E Math Paper 2

00062720080 1 4052/01/O/N/26 [Turn over SECONDARY 4 PRELIMARY EXAMINATION in preparation for the General Certificate of Education Ordinary Level CANDIDATE NAME CENTRE NUMBER S . INDEX NUMBER MATHEMATICS 4052/02 Paper 2 October/November 2026 2 hours 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your Centre number, index number and name on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. DO NOT WRITE ON ANY BARCODES. Answer all the questions. The number of marks is given in brackets [ ] at the end of each question or part question. If working is needed for any question it must be shown with the answer. Omission of essential working will result in loss of marks. The total of the marks for this paper is 90. The use of an approved scientific calculator is expected, where appropriate. If the degree of accuracy is not specified in the question and if the answer is not exact, give the answer to three significant figures. Gives answers in degrees to one decimal place. For π, use either your calculator value or 3.142. This document consists of 21 printed pages and 1 blank page. 0006270

00062720080 2 4052/01/O/N/26 Mathematical Formulae Compound interest Total amount = P(1+ r 100) n Mensuration Curved surface area of a cone = πrl Surface area of a sphere = 4πr2 V olume of a cone = 1 3 πr2h V olume of a sphere = 4 3 πr3 Area of a triangle ABC = 1 2 ab sin C Arc length = rθ, where θ is in radians Sector area = 1 2 r2θ, where θ is in radians Trigonometry a sin A = b sin B = c sin C a2 = b2 + c2 – 2bc cos A Statistics Mean = Σ fx Σ f Standard deviation = √Σ fx 2 Σ f − (Σ fx Σ f ) 2

00062720080 3 4052/01/O/N/26 [Turn over TURN OVER FOR QUESTION 1

00062720080 4 4052/01/O/N/26 1 (a) Express as a single fraction 3x + 5 3 − 7x − 4 2 . Answer ………………………………. [2] (b) Solve 9x + 4 ≥ 6 − 2x > 3x. Answer ………………………………. [3] (c) It is given that a = b − c2 2b . (i) Find a when b = 1.2 and c = −3. Answer a = ..…………………………. [1] (ii) Express b in terms of a and c. Answer b = ..…………………………. [3]

00062720080 5 4052/01/O/N/26 [Turn over (d) Simplify 5ab2 3c ÷ 20b4 9a3c2 Answer ………………………………. [2] (e) Solve the equation 2x x + 2 − x 2x2 + 3x − 2 = 1. Give your solutions correct to 2 decimal places. Answer x = ……………… or ……………… [5]

00062720080 6 4052/01/O/N/26 2 ABCD is a park on horizontal ground crossed by a path BD. CD = 450 m and AB = 230 m Angle BCD = 80°, angle ABD = 42° and angle BAD is obtuse. The bearing of C from B is 075°. The bearing of D from B is 110°. (a) Calculate BD. Answer …………………………… m [3] A B D C 42° 80° North 450 230

00062720080 7 4052/01/O/N/26 [Turn over (b) Calculate the area of the park. Answer …………………………… m2 [3] (c) A vertical 170 m-tower stands at B. Peter walks from P to Q along BD. The angle of elevation of the top of the tower from Q is 035°. The distance between P and Q is 300 m. Find the angle of elevation of the top of the tower from P. Answer ………………………………. [4]

00062720080 8 4052/01/O/N/26 3 The diagram shows part of a number grid. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 (a) A zig-zag outlining five numbers, as shown, is placed on the grid. The zig-zag is placed in a different position on the grid. The sum of the largest and smallest of the numbers outlined is 154. Complete the zig-zag to show the numbers outlined. Answer [3]

00062720080 9 4052/01/O/N/26 [Turn over (b) The zig-zag is placed in a different position on the grid. The difference between the product of the top right and bottom left numbers and the product of the left and right numbers is found. Show that this difference is always 24. [3]

00062720080 10 4052/01/O/N/26 4 The masses, in grams, of 350 apples in bag A are recorded. The cumulative frequency curve shows the distribution of the results. (a) Use the curve to estimate (i) the percentage of the apples from bag A which mass is over 150 g. Answer …………………………… % [1] (ii) the 90th percentile for bag A. Answer ………………………………. [1] 100 120 v 140 v 160 v 180 v 200 0 50 100 150 200 250 300 350 Mass (g)