Number and language. Accuracy. Cambridge IGCSE Mathematics Core and Extended Practice Book Answers. Exercises Exercises Exercise 1.

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1 Cambridge IGCSE Mathematics Core and Etended Practice Book Answers Number and language Eercises..,, (a),,,,,,,,,,,,,,,,,, (a) (a) (a) Eercise. (a) Rational Rational (c) Irrational (d) Rational (e) Rational (f) Irrational (g) Rational (a) Student s shapes e.g. cuboid, triangular prism, pramid (a) Student s shapes likel to include a circle/ semicircle (a) Student s shapes e.g. sphere, cone, clinder Eercises.. (a). (a) - Eercise. (a) m m m Accurac Eercises.. (a) (c) (a).. (c). (a). (c). Eercise. Answers ma var (a) cm² Eercise.. m.. (a).,..,. (c).,. (d).,. (e).,..,. ( d.p.) Eercise..,. km² (a).%,.% A percentage error of. out of is more significant than a percentage error of. out of. km,. km Eercise. (a).,..,. (c).,. (d)., (e).,. ( d.p.) Hodder & Stoughton Ltd

2 Cambridge IGCSE Mathematics Core and Etended Practice Book Answers Calculations and order Eercises... t..,.,.,.,.,. Eercises.. (a) (c) - (a) no brackets needed ( + ) =. (c) ( + ) =. Integers, fractions, decimals and percentages Eercises.. (a) (c). (a) (a) (a).. (c). (a) %. % (c). (d) % (e) i. i.% i (f).% Eercise. (a).. Eercises.. (a) (a) (a) - i.. Eercise. (a) - = Further percentages Eercises.. (a) % % (c).% (d).% (a) (c) (d) $ (e) $ (f) (a) % % (a) (i) (ii) % (i) (ii) % (c) (i) i (ii).% Ahmet = %, Jo = %, Anna = %.% ( d.p.) (a) $..% Eercise. (a) (c) (a) (c) (a) $ Eercise. (a) $ $ (c) % (d) % cm Hodder & Stoughton Ltd

3 Chapter Ratio and proportion Ratio and proportion Eercise. Eercises.. (a) (a) :. kg g cm and cm kg (c) (a) litres of petrol, litres of oil ml $, $, $, $ Speed (km/h). Time (h)... (a) (i) hrs (i) people hrs hours quicker Eercise. (a) (a).. (a) Eercise. (ii) hrs (ii) people cm : (a) (i) cm² (ii) cm² : (a) (i). cm³ (ii) cm³ : Indices and standard form Eercises.. (a) (c) (d) (a) (c) (d) (a) (c) (d) (a) (c) (d) (a) (c) - (d) - (a). (c). (d) (a) (c) (d). (a) (c) (d) (a) (c). (d) Eercises.. (a)... (a). km. km (a) (a) Eercise. Eercise. = Hodder & Stoughton Ltd

4 Cambridge IGCSE Mathematics Core and Etended Practice Book Answers Mone and finance Eercise. (a).. (c) NZ $. Eercises.. (a).. (a) Option : $ etra Option : $ etra e.g. The customer ma not be able to afford the initial deposit % % Eercise. % ears Eercise. $. $ $..%.% (a). ears Time Eercise. (a) hrs mins Monda (c) Set notation and Venn diagrams Eercise. Eercise. (a) Capital cities Student s two capital cities (a) Currencies Student s two currencies Student s coordinates which satisf = + e.g (, ) (a) Numbers from up to but not including Student s numbers (a) P c e a m d b g i r t h o n Q Eercise. (a) B = {,,,} C = {,,} (a) {a, b, c}, {a, b}, {a, c}, {b, c}, {a}, {b}, {c}, {ø} {a, b}, {a, c}, {b, c}, {a}, {b}, {c} Eercise. Girl s names not beginning with the letter A (a) (i) even numbers up to (ii) multiples of up to (iii) multiples of up to (i),,,, (ii),,,,,,,,,,,,, (iii) (iv),, (a) (i),,,,,,,,, (ii),,, Z (a) (i) {b,r,i,g,h,t,o,n,d,u,a,m} (ii) {r} (iii) {h,t,o,n} (i) (ii) Eercise. A u (a) (i) z = (ii) = (iii) = R Hodder & Stoughton Ltd S

5 Topic Eam focus Topic Eam focus Rational as = (a). cm². cm (c). cm (a) (c) (d) : (a) (a) (i). ( d.p.) (ii). ( d.p.) (iii). ( d.p.).. - kg (a) $ $ (c) $ (d) $ (a) (i),,, (ii),, (iii), No, as is an element in R but not P Algebraic representation and manipulation Eercises ab + a c - -a + a b a p - q + r + qr - + z - z + a + ab p - pq a + a + b - c - c + - m + m jk - jm + k - km Eercise. (a + b) -(c + d) ( - ) m(m - mn - n ) Cannot be factorised Eercise. - - Eercise. c = d - ab b d + = c a m = (r - ) q = r(p - s) p q = r + s Eercise. d - e - e + f - g - h + - Eercise. (a + b)(c + ) (d + e)(c + ) (f - )(g - ) (p - r)(p - q) (m + )(m + n) Eercise. (m - n)(m + n) ( - )( + ) (a - b )(a + b ) (m - n)(m + n) Eercise. ( - )( + ) = ( - )( + ) = = ( - )( + ) = = Hodder & Stoughton Ltd

6 Cambridge IGCSE Mathematics Core and Etended Practice Book Answers Eercise. (a + )(a + ) (b - )(b + ) (c - )(c - ) (d - )(d - ) or (d - ) (e + )(e + ) (f - )(f + ) (g + )(g - ) (h + )(h - ) (j + k)(j + k) or (j + k) Eercises.. pr a = q a = m bt r a = ( ) p b a = t b c a = ( ) Eercise. C (a) r = p r =. cm ( d.p.) A (a) r = p r =. cm ( d.p.) (a) p = A l p = cm A (a) h = - r p r. cm ( d.p.) V (a) h = p r. cm ( d.p.) Eercise. a de Eercises.. a + b c a -e f Eercise. p + ( p+ )( p-) a b a a + a a + a Algebraic indices Eercises.. (a) a b c p q r (c) m (d) a b e (a) a c m (c) b (d) b Eercise. (a) a (a) ( ) - (a) (c) b a - a - a ( b) a - Equations and inequalities Eercise. a = b = - c = - d = e = f = g = h = j = k = Hodder & Stoughton Ltd

7 Eercise.,,,, = cm, cm, cm,,,,, j =,,,,,,, Eercises.. a = b = c = d = e = f = g = - h = - p = q = r = - s = - w = = - =. =. a = b = c = d = e = - f = - g = =. h =. j = k =. l = m = n = - p = q = r = s = t = w =.,, - and a = b = (a) = = - (a) units units rs and rs Eercise ± (a) -, + Zach = rs, Leda = rs, Spot = rs,,, ± Eercise. Eercise. -, - -, Chapter Equations and inequalities, -, -, - Number line showing -, - < < -, Number line showing < <, < < ± Number line showing < < ± Hodder & Stoughton Ltd -, - ± ± No solution No solution ± ± ± ± No solution Eercise. $ base = cm, height = cm and and balls Eercise. -, - -., -.., -.., -., - -, -.,. -, -, - Eercises.. + < Number line showing < - + Number line showing - Number line showing - < Number line showing <

8 Cambridge IGCSE Mathematics Core and Etended Practice Book Answers < - < Number line showing < < + < Number line showing < - Number line showing.. Linear programming Eercise. - < - Eercise. Eercise. Eercise. (a) > > + (c) male + female male + female male + female Sequences Eercises..,,, (a) Number of white squares Number of shaded squares (c) n (d) (a) (i), (ii) square numbers (i), (ii) term to term + (c) (i), (ii) add the two previous terms together (Fibonacci sequence) (a) n + n + (c) n + Hodder & Stoughton Ltd

9 Chapter Variation Eercise. (a), n - (a), n + Eercise.,.,., (a) u =, u =, u = n = (a) n- (c) un = ( ) (d) Variation Eercise. (a) d = kp k = (c) (d) k (a) a = b a = (a) p =. or p = q q. (c) ± k p = r Eercise. Eercise. (a) b.h.p. kg m/s N Graphs in practical situations Eercise. (a) (a) Cost ($) Percentage, (c) Units The following method should be clearl seen in student s work. Mark Cost ($) Units $. (c). units Hodder & Stoughton Ltd

10 Cambridge IGCSE Mathematics Core and Etended Practice Book Answers, (c) Percentage % (c) marks The following method should be clearl seen in student s work. Mark Eercise. (a) m/s km/h (a) m m or. km (a). h or. min s Eercises.. (a) m/s. m/s (c) m (d) stationar (e) m/s (a) km (c) Distance (km) Time (d). km/h Eercises.. (a) acceleration of m/s deceleration of m/s (a) Running at a constant speed of m/s acceleration of m/s (c) deceleration of m/s Eercise. (a) Speed (m/s) (c) m (d) m (a) Speed (m/s) Time (s) Speed (m/s) B seconds (c) m Time (s) Time (s) A Hodder & Stoughton Ltd

11 Graphs of functions Eercise. Eercise. = - and = and = - and Eercise. = and = and = - and Chapter Graphs of functions Hodder & Stoughton Ltd

12 Cambridge IGCSE Mathematics Core and Etended Practice Book Answers Eercise Eercise. (a) Gradient = (a) Eercises.. (a) f()..... Gradient = Eercise. (a) (a) f()..... Hodder & Stoughton Ltd

13 Chapter Functions Rearrange the equation to give - =- + Superimposing the graph of = - + gives Therefore -., - and. (a) Rearrange the equation to give + = + Superimposing the graph of = + gives Therefore -. and. Functions Eercise. (a) (c) (d) (e) (f) (a) (c) (d) -. (a). (c). (d). Eercise. (a) (c). (d). (a) - (c) - (d) -. (a) -. - (c) (d). Hodder & Stoughton Ltd

14 Cambridge IGCSE Mathematics Core and Etended Practice Book Answers Eercise. (a). (c) (d) (e) (a) (c) (d) - (a) - (c) (d) - Eercise. (a) + - (c) + (d) + (a) - - (c) - (d) - + Eercise. (a) f - () = - - f ( ) = (a) ( + ) g ( ) = g ( ) = (c) - + g ( ) = Eercise. (a) (a) - - Eercise. (a) fg() = ( + ) fg() = (a) pq() = ( + ) pq() = + - (a) jk( ) = jk() = - (a) no solution Topic Eam focus (a) (a + b)(a b) (d + )(d ) (c) mb a a = c - (d) n a - r =. cm ( d.p.) (a) a a b (c) a (d) a (a) + = = (a) ( - ) - = =. and. (a) + + > < = (a) Stage A km/h² (c) Stage D. As deceleration in stage B is km/ h², whilst deceleration in stage D is. km/h² ( d.p.). The graph of stage D is steeper than that of B. (d) km (e) = km + - = can be rearranged to form - = + Superimposing the two graphs gives -., - and. (c) chickens and ducks (a) (i), (ii) u n = n (i), (ii) u n = -n + ( ) (c) (i),- (ii) un = - (d) (i), (ii) u n n- = ( ) n- (a) gh() = - - Hodder & Stoughton Ltd

15 Chapter Geometrical vocabular Geometrical vocabular Eercise. (a) Definitel congruent as all three angles the same and corresponding side Not necessaril congruent e.g. the side opposite the angle could be drawn in a different position and still be cm long Eercise. Rhombus Parallelogram Kite Opposite sides equal in length Yes Yes No All sides equal in length Yes No No All angles right angles No No No Both pairs of opposite sides Yes Yes No parallel Diagonals equal in length No No No Diagonals intersect at Yes No Yes right angles All angles equal No No No Eercise. A and B can be folded to form a cube. Diagram C has squares so is not a net of a cube. Geometrical constructions and scale drawings Eercises.. Student s construction Student s construction (a) Student s construction Circle passing through A, B and C, with its centre at the point of intersection of the three perpendicular bisectors constructed in (a) Eercise. (a). km cm (a) :. cm Similarit Eercise. (a) Angles in both triangles are the same:, and. (c) =. cm (d) = cm (a) a =. cm ( d.p.) b =. cm ( d.p.) Eercises.. (a). cm (c). cm ( d.p.) (a).. (c). cm (a) cm m Eercise. (a) (i) cm (ii). cm Rectangle H. cm Hodder & Stoughton Ltd

16 Cambridge IGCSE Mathematics Core and Etended Practice Book Answers Smmetr Eercise. (a) Several answers possible. Two are given below: Eercise. (a) AB = CD (given). OA = OB = OC = OD (all radii of the circle) All three corresponding sides the same length, therefore congruent. Isosceles (c) Rotational smmetr of order Eercise. p = Angle OXZ = as it s the angle between a tangent and a radius at a point. Angle XOZ = - - = Triangles OXZ and OYZ are congruent, therefore angle YOZ = XOZ. Therefore p = Angle properties Eercises.. a = b = c = d = e = p = q = Eercise. (a) (a) Eercise. = = Eercise. = = Eercise. (a) (c),,,, (a) = - = or + = (c) (d) Eercise. = = = Eercise. = = = = z = Eercise. p = q = = = z = Hodder & Stoughton Ltd

17 Chapter Loci Loci Eercises.. m A m C m B m m A B C Topic Eam focus There are several possible solutions. Two are shown below: A B. m m (a) m cm (a). cm³ (a).. (c). ( d.p.) (d). cm³ ( d.p.) = sides (a). cm ( d.p.) (a) = = (a) n = m = D m Note: the centre of the path is the perpendicular bisector of AC. As the path is m wide, the edges of the path are. m from its central line measured at right-angles. C Hodder & Stoughton Ltd

18 Cambridge IGCSE Mathematics Core and Etended Practice Book Answers Measures Eercises.. (a) mm. km (a). kg kg (a). litres ml. km (a) cm (i) mm (ii). m Perimeter, area and volume Eercises.. circumference =. cm area =. cm (a) cm. cm. cm. cm (a) cm. cm (c). cm. cm Eercises... cm. cm (a) h + p + ph (c). cm ( d.p.) cm (a). cm p - p or p( - ) (c). cm ( d.p.) Eercises.... cm (a) = r. Eercise.. (a). cm :. (a).. cm (c) cm (d) cm Eercises... cm (a) Volume of outer hemisphere - volume of inner hemisphere. Radius of inner hemisphere = ( - ) cm p( - ) (c) Student s proof (d). cm Eercise. (a). cm. cm (a). cm. cm Eercises.. (a) cm. cm (a) cm. cm (c). cm Eercises.. (a) cm. cm (c). cm (a). cm. cm (c). cm (d). cm (a). cm. cm (c). cm Topic Eam focus. km cm (a). cm. cm (c) :. (a). cm. (a). cm.% (a) cm (i). cm (ii). cm (c) (i). cm (ii). cm Hodder & Stoughton Ltd

19 Straight-line graphs Eercises.. (a) gradient = = - (a) gradient = = - (a) gradient = = (a) gradient is infinite = - (a) gradient = - =- + = + Chapter Straight-line graphs = - =- - =- = + m represents the gradient of the straight line. c represents the intercept of the line with the ais. Eercise. (a) gradient = -intercept = - gradient = - -intercept = - (a) gradient = - -intercept = gradient = - -intercept = (a) gradient = - -intercept = gradient = - -intercept = - (a) gradient = -intercept = - gradient = -intercept = (a) gradient = -intercept = gradient = -intercept = - Eercise. = = Eercise. Hodder & Stoughton Ltd Eercise. = - and =

20 Cambridge IGCSE Mathematics Core and Etended Practice Book Answers = and = - Eercise. (a). (, ) ( ) (a)., (a). (, -) ( ) (- - ) (a)., (a)., Eercise. = - = - + = =- = = + =- - Eercise. (a) - (c) =- + (a) - (c) = + (a) - (c) =- - (a) infinite (c) = (a) - (c) = + (a) infinite (c) = Topic Eam focus =- + (a) gradient = - -intercept = (a) (, -) = - + gradient = -intercept = (a) = Bearings Eercise. (a) Student s scale drawing (i). km (ii) Hodder & Stoughton Ltd

21 Chapter Trigonometr Trigonometr Eercises... cm. cm.. cm.. cm.. cm Eercises.. a =. cm b =. cm c =. cm d =. cm (a). km. km (a). km. km (c). km (d) (a). m. m (c). Eercise. (a). m (c) :. (a). m. (c). m Eercises.. (a) sin sin (a) -cos -cos (a),, (a) cos cos Further trigonometr Eercises... cm. cm. cm Eercise. (a). m Topic Eam focus. m Eercise.. cm² cm Eercise.. (a). cm. cm (a). cm (c). cm (d) (a) cm (c). cm (d) (a). cm (c). cm (a). m. m (c) m² (a) cm Vectors Eercise. ( ) (c) - ( ) (a) - (e) - (- ) - ( ) (d) ( ) - Eercise.. (a) ( ) ( ) Hodder & Stoughton Ltd (c) - - (d) ( ) -

22 Cambridge IGCSE Mathematics Core and Etended Practice Book Answers (a) a + b b a Eercise. - (a) (- ) - ( ) therefore magnitude is. therefore magnitude is. Eercises.. (a) a (c) a+ b b (d) b- a (a) a + b b b c + b c (c) a+ b (d) a+ b Matrices Eercise. (a) Class Class Black Brown Blonde Ginger Eercise. - ( ) (a) ( ) + ( ) + ( ) ( ) Eercises.. (a) - - ( ) - (a) () - ( ) - (a) Eamples of possible multiplications are AC, BA or CB Eamples of multiplications not possible are CA, AB or BC Eercises.. (a) B = ( ) The identit matri (a) (a) ( -) Eercise. - (a) - ( ) Hodder & Stoughton Ltd

23 Chapter Transformations Transformations Eercises.. (a) (i) (i) (ii) = + Eercises.. (a) (ii) = - = - + (a) Rotation clockwise or anticlockwise Hodder & Stoughton Ltd

24 Cambridge IGCSE Mathematics Core and Etended Practice Book Answers Eercises.. ( ) ( ) ( ) B = - C = - - D = - Rotation clockwise / anticlockwise Eercise. (a) Centre of rotation (, -) anticlockwise about O O (a) Centre of rotation (, ) anticlockwise about O O Hodder & Stoughton Ltd

25 Chapter Transformations Eercises.. (a) A B C A B O C Scale factor of enlargement =. A Eercise. X B Y C C Z Z B A Y X Scale factor of enlargement = Scale factor of enlargement = - Eercise. C A A C A B B A C Hodder & Stoughton Ltd B B C

26 Cambridge IGCSE Mathematics Core and Etended Practice Book Answers Eercises.. (a) A B C ( - ) ( )( ) = - ( - - ) - (c) A B C C (d) (i) Enlargement of scale factor - with centre of enlargement at the origin (ii) Rotation of with centre of rotation at the origin (a) units² A' A B B A B' C C' (c). (d). =. units² Eercise. (a) (e) B' C' C D B A C' D' B'' A'' C'' D'' (c) ( ) - (d) ( ) - Hodder & Stoughton Ltd

27 Topic Eam focus (a) ( - ) (a) - ( ) - - ( ). ( d.p.) (a) b a+ (c) a+ b b (d) a- b (a) QP is possible as the number of columns in Q is the same as the number of rows in P (a) - - ( ) (a) - - O (a) B C O = (, ) Scale factor = (c) = units Topic Eam focus A D O D C A B Centre of rotation O = (, ) anticlockwise about O (or clockwise) Hodder & Stoughton Ltd

28 Cambridge IGCSE Mathematics Core and Etended Practice Book Answers (a) (i) A B C ( ) (a) (ii), B C A A B B C C (c) ( - ) (d) units² A (e) - Probabilit Eercises.. (a) (c) (e) (d) (f) (a) = Not ever month has the same number of das (c) (a) (c) (a) (d) Further probabilit Eercise. (a) (c) (d) Student s answer (a) (i) (i) (a) (a) (a) (i) (ii) (ii) (ii) Eercise. (iii) (a) (a) (c) (d) (a) (i) (a) (ii) It will depend on how good the opposition is. Hodder & Stoughton Ltd

29 Topic Eam focus Eercise. (a) (c) (d) Topic Eam focus (e) Within the first three throws it is certain that a plaer will either start or not start (a).. (c). (a).. =. ( d.p.) (a) (c) (a) (d) (a) (a).%.% (a) r rr ( -) r + b ( r + b)( r + b-) (c) rb ( r + b)( r + b-) Mean, median, mode and range Eercises.. (a). (c) (d). kg (a) (c). ( d.p.) (d) (e) Eercise. (a) mins s Collecting and displaing data Eercises.. (a) Moderate positive correlation as taller people tend to be heavier. M Height (cm) Mass (kg) (c) (i). cm (ii). kg (iii) see graph for position of M (d) See graph for line of best fit (e) (i) Moderate positive correlation (ii) Student s comparison Hodder & Stoughton Ltd

30 Cambridge IGCSE Mathematics Core and Etended Practice Book Answers Eercises.. (a) Age (ears) Frequenc Frequenc densit... Frequenc densit..... Age (ears) Cumulative frequenc Eercises.. (a) Time (mins) Frequenc Cumulative frequenc Cumulative frequenc q q q Time (mins) (c) Median minutes (see graph) (d) (i) Upper quartile minutes (see graph) (ii) Lower quartile minutes (see graph) (iii) Interquartile range minutes Topic Eam focus (e) Yes the data does support his aim, as the middle % corresponds to the interquartile range. The IQR < mins. Several answers are possible Check + = kg, median = kg and range = kg e.g. = kg and = kg Hodder & Stoughton Ltd

31 Topic Eam focus (a) Fuel consumption (kpl) M Moderate negative correlation (c) (i) kg (ii) kpl Mass (kg) (d) See graph above for M (e) See graph above for line of best fit (f) Average fuel consumption kpl (see graph above) (a) Bus lateness (mins). Frequenc Frequenc densit. Frequenc densit Lateness (mins) (a) Reaction time (s) Frequenc Cumulative frequenc Reaction time (s) Frequenc Cumulative frequenc Hodder & Stoughton Ltd

32 Cambridge IGCSE Mathematics Core and Etended Practice Book Answers Cumulative frequenc Full sleep No sleep (c) Full sleep median reaction time. s No sleep median reaction time. s (d) Full sleep IQR. s No sleep IQR. s (e) Student s conclusions ma var. Median reaction time is greater with no sleep. Greater spread of results with no sleep. q q q q q q Reaction time (s) Hodder & Stoughton Ltd