2023 Sec 3 Express E Math EOY Anglo Chinese School (Barker) with Answer

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3 Full Name Class Index No ~¼lln--4rqittes~ ~tqnnl (~arker ~ab} END-OF-YEAR EXAMINATION 2023 SECONDARY THREE EXPRESS MATHEMATICS 4052 PAPER 1 1 HOUR 45 MINUTES Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST - Write your index number and name on all the work you hand in. Write in dark blue or black pen. Answer all questions. 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 use of an approved scientific calculator is expected, where appropriate. Class 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. Give answers in degrees to one decimal place. For 1r, use either your calcu_lator value or 3.142, unless the question requires the answer in terms of Jr. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 70. For Examiner's Use Thi~ question paper consists of 16 printed pages. BP-3

Compound interest Mensuration Trigonometry Statistics End-of-Year Examination 2023 4 Mathematical Formulae Total amount = P ( l + ~)n 100 Curved surface area of a cone = 1rrl Surface area of a sphere = 4nr 2 1 Volume of a cone = - nr 2 h 3 4 3 Volume of a sphere = - nr 3 Area of triangle ABC = ..!_ ab sin C 2 Arc length = r0, where 0 is in radians Sector area = ..!_ r2 0 , where 0 is in radians 2 a b C = = sinA sinB sinC a2 =b2 +c2 -2bccosA Mean= ~fx Lf Standard deviation = 2 Secondary 3 Express Mathematics 4052 Paper 1 BP-4

5 1 Expand and simplify ( 2x - 3 y )2 . Answer [2] ---------- 2 The first 4 terms in a sequence are 6, 10, 14, 18, .. .. (a) Write down an expression, in terms of n, for the nth term, Tn, of this sequence. Answer [1] ---------- (b) Evaluate T 11 . Answer --------------- [1] ( c) Explain why T n is always an even number , for all values of n. Answer 3 End-of-Y ear Examina tion 2023 [1] Secondary 3 Express Mathematics 4052 Paper I BP-5

6 3 The population of Zimbabwe was 15.99 million with a land area of 390 745 km2 in 2021. (a) Write 15.99 million in standard form. Answer -------------- (b) Calculate the number of people per square kilometre , co1Tect your answer to the nearest whole number. Answer -------------- 4 (a) Express 540 as the product of its prime factors. (b) The number 540 p is a perfect cube. q p and q are prime numbers. Answer Find the value of p and the value of q. -------------- Answer p = __________ _ q= ________ _ 4 [l] [2] [l] [2] End-of-Year Examination 2023 Secondary 3 Express Mathematics 4052 Paper I

7 5 (a) The time taken to put together a wooden crate is inversely proportional to the number of workers. Four workers take 12.5 hours. Find the time it would have taken 5 workers to put together a wooden crate. Answer hours [1] (b) A quantity y is directly proportional to .x3. If x is increased by 200%, calculate the percentage change iny . Answer ___________ ....:o/c~o_ [2] 6 If 2x g x-2 42x+3 1 -a- x = - , find the value of x. 16 End-of-Year Examination 2023 Answer [3] -=========- 5 Secondary 3 Express Mathematics 4052 Paper I BP-7

8 7 (a) Express x2 -6x + 4 in the form ( x - p )2 + q . 8 Answer -------------- (b) Write down the coordinates of the minim m point of the graph of y = x2 - 6x + 4. Answer --"--------'------~ u In the diagram, ST II VW, angle TUV= 95° and angle UVW= 128°. Calculate angle STU. Give a reason for each step of your working. [2] [l] Answer _____________ 0_ [3] 6 End-of-Year Examination 2023 Secondary 3 Express Mathematics 4052 Paper I BP-8

9 9 The graph of y = -x 2 + x + 6 is drawn on the grid. (a) Write down the equation of the line of symmetry of the curve. Answer --------------- 2 (b) The equation -x + x + 2 = 0 can be solved by drawing a suitable straight line on 2 the grid. (i) Find the equation of the straight line. Answer --------------- 7 [1] [1] End-of-Year Examination 2023 Secondary 3 Express Mathematics 4052 Paper 1

10 10 (a) 2 (ii) By drawing this straight line, solve the equation -x + x + 2 = 0. 2 Answer x= or --------------- -f h2 -4k2 Given that p = ---- , express kin te1ms of h, n and p . n Answer --------------- (b) Hence, find the values of k when p = -1, h = 9 and n = 2. Answer k= or --------------- 8 (3] (3] [2] End-of-Year Examination 2023 Seconda1y 3 Express Mathematics 4052 Paper I BP-10

11 11 A B C The diagram shows the interior angles of each of three regular polygons , A, Band C. A is a square, B is a regular pentagon and C is a regular n-sided polygon. The polygons fit together at 0. Find the value of n. Answer _n_= ___________ [4] 9 End-of-Year Examination 2023 Secondary 3 Express Mathematics 4052 Paper I BP-11