4016/01 October/November 2011

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1 ELEMENTARY MATHEMATICS Paper 1 Suggested Solutions 1. Topic: Arithmetic (Approximation & Estimation) /01 October/November ( sig. fig.) Answer 1.05 [2] 2. Topic: Integers 2 ( 7) = = 5. Topic: Arithmetic (Percentage) = = 600 Answer 9 C [1] 5 C [1] of sector in pie chart its given data Answer 600 [2] 4. Topic: Matrices = Answer 5. Topic: Algebra x 1 litre 1 1 x litre litre x $y 100y litre x [1] The total amount of money collected for each match, i.e. $1200 for the first match and $1401 for the second match [1] Answer 6. Topic: Arithmetic (Fractions & Percentages) 12 2 = 18 cm x a b c d e f y z aa + bb + cc = dd + ee + ff 100y x litres [2] 6 100cm 100% = 0.5 % Answer 18 glasses [1] Difference between angles of Mathematics and Chemistry sectors in pie chart. 1 m = 100 cm 0.5 % [2] Copyright 2011 ϕ exampaper.com.sg. All rights reserved. 1 / 9

2 7. Topic: Factors and Multiples p = 2 6 = 2 2 = 18 LCM = (c) HCF = 2 = 6 8. Topic: Algebra 5c 20c2 2 d = 5c 2 d 20c 2 = d 8c n a m = a m n 6x x 12 = 2(x 2 + 7x 6) = 2(x 2)(x + ) Answer 18 [1] [1] (c) 6 [1] By inspection, x 2 2x x 9x x 2 6 7x Answer 8c [1] 2(x 2)(x + ) [2] d 9. Topic: Maps and Scales 1 cm : cm 1 cm : 0.25 km 1cm : 0.25 km 0 cm : = 7.5 km (c) From, (1 cm) 2 : (0.25 km) 2 1 cm 2 : km 2 40 cm 2 : 2.5 km Topic: Congruency and Similarity Since ABC and ACN are similar, AB AC 9 AC = AC AN = AC 4 AA 2 = 6 AC = 6 or 6 (rej) Answer n = 0.25 [1] 7.5 km [1] (c) 40 cm 2 [1] If ABC and ACN are similar, AA AA = BB CC = CC B NN = k 1 km = 1000 m = cm C A A C N Answer In triangles ABC and ACN ABC = ACN (given) BAC = CAN (common) ABC is similar to ACN. [1] AC = 6 m [2] Copyright 2011 ϕ exampaper.com.sg. All rights reserved. 2 / 9

3 11. Topic: Trigonometry cos p = cos AA D = 4 x Area of trapezium ABCD = 5 Area of ADC Area of trapezium sum of // sides height = (AA + DA) AD = 5 1 AD DA (AA + 4) = AA + 4 = 5 4 AB = Topic: Approximation & Estimation Answer cos p = 4 x [1] AB = 16 cm [2] Greatest possible mass of 1 cubic centimetre of the glass = = greatest possible mass least possible volume g ( sig. fig.) cos (180 θ) = cos θ 42.5 g mass of glass block < 4.5 g 14.5 cm volume of glass block < 15.5 cm Answer 42.5 g [1].00 g [2] 1. Topic: Set Language & Notation A R (A has a 90 angle) A S (A has two 45 angles isosceles) B R (By Pythagoras Theorem, not a right-angled triangle) B S (B has two equal 7 cm sides) C R (By Pythagoras Theorem, = 5 2 right-angled triangle) C S (C has three unequal sides) Answer ξ R S A C B [] 14. Topic: Geometry (i) From MDC, MD A = 180 DM A DA M (sum of interior s in ) = x = 152 x (ii) From BNC, CA A = 180 AC A AA C (sum of interior s in ) = x = 158 x Alternative Method: [using answer from (i)] CA A = 180 MD A (opposite s in cyclic quad) = 180 (152 x ) = 28 + x Copyright 2011 ϕ exampaper.com.sg. All rights reserved. / 9

4 CA A + MD A = 180 (opposite s in cyclic quad) A B 16. Topic: Algebra (a 4) = 1 ( a) 152 x x = 180 2x = 10 D C a 12 = 1 + a 2a = 10 x = 65 a = 5 Alternative Method: y = x 7 (1) From BNC, x = y (2) AC A + CA A + AA C = 180 (sum of interior s in ) Sub (2) into (1), x + x = 180 y = (y + 4) 7 2x = 10 y = y x = 65 2y = 5 Answer (i) MD A = 152 x [1] (ii) CA A = 158 x or 28 + x [1] x = 65 [1] y = 2.5 Sub y = 2.5 into (2), x = Topic: Mensuration = 1.5 Area of the minor sector AOB = 1 2 (4)2 (2.5) = 20 (i) Reflex angle AOB = 2π 2.5 (ii) Length of arc ACB = 4(2π 2.5) = 8π 10 Area of sector = 1 2 r2 θ Length of arc = rθ Answer a = 5 [2] x = 1.5 y = 2.5 [2] Answer 20 cm 2 [1] (i) (2π 2.5) radians [1] (ii) (8π 10) cm [1] Copyright 2011 ϕ exampaper.com.sg. All rights reserved. 4 / 9

5 17. Topic: Geometry (i) (iii) AA D = FD F (corresponding s, FD // BC) = 44 (ii) AD F = AA D = 56 (alternate s, FD // BC) AA D = AD A = (adjacent s on straight line) = 80 AF D = 60 AA F AA D AD F (sum of interior s in quadrilateral) = = 12 Answer (i) AA D = 44 [1] (ii) AA D = 80 [1] (iii) AF D = 12 [1] AF is not parallel to BD because BA F + AB D 180, since these two interior angles have to be supplementary in order for AF to be parallel to BD. [1] 18. Topic: Indices (i) 7 12 = 7 9 (ii) (iii) 1 49 = = 7 2 = k = k = 0 k = 2 a m a n = a m n 1 am = a m n a m a 0 = 1 = a m n Answer (i) 7 9 [1] (ii) 7 2 [1] (iii) [1] k = 2 [1] Copyright 2011 ϕ exampaper.com.sg. All rights reserved. 5 / 9

6 19. Topic: Coordinate Geometry x = 8 (1) (c) y = 6 x.. (2) Sub (1) into (2), y = 6 8 = 2 A (8, 2) x = 8 2y = x + 2 () Sub (1) into (), 2y = (8) + 2 y = 1 B (8, 1) y = 6 x m = 1 k = 1+( 2) 2 = 5.5 Equation of straight line with gradient m and y-intercept c: y = mx + c k is the y-coordinate of the midpoint of AB i.e. y A+y B Topic: Geometrical Construction Answer A is ( 8, 2 ) [1] B is ( 8, 1 ) [1] 1 [1] (c) k = 5.5 [1] Copyright 2011 ϕ exampaper.com.sg. All rights reserved. 6 / 9

7 21. Topic: Graphs of Quadratic Equations When y = 0, (x )(x + 1) = 0 x = 0 or x + 1 = 0 x = x = 1 When x = 0, y = (0 )(0 + 1) = line of symmetry: x = 1+ = 1 (c) Sub x = 1 into y, y = (1 )(1 + 1) = 4 Maximum point (1, 4) 2 x-intercepts y-intercept Line of symmetry of quadratic graph passes through the max/min point. 22. Topic: Standard Form seconds = seconds = 14 nanoseconds (i) = = 10 6 ( ) = (ii) 27% % = nano = When quantities are multiplied or divided, the no. of sig. fig. is the answer equal to the no. of sig. fig. in the quantity with the smallest no. of sig. fig. Answer Coefficient of x 2 < 0 graph has max point with shape 4 y y = (x )(x + 1) Answer k = 14 [1] (i) [2] (ii) [2] 1 0 x x = 1 [2] x = 1 [1] (c) ( 1, 4 ) [1] Copyright 2011 ϕ exampaper.com.sg. All rights reserved. 7 / 9

8 2. Topic: Statistics (Cumulative Frequency) From graph, No. of students scoring < 75% Lower quartile = 18 Upper quartile = 2 Interquartile range = 2 18 = 14 No. of students gaining 75% Interquartile range = Upper quartile Lower quartile = total no. of students no. of students gaining < 75% = = 140 Answer 14 marks [2] 140 [2] (c) 4 [1] (d) Paper 1 was more difficult because its median mark of 26 is lower than the median mark of 1 for paper 2. [1] Lower quartile (Paper 1) Upper quartile (Paper 1) Median mark (Paper 1) Median Mark (Paper 2) Copyright 2011 ϕ exampaper.com.sg. All rights reserved. 8 / 9

9 24. Topic: Kinematics Ali s speed as he runs to the shop = (c) Ali s speed as he walks home = Answer Distance from home (metres) km 5 60 hr = 9.6 km/h 0.8 km hr = 4.8 km/h Ali running to shop Time (minutes) [1] 9.6 km/h [2] (c) 10 Speed (km/h) Speed = Distance Time taken Ali at rest Ali walking home Time (minutes) [2] Copyright 2011 ϕ exampaper.com.sg. All rights reserved. 9 / 9

CAMBRIDGE IGCSE MATHS EXAMINATION BOARD COVERAGE

CAMBRIDGE IGCSE MATHS EXAMINATION BOARD COVERAGE TIER TOPIC HEADING SUB HEADING Both Number Integers Ordering numbers Both Number Integers Rounding numbers Both Number Integers Adding and subtracting whole