CHS 2020 Y4 EOY Math P1 solutions

Name: Index Number: Class: CATHOLIC HIGH SCHOOL Preliminary Examination Year 4 (Integrated Programme) – Solutions MATHEMATICS Paper 1 5 OCTOBER 2020 2 hours Candidates answer in the space provided on the Question Paper. 1 (a) Find the fraction which is exactly halfway between 3 7 and 6 7 . Answer …………. 9 14 ……………… [1] (b) Calculate 2 33.595 0.0875 , correct your answer to 4 significant figures. Answer ……… 0.09305 ………… [1] 2 Factorise fully 3 12 2 18 .ax by bx ay              3 12 2 18 3 2 6 2 3 3 2 6 3 2 6 3 2 ax by bx ay x a b y b a x a b y a b x y a b               Answer ……………………………… [2]

2 3 (a) Simplify 2 2 2 2 6 3 bab a      . 2 2 4 3 2 2 6 2 3 27 bab a b a       (b) Given that    49 50 02 2 2 2 4 x   , find the value of x without using calculator.       49 50 0 49 2 2 2 2 2 4 2 1 2 1 2 2 124 2 x x x        Answer ……………………………… [2] Answer x = …………………………. [2]

3 4 (a) Matthew bought a pair of limited edition sports shoes for $199 and made a profit of 250% of his cost. Find his selling price.   Selling Price = 199 350% = $696.50 OR   Selling price 250% 199 199 =$696.50   (b) A rectangular piece of fabric which measures 270 cm by 420 cm is cut into identical squares to make masks. Find the largest possible area of each square such that there is no leftover fabric.   3 2 2 270 2 3 5 420 2 3 5 7 Largest area 2 3 5 900            Answer $ ………………………… [2] Answer ……………………………… cm2 [3]

4 5 Tom invested some money in a savings account for 2 years. The rate of compound interest was fixed at 2.88% per annum compounded quarterly. At the end of the 2 years, there was $9427 in his account. How much did Tom invest in the account? Leave your answer to the nearest dollar. 2 4 8 2.88 41 100 0.729427 1 100 $8901 A P P P                  6 Mr Lim bought a system 4 aircon for his new home which cos t $4259 on hire purchase. He paid a down payment of $1500. The remaining sum is to be paid in monthly instalments over 3 years at 1.4% per annum. Find the amount of his monthly instalment. Interest =    4259 1500 1.4 3 100  = $115.878 Monthly instalment = 4529 1500 115.878 36   Answer $……………………………… [2] Answer $……………………………… [3]

5 7 The point (1, 1) is marked on each diagram in the answer space. On these diagrams, sketch the graphs of (i) 1y x , [1] (ii) 3xy . [1] y x y x –1

6 8 The scale of a map is 4 cm : 2.5 km. (a) Write this scale in the form of 1 : n. 1 : 62500 (b) A plot of land is represented by an area 8.5 cm2 of on the map. Calculate the actual area of lake in m2, leaving your answers in standard form. 2 2 2 6 2 1cm : 390625m 8.5cm : 3.32 10 m 9 (a) Solve the inequalities 1 4 32 x    and represent the solutions on the number line provided. 1 4 32 10 2 [B1] x x        (b) It is given that 5 1 y   and x and y are integer values. Using the answers found in (a), find the maximum value of (i) 2x y ,     22 10 5 105x y      (ii) y x . 5 2 13 3 y x   Answer …………………………….. [1] Answer ……………………………… m2 [2] Answer ………………………………. [1] Answer ………………………………. [1] Answer ………………………………. [1] x –10 –2

7 10 p is directly proportional to square root of q. q is increased by 125%. Find the percentage increase in p. 2.25% increase 100% 50% p k q k q k q k q     11 In the diagram, ABC and CDEF are straight lines and are perpendicular to each other. Lines BD and AE are parallel lines. Given that tan ˆDBC = x, find the value of cos AEF in terms of x. 2 2 1 ˆcos 1 BD x xAEF x     Answer ……………………………… % [2] Answer ……………………………… [2] A B C D E F

8 12 The diagram shows a circle ABCE, with centre O. Lines AOD and BOE are straight lines. Line AOD is the perpendicular bisector of chord CE. Given that angle BAC = 46°, find, giving reasons for each answer, (a) angle CEB, angle CEB = 46° (angles in same segment) (b) angle CAE, angle CAE = 90° – 46° = 44° (right angle in semi-circle) (c) angle ABC. angle AEC = 180 44 68 (base angles of isosceles ) 2      Angle ABC = 180° – 68° = 112° (supplementary angles in opposite segments) Answer ……………………………… ° [1] Answer ……………………………… ° [1] Answer ……………………………… ° [2] A D E O B C 46°

9 13 The diagram (not drawn to scale) shows one interior angle of each of three regular polygons A, B and C. The polygon fit together at O. It is given that C is an equilateral triangle and the number of sides polygon A has is 1.5 times that of polygon B. (a) Find the number of sides of polygon B.    180 2 180 2 180360 3 2 2 1 2 3 1.5 2 2 5 1.5 3 3 4 2 5 3 3 3 4 3 6 5 10 a b a b a b a b b b b b b b b b b b b b                        (b) Find the exterior angle of polygon A. 10 1.5 15 360Ext angle of A = 24 15 a      Answer ……………………………… [3] Answer ……………………………… ° [1] C A B O

10 14 Three ships, P, Q and R are such that Q is due east of P. A map is being drawn to a scale of 1 cm : 2 km. The positions of P, Q and R are shown below. Another ship, S, is 18 km from R and 20 km from P. (a) Using a ruler and compass only, complete the map to show the position of ship S. [1] (b) Measure the bearing of S from R. [1] (c) A lighthouse is located I equidistant from P and Q, II equidistant from PS and RS. Mark the location of the lighthouse with a cross on the map and label it “L”. [3] P Q R N