2023 Sec 3 Express E Math EOY Ahmad Ibrahim Secondary with Answer

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45 AHMAD IBRAHIM SECONDARY SCHOOL END-OF-YEAR EXAMINATION 2023 SECONDARY 3 EXPRESS I Name I Class I Register No.: MATHEMATICS Paper1 Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST 4052/01 3 October 2023 2 hours 15 minutes Write your name, class and index number 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. 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, gives the answer to 3 significant figures. Gives answers in degrees to one decimal place. For rr, use either your calculator value or 3.142 unless the question requires the answer in terms of 1r. For Examiner's Use /90 This document consists of 22 printed pages. AISS EOY/SEC 3E/P1/2023 [Turn over

Compound Interest Mensuration Trigonometry Statistics 46 2 Mathematical Formulae Total amount = P (l + _r_) n 100 Curved surface area of a cone = rrrl Surface area of a sphere = 4rrr2 1 Volume of a cone = - rrr2h 3 4 Volume of a sphere = - nr3 3 1 Area of triangle ABC = - ab sin C 2 Arc length = r0, where 0 is in radians Sector area= _! r20, where 0 is in radians 2 a b C sin A sin B sin C a2 = b2 + c2 - 2bc cos A Mean= "i,fx "i,f Standard deviation= Ifx 2 -("i,fx) 2 "i,f "i,f AISS EOY/SEC 3E/P1/2023 BP-46

BP-47 3 Answer all the question s. 1 (a) I 1 154 2 • • 3 . .fi fi Ca cu ate , ,.-;:;-; , g1vmg your answer correct to s1gm 1cant 1gures. -v )j) - 2.67 Answer ... ....... .. .. .... ....... .. ... .... . [!] (b) The mass of a cone is 25.0 g, rounded off to the nearest 1 decimal place . Write down the minimum mass of the cone. Answer .. ... ........ ........... ...... g [1] 2 The length of each side of a cube is decreased by 20%. Find the percentage change in the volume of the cube. Answer ... .. .... ........ .... ... ... % [2] AISS EOY/SEC 3E/P1/2023 [Turn over 47

4 3 In a regular polygon , the ratio interior angle : exterior angle = 7 : I. Calculate the number of sides of the polygon. Answer ...... ... ... ........ ... .. ..... .. .. [3] 4 (a) Factorise completely p 2 + p-6. Answer .......... ..... ...... ..... ..... . [I] b) H I 5p+l5 . I f . . . . l ( ence express --+ 2 as a smg e ract10n m its s1mp est terms. 2- p p + p-6 Answer ................................ [2] AISS EOY/SEC 3E/P1/2023 48

49 5 5 The data below shows the number of accidents that happened from April to August in district Z. Decline in the number of accidents Number of accidents 50 20 April May June August Month State one aspect of the graph that may be misleading and explain how this may lead to a misinterpretation of the graph . Answer 6 Xander deposited $17 000 in an account that pays 5.5% compound interest per year. Find the total amount in the account after 6 years if the interest is compounded half-yearly. Answer $ . . . . . . . . . .. . . . . . . . . . . . . . . . . . . [3] AISS EOY/SEC 3E/P1/2023 [Turn over

50 6 7 (a) Express 540 as a product of its prime factors . Answer ... .... ..... ........ .... .. ..... .. [I] (b) Explain why 540 is not a cubic number. Answer .... .. ... ... ......... .... ... ... .. ... .... .... . .... .. ........ . ... .... ...... ... ........ ... ...... .... .. .... ..... .. . ... ... ... ... ... ... .. . ... ... ... ... ... ... ... .. . ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... .. . ... ... . [I] (c) Find the smallest integer k such that 540k is a perfect square. Answer ..... .......................... . [1] ( d) Written as the product of its prime factors , 84 = 2 2 x 3 x 7 . Find the highest common factor (HCF) and lowest common multiple (LCM) of 84 and 540, giving your answer in index notation. Answer .......... ... .. .. ............. ... [2] AISS EOY/SEC 3E/P1/2023 BP-50

BP-51 7 8 (a) Factorise completely 3p4 -4p 3q-20q 2 +I5pq. Answer .... ... ............. ........ .. .. [2] (b) Rearrange the formula a = k ✓ a: 1 to make b the subject. Answer b = ......... ........ .. ....... . [3] AISS EOY/SEC 3E/P1/2023 [Turn over 51

52 8 9 (a) Express x 2 +2x -2 in the form (x +a)2 +b. Answer ... .. ..... ............. .. .... .. . [2] (b) Sketch the graph of y = x~ + 2x - 2 on the axes below. Indicate clearly the coordinates of the points where the graph crosses the axes and the minimum point on the curve. Answer y 0 X [3] (c) Explain how your graph shows that there are more than one solution of the equation x2 +2x -2 =0. Answer ...... ...... ................ ... ....... .... .... ........... ......... ..... ........ .......... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . [ 1] AISS EOY/SEC 3E/P1/2023

53 9 10 If 3x = 5 y , find the ratio x 2 : y2 . 11 (a) Solve the inequality .!.. (x -1):::; 3 + 2x < 10. 3 Answer [2] Answer ........ .... ..... .. ............ [3] (b) Represent your answer on the number line below . [1] • 0 4 ··- r I I r- -I i T 1 ·-· 1 - .. - 4 -2 0 2 4 6 AISS EOY/SEC 3E/P1/2023 [Turn over BP-53