grade 10 whose home language is Bahasa and Chinese. 18 30 The favourite sports of students in Grade 10, separated by class athletics f g athletics 9 b c d 10 Hot porridge Grade 11 Cereal 0 4 8 12 16 20 24 28 32 Frequency 5 a d cars b 17% handcarts and bicycles 6 a b Pie chart with sector sizes: A − 18°; B − 43°; C − 148°; D − 90°; E or lower − 61° 6 c 50 d C a b c d e f g 29.7 ± 0.1° C April–November northern hemisphere no 10 mm February There is little or no rain. 7 c 20 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Review exercise 1 a b c survey or questionnaire discrete; you cannot have half a child quantitative; it can be counted d No. of children in family 0 Tally | | | | | | Frequency 2 1 7 Pie chart with sector sizes: 0 − 53°; 1 − 75°; 2 − 83°; 3 − 90°; 4 − 37°; 5 − 15°; 6 − 7° f The number of families that have three or fewer children is five times greater than the number of families with four or more children. Pulse rate before exercise Pulse rate after exercise Stem 5 5 0 5 9 9 7 4 6 4 3 7 0 8 4 9 5 7 8 10 3 11 3 5 5 12 0 1 3 | | | | | | | | | | | | | | | | | | | | | | | | | | | e a 2 10 11 5 a c e 6 a 12 4 5 6 | | | | | | | | | 5 2 1 b d Downtown $2500 15% $4750 $3750 Rice Not rice Pasta 13 24 Not pasta 32 6 b 49% 7 a b Student’s own chart Student’s own chart 8 a 49.6% b $3 600 Key: Before exercise0 | 5 represents 50 beats per minute After exercise8 | 4 represents 84 beats per minute b 3 Student’s own pictogram 4 a b c d e f g 11 In every person, the pulse rate increased after exercise. compound bar chart It shows how many people, out of every 100, have a mobile phone and how many have a land line phone. No. The figures are percentages. Canada, USA and Denmark Germany, UK, Sweden and Italy Denmark Student’s own opinion with reason. Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Chapter 5 Exercise 5.1 5 1 a d 2 5 5 __ 3 3 __ a __ , 1 __ , , __ , 1 3 8 4 8 8 5 13 7 ___ 11 , __ , ___ , ___ , 4 b ___ 9 9 24 18 15 13 2 __ 5 3 ___ 17 c ___ , 2 __ , , __ , 3 3 6 4 24 x = 65 x = 117 b e x = 168 x = 48 c f x = 55 x = 104 2 3 4 12 25 a ___ 8 15 d ___ 4 33 g ___ 10 b 17 ___ 11 59 e ___ 4 29 h ___ 4 c f 59 ___ 63 ___ 13 c 14 e 3 f 6 ___ g 120 h i 72 j 3 k 3 ___ 14 233 ____ 50 7 l __ 4 19 ___ c b e h k 24 b 10 d ___ 27 e g h 2 f 0 6 a $525 b $375 7 a 300 b 6 hours 56 min 8 28 000 litres 60 183 ____ 56 41 ___ 40 − 10 ____ 3 96 ___ 7 32 ___ 45 3 __ 5 1 2 b a c g 5 25 ___ 9 108 a ____ 5 28 d ___ 5 13 a ___ 24 35 d ___ 6 18 g ___ 65 −5 j ___ 6 4 __ 5 25 e ____ 576 11 h ____ 170 b i 39 ___ 7 215 ____ 72 187 ____ 9 Exercise 5.3 Exercise 5.2 1 38 a ___ 9 19 d ___ 4 f i l 19 3 4 7 c ___ 96 9 f ___ 14 152 i ____ 39 16.7% b 62.5% c 29.8% d 30% e 4% f 47% g 112% h 207% i 125% j 250% k 1750% l 103.8% b __ 1 c 49 ___ c 9.05% 1 a __ 8 3 d __ 5 a 53.33% a c e g i k 60 kg 150 litres $64 18 km 0.2 g 475 m3 5 a c e g 6 7 19 ___ 21 161 ____ 20 29 ___ 21 − 26 ____ 9 a e b 2 ___ 11 50 37.62% b d f h j $24 55 ml $19.50 $108 $2.08 l 99 km +20% +53.3% −28.3% +2 566.7% b d f −10% +3.3% +33.3% a c e $54.72 $32.28 $98.55 b d f $945 $40 236 $99.68 a c e $58.48 $83.16 $76.93 b d f $520 $19 882 $45.24 50 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK 8 28 595 tickets 9 1800 shares 4 a c e g i 1.2 × 1031 3.375 × 1036 2 × 1026 1.2 × 102 3 × 10−8 b d f h 4.5 × 1011 1.32 × 10−11 2.67 × 105 2 × 10−3 5 a the Sun b 6.051 × 106 6 a b 500 seconds = 5 × 102 seconds 19 166.67 seconds = 1.92 × 104 seconds 10 $129 375 11 21.95% 12 $15 696 13 $6228 14 2.5 g 7 15 ___ = 28% increase, so $7 more is better 25 16 $50 17 a 1 200 b 960 18 $150 19 a b 2 hrs 54 mins (174 mins) 4 hrs 46 mins (286 mins) Review exercise 1 a b 2 1 a __ 6 3 d ___ 44 361 g ____ 16 14 j ___ 9 20 26.59 grams (two decimal places) 21 a $12 b 27 750 c $114 885 Exercise 5.4 1 13 a c e g i k 4.5× 104 8 × 10 4.19 × 106 6.5 × 10−3 4.5 × 10−4 6.75 × 10−3 b d f h j l 8 × 105 2.345 × 106 3.2 × 1010 9 × 10−3 8 × 10−7 4.5 × 10−10 2 a c e g i 2500 426 500 0.00000915 0.000028 0.00245 b d f h 39 000 0.00001045 0.000000001 94 000 000 3 a c e g i 6.56 × 10−17 1.44 × 1013 5.04 × 1018 1.52 × 1017 4.50 × 10−3 b d f h 1.28 × 10−14 1.58 × 10−20 1.98 × 1012 2.29 × 108 Any multiple of 8 (8, 16, 24 etc.) Two trays b 63 c e 31 ___ 48 334 ____ 45 f h 3 $10 000 4 a 5 67.7% 6 8.15% 7 a 5.9 × 109 km b 5.753 × 109 km a b c 9.4637 × 1012 km 1.6 × 10−5 light years 3.975 × 1013 km 8 719 b i 5 __ 3 71 ___ 6 68 ___ 15 11 779 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Chapter 6 Exercise 6.1 1 a 3 b x=4 d x=4 f x=5 h x = −5 j 3 = − __ = −1 __ x 1 1 k x = ___ 11 = 5 __ l x=3 a b x = −2 8 c x = − __ = −2 __ 2 3 3 d e x=8 f g x = −4 h 1 x = __ 4 = 1 __ 3 3 1 __ x = 4 x = −9 i x = −10 j x = −13 x=3 9 c x = __ = 4 __ 1 2 2 18 3 36 ___ ___ e x = = = 3 __ 5 5 10 g i x=2 x=4 2 2 3 2 x = 10 2 a x(x + 8) b a(12 − a) c e g i k x(9x + 4) 2b(3ab + 4) 3x(2 − 3x) 3abc2(3c − ab) b2(3a − 4c) d f h j l 2x(11 − 8x) 18xy(1 − 2x) 2xy 2(7x − 3) x(4x − 7y) 7ab(2a − 3b) 4 a c e g i k (3 + y)(x + 4) (a + 2b)(3 − 2a) (2 − y)(x + 1) (2 + y)(9 − x) (x − 6)(3x − 5) (2x + 3)(3x + y) b d f h j l ( y − 3)(x + 5) (2a − b)(4a − 3) (x − 3)(x + 4) (2b − c)(4a + 1) (x − y)(x − 2) (x − y)(4 − 3x) 5 a c e (2 + a)(2x + 3) (b + 4)(2c + 3a) (2y + 3x)(x2 + y2) b d f (x − 3)(x + 2y) (3x2 + 4)(2x + 1) (a + 9)(2 − b) 2 Exercise 6.3 k x = −34 l 7 20 x = ___ = 1 ___ a x = 18 b x = 27 2 m = __ D k c = y − mx c x = 24 d x = −44 e f P+c b = ____ a x = 17 g x = −1 h 23 5 x = ___ = 3 __ 6 6 x=9 3 4 a−c b = ___ x 3 16 i x = ___ = 1 ___ 13 13 5 a j x = 10 k l x = ____ − 11 2 1 x = __ 5 x = −1 x = 42 m x=2 n o p x=1 13 13 1 14 a d g j 3 a 4xy xy2z 2 a c e g i 12(x + 4) 4(a − 4) a(b + 5) 8xz(3y − 1) 2y(3x − 2z) b e h k c f i l 8 3y pq ab3 b d f h j f 5 5ab 7ab 3xy 2(1 + 4y) x(3 − y) 3(x − 5y) 3b(3a − 4c) 2x(7 − 13y) b a = 2c + 3b c+d d−c c a = ____ d a = ____ b b e a = bc − d (or a = −d + bc) Exercise 6.2 1 a=c−b 6 7 8 a = d + bc g de − c h a = ____ b i ef − d j a = ____ bc k cd − b a = _____ 2 e+d a = ____ bc c ( f − de) a = ________ b d(e − c) d l a = ________ m a = __ c + b b c n a = __ − 2b d a w = __ P − l b w = 35.5 cm 2 C b 9 cm c 46 cm a r = ___ 2π use b = ___ 2A − a; b = 3.8 cm h Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK 9 a i b 11 656 kg 70 kg ii 12 kg b 6 seconds 3 a c e g i 4(x − 2) −2(x + 2) 7xy(2xy + 1) (4 + 3x)(x − 3) (a2 + 10)(a − 6) 4 a b c d 4(x − 7) = 4x − 28 2x(x + 9) = 2x2 + 18x 4x(4x + 3y) = 16x2 + 12xy 19x(x + 2y) = 19x2 + 38xy 5 a b x = 15°, so ∠DEG = ∠FEH = 135° x = 26°, so ∠ABC = 26°, ∠ACB = 94°, ∠BAC = 60° x = 30°, so ∠ADB = ∠ADC = 135° T − 70P = B c ________ 12 d 960 kg 10 a √ __ h t = __ 5 Review exercise 1 2 a c e g x = −3 x=9 x=2 x = 1.5 b d f h x = −6 x = −6 x = −13 x=5 m+r a x = _____ np b mq − p x = ______ n c 3(4x − y) 3x( y − 8) (x − y)(2 + x) 4x(x + y)(x − 2) y × a; Young’s Rule: d = ______ y + 12 y Dilling’s Rule: d = ___ × a 20 6 a b c 15 b d f h Young’s Rule: 6.77 mg/6–8 hours; Dilling’s Rule: 5.25 mg / 6–8 hours. Clark’s rule: 6.75 mg/6–8 hours. Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Chapter 7 Exercise 7.1 Exercise 7.2 1 a c e 120 mm 128 mm 36.2 cm b d f 45 cm 98 mm 233 mm 2 a c e g 15.71 metres 53.99 mm 18.85 metres 24.38 cm b d f h 43.98 cm 21.57 metres 150.80 mm 23.00 cm 3 90 m 4 164 × 45.50 = $7462 5 9 cm each 6 about 88 cm 7 8 a a c e g 63π cm 332.5 cm2 399 cm2 59.5 cm2 2 296 mm2 b b d f h 70π cm 1.53 m2 150 cm2 71.5 cm2 243 cm2 9 a c e 7853.98 mm2 7696.90 mm2 167.55 cm2 b d 153.94 mm2 17.45 cm2 10 a c e g i 288 cm2 373.5 cm2 366 cm2 272.97 cm2 5640.43 cm2 b d f h 82 cm2 581.5 cm2 39 cm2 4000 cm2 11 a c e 30 cm2 33.6 cm2 720 cm2 b d f 90 cm2 61.2 cm2 (625π + 600) cm2 b 15π cm 1 a b c d cube cuboid square-based pyramid octahedron 2 a b c cuboid triangular prism cylinder 3 The following are examples; there are other possible nets. a b 12 11.1 m2 13 70 mm = 7 cm 14 a 14π mm 8 c __ π mm (or 2.6π mm) 3 15 6671.70 km 16 a c 24π cm2 (81π − 162) mm2 b 233.33π cm2 17 61.4 cm2 16 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK 9 c a 5.28 cm3 c e 25.2 cm3 65 144.07 mm3 b d 33 510.32 m3 169.65 cm3 b 1868.36 cm2 b 21π cm b d f h 33 000 mm2 80 cm2 35 cm2 159.27 cm2 10 a i 1.08 × 1012 km3 ii 5.10 × 108 km2 b 1.48 × 108 km2 11 a 0.498 m2 Review exercise 1 d 3 65 π cm √ ___ a 2000 mm2 c e g 40 cm2 106 cm2 175.93 cm2 4 15 metres 5 243 cm2 6 a b c d Exercise 7.3 Cuboid B is smaller 14 265.48 mm3 student’s own diagram cylinder 7539.82 mm2, cuboid 9000 mm2 a c 2.56 mm2 13.5 cm2 b d 523.2 m2 128π mm2 7 42 2 a 384 cm2 b 8 cm 8 3 a c 340 cm2 4 tins b 153 000 cm2 volume pyramid = 30 cm3 15 volume cone = ___ π cm3 2 difference = 6.44 cm3 4 a c e g 90 000 mm3 20 420.35 mm3 960 cm3 1800 cm3 b d f h 60 cm3 1120 cm3 5.76 m3 1.95 m3 9 5 332.5 cm3 729 π cm3 volume 3 balls = ____ 2 14812 π cm3 volume tube = ______ 25 space = 716.22 cm3 6 a b 44 people 7 67.5π m3 8 Various answers – for example: 224 m3 10 a b Volume (mm3) 64 000 64 000 64 000 64 000 17 110.25π cm2 ___ 2 1 a Length (mm) 80 50 100 50 Breadth (mm) 40 64 80 80 Height (mm) 20 20 8 16 13 014.57 mm3 For example: the cylinder may be hollow, or, part of the sphere will be removed where it joins the cylinder. 11 37.7 cm3 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Chapter 8 Exercise 8.1 1 a b Exercise 8.2 9 17 3 , green = ___ red = ___ , white = ___ 25 50 10 1 30% c 1 d __ 3 1 2 a A: 0.61, B: 0.22, C: 0.11, D: 0.05, E: 0.01 b i highly likely ii unlikely iii highly unlikely 3 4 4 or equivalent a ___ 18 4 or equivalent b __ 9 7 c __ or equivalent 9 a 1, 2, 3, 4, 5, 6, 7, 8, 9 or 10 9 i H HH HT T TH TT 3 a __ 4 2 Yellow 3 c 0.6 b 0.97 c 11 2 3 1 1, 1 1, 2 1, 3 2 2, 1 2, 2 2, 3 3 3, 1 3, 2 3, 3 vi 10 __ 1 2 ix 0 a cola, biscuit Drink fruit juice, biscuit water, biscuit 2 __ 2 5 d Snack cola, cake fruit juice, cake water, cake cola, muffin fruit juice, muffin water, muffin 2 c __ 3 1 b __ 9 __ 1 1 d __ 3 1 c __ 3 3 ___ iii c 1 9 Exercise 8.3 1 a 0.73 12 a 1 b __ 4 a b 5 10 __ 8 11 a 0.16 b 0.84 c 0.6 d strawberry 63, lime 66, lemon 54, blackberry 69, apple 48 114 2 3 4 18 T Green ___ 1 ii 1 10 3 2 iv ___ v __ 5 10 9 3 ___ ___ viii vii 10 10 2 5 a __ 5 3 b no sugar; probability = __ 5 1 6 a __ b __ 1 4 2 7 b __ 1 7 a ___ 20 2 3 ___ __ e 1 d 5 10 13 8 ___ 40 b H 4 b ___ 15 7 a ___ 13 1 a __ 8 A E A C CA CE CA N NA NE NA B BA BE BA R RA RE RA R RA RE RA 1 __ 5 6 b ___ 13 1 b __ 8 c d ___ 4 15 9 c ___ 13 3 c __ 8 Removing a flavour has an effect on the second choice (there are fewer left to choose from) so the events are not independent. Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Review exercise a 10 000 b heads 0.4083; tails 0.5917 1 c __ 2 d The coin could be biased – probability of the tails outcome is higher than the heads outcome for a great many tosses 2 3 1 a __ 2 9 e ___ 10 1 a ___ 36 2 b __ 5 9 f ___ 10 b 7, __ 1 6 c ___ 1 10 1 g __ 2 1 c __ 2 d d a Josh Carlos 1 4 0 __ 1 6 5 $1 $1 $1 50c 50c $5 20c 20c $5 6 6 6 5.5 5.5 10 5.2 5.2 $5 6 6 6 5.5 5.5 10 5.2 5.2 $5 6 6 6 5.5 5.5 10 5.2 5.2 $5 6 6 6 5.5 5.5 10 5.2 5.2 $2 3 3 3 2.5 2.5 2.2 2.2 50c 1.5 1.5 1.5 1 1 5.5 0.7 0.7 50c 1.5 1.5 1.5 1 1 5.5 0.7 0.7 3 b ___ 14 1 c __ 4 a b 0.4 1 6 __ 8 7 a 40 b i 0.025 c i 1 19 7 35 d ___ 56 0.85 ii ii 0.3 0.625 iii 0.925 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Chapter 9 Exercise 9.1 1 2 3 4 5 6 7 a b c d e f g a c n = 24 h a 7, 9, 11, 13 c e 1, __ 1 , __ 1 , __ 1 d 2 4 8 100, 47, 20.5, 7.25 a b c d e f 5, 7, 9 T35 = 73 1, 4, 9 T35 = 1225 5, 11, 17 T35 = 209 0, 7, 26 T35 = 42 874 0, 2, 6 T35 = 1190 1, −1, −3 T35 = −67 2 1 They are all prime numbers. They have no square number factors. a d 8n − 6 b 1594 c 30th T18 = 138 and T19 = 146, so 139 is not a term. 2 a 3√ 3 b 4 √ 3 4 √ 7 d 15 √ 2 e 9√ 2 f − 8 √ 6 h 24 √ 6 √ a 27 b √ 216 √ 20 d − √ 175 a b c d e 2n + 5 3 − 8n 6n − 4 (n + 1)2 1.2n + 1.1 a n Tn b 5, 11, 23, 47 1 T50 = 105 T50 = −397 T50 = 296 T50 = 2601 T50 = 61.1 _ _ 3 _ 4 a __ 9 103 ____ d 900 _ b e _ c g 3 c 5 6 6 11 16 21 26 31 3, 4, 7, 12, 19 _ a √ 16 , √ 12 , 0.090090009… 74 ___ c 99 943 ____ 999 f 79 ___ 90 928 _____ 4995 Exercise 9.3 4 5, 10, 15 9, 6, 3 2, 1, __ 1 2 3 Tn = 3n2 + 1 √ b 45 , √ 90 , π, √ 8 3 a c b Tn = n2 Exercise 9.2 2 Tn = 5n + 1 496 11 a 37, 32, 27, 22 1 b c 10 a First difference: 7, 9, 11, 13 Second difference is 2, which is constant, so sequence is quadratic. b 65 c Tn = n2 + 4n + 5 d 2705 d 55th b d 7, 10, 13 −20, −16, −12 f 1, 2, 4 _ _ _ − 10 √ 3 _ _ _ _ _ _ _ _ _ _ _ _ _ 4 3 , 6 √ 5 , 3 √ 8 , 3 √ 3 , √ 12 9 √ 5 a 6√ 7 + 3 √ 5 _ c _ _ 3 √ 6 _ _ √ 10 − 2 √ 7 _ a 4√ 2 _ c 7 √ 2 _ √ a 21 _ c √ 10 _ e 4 √ 2 b d e 6 7 g 20 b un = 8 − 3n u30 = −82 17, 19, 21 (add 2) 121, 132, 143 (add 11) 8, 4, 2 (divide by 2) 40, 48, 56 (add 8) −10, −12, −14 (subtract 2) 2, 4, 8 (multiply by 2) 11, 16, 22 (add one more each time than added to previous term) 21, 26, 31 (add 5) e 8 9 78 _ _ _ √ 3 − √ 7 b _ √ 5 _ − √ 2 _ √ 22 d 4 f 6 √ 35 h 15 √ 15 b d _ 3 √ 6 + 3 √ 2 _ _ Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK 8 _ b _ √ 3 1_ ___ √ 3 d 1 __ 2 e 3 f 6 √ 3 g 8 h 4 √ 3 a 2√ 2 c _ 2 e f {2} {10, 12} 3 a b c d e f {} {1, 3, 5, 6, 7, 9, 11, 12, 13, 15, 18} {1, 3, 5, 7, 9, 11, 13, 15} {2, 4, 8, 10, 14, 16, 17, 19, 20} {2, 4, 6, 8, 10, 12} {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 15, 18} 4 a b {−2, −1, 0, 1, 2} {1, 2, 3, 4, 5} 5 a b {x: x is even, x < 10} {x: x is square numbers, x < 25} 6 a It is the set of ordered coordinate pairs on the straight line y = 5x − 2. There are an infinite number of points on the line so it is not possible to list them all. _ _ 2√ 3 ____ b 5 3 _ _ √ √ − 7 6 ____ ___ c d 7 3 _ _ − 4 √ 3 2√ 21 e _____ f ______ 3 9 _ _ 2√ 3 + 3 2 √ 3 + 3 h ________ g ________ 3 6 10 a Incorrect multiplication when expanding brackets. 9 b c d The set of even numbers from two to twelve. 6 {2} {2, 4, 6, 8} _ 6√ 5 a ____ b Student B would get full marks. Student C did not multiply by ___ − 1 to fully −1 simplify the fraction. _ 1+√ 5 11 a ______ 4 _ _ 12 a √ 15 + 7 √ 3 c _ 18 √ 5 _ _ _ b − 6 − 3 √ 5 b 8 √ 3 − 2 √ 6 d 12 √ 3 − 6 _ _ a b _ 13 √ 54 = 3 √ 6 cm 7 _ a 14 2π √ 5 cm b d f 15 5 √ 3 cm p _ 16 100 √ 3 metres √ 2 200 10 √ ____ _ = _____ cm _ l √ π 18 40 √ 5 cm _ 8 a b c d e f 9 a _ _ 19 a P = ( 2 √ 2 + √ 5 + √ 3 )cm _ √ 15 cm2 b A = ____ 2 _ _ 20 a V = ( √ 110 + 3 √ 55 ) m3 b _ _ _ ( 2 √ Surface 55 + 2 √ 10 + 6 √ 5 _area = _ + 2√ 22 + 6 √ 11 )m2 n o a d g false true false q u v w x z M b e h true false true c f false true S 78 − x x c 0.57 36 − x 7 b 21 C 9 20 {c, h, i, s, y} {c, e, h, i, m, p, r, s, t, y} {a, b, d, f, g, j, k, l, n, o, q, u, v, w, x, z} {c, h, i, s, y} Exercise 9.4 1 k _ ____ π j t e m r h i s c y _ 17 g P 21 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK _ 11 a 3√ 3 10 a x=4 b i iv ii v 12 3 23 7 iii 11 Review exercise 1 2 a b c 5n − 4 26 − 6n 3n − 1 a b c −4, −2, 0, 2, 4, 8 174 T46 54 = 3 √ 6 PR = √ _ _ 27 1 __ c Area = (3 √3 )(3 √3 ) = __ 1 (9 × 3) = ___ 2 2 2 = 13.5 cm2 12 a B b 21 4 u51 = 44 d i 5 a b u4 = 105 ml The volume of medication in the blood after 24 hours (four six−hour periods). 6 a b c 44, 60 Tn = n2 + 5n − 6 12th 7 a Student A multiplies each term by 3 to get the next term in the sequence. Student B adds 4, then 12, then 20 and has a constant second difference of 8. A: Tn = 2 × 3n − 1 B: Tn = 4n2 − 8n + 6 146 T10 b 286 ____ 999 c 17 ___ 40 59 ___ iv 80 13 a b c 18 14 16 41 ___ 80 ___ v 21 80 ii iii 1 __ 5 (A ∩ C) ∩ B9 B∪C A ∪ (B ∩ C) Sequence 1st term 2nd term 3rd term A 1 8 27 B 2 16 54 C −1 10 45 Sequence 4th term nth term A 64 n3 B 128 2n3 C 116 2n3 − 3n _ 0.213231234…, √ 2 , 4π 23 a ___ 99 10 n = 4 9 16 21 2, 0, −2 8 C 25 3 b c d 22 T120 = 596 T120 = −694 T120 = 359 _ _ b Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Chapter 10 Exercise 10.1 1 a b c d e 6 g h j 0 1 2 3 b y 4 5 6 7 8 c x −1 0 1 2 3 y 1 −1 −3 −5 −7 x −1 0 1 2 3 y 9 7 5 3 1 x −1 0 1 2 3 y −1 −2 −3 −4 −5 x 4 4 4 4 y −1 0 1 2 d g m = __ 1 , c = __ 1 2 4 4 __ m = , c = −2 5 m = 0, c = 7 h m = −3, c = 0 i j m = − __ 1 , c = ___ 14 3 3 m = −1, c = −4 4 k m = 1, c = −4 3 l m = −2, c = 5 x −1 0 1 2 3 y −2 −2 −2 −2 −2 x −1 0 1 2 3 y 1.5 e f x −1 1 −1.2 −0.8 −0.4 2 3 0 0.4 x −1 0 1 2 3 y −1 −0.5 0 0.5 1 x −1 0 1 2 3 y 0.5 −0.5 −1.5 −2.5 −3.5 3 y=x−2 4 a d g h no b yes no e no yes (horizontal lines) yes (vertical lines) a m=1 6 m = __ 7 undefined g 23 0 student’s graphs of values above d m m = −2, c = −20 7 a y = −x b c d f y = 2x + 1 g y = 2.5 1 x −1 y = __ 2 x=2 1 x y = __ 2 y = −2x −1 h i y = −2x j y = − __ 1 x + 2 3 y=x+4 k y = 3x − 2 l y=x−3 a x = 2, y = −6 b x = 6, y = 3 c x = −4, y = 6 d x = 10, y = 10 e −5 x = ___ , y = −5 2 1 b 1 e −0.5 −2.5 −4.5 −6.5 2 5 m = −1, c = −1 m=− __ 1 , c = 5 2 m = 1, c = 0 −1 y i m = 3, c = −4 x (in fact, any five values of y are correct) f a 8 9 a d 10 a b c f yes no b m = −1 c m = −1 e m=2 f m=0 h m = ___ 1 16 11 a b c 12 a c −1 1 2 e 0 f __ 2 a: (0, 0), b: (−1.5, 0.5), c: (−2, 3) d: 13.42 units, e: 3 units, f: 6.71 units AD: y = x + 3, AB: y = −x + 3, BC: y = x − 3, DC: y = −x − 3 (−1.5, 1.5) ABCD is a _ square; side lengths are all equal to √ 18 and gradient of adjacent sides has a product of −1, so sides are perpendicular. y = 3x − 10 _ 13 a 2 √ 26 cm b y = 2x − 6 b 10.20 cm Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK k (x + 5)(x − 2) m (x − 3)(x − 4) o (x + 9)(x − 6) l n p (x + 4)(x − 8) (x + 4)(x − 3) (4x + 1)2 q s (x + 6)2 (5x − y)2 r t 2(3x − 1)2 (2x + 3y)2 6 a c e g i 5(x + 2)(x + 1) 3x(x − 3)(x − 1) x(x + 10)(x + 2) x(x + 7)(x − 2) −2(x + 4)(x − 6) b d f h j 3(x − 4)(x − 2) 5(x − 2)(x − 1) x2y(x + 2)(x − 1) 3(x − 3)(x − 2) 2(x + 7)(x − 8) 7 a b c d e f g h i j k l m n (x + 3)(x − 3) (4 + x)(4 − x) (x + 5)(x − 5) (7 + x)(7 − x) (3x + 2y)(3x − 2y) (9 − 2x)(9 + 2x) (x + 3y)(x − 3y) (11y + 12x)(11y − 12x) (4x + 7y)(4x − 7y) 2(x + 3)(x − 3) 2(10 + x)(10 − x) (x2 + y)(x2 − y) (5 + x8)(5 − x8) (xy + 10)(xy − 10) 14 Write the formula with (4, 6) as one of the points and (x, 0) as the other point and solve for x. The two points are (12, 0) and (−4, 0). _ 15 2 √ (x 2 + y 2) Exercise 10.2 1 a c e g i x2 + 5x + 6 x2 + 12x + 35 x2 − 4x + 3 y2 − 9y + 14 2x4 − x2 − 3 b d f h j x2 − x − 6 x2 + 2x − 35 2x2 + x − 1 6x2 − 7xy + 2y2 x2 + x − 132 k 1 − __ 1 x2 l −3x2 n x2 + 8x + 16 4 m −12x2 + 14x − 4 2 a c e g i k m x2 + 8x + 16 x2 + 10x + 25 x2 + 2xy + y2 9x2 − 12x + 4 4x2 + 20x + 25 9 − 6x + x2 36 − 36y + 9y2 b d f h j l x2 − 6x + 9 y2 − 4y + 4 4x2 − 4xy + y2 4x2 − 12xy + 9y2 16x2 − 48x + 36 16 − 16x + 4x2 3 a c e g i x2 − 25 49y2 − 9 9x2 − 16 16x4y4 − 4z4 16x2y4 − 25y2 b d f h j 4x2 − 25 x4 − y4 x6 − 4y4 4x8 − 4y2 64x6y4 − 49z4 a b c d e f g h i j k l x3 + 5x2 + 11x + 15 x3 + 3x2 + x − 5 x3 − 3x2 − 6x + 8 x3 − 14x2 + 64x − 96 x3 + 2x2 − 5x − 6 x3 − 4x2 + 3x x3 − 5x2 + 8x − 4 x3 − 3x2 + 3x − 1 2x3 − 11x2 + 12x + 9 3x3 − 36x2 + 144x − 192 −2x3 − 6x2 − 6x − 2 8x3 − 27 a c e g i (x + 2)(x + 2) (x + 3)(x + 3) (x + 3)(x + 5) (x − 5)(x − 3) (x − 26)(x − 1) 4 5 24 + 11x − 6 b d f h j (x + 4)(x + 3) (x + 1)(x + 4) (x − 1)(x − 8) (x − 1)(x − 3) (x − 8)(x + 1) 5x 8w 5x 8w o ___ + ___ − ___ z ___ z ( y 2 )( y 2 ) p (5x5 + 1)(5x5 − 1) q (1 + 9x2y3)(1 − 9x2y3) _ _ r (x + √ 2 )( x − √ 2 ) 8 9 a x=2 b c x=1 d e x=1 f a x = 0 or x = 3 b c x = 0 or x = 2 d e x = −1 or x = 1 f g h x = −4 or x = −2 i 1 or x = __ x = − __ 1 2 2 x = −4 or x = −1 j x = 5 or x = −1 k x = 5 or x = −4 l x = −10 or x = 2 m x = 5 or x = 3 n x = 20 or x = −3 o x = 7 or x = 8 p x = 10 q x=2 r x = −7 or x = 2 x = −10 or x = 1 3 x = __ 2 x = −12 x = −2 or x = 2 x = 0 or x = − __ 2 3 7 7 __ x = − or x = __ 2 2 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Review exercise a b c d y = __ 1 x 2 40 x −1 0 1 2 3 y −0.5 0 0.5 1 1.5 3 25 30 2 x −1 0 1 2 3 y 2.5 3 3.5 4 4.5 x −1 0 1 2 3 20 15 y 2 2 2 2 2 y − 2x − 4 = 0 x −1 0 1 2 3 y 2 4 6 8 10 5 x 0 m = −2, c = −1 b c m = 1, c = 8 d e 2 , c = 2 m = − __ 3 f m = −1, c = 0 a y=x−3 b c y = −x − 2 d e y = 2x − 3 f y = − __ 2 x + __ 1 3 2 4 y = − __ x − 3 5 y = −x + 2 g y=2 h x = −4 j y = −4x + 34 b y=7 d x = −10 8 f y = −3 9 4 A 0, B 1, C 2, D 1, E 4 5 a y = −2x − 6 c y = __ 4 x + 4 3 e y = −x m = 1, c = −6 m = 0, c = − __ 1 2 t 0 2 4 6 D 0 14 28 42 2 4 6 Time, hours c y = 7x d 7 e i 3 hours ii 1 h 26 min iii 43 min f i 28 km ii 17.5 km iii 5.25 km a a 25 10 y=2 i y = − __ 1 x + 1 2 6 35 y = __ 1 x + 3 All four plotted on the same graph. 2 Caroline’s distance at 7 km/h y 45 Distance, km 1 b 7 a b c i 1 (0.5, 6.5) 4.243 ii 2 (0, 5) 4.472 iii −1 (1, 3) 2.828 iv 4 − __ 3 (−0.5, 3) 5 v undefined (−1.5, 0.25) 3.5 1 a(0, __ 2) b _ √ 89 a b c d e f g x2 − 16x + 64 2x2 − 2 9x2 − 12xy + 4y2 1 − 12y + 36y2 9x2 − 4 4x2 + 20x + 25 9x4y2 + 6x2y + 1 h x 2 + xy + __ 1 y 2 4 1 __ 2 i x − 4 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK 1 − 4 j ___ x 2 k l m n o p 10 a b c d e f g 26 h i j k l 10x − 45 −2x3 + 16x2 − 8x 2x3 + 8x2 + 16x x3 − 6x2 + 12x − 8 3x3 − 6x2 − 3x + 6 −x3 + 12x + 16 a(a + 2)(a − 2) (x2 + 1)(x + 1)(x − 1) (x − 2)(x + 1) (x − 1)(x − 1) (2x − 3y + 2z)(2x − 3y − 2z) (x + 12)(x + 4) x x x 2 + __ x 2 − __ ( 2 )( 2) 11 a b c d e f g h i (x + 1)(x − 6) 4(x + 3)(x − 4) 2(x − 3)(x − 4) 5(1 + 2x8)(1 − 2x8) 3(x + 3)(x + 2) x = −5 or x = −1 x = −2 or x = 2 x = 2 or x = 1 x = −1 x = 5 or x = −1 x=2 x = 6 or x = −4 1 or x = 6 x = __ 2 x=7 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Chapter 11 Exercise 11.1 1 2 9:4 a c e g 5 cm 12 mm 1.09 cm 8.49 cm b d f h 17 cm 10 cm 0.45 cm 6.11 cm 3 a 254.48 cm2 b 529 mm2 4 a x = 2 cm b x = 15 m 5 28 000 cm3 a c e 55.7 mm 5.29 cm 9.85 cm b d f 14.4 cm 10.9 mm 9.33 cm 6 a Exercise 11.4 3 a no c no 4 a √ 32 = 5.66 b √ 18 = 4.24 c √ 32 = 5.66 d √ 180 = 13.4 e f √ 45 = 6.71 2 _ b yes _ 3 _ d yes _ 20 mm 6 44 cm 7 height = 86.6 mm, area = 4330 mm2 8 13 metres and 15 metres 9 310 cm b c 25 : 1 125 : 1 1 x = 2.9 cm 2 x = 3 cm 3 BCA = EFD (corresponding angles in congruent triangles) So 2x + 15 = 3x − 2 and x = 17° So, ABC = DEF = 29°, BCA = EFD = 49° and CAB = FDE = 102° 4 a _ 5 5:1 Yes b 76.2 cm 5 Exercise 11.2 1 a c e f g h 2.24 cm b 6 mm 7.5 mm d 6.4 cm y = 6.67 cm, z = 4.8 cm x = 5.59 cm, y = 13.6 cm x = 9 cm, y = 24 cm x = 50 cm, y = 20 cm 2 angle ABC = angle ADE (corr angle are equal) angle ACB = angle AED (corr angle are equal) angle BAC = angle DAE (common) ∴ triangle ABC is similar to triangle ADE 3 25.5 metres 4 Angle ACB = angle ECD (vertically opposite angles) Angle ABC = angle EDC (alternate angles) Angle BAC = angle DEC (alternate angles) Three equal angles so triangles are congruent. Length AE = 28 cm Review exercise 1 a 2 102 = 62 + 82 ∴ triangle ABC is right angled (converse Pythagoras) 3 a √ 18 = 4.24 b √ 20 = 4.47 c √ 8 = 2.83 d 5 27 a b x = 18 cm x = 27 cm, y = 16 cm b 1:9 _ _ e b 130 metres _ 3.5 4 P = 2250 mm 5 a b c x = 3.5 cm x = 63°, y = 87° x = 12 cm 6 a 4:1 Exercise 11.3 1 sketch Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK 7 18 cm2 8 23 750 mm2 9 a b 10 a b c d 11 a b 13 a 3 cm height = 12 cm, area of base = 256 cm2 68 mm triangle ABC is congruent to triangle HGI triangle ABC is congruent to triangle DEF triangle ACB is congruent to triangle EDF triangle CAB is congruent to triangle GIH The lines are perpendicular. It is a rectangle or a square. 140 mm 560 mm 420 mm 140 mm b 156 mm 12 5.63 metres 28 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Chapter 12 Exercise 12.1 1 2 2 a b c d e f mean 6.14 27.44 13.08 5 4.89 5.22 median 6 27 13 5 5 5 mode 6 27 and 38 12 no mode 4 6 a iii and vi b Sensible answer from student, e.g. different sets can still add up to the same total as another set. If divided by the same number they will have the same mean. a b 3 a b mean = 12.8, median = 15, mode = 17, range = 19 mode too high, mean not reliable as range is large Runner B has the faster mean time; he or she also achieved the faster time, so would technically be beating Runner A. A is more consistent with a range of only 2 seconds (B has a range of 3.8 seconds). 4 Median. The mean will be affected by the very high value of 112 minutes and the mode has only two values, so unlikely to be statistically valid. The median is 21 minutes which seems reasonable given the data 3 255 Exercise 12.3 4 15 1 5 a c 6 Need to know how many cows there are to work out mean litres of milk produced per cow. b d 14 metres 10 metres b 8.6 metres 10 metres 7 a 2.78 8 a d e $20.40 b $6 c $10 2 (only the Category B workers) The mean is between $20 and $40 so the statement is true. 1 Exercise 12.2 1 a b c a 2 Mean = 4.3, median = 5, mode = 2 and 5. The data is bimodal and the lower mode (2) is not representative of the data. Mean = 3.15, median = 2, mode = 2. The mean is not representative of the data because it is too high. This is because there are some values in the data set that are much higher than the others. (This gives a big range, and when the range is big, the mean is generally not representative.) Mean = 17.67, median = 17, no mode. There is no mode, so this cannot be representative of the data. The mean and median are similar, so they are both representative of the data. Score Frequency Score × frequency (fx) 0 6 0 1 6 6 2 10 20 3 11 33 4 5 20 5 1 5 6 1 6 Total 40 90 2.25 Data set mean b 3 a B C 3.5 46.14 4.12 3 40 4.5 3 and 5 40 6.5 Stem Leaf 1 679 2 125599 3 0458 4 19 6 Key: 1 | 6 represents 16 years 4 b 33 years b 29 years a 8 years b 4 years d 5 years 288 c ____ = 5.3 years 54 29 d 2 A median mode c 3 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK 5 a Group A Leaf Group B Leaf Stem 4 077899 98776 5 123446778999 986666542110 6 2344566678 76544322100 7 12 10 8 Key: (Group A) 6 | 5 represents 65 kgand (Group B) 4 | 0 represents 40 kg b Range for group A is 81 − 56 = 25; for group B 72 − 40 = 32. Median for group A is 67 kg, for group B is 58.5 kg. In general, group A are h eavier than group B. The distribution for group A is more clustered around the higher values and only five competitors in group A weigh less than 60 kg. 18 competitors in group B have a mass of less than 60 kg and only two have a mass of 70 or more kilograms while 13 group A competitors weigh 70 or more kilograms. Exercise 12.4 1 a Marks (m) Mid-point Frequency ( f ) 0 , m < 10 5 2 10 10 , m < 20 15 5 75 20 , m < 30 25 13 325 30 , m < 40 35 16 560 40 , m < 50 45 14 630 50 , m < 60 55 13 715 63 2315 Total b c 2 36.75 (2 d.p.) 30 , m , 40 Words per minute (w) Mid-point Frequency 31 , w < 36 33.5 40 1340 36 , w < 41 38.5 70 2695 41 , w < 46 43.5 80 3480 46 , w < 51 48.5 90 4365 51 , w < 55 53.5 60 3210 55 , w < 60 58.5 20 1170 360 16 260 Total a b 30 Frequency × mid-point f × mid-point 45.17 (2 d.p.) 46 , w , 51 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Exercise 12.5 1 a b c d Q1 = 47, Q2 = 55.5, Q3 = 63, IQR = 16 Q1 = 8, Q2 = 15, Q3 = 17, IQR = 9 Q1 = 0.7, Q2 = 1.05, Q3 = 1.4, IQR = 0.7 Q1 = 1, Q2 = 2.5, Q3 = 4, IQR = 3 3 C – although B’s mean is bigger it has a larger range. C’s smaller range suggests that its mean is probably more representative. 4 a c 4.82 cm3 5 cm3 5 a b 36.47 years 40 < a , 50 c don’t know the actual ages a b c d 19 5 Q1 = 18, Q3 = 23, IQR = 5 fairly consistent, so data not spread out Review exercise 1 2 31 a b c mean 6.4, median 6, mode 6, range 6 mean 2.6, median 2, mode 2, range 5 mean 13.8, median 12.8, no mode, range 11.9 a 19 b 9 and 10 c 6 5.66 b 5 cm3 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Chapter 13 Exercise 13.1 1 Student’s own diagrams 2 a c e 2600 metres 820 cm 20 mm b d f 230 mm 2450.809 km 0.157 metres 3 a c e 9080 g 500 g 0.0152 kg b d f 49 340 g 0.068 kg 2.3 tonne 4 a b c d e f 19 km 9015 cm 435 mm 492 cm 635 metres 580 500 cm 5 a c e 1200 mm2 16 420 mm2 0.009441 km2 b d f 900 mm2 370 000 m2 423 000 mm2 6 a c e g 69 000 mm3 30 040 mm3 0.103 cm3 0.455 litres b d f h 19 000 mm3 4 815 000 cm3 0.000 046 9 cm3 42 250 cm3 7 220 metres 8 110 cm 9 42 cm 100 metres 15 cm 2 mm 63 cm 35 metres 500 cm 10 88 (round down as you cannot have part of a box) Exercise 13.2 1 32 Name Time in Time out Lunch (a) Hours worked (b) Daily earnings Dawoot __ 1 past 9 Half past five 3 __ hour 4 7__ 1 hours 2 $100.88 Nadira 8.17 a.m. 5.30 p.m. __ 1 hour 8 h 43 min $117.24 John Robyn Mari 08 23 7.22 a.m. 08 08 17 50 4.30 p.m. 18 30 8 h 42 min 8 h 8 min 9 h 37 min $117.02 $109.39 $129.34 4 2 45 min 1 hour 45 min Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK 2 6 h 25 min Exercise 13.4 3 20 min 1 4 a c 5 h 47 min 12 h 12 min 5 a d e 09 00 b 1 hour c 10 05 30 minutes It would arrive late at East Place at 10 54 and at West Lane at 11 19. 6 b d 10 h 26 min 14 h 30 min a b i ii iii 2 2 hours, 1 minute and 39 seconds (or 02:01:39) i a d Temperature in degrees F against temperature in degrees C i 32 °F ii 50 °F iii 210 °F Oven could be marked in Fahrenheit, but of course she could also have experienced a power failure or other practical problem. Fahrenheit scale as 50 °C is hot, not cold a c 9 kg i 20 kg b c 2 The upper bound is ‘inexact’ so 42.5 in table means ,42.5 Upper bound Lower bound a 42.5 41.5 b 13 325.5 13 324.5 c 450 350 d 12.245 12.235 e 11.495 11.485 f 2.55 g h a b ii Aus$38 b Aus$304 45 kg ii 35 kg iii 145 lb Exercise 13.5 1 a c e US$1 = ¥115.76 €1 = IR84.25 ¥1 = £0.01 2.45 2 a 3800 b 50 550 c 9650.10 395 385 3 a 13 891.20 b 64 160 c 185 652 1.1325 1.1315 4 US$294.50 5 $0.70 or 70c 6 C$676 71.5 < h , 72.5 Yes, it is less than 72.5 (although it would be impossible to measure to that accuracy). 3 upper bound: 28.0575 m2 lower bound: 26.9875 m2 4 a a b d f £1 = NZ$1.97 Can$1 = €0.71 R1 = US$0.07 Review exercise 1 195.5 cm < h , 196.5 cm 93.5 kg < m , 94.5 kg b maximum speed greatest distance _____ 405 = = _______________ 33.5 shortest time = 12.09 m/s a c e g i k 2 23 min 45 s 5 3 2 h 19 min 55 s 4 1.615 metres < h , 1.625 metres 5 a No, that is lower than the lower bound of 45. b Yes, that is within the bounds. b 6 33 3 525 000 rupiah 1 050 000 rupiah 5 250 000 rupiah c Exercise 13.3 1 1 cm per 100 000 rupiah upper bound of area: 15.5563 cm2 lower bound of area: 14.9963 cm2 upper bound of hypotenuse: 8.0910 cm lower bound of hypotenuse: 7.9514 cm 0.4425 cm2 2700 metres 6000 kg 263 000 mg 0.24 litres 0.006428 km2 29 000 000 m3 b d f h j l 690 mm 0.0235 kg 29 250 ml 1000 mm2 7 900 000 cm3 0.168 cm3 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK 6 a c 3.605 cm to 3.615 cm 2.565 cm to 2.575 cm lower bound of area: 9.246825 cm2 upper bound of area: 9.308625 cm2 lower: 9.25 cm2, upper: 9.31 cm2 7 a b 21 600 m3/hr 31.46 m3/m2 8 a b c d Brigid Kosgei 3 minutes 53 seconds 3 minutes 41 seconds faster 3 minutes 11 seconds per kilometre b 9 a conversion graph showing litres against imperial gallons (conversion factor) b i 45 litres ii 112.5 litres c i approximately equal to 3.5 gallons ii approximately equal to 26.5 gallons d i 48.3 km/gal and 67.62 km/gal ii 10.62 kilometres per litre and 14.87 kilometres per litre 10 €590.67 11 a b c US$1 = IR76 152 000 rupees US$163.82 12 £4046.25 34 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Chapter 14 Exercise 14.1 b 1 a c x = 3, y = 2 x = 3, y = −1 b d x = 1, y = 2 x = 3, y = 5 2 a c x = 2, y = 1 x = 5, y = 2 b d x = 3, y = −1 x = 3, y = 2 4 5 x = 2, y = 1 x = 5, y = 2 e x = 7, y = −4 f g i k m o q x = 3, y = 2 x = 2, y = −1 x = 2, y = 1 x = 3, y = 2 x = 4, y = 2 x = 0.5, y = −0.5 h j l n p r x = __ 1 , y = −2 3 x = 3, y = 3 x = 5, y = 1 x = 2, y = 2 x = 3, y = 2.5 x = 5, y = 3 x = −9, y = −2 a c x = 15, y = 30 x = 2, y = 1 b x = 4, y = 2 x = 70 and y = 50 7 Pack of markers is 150 grams, notebook is 80 grams. 8 a b 9 x + y = 23; 8x − 15y = 92, x = 19 people took a class c + d = 15, 50c + 120d = 960 3 desks and 12 chairs 7 −8 4 6 5 −6 −5 6 7 x x x 5 x x < −15 −17 2 13 x,6 f b d 12 x > −7 x = 1, y = −2 x = 3, y = 1 Exercise 14.2 a −16 −15 −14 x x>4 x b 3 4 5 x<6 c 3 4 5 6 7 x x>6 d 4 5 6 7 8 9 10 x x,8 e 7 8 9 −6 −5 x x > −6 −7 x f x < 18 __ 1 3 18 18 1 3 18 2 3 x x,6 35 8 e x = −2, y = −2 x = 3, y = 3 x = 3, y = −2 x = −1, y = 6 x = 2, y = 0 11 x<7 −7 a c a c d 6 1 10 3 a A: y = −2 B: y = x C: y = 3x − 6 D: y = −7x − 1 E: y = −2x + 4 b i ii iii iv v x > 11 7 6 5 4 x Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK 5 g x . − __ 8 − h c 6 8 − 5 8 − 4 8 y 6 x 4 x < −1 i −3 2 −2 −1 0 x −6 −2 , x < 1 −4 −2 0 2 4 6x 2 4 6x 4 6x −2 j −3 −2 −1 0 1 2 x y = 2x + 2 1 2 3 4 5 −6 x d 3 x > 39 4 1 , x , 11 __ 1 1 __ 2 2 1 but she cannot buy __ x > 3 __ 1 cookie, so she 4 4 has to buy at least four. 5 6 −4 2,x,4 y 6 2y + x = 6 4 2 p < 6.2 As she can only buy whole pizzas, the most she can buy is six to still have enough money for a cake. −6 −4 −2 0 −2 Exercise 14.3 1 a −4 y 2 1 y=x−3 −6 y>x−3 −2 −1 0 −1 1 2 3 4 x e y 6 −2 −3 4 −4 −5 b 2 y 5 y = 2x 4 (2, 4) 3 2 0 −3 −2 −1 −1 −4 −4 −2 0 2 −4 1 2 3x −6 −2 −3 −6 −2 (1, 2) 1 36 2x + y = 4 y < 2x Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK f y 6 4 1 y = –x + 2 2 2 −6 −4 0 −2 2 6x 4 −2 −4 −6 2 a y > 2x + 1 y , − __ 1 x + 2 3 2x x > 3 and y , ___ − 1 3 c 3 4 b y . 2x − 1 d 3x y > ___ + 3 2 y 8 7 6 5 4 This is solution region 3 2 y>1 1 −7 −6 −5 −4 −3 −2 −1 0 −1 1 2 3 4 5 6 7 8 9 10 x −2 −3 −4 y<−x+5 −5 −6 −7 −8 37 x 1 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK 5 y 8 7 x > −4 6 5 4 3 2 x−y<7 1 −8 −7 −6 −5 −4 −3 −2 −1 0 −1 1 2 3 4 5 6 8x 7 −2 −3 −4 −5 −6 −7 2x + y < 4 −8 Exercise 14.4 1 a x = 4, x = −1 b x=√ 6 − 1, x = − √ 6 − 1 c 3 3 − ___ x = __ + ___ 11 , x = __ 11 2 2 12 12 _ _ √ √ 2 + 2 − 10 10 x = _______ , x = _______ 3 3 d 2 a b c d e f _ √ 2 _ ___ √ x = 2, x = −0.5 x = 3, x = 1 x = 2.53, x = −0.53 x = 3, x = −0.5 x = 7.47, x = −1.47 x = −2.27, x = 1.77 Exercise 14.5 1 38 a b c d e f g h x = 1.85 or x = −0.180 x = 1.18 or x = − 0.847 x = 0.922 or x = −3.25 x = 1.70 or x = − 4.70 x = 1.45 or x = −3.45 x = 4.44 or x = 0.564 x=1 x = −0.618 or x = 1.62 ___ _ _ a x = −2 − √ 7 or x = √ 7 − 2 b x = −4 − √ 10 or x = √ 10 − 4 c 1 + √ 13 1−√ 13 or x = _______ x = _______ d √ −1 − √ 7 7 − 1 x = ________ or x = ______ _ _ _ 3 _ _3 _ 2 2 _ _ √ b 2 − −b + b 2 − 4ac 4ac − b − √ 3 _______________ − _______________ 2a _ 2a _ − b + √ b 2 − 4ac + b + √ b 2 − 4ac = _____________________________ 2a _ 2 − 4ac √ 2 b = ___________ 2a _ √ b 2 − 4ac = __________ a Exercise 14.6 1 a c e (2x + 1)(x + 1) ( y + 2)(5y − 1) (3x + 5)(2x − 1) b d f (x + 2)(3x − 1) ( y − 1)(5y − 3) (3x + 2)(4x − 3) 2 a c e g i 2(x + 2)(2x + 1) (x − 3) (2x − 3) (3x + 2) (4x + 5) (x + 3)(x + 2) (2y − 7)(2y − 1) b d f h 4(x + 6)(x − 3) 2(x + 1) (5x − 7) 6(x + 2) (x − 1) (3x + 8)(x − 4) 3 (3x + 1) cm 4 (3x − 1) cm Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Exercise 14.7 1 2 3 e 8x b ___ 28 a − ___ x d 36xy 2 3y x 4 _____ e 3 3 y z a d g b e h xy 2x2 + 3x x−1 c 7x y − _____ 2 2 z f 5z f ___3 x c f y x+3 2x − 1 x − 2xy x+1 45 30 46 30 47 30 48 30 x x 4 3x − y > −6 2x + y , 4 −2 6 x 2 y 11 10 y + x < 10 9 8 7 x.0 6 x + 2y < 16 5 3 2 1 3 $5000 at 5% and $10 000 at 8% 3 a x < − __ 4 − 4 5 6 x , 9 7 −2 −1 0 −1 1 2 3 4 − − − 4 4 4 4 x , 5 3 d −6 4 x = −2, y = 5 c −7 y x = 2, y = −5 b −8 6 (2x − 1) a ________ ( x + 1) x(2x + 1) b _______________ 6(x + 1)( 4x − 5) x+2 c _____ 2 7x − 11 d _____________ ( x + 3)( x − 5) 2x + 7 e ________2 (x + 4) (x 2 + 4) 2 f _________ ( x 2 − 4) 2x 3 − 18x 2 − 13x + 117 g _______________________ x 4 − 13x 2 + 36 4x 2 − 3x + 3 h ____________ x − x 3 2 i ___________________ ( x − 4)( x − 2)( x + 1) 2 4 47 x < ___ 30 −9 5 Review exercise 1 x , −7 8 9 10 4 − x 7 8 x 9 x 7 x > − __ 8 7 6 5 − − − 4 4 4 4 −2 1 2 3 4 5 6 7 8 9 10 11 x y>0 _ _ −5 − √ 17 −5 + √ 17 or x = _________ = _________ x 2 2 _ _ √ √ 14 ____ 14 ____ or x = −1 − x = − 1 + 2 2 2(x + 5) 3x + 19 a ________2 b ________ x+4 (x + 4) 10 Pencil = $1.20 and ruler = $2.00 x 11 a i (1 + 3)(1 + 7) = 4 × 8 = 32 ii (−4 + 3)(−4 + 7) = −1 × 3 = −3 iii (−8 + 3)(−8 + 7) = −5 × −1 = 5 b when x = −7 answer is zero c −3 > x > −7 12 x = __ 2 , y = __ 1 3 4 39 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Chapter 15 Exercise 15.1 1 1 cm 0.5 cm 0.5 cm 0.5 cm 0.5 cm 0.4 cm 2 3.3 cm 2.1 cm 5.4 cm 5.4 cm 5.4 cm 3.3 cm 3 a i 100 mm iii 250 mm b 1 : 200 ii iv 200 mm 125 mm 4 a c b d 10 metres 2 metres 5 13 mm or 1.3 cm 6 0.32 mm ii 333° ± 1° b 036° ± 1° 16 metres 12.4 metres Exercise 15.2 1 a b c B i 115° ± 1° 022° ± 1° 2 329° ± 1° 3 a 4 6 km 200 metres Exercise 15.3 1 Triangle Hypotenuse Opposite u Adjacent u ABC AB BC AC DEF DF EF DE XYZ XZ XY YZ 2 40 a b c d e f i sin u 0.6 0.385 0.814 0.96 0.471 0.6 ii cos u 0.8 0.923 0.581 0.28 0.882 0.8 iii tan u 0.75 0.417 1.400 3.429 0.533 0.75 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK 3 a d g 0.743 0.416 0.185 a c e 5.75 cm 7.27 metres 61.44 cm 5 a d 32° 39° b e 12° 73° c f 44° 50° 6 a d 36.9° 66.0° b e 23.2° 68.0° c f 45.6° 9.6° 4 b e h c f 0.978 0.839 0.993 b d f 2.605 0.839 26.26 mm 7.56 cm 7.47 metres Exercise 15.4 1 2 3 √ 2 + 2 √ 4 √ 3 3 d _________ e ____ f 2 3 1 b __ 1 c a __ 4 3 d 0 √ 3 a √ 3 3 1 __ __ LHS = __ 1 + ( ___ ) = + 1 _ b _ e (2) 2 √ 3 _ c f 1 _ 2 2 1 a c e cos 88° sin 121° −cos 45° 2 a d 135° 630° 3 a b c d e f g h i j k l x = 108° or 288° x = 60° or 120° x = 135° or 225° x = 120° or 300° x = 180° x = 90° or 270° x = 98° or 278° x = 40°, 80°, 160°, 200°, 280° or 320° x = 120° or 240° x = 60° or 300° x = 49° or 131° (nearest degree) x = 60° or 300° 4 a b 10°, 50°, 130°, 170°, 250° or 290° 90°, 210° or 330° _ _ √ 2 + 1 ___ 2 1 1 __ 2 __ 1 2 a Exercise 15.6 4 _ 4 = 1 = RHS b d f b e 240° 300° −cos 140° sin 99° −cos 150° c f 235° 350° Exercise 15.7 _ √ 3 _ ___ _ √ 3 __ 2 = ___ × 2 = √ 3 ; b LHS = ___ 2 1 __ 1 2 __ RHS = √3 , so LHS = RHS. 1 sin Q _____ sin R sin P _____ _____ = = 2 a x = 10.46 cm b x = 8.915 cm 3 a c e g i k m o x = 9.899 cm x = 5.477 cm x = 328.3 mm x = 14.51 cm x = 10.95 cm x = 108.1° x = 22.19° x = 7.756 cm b d f h j l n p x = 11.20 cm x = 106.6° x = 134.5° x = 136.1 mm x = 61.50° x = 4.396 metres x = 17.28 cm x = 23.45° 4 a b x = 74.6° or x = 105.4° x = 47.0° or x = 133.0° 5 a b QP = 8.401 metres QS = 7.928 metres 6 x = 1081 cm 10 1.14 metres 7 AB = DC = 19.8 m, AD = BC = 7.7m 11 4.86 metres 8 139 metres 9 22 cm Exercise 15.5 1 a 2 6.06 metres 3 16.62 cm 4 9 + 4√ 3 metres 5 52.43 km 6 a 7 185 metres 8 a 9 50.3° 15.08 metres b 30.16 cm _ 1689 metres 64.2° b b 975 metres 4.36 metres p q r 10 0° − 20° 41 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Exercise 15.8 1 a c 5.85 cm2 25.82 cm2 b d 18.21 cm2 41.93 cm2 2 a 106.5 cm2 b 2226.43 cm2 3 65.0 cm2 3 a 150° 4 a b c d e f g h i j x = 30° or x = 150° x = 120° or x = 240° x = 44.4° or x = 135.6° x = 60° or x = 240° x = 210° or x = 330° x = 30° or x = 60° or x = 210° or x = 240° x = 30° or x = 210° x = 135° or x = 225° x = 45° or x = 225° x = 40° or x = 80° or x = 160° or x = 200° or x = 280° or x = 320° 5 a b c x = 190° or x = 310° x = 56.3° or x = 236.3° x = 72.2° or x = 117.8° or x = 297.8° or x = 252.2° 6 approximately equal to 16 metres Exercise 15.9 1 24.22 cm 2 DB = 37.30 metres tall 3 a b 4 a CD = 74.69 metres Area ACD = 1941.52 m2 In triangle AFB: FB 2 = h2 + w2 (Pythagoras’ theorem) FB = DB (diagonals of congruent rectangles) FD2 = FE 2 + ED2 = w2 + w2 = 2w2 So using the Cosine rule lookout (L) 2(w 2 + h 2) − 2w 2 cos u = ________________ 2(w 2 + h 2) h 2 = ________ 2 w + h 2 b 50° u = 50.21° Lines drawn accurately to the following lengths: a 1 cm b 2 cm c 3.4 cm d 1.4 cm e 3.6 cm f 1.8 cm 2 (v) (i) N (iv) 160° 25 m Review exercise 1 b control tower (ii) base of lookout (B) 7 5m swimmer (W) shark (S) RS = 591 metres cos 60° + sin 30° = __ 1 + __ 1 = 1 2 2 _ _ √ √ 3 √_ 3 ___ ___ = 3 b cos 30° + sin 60° = + 2 2 _ 2 2 3 1 + √___ c (sin 30°)2 + (cos 30°)2 = ( __ ( 2) 2) 3 1 + __ = __ = 1 4 4 9 a 2 metres b Greatest depth: noon and midnight Empty: 6.00 p.m. c Between noon and 2.00 p.m. and from 10.00 p.m. onwards (to 2.00 a.m. the next day). 8 a 10 AB = 9.90 cm, AC = 5.43 cm 11 E = 22.2°, F = 34.8°, DE = 89.2 mm (iii) 200 km 42 12 31.37 km 13 a 869 mm2 b 585 mm2 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK 14 54 metres 15 10.2 cm 43 16 a c 5.19 metres 5.52 metres b d 17 a b 9.28 km (three significant figures) 268.0° (one decimal place) 18 a b A = 150° B = 190° A = 134.730 km, B = 153.209 km 62.0° 6.38 metres Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Chapter 16 Exercise 16.1 Review exercise 1 1 a 2 a a b c d e 2 a d e student’s own line (line should go close to (160, 4.2) and (175, 5.55)); answers (b) and (c) depend on student’s best fit line approximately equal to 4.7 metres Between 175 cm and 185 cm. This is not a reliable prediction because 6.07 metres is beyond the range of the given data. fairly weak positive taller athletes can generally jump further a distance (metres) b c 3 A strong negative correlation. The more hours of watching TV, the less the test score. A strong positive correlation. The longer the length of arm, the higher the bowling speed. Zero correlation. The month of birth has no effect on mass. A strong negative correlation. The more cigarettes smoked daily, the less the length of life. A fairly strong positive correlation. Usually the taller one is, the bigger the shoe size. b 600 b c d e 3 a b There a strong negative correlation at first, but this becomes weaker as the cars get older. approximately equal to 3 years It stabilises around the $6000 level. 2−3 years $5000−$9000 This is not very reliable as there is limited data from only one dealership. There is no correlation. As one variable increases (x), there is no increase or decrease in the other variable. There is no correlation. As one variable increases ( y), there is no increase or decrease in the other variable. d 500 Distance (m) the number of accidents at different speeds b average speed c answers to (c) depend on student’s best fit line i approximately equal to 35 accidents ii , 45 km/h d strong positive e There are more accidents when vehicles are travelling at a higher average speed. 400 300 200 100 0 c e f g 44 0 6 8 10 12 14 16 Age (years) weak positive 12 years old Not very reliable because correlation is very weak and beyond the range of the data 600 metres Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Chapter 17 Exercise 17.1 Review exercise 1 $19.26 1 a 12 h b 40 h c 2 $25 560 2 a $1190 b $1386 c 3 a c $930.75 $765 b d $1083.75 $1179.38 3 a $62 808 b $4149.02 4 a $1203.40 b $830.72 4 Student’s own graph showing values: 5 $542.75 6 a $625 b c $25 Years $506.50 Exercise 17.2 300 300 5 1500 1592.74 10 3000 3439.16 A comment such as, the amount of compound interest increases faster than the simple interest 2 5 years 5 $862.50 3 2.8% 6 $2678.57 4 $2800 more 7 a $1335, $2225 5 $2281 more 6 a d b c $1950, $3250 $18 000, $30 000 8 a $4818 9 $425 7 $562.75 8 a $2000 b e b $160 $343.75 $187.73 $346.08 c 1 a d $7.50 $574.55 b e Simple interest Compound interest 1 $7.50 $448 c $210 $225.75 $9000 b 120% 10 $272.73 1 %, year 3: 50% 9 Year 1: 25%, year 2: 33 __ 3 10 a $184 000 b $117 760 11 $43.36 (each) 11 a b 160 mg (50% of original amount) 35.4% of original amount 13 161 12 a c $2.04x $200 000 b 25 __ 1 h 2 $1232 12 $204 14 326.84 hPa (using power 8.849 in formula) $3.1216x Exercise 17.3 45 1 $64.41 2 a $179.10 b $40.04 c $963.90 3 a d $100 $900 b $200 c $340 4 $300 5 $500 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Chapter 18 Exercise 18.1 1 a b c x −6 −4 −3 −2 −1 0 1 2 3 y −33 −22 −13 −6 −1 2 3 2 −1 −6 x −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 y 50 37 26 17 10 5 2 1 2 5 10 17 26 x −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 y 4 1 0 1 4 9 16 25 36 49 64 81 100 −5 50 iii b i ii iii (−1, 8) x = −4 and x = 0 x = −2 (−2, 4) 40 4 80 70 60 30 20 10 0 −6 −5 −4 −3 −2 −1 −10 1 2 3 4 5 6x a b c d e y = 3(x + 1)2 + 0 (0, 3) x = −1, vertex (−1, 0) (−1, 0) axis of symmetry x = −1 y −20 y = 3x2 + 6x + 3 −30 (a) (0, 3) y-intercept −40 2 a 6 −13 −22 −33 x = −3 or x = 1 x = −1 90 (c) 5 3 a i ii y 100 (b) 4 y x-intercept −1 turning point, (−1, 0) minimum y = x2 − 4x + 3 3 5 a y y= 0 1 3 −1 46 1 2 1 x − 2 2 x −1 b y = −1 [when x = 2] c x=2 x 0 0 1 x −1 2 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK b e y y =−2x2 + 8 y 5 8 4 3 0 −2 x 2 2 1 y = x2 − x + 1 −2 c y y= f 1 2 x +2 2 −1 0 1 2 3x y 5 4 3 2 2 x 0 1 0 d y −1 6 −2 4 6 2 −4 −2 0 −2 2 4 6 8 x a b c d e 5x y = x2 − x + 1 8 metres 2 seconds 6 metres just short of 4 seconds 3 seconds −4 −6 −8 y = −x + 4x + 1 2 −10 −12 47 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Exercise 18.2 1 a x 2 y = __ x −5 −4 −0.4 −3 −0.5 −0.67 −2 −1 1 2 3 4 5 −1 −2 2 1 0.67 0.5 0.4 y 2.0 1.5 1.0 y= 0.5 −5 −4 −3 −2 −1 0 −0.5 1 2 3 2 x 4 5x −1.0 −1.5 b −2.0 x −5 −4 −3 −2 −1 1 xy = −1 0.2 0.25 0.33 0.5 1 −1 2 3 4 5 −0.5 −0.33 −0.25 −0.2 y 1.0 0.8 0.6 0.4 0.2 −5 −4 −3 −2 −1 0 −0.2 1 2 3 4 5x −0.4 −0.6 −0.8 xy = −1 −1.0 c x −5 −4 −3 −2 −1 1 2 3 4 5 4 y = __ x + 2 1.2 1 0.67 0 −2 6 4 3.33 3 2.8 y 7 6 5 4 y= x+2 4 3 y=2 2 1 −5 −4 −3 −2 −1 0 −1 48 1 2 3 4 5x −2 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK d x −5 9 y = − __ x − 3 −4 −3 −2 −1 1 2 3 0 1.5 6 −12 −7.5 −6 −1.2 −0.75 4 5 −5.25 −4.8 y 6 y =− 9 −3 5 x 4 3 2 1 −8 −7 −6 −5 −4 −3 −2 −1 0 −1 1 −2 2 3 4 5 6 7 8x y = −3 −3 −4 −5 −6 −7 −8 −9 −10 −11 −12 2 a y 3 y=1 −4 −2 b 1 y= x+1 2 1 0 −1 y 3 2 1 c −2 y 4 2 −3 −2 −1 0 −2 1 +1 x y=1 y =− 2 −4 4x 0 −1 2 4x 2 y= x−1 1 2 3x −4 y = −3 −6 −8 −10 49 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK 3 a Length 1 2 3 4 6 8 12 24 Width 24 12 8 6 4 3 2 1 Width (m) b c d 24 22 20 18 16 14 12 10 8 6 4 2 0 b i ii iii y x 0 2 4 6 8 10 12 14 16 18 20 22 24 Length (m) The curve represents all the possible measurements for the rectangle with an area of 24 m2 approximately equal to 3.4 metres Exercise 18.3 1 2 a b c a a&c y y = x2 − x − 6 (iii) y = 6 (ii) y = 0 x 1 2 3 4 5 (i) y = –6 y 12 10 y 14 y = x2 − x − 6 13 12 11 10 9 8 7 6 5 4 3 2 1 x 0 −5−4−3−2−1 −2 −3 −4 −5 −6 −7 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 −4 −2−1 −2 −3 −4 −5 −6 −7 −8 3 x = 1, x = 3 x = 0, x = 4 x = 4.2, x = −0.2 x = 1, x = 0 x = 3, x = −2 x = 4, x = −3 8 y = 2x2 + x − 3 6 4 y = 2x + 1 2 −3 −2 −1 0 1 2x 1 2 3 4 5 2 4 b x = 1 and x = −1.5 (answers within the range of −1.5 to − 1.6 are acceptable) d (1.7, 4.4) and (−1.2, −1.4) (1 dp) e At the points of intersection, the two equations are equal, so: 2x2 + x − 3 = 2x + 1 If you rearrange this equation, you get 2x2 − x − 4 = 0. 50 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK 4 a&b 6 y 12 y = 3x − 5 and x2 + y2 = 5 Substituting x = 2 and y = 1 shows point of intersection at (2, 1) Substituting x = 1 and y = −2 shows point of intersection at (1, −2) 10 y = x2 = 2x + 3 8 Exercise 18.5 1 6 a y 8 y = x3 6 4 4 2 2 −2 −1 0 −2 −3 −2 −1 0 1 2 3 1 2x −6 −8 b 4 2x −4 y = −2x + 5 2 c 4x 1 y 8 6 ±1.41 4 Exercise 18.4 2 1 a b 2 x = 1, y = 0 or x = 3.5, y = 1.25 (1, −4) and (2, −5) x = 1, y = −4 and x = 2, y = −5 3 −6 c 2 y=x+2 6 4 −2 −1 −0.4 −0.6 1x x = −0.4, y = 1.6 and x = −2.6, y = −0.6 51 12 8 1 5 y = 2x3 10 −1.6 −2.6 a b c d y 16 14 1 4 y = −x3 −8 3 −3 −4 y 4 y = x2 + 4x + 3 −4 −2 −1 0 −2 (−0.5, 3.25) and (6, 0) (−3, −8) and (2, −3) (−5, 4) and (−2, −2) (3, 4) and (4, 3) x = −2 or x = 1; y = −4 or y = 5, points of intersection are (−2, −4) and (1, 5) 2 −2 −1 0 −2 1 2x −4 −6 −8 −10 −12 −14 −16 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK 2 a x y −2.5 −2 −1.5 −1 −36.875 −18 −4.625 b 50 4 −0.5 0 0.5 8.625 10 8.875 y 1 6 5 1.5 a&b i x 1 2 3 4 5 300 Number of organisms 20 −4 −3 −2 −1 0 −10 6 −20 −30 −40 y = x3 − 5x2 + 10 c i ii iii 3 −50 b ii c i ii y y = 2−x 3 4 5 6 −6 10 46 y y = 3x 250 200 150 100 50 y = 12x + 1 −1 0 x = −1.3, 1.8 or 4.5 x = 0 or 5 x = −1.6, 2.1 or 4.5 a–d 2.5 2.125 −2 −5.62 −8 40 30 10 2 1 2 3 4 Time (hours) 5 x 6 12 per hour approximately equal to 3.4 hours approximately equal to 42 Exercise 18.6 y = 2x + 1 1 y = 2x a b approximately equal to −4 approximately equal to 12 2 y 6 2 y = x2 − 2x − 5 4 1 2 x −4 −1 −2 0 2 4 6x −2 y = −2x −4 −6 a i 4 ii −6 b x = 3.8, x = −1.8 (one decimal place) 4 y 3 y = 4x − 5 y = −2x3 + 2 2 0 52 1 x Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Exercise 18.7 1 a c e g i Review exercise 3x2 6 6x 6x2 + 4 4x3 − 6x2 b d f h j −4x −2 −x 15 − 12x 6x2 − 12x k 6x − 10 l 2 a x = 1, x = −1 b 9 _____1 + 2 4x 4 x=2 3 a (−1, 1) b y = −8x − 7 4 y 2 1.5 1 1 a x −1 −0.5 0 0.5 x3 −1 −0.125 0 0.125 2x −2 −1 0 1 y = x3 − 2x 1 0.875 0 −0.875 x 1 1.5 2 2.5 x3 1 3.375 8 15.625 2x 2 3 4 5 y = x3 − 2x −1 0.375 4 10.625 y 11 0.5 0 −1 −0.5 −0.5 0.5 10 1 9 8 −1 a(__ 1 , −1)(− __ 1 , 1) b 2 2 7 y = 9x − 8 6 Local max. = 1 at x = − __ 1 2 1 __ Local min. = −1 at x = 2 5 5 1 c a y 4 4 3 2 y = x3 − 3x3 0 −2 −1 −1 3 2 1 (0, 0) −3 −2 −1 0 −1 1 (3, 0) 2 3 4 5x −2 −3 −4 b (2, −4) y 4 3 y = x(x − 1)(x + 1) 2 (−0.58, 0.38) 1 (−1, 0) (0, 0) (1, 0) −3 −2 −1 0 1 2 3 4x −1 (0.58, −0.38) −2 −3 −4 53 1 2 3x −2 b x −1 −0.5 0 0.5 x2 1 0.25 0 0.25 1 __ x −1 −2 − 2 1 y = 2 + x2 − __ x 4 4.25 − 0.25 x 1 1.5 2 2.5 x2 1 2.25 4 6.25 __ 1 x 1 0.67 0.5 0.4 1 y = 2 + x2 − __ x 2 3.58 5.5 7.85 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK 4 y 10 a y y=x+2 9 6 8 4 7 2 6 5 −4 4 −2 4 2 x −2 3 2 1 −1 2 a b 0 y= −x2 c y = __ 4 x 3 1 2 +1 y 4 y =− x 3x b y= d xy = −6 2−x −4 −6 −2 A: y = x + 2 B: y = −2x + 10 8 C: y = __ x or xy = 8. b i x = 2, y = 4 and x = −4, y = −2 ii x = 1, y = 8 and x = 4, y = 2 c x 6 y 8 Substitute x and y coordinates of each point of intersection into the original equations: y = −2x + 10 (4, 2): 2 = −2(4) + 10 2 = −8 + 10 = 2 LHS = RHS (1, 8): 8 = −2(1) + 10 8 = −2 + 10 = 8 LHS = RHS 8 y = __ x , so xy = 8 y = 3x 6 4 (1, 3) 2 (0, 1) −2 −1 2 1 d x y y = −x2 + 3 3 2 1 −2 –√3 −1 √3 1 2 x −1 (4, 2): 5 a&b y=x 2 1 × 8 = 8, so RHS = LHS d 4 −5 c 4 × 2 = 8, so RHS = LHS 2 (2, −2) a (1, 8): 5 (−2, 2) y 4 2 y=0 −3 −2 −1 y = 2x = 1 0 1 2x −2 −4 54 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK c d 6 e x=1 It is the tangent to the curve at the point (1,1). 2 a (0, 1) Many possibilities, for example ( 1, __ 1 ) 2 1 __ and ( 2, ) 4 c Decreasing because for larger x-values the y-values are decreasing and the graph slopes down to the right. d y = 2x b 7 a y 3 2 y = 2x − 1 1 −4 −3 −2 −1 0 −1 2 y= x−1 −2 −3 −4 b c 55 x = 1 and x = −1 1.5 units 1 2 3 4x 8 2x + 6 9 −3 10 a b y = 1 and gradient = 2 y = −5 and gradient = 4 11 a local maxima – the maximum height of the rocket b (1.4, 12.8), maximum height reached is 12.8 m after 1.4 s c minimum height, h is 0, maximum h is 12.8 minimum time, t is 0, maximum t is 2.8 dy 12 a ___ = −6x 2 + 6x + 12 dx b (−1, −7) and (2, 20) c (−1, −7) is a minimum, (2, 20) is a maximum 13 Differentiate and set equal to 0 to get t2 − 5t + 4 = 0, so t = 1 and t = 4 are the turning points. t = 1 is a local maximum, t = 4 is a local minimum, so substitute t = 1 into equation to get max level is 51.83 metres Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Chapter 19 Exercise 19.1 1 a A B 2 C D E F G 3 A = 0, B = 3, C = 4, D = 4, E = 5, F = 2, G = 2, H = 2 2 a b 2, student’s diagram 2 3 Student’s own diagrams but as an example: 2 Infinite number corresponding to the number of diameters of the sphere a 4 b 3 c 1 d infinite e 4 f 8 a Shape A has a limited order of rotational symmetry (order 4) about a vertical and horizontal axis (order 2) because it has vertices, it also has only five planes of symmetry. Shapes B and C have an infinite order of rotational symmetry about a vertical axis and none about a horizontal axis. This means they also have an infinite number of vertical planes of symmetry and no horizontal ones. Answers will vary, but can only involve shapes based on circles. For example: b H has no lines of symmetry b g h Exercise 19.3 a b c d e f 56 a 7.75 cm b 13.9 cm 2 a x = 25° b x = 160°, y = 20° 3 6.5 cm 4 a b 177.72 cm 49.07 cm c 25.4 mm Exercise 19.4 Exercise 19.2 1 1 3 4 Infinite number corresponding to the number of diameters of the circle face (+1 parallel to the circular face) Infinite number correponding to the number of diameters of the circle face 2 3 (all dimensions different), 5 (two dimensions equal) or 9 (3 dimensions equal) 1 144° 2 a b c d 15° (isosceles triangle) 150° (angles in a triangle) 35° (angle MON = 80°, and triangle MNO in isosceles, so angle NMO = angle MNO = 50°, so angle MNP = 35°) 105° (angle PON = 210° so angle PMN = 105° − half the angle at the centre) Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK 3 a b c 55° (angles in same segment) 110° (angle at centre twice angle at circumference) 25° (angle ABD = angle ACD, opposite angles of intersecting lines AC and BD, so third angle same) 3 a c true false 4 a x = (w + z) = 90° (angle in semicircle) so AB // DC, z = 28° (alt) and and w = 62° (base angle isosceles triangle, alt), y = 62° (angles in a triangle) x = 100° (reflex angle ADB = 200°, angle at circumference = half angle at centre) x = 29° (angle ADB is angle in a semicircle so angle BDC = 90°, then angles in a triangle) x = 120° (angle at centre), y = 30° (base angle isosceles triangle) angle QPR = 39° (alternate segment theorem), therefore x = 180 − (39 + 66) = 75° (angle sum of triangle) angle OTB = 90° (tangent and radius), angle CTO = 60° (90° − 30°), angle OCT = 60° (isosceles triangle), angle BCT = 120° (angles on straight line), so x = 30° (angles in triangle) angle at circumference = 180° − 108° = 78°, so x = 156° (angle at centre) angle QLN = 78° (alternate angles), so x = 78° (alternate segment) 4 angle DAB = 65°, angle ADC = 115°, angle DCB = 115°, angle CBA = 65° b 5 35° c 6 59.5° 7 a 22° b 116° c 42° 8 a 56° b 68° c 52° 9 a angle NDF = 40° (alternate segment theorem) angle NEF = 40° (alternate segment theorem) angle DNF = 90° (angle in a semicircle), so angle DFN = 180° − (90° + 40°) = 50° (angle sum of triangle) b c d e f g Review exercise 1 2 57 a b c d e i i i i i a b c d a hexagonal prism the axis of rotational symmetry 6 7 1 1 4 8 1 ii ii ii ii ii none none four eight none h 5 a b b d true true x = 7.5 cm, y = 19.5 cm x = 277.3 mm, y = 250 mm Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Chapter 20 Exercise 20.1 Frequency density 1 2 y 1.0 a b c d 166 cm Q1 = 156.5, Q3 = 176 19.5 12.5% 0.5 Review exercise 0 0 10 20 30 40 50 60 70 80 90 100 x 1 a Time (t) in minutes Frequency 125 < t < 140 6 140 , t < 160 16 160 , t < 170 28 170 , t < 195 35 195 , t < 235 8 235 , t < 285 5 Mass (in grams) a b c 3 Eight students 4 P(,5 km) = 0.70 Frequency density 2.5 a b 2.0 1.5 c 1.0 2 0.5 0 4 Ages of internet cafe users y 3.0 b 300 Number of students a b c d e 58 a 15 20 25 30 35 40 45 50 55 x Age (years) 240 c 100 Exercise 20.2 1 Slowest is 285 minutes and fastest is 125 minutes. Approximately 50 runners 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 0 b y Seconds Frequency 1 < t < 21 8 21 , t < 31 10 31 , t < 41 9 41 , t < 46 3 21 < t , 31 c Seconds Frequency Frequency density 1 < t , 21 8 0.4 21 , t < 31 10 P60 31 , t < 41 9 0.9 Q2 41 , t < 46 3 0.6 P80 Q3 Q1 x 0 10 20 30 40 50 60 70 80 90 100 Percentage Median = 57%, Q1 = 49% and Q3 = 65% IQR = 16 91% 60% of students scored 59 or less; 80% of the students scored 67 or less. Frequency density 2 1 Histogram to show how long Sandra’s classmates can hold their breath y 1.0 0.8 0.6 0.4 0.2 0 0 5 10 15 20 25 30 35 40 45 50 x Time (seconds) Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK 3 a Mass 0,m,3 Cumulative frequency b 3 < m , 3.5 3.5 < m , 4 4 < m , 4.5 4.5 < m , 6 8 57 92 99 100 y 100 90 Cumulative frequency 80 70 60 50 40 30 20 10 0 c i iii v 4 a 0 1 2 3 4 Mass of baby (kg) ii iv 3.4 kg 0.5 kg 3.8 kg 6x 5 3.7 kg 43 6.5 cm b Cumulative frequency of plant heights Cumulative frequency y 30 20 Q3 10 Q2 Q1 0 0 1 2 3 4 5 6 7 8 9 10 11 12 x Height (cm) median height = 6.8 cm c d 59 IQR = 8.3 − 4.7 = 3.6 13.33% Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK 5 Frequency density 0 , x < 10 3 10 , x < 15 9 15 , x < 25 4.1 25 , x < 30 6.6 30 , x < 40 2.5 Histogram to show the distribution of swimming times y 10 Frequency density Swimming time (x minutes) 5 0 0 5 10 15 20 25 30 35 40 x Time (minutes) 60 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Chapter 21 Exercise 21.1 1 2 10 a a c e 3:4 7:8 1:4 b d f 6:1 1:5 31 : 50 : 45 a c e g i k x=9 x = 16 x=4 x = 1.875 x=7 x = 6, y = 30 b d f h j l x=4 x=3 x = 1.14 x = 2.67 x = 13.33 x = 3, y = 24 3 60 cm and 100 cm 4 a b c 20 ml oil and 30 ml vinegar 240 ml oil and 360 ml vinegar 300 ml oil and 450 ml vinegar 5 60°, 30° and 90° 6 810 mg Exercise 21.2 1 a 1 : 2.25 b 1 : 3.25 c 1 : 1.8 2 a 1.5 : 1 b 5:1 c 5:1 3 240 km 4 30 metres 5 a 6 1 cm : 90 km 7 a 5 cm b 3.5 cm b A is 6 metres (6000 mm acceptable) B is 12 metres (12 000 mm acceptable) C is 15.75 metres (15 750 mm acceptable) 61 8 a b c 4:1 14.8 cm 120 mm or 12 cm 9 a b 3.5 : 1 = 7 : 2 2.14 cm b 1120 cm2 c 4:1 Exercise 21.3 1 25.64 litres (2 d.p.) 2 11.5 kilometres per litre 3 a b c 78.4 km/h 520 km/h 240 km/h (or 4 km/minute) 4 a c 5h 40 h b d 9 h 28 min 4.29 min 5 a c 150 km 3.75 km b d 300 km 18 km 6 167 seconds or 2.78 minutes 7 15.658 g/cm3 (three d.p.) 8 60 000 N/m2 Exercise 21.4 1 i 100 km ii 200 km a iii 300 km b 100 km/h d 250 km 2 A is 8 mm B is 16 mm C is 21 mm 280 cm2 a b c c e vehicle stopped 125 km/h 2 hours 190 min = 3 h 10 min 120 km/h d i 120 km ii 80 km e 48 km/h f 40 min g 50 min h 53.3 − 48 = 5.3 km/h i Pam 12 noon, Dabilo 11.30 a.m. Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Exercise 21.6 3 a i 40 km/h ii 120 km/h b 3.5 min c 1200 km/h2 d 6 km a i y ∝ x 2 ii y = kx2 b i y ∝ ___ 12 x ii k y = ___2 x c i m ∝ T ii m = kT d i ii e i 1 A ∝ ___ M 1 y ∝ ___ x 3 k A = ___ M k y = ___3 x 2 a k=7 3 m Ratio of m to T is constant, __ = 0.4587, T so m varies directly with T 4 4 a 3 5 4 a = 2, b = 8, c = __ 3 a y=2 1 4 a c 0−30 s, 0.83 m/s2 90 km/h 5 a Speed changes from 0 m/s to 3.5 m/s over a period of 10 seconds. 17.5 metres 0.35 m/s2 b c a after 70 s, 0.5 m/s2 2 km y 5 Velocity (m/s) 6 b d 2 a b c b m = 4.5 b x = 0.5 b y = 1250 7 a = 17 __ 9 x=2 0 7 a c y= x=9 8 a b c y√ x = 80 y=8 x = 15.49 9 a b = 40 b 10 a y = 2.5 b 11 a xy = 18 for all cases, so relationship is inversely proportional 18 xy = 18 or y = ___ x y = 36 0 10 20 30 40 0.33 m/s approximately equal to 17 metres Yes, __ A = ____ 1 B 150 8 No, ___ is not = __ 1 2 15 10 A = ___ Yes, __ B 1 $175 b 50 x b c 2x2 __ 2 a 3 $12.50 4 60 metres 5 a c 75 km 3 h 20 min b 375 km 1 a b 6 a 15 litres b 540 km 2 1 : 50 7 a inversely proportional 3 x = 6 or x = −6 b 2 __ 1 days 2 1 __ ii day 2 12 days 4 a b i 85 km i 0.35 h 5 a b c d e 150 km after two hours; stopped for one hour 100 km/h 100 km/h 500 km $250 8 a 9 5 h 30 min 12 8192 Review exercise i 10 1200 km/h 62 F = 40 a = 84 6 Exercise 21.5 1 b 1 Time (s) b c ii b 5 days 90 mm, 150 mm and 120 mm Yes, (150)2 = (90)2 + (120)2 ii 382.5 km ii 4.7 h iii iii 21.25 km 1.18 h Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK 6 a c 7 4.5 min 8 187.5 g 20 seconds 200 metres b d 2 m/s2 100 metres k k y ∝ ___ 13 , so y = ___ 3 and 1728 = ___ 3 , so k = 1728 x x 1 1728 Substitute x = 4 into y = _____ 3 to give x 1728 1728 = 27 y = _____ 3 = _____ 64 4 k 10 a P = __ v or PV = k b P = 80 11 a F = 0.02125 v2 b 200 m/s 9 63 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Chapter 22 _ Exercise 22.1 3 b y − 2 a 3 V a I = __ R b l = g(___ T ) 2π b 20 amps 2 1 a c x−4 A = x2 − 4x 2 a S = 5x + 2 3 a c x+2 S = 3x − 1 4 80 silver cars, 8 red cars 5 father = 35, mother = 33 and Nadira = 10 6 X cost 90c, Y cost $1.80 and Z cost 30c Exercise 22.3 7 9 years 1 8 97 tickets a c 11 5 9 x + y = 112 and x − y = 22 2 a b i 17 ii 53 iii 113 f(2) + f(4) = 17 + 53 = 70 ≠ f(6) which is = 113 P = 4x − 8 5x + 2 b M = ______ 3 b x−3 4 10 x + (x − 5) = 30, so 2x = 35 Length = 17.5 metres and width = 12.5 metres 11 x = 13 and y = 2 12 6 and 8 13 −9, −8 or 8, 9 √ __ 5 a r = __ A π (note, radius cannot be negative) b r = 5.64 mm 6 9 a F = __ C + 32 5 c 323 K x = 67 and y = 45 b d b 80.6 °F −1 2m + 5 c i 3a2 + 5 ii 3b2 + 5 iii 3(a + b)2 + 5 d a = ±3 3 a h(1) = ±2 b h(−4) = ±3 4 a 4(x − 5) b 4x − 5 15 0.98 metres 5 18 16 b2 + 25b = 2000. Using the quadratic formula, b = 339 or −589, but as this is a length, −589 is an impossible answer, so the width is 339 mm. 6 a f−1(x) = x − 4 b f−1(x) = x + 9 x f−1(x) = __ 5 f−1(x) = −2x 14 17 cm (x = 8, x cannot be 0 as it’s the length of a side) 1 2ab − P a h = ________ 2a 2y c h = _____ 1−y 2 a a b = ______ 1 − 2a 3p c q = _____ p−1 6n + 1 e m = ______ 5 c d Exercise 22.2 64 √ x = ______ S − πr 2 b h = _______ πr E − __ 1 mv 2 2 dh = __________ mg 2m bn = ______ 1−m d a = 2x − 3y x a __ − 3 2 d 2x + 3 e 8 a b 9 a 3√ x +1 +1 7 b x _ x−3 ____ 2 2x + 3 c 2(x + 3) f 2(x + 3) x+1 _____ x−1 c 9 __ 7 _ b 1 ± √ 5 x = ______ 2 a 2 fy = _____ a−b Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK c 5 a (2x + 1)(x − 3) = 60 2x2 − 6x + x − 3 = 60 g−1(x) = x2−1 y 2x2 − 5x − 63 = 0 b Sides are 4 metres and 15 metres. c y = x2 −1 d y = x + 1 for x > −1 1 0 −1 x 1 −1 d Note that the curves are symmetrical about y = x when x > 0 for y = x2 − 1 _____ and x > − 1 for y = √ x + 1 . Solve simultaneously: 3a + 2 = 2b − a and 2b − a = b + 3. Side length are 8 cm (a = 2 and b = 5), so perimeter = 24 cm. 7 4.00 p.m. 8 80 km 9 a b = ±√ a 2 + 2ac _ 9a − 26 b b = ______ 8 a 2 − 4 c b = _____ 17 10 a 2.07 b 2.43 11 15 12 96 km 10 a b c d e f x = −2 and x = −6 x . 1 and x , −1 −3 < x < 3 −2 , x , 3 −4 , x , 1.5 all values can be included 13 a 11 a a = 35, b = 80, c = 75 and d = 160 5 x f −1(x) = __ 8 5x + 3 14 f−1(x) = _____ 2 x−4 15 a f−1(x) = ____ 3 c a=6 e 37 b Review exercise 65 6 1 Four years 2 Sindi puts in $40, Jonas $20 and Mo $70 3 44 children 4 kiwi fruit = 40c and plum = 15c b c 16 a b Domain: {x: x is a real number} Range: { y: y is a real number} Domain: {x: x . 0 and x is a real number} Range: { y , 4 and y is a real number} Domain: {x: x is a real number} Range: { y: y is a real number and y ≠ 0} 5 i __ 3 x = −3 ii −5 b 3 d 9x + 16 iii 1 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Chapter 23 Exercise 23.1 1 5 A' B 10 B' 8 D C C' C'' A'' 10 A' 6 I'' 6 c ii 2 H c i 4 6K' 8 I x K J A y B b i C –8 S' –6 S'' X P 6 4 Q' Q 2 P'' R' –4 –2 0 –2 b ii Q'' –4 R'' –6 –8 66 7 J' 8 A P' A'' A: centre (0, 2), scale factor 2 B: centre (2, 0), scale factor 2 C: centre (−4, −7), scale factor 2 D: centre (9, −5), scale factor __ 1 4 a i F −8 3 x 10 A' −6 G K'' I' E −4 D 4 J'' C'4 H'' 2 B C F' G' b −10 −8 −6 −4 −2 0 D' E' −2 8 −10 8 B' B 6 −8 y 9 a A D'' 4 2 −6 B'' 2 2 −10 −8 −6 −4 −2 0 −2 C −4 (b) B'' 4 C'' D' D D'' A 6 (a) A y ii S R 2 4 6 A' a A 8 x A'' X B' C' A: y = 5 B: x = 0 C: y = −1.5 D: x = −6 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK b Exercise 23.2 i 1 B' a y A' B X B' ii B B x 1 2 3 4 5 –2 C'' –3 B'' –4 –5 –6 A'' –7 X i C' b C 2 rotation 180° about (0, 0) or enlargement scale factor −1, using (0, 0) as centre a y 10 X 8 ii C 6 C C'' A 2 −4 i b 3 D' B 4 X d C –5 –4 –3 –2 –1 0 B'' c A 7 6 5 4 3 C' 2 1 D a x 0 −2 2 4 6 8 enlargement scale factor 2, using (8, −1) as centre y 10 X 8 F' 6 B A 4 ii 2 X D'' D 0 b 67 D 0 C 2 x 4 6 8 10 rotation 180° about (4, 5) Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK 4 a b 2 Scale factor 3, centre of enlargement (−4, 1). Scale factor − __ 1 , centre of enlargement 2 (−1, 1). 5 B A 1 , centre of enlargement Scale factor − __ 2 (1, 2). c a b D y 6 C 4 C' c F 2 −8 −6 −4 A' −2 0 A' −2 −4 2 4 B 6 10 12 x B' 8 E C d 6 G y 5 4 H 3 S' R' 2 P 3 Q 1 Q' −4 P' −3 −2 −1 0 −1 1 −2 2 3 4 5 R S −3 ⟶ i AB = ( 5 ) 0 ⟶ iii AE = ( 0 ) −6 ⟶ 1 ) v DB = ( 6 ⟶ vii CD = ( −5 ) −6 b they are equal a 4 B (2 ) 3 D (−3 ) −3 E (9 ) 3 C ( 4 ) −3 a (−8 ) 16 b (2 ) 6 c ( 0) 12 d (−1 ) 7 e (−2 ) 1 f (−1 ) 4 g (−4 ) 18 h (−8 ) 22 i ( 0 ) −20 j ( 10 ) −16 Exercise 23.3 1 6 x A (8 ) 1 ⟶ BC = ( 4 ) 0 ⟶ iv BD = ( −1 ) −6 ⟶ vi EC = ( 9 ) 6 ⟶ viii BE = ( −5 ) −6 ii c (9 ) 0 d (−5 ) −6 e Yes 68 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK 5 6 a d g −a b 2b 2c e 2b b h −c b __ j + 3c 2 a–e student’s own diagrams 7 a c 6.40 cm 15 cm b d 7.28 cm 17.69 cm 8 a c 5.10 8.06 b d 5 9.22 9 a c f i −a + c 2c −7a + 7c A(−6, 2), B (−2, −4), C (5, 1) ⟶ b AB= ( 4 ) −6 ⟶ BC= ( 7 ) 5 ⟶ CA= ( −11 1 ) ⟶ 10 XZ = x + y ⟶ ZX= −x − y ⟶ __ MZ = x + y 2 11 a i x = (2 ) 7 −3 ii y = ( ) −3 iii z = ( 10) −4 b i ii iii 7.28 4.24 21.5 ⟶ 12 a i XY = b − a ⟶ 1 ii AD = __ (a + b) 2 ⟶ iii BC = 2(b − a) ⟶ ⟶ b XY = b − a and, BC = 2(b − a) so they are both multiples of (b − a), and hence ⟶ ⟶ parallel, and XY is half BC ⟶ 13 a MN = 4a + 6b ⟶ b MP = (2a + 3b) × 7 = 14a + 21b ⟶ 3 3 ⟶ __ 3 14 a AD = − __ a + __ b; OD = 1 a + __ b 2 4 2 4 ⟶ b OB = 2a + 3b ⟶ 1 ⟶ ⟶ OD = __ ( 2a + 3b)= __ 1 OB , so OD is 4 4 ⟶ parallel to OB , point O is common and the points must be on a line. Review exercise 1 a i ii iii reflect in the line x = −1 rotate 90° clockwise about the origin reflect in the line y = −1 b irotate 90° anti-clockwise about (0, 0) then translate ( −2 ) −1 ii reflect in the line y = −1 then translate (−8 ) 0 iii rotate 180° about origin then translate (6 ) 0 iv reflect in the line x = 0 ( y−axis) then translate ( 0 ) −2 2 y 5 4 D' G' 3 2 1 E' F' −5 −4 −3 −2 −10 1 2 3 4 5 F −2 G a&b −3 −4 D −5 −6 −7 G'' F'' E D'' 3 10 E'' y d B''' 8 B' A''' a 4 A' D''' C' −10 −8 B −6 D'−4 B9(−6, 6) B09(−1, 8) C''' D'''' −2 D'' −2 C'''' C A'' 2 −4 a c B''' A'''' 6 c x x 2 b 4 6 8 10 B'' C'' b d B0(6, −2) B00(3, 9) 15 28.3 (1 d.p.) 69 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK 4 iii y 5 F' 4 G' E' a b a b a−b 3 D' 2 D 1 −4 −3 −2 G −1 0 −1 1 2 3 4 5 x 6 iv E −2 −3 F −4 5 a b c (11, 5) (8, 4) (9, 8) (3, −2) (2, 1) (6, 0) (−3, −6) (−2, −3) (−6, −4) ( 0 ) −8 iv (12 ) 0 ( 6) 12 iii ( 1) 10 6 a b ii i i 2a + 3b ⟶ i ED = y ⟶ ii DE = −y ⟶ iii FB = x + y ⟶ iv EF = x − y ⟶ v FD = 2y − x 7 a 2a 8 b c b+c 70 b 4. 47 a c 26.4 14.9 b d 3.0 11.1 ⟶ i = −a + b AF ⟶ ii OE = −a + b ⟶ ⟶ ⟶ ⟶ + OD = −2a, BC = −a, b AD = AO ⟶ ⟶ so AD = 2 BC ⟶ 10 a OQ = 2a − 6b ⟶ b AB = 2b + a − 3b = a − b ⟶ BR = a − 3b + 2a = 3a − 3b ⟶ ⟶ ⟶ ⟶ So, BR = 3 AB , so BR and AB are parallel and they have a common point B, so ABR is a straight line and the points are collinear. 9 ii a a Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Chapter 24 Exercise 24.1 1 2 Card G B 1 2 2 3 4 1 2 3 0.4 0.6 7 11 1 6 1 b __ 4 71 1 2 T H 0.054 Green 4 11 Yellow 0.7 0.35 C 0.245 8 11 Green D 0.455 3 11 Yellow B 0.65 4 a First fruit Second fruit 4 15 Bus 4 15 0.9 Walk 1 3 0.1 Bus 5 16 7 16 1 2 H 1 2 1 2 T H 1 2 1 2 T H 1 2 T 1 c ___ 12 Plum Mango P 7 15 1 3 Banana 1 5 1 2 1 2 1 2 H 1 2 T T H M B P 6 15 4 15 1 4 Black T D 0.95 Yellow 1 2 1 2 H 0.18 Not Rain 1 3 T A Walk Blue 1 2 1 2 H 0.3 Rain 1 2 T 0.246 0.05 a 1 2 1 2 C Exercise 24.2 1 T H 0.82 Yellow 4 H 1 2 1 1 1 b __ c __ d __ 2 2 8 e 0, not possible on three coin tosses Green 1 3 1 2 T T a&b 2 3 1 2 1 2 G H A B C D E F 1 H H H T H T H T H T Y 3 1 2 Coin R 2 a M B P 7 15 M B 1 b ___ 12 5 d ___ 12 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Exercise 24.3 1 2 Even 3 M3 6 12 2, 4, 8, 10 3, 9 4 1, 5, 7, 11 1 a __ 2 2 2 b __ 3 a c __ 1 d 6 W __ 1 3 1 3 a __ 7 6 G 5 5 5 2 2 b __ c __ d __ 1 a __ 5 3 9 9 1 2 1 1 d ___ b ___ c ___ a ___ 45 30 15 15 8 7 3 e ___ f ___ g ___ 15 15 10 28 5 40 40 a ___ b ____ c ____ d ____ 17 153 153 153 e The four situations represent all the possible outcomes, so they must add up to one. b 0.1 Fail 0.8 0.9 Don’t fail 0.2 0.15 Fail A B 3 a i __ 4 5 1 ii __ 4 iii Science Museum 5 3 11 b 3 __ 11 ___ 20 London Eye 0.85 Don’t fail 3 P(B given it failed test) = ___ 11 5 __ 7 8 8 a Train Bus 130 20 10 10% 45% 30 20 30 b 30% Madame Tussauds 130 c 0 15% d 160 30 __ = 1 However, this is a small Yes, ____ 240 8 sample for a busy city like London and the answer can only apply to this group and not to tourists as a whole. 9 2 b ___ 11 c a 0.2 b 0.56 b e 10 a 2 __ 5 __ 2 7 0.35 Exercise 24.4 1 72 66 a ____ = 0.413 160 19 b ___ = 0.288 66 51 ___ c = 0.543 94 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023 CAMBRIDGE IGCSE™ MATHEMATICS: EXTENDED PRACTICE BOOK Review exercise 1 a&b 1 6 1 6 1 6 1 6 1 2 3 4 1 6 1 6 5 2 1 2 H 1 2 T 1 2 H 1 2 T 1 2 H 1 2 T 1 2 H 1 2 T 1 2 H 1 2 6 1 c __ 8 3 T 1 2 H 1 2 T 1 2 1 2 1 2 H 4 T H 5 1 2 T 1 2 1 2 1 2 H 1 2 T H 1 2 T 5 7 10c 5 5 =1 c 9 ___ 13 F 1 3 6 0 4 M b i ___ 2 15 ___ iii 2 15 1 6 a __ 6 10c 5 6 P 1 T H a&b 2 7 a 11 1 d ___ 12 5c b T H 1 2 1 2 1 2 1 6 4 ___ 13 1 b ___ 12 1 a ___ 52 5 a __ 8 4 8 ___ 15 3 __ iv 8 b __ 1 4 ii __ 1 7 3 5c 10c 5 1 c __ d ___ 7 21 e 1 (there are no 5c coins left) 73 Cambridge IGCSE™ Mathematics – Morrison © Cambridge University Press & Assessment 2023