OPSS MYE 2018 2E Math QP

1 ORCHID PARK SECONDARY SCHOOL Mid-Year Examination 2018 CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS Papers 1 & 2 Secondary 2 Express Setter: Mr Benny Leong & Mr Wong Yiu Hang 4048 4 May 2018 2 hours 30 minutes 100 Marks Additional Materials: Writing Papers, Graph Paper and Answer Cover Page READ THESE INSTRUCTIONS FIRST Write your name, class and index number on all the work you hand in. Write in dark blue or black pen. Use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid/tape. Section A Answer all questions in the spaces provided in the question paper. Section B Answer all questions in the writing papers provided. If working is needed for any question it must be shown with the answer. Omission of essential working will result in loss of marks. 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 π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 100. This document consists of 16 printed pages For Examiner’s Use Total Calculator Model:

2 Mathematical Formulae Compound interest Total amount = n rP      + 1001 Mensuration Curved surface area of a cone = rlπ Surface area of a sphere = 24 rπ Volume of a cone = h r2 3 1π Volume of a sphere = 3 3 4 rπ Area of triangle ABC = C absin2 1 Arc length = θr , where θ is in radians Sector area = θ2 2 1 r , where θ is in radians Trigonometry C c B b A a sin sin sin= = A bc c b acos22 2 2− + = Statistics Mean = ∑ ∑ f fx Standard deviation = 22       − ∑ ∑ ∑ ∑ f fx f fx

3 1 (a) Calculate 62.332+38.2 0.3141+√579. Write down all the figures on your calculator display. Answer ……….……………………………. [1] (b) Write your answer to part (a) correct to 3 significant figures. Answer ……….……………………………. [1] ___________________________________________________________________________ 2 (a) Alvin’s age is 6 years less than 1 2 times the present age of Ben. If Ben is x years old now, express, in terms of x, Alvin’s present age. Answer ……….……………………………. [1] (b) John made a statement that a bicycle travelling at 20 km/h is as fast as a motorcycle travelling at 20 m/s. Is the statement made by John correct? Justify your answer. Answer ………………………………………………………………………… ……………………………………….……….……………………………. [2] ___________________________________________________________________________ Section A (50 marks) Answer all the questions. [Turn over

4 3 (a) Express 2160 as the product of its prime factors in index notation. Answer ……….……………………………. [1] (b) Using your answer in part (a) find the smallest k such that 2160k is a perfect square. Answer k = …..……………………….……. [1] ___________________________________________________________________________ 4 y is directly proportional to (2𝑥𝑥 − 2). Given x = 10, y = 36 (a) Write an equation connecting x and y. Answer ……….……………………………. [2] (b) Find the value of y when x = 3 Answer y = .….……………………….……. [1] ___________________________________________________________________________

5 5 Solve the following simultaneous equations 3𝑥𝑥 − 2𝑦𝑦 = 12 5𝑥𝑥 − 3𝑦𝑦 = 21 Answer x = ……..….… , y = ……………… [3] ___________________________________________________________________________ 6 Simplify the following expressions. (a) (2𝑥𝑥 + 3𝑦𝑦) 2, Answer ……….……………………………. [2] [Turn over

6 6 (b) (𝑥𝑥 + 2) − (2𝑥𝑥 − 4)(𝑥𝑥 − 3) Answer ……….……………………………. [3] ___________________________________________________________________________ 7 One of the solution of 𝑥𝑥 2 − 𝑘𝑘𝑥𝑥 − 20 = 0 is x = 5. Find (a) the value of k, Answer k = .….……………………….……. [1] (b) the other solution of the equation. Answer x = .….……………………….……. [2] ___________________________________________________________________________

7 8 (a) Factorise 𝑥𝑥2 − 16. Answer ……….……………………………. [1] (b) Hence, find the 2 factors of 3584, other than 1 and 3584 Answer ……….……… and ………………. [2] ___________________________________________________________________________ [Turn over

8 9 The diagram below shows the graph of 𝑦𝑦 = 𝑥𝑥2 − 𝑥𝑥 − 12. (a) The graph cuts the x – axis at B and C. Find the coordinates of B and C. Answer B (……….……… , …….……….) [1] Answer C (……….……… , …….……….) [1] (b) Find the gradient of line AC. Answer ……….……………………………. [2] (c) Find the equation of the line of symmetry. Answer ……….……………………………. [1] ___________________________________________________________________________ y x B C A

9 10 Make r the subject of the formula 𝑣𝑣 = 1 3 𝜋𝜋𝑟𝑟2ℎ. Answer ……….……………………………. [3] ___________________________________________________________________________ 11 Factorise the following expressions. (a) 3𝑥𝑥𝑦𝑦 2 − 18𝑥𝑥2𝑦𝑦, Answer ……….……………………………. [1] (b ) 10𝑥𝑥 𝑦𝑦 − 20 𝑥𝑥 + 5𝑦𝑦2 − 10𝑦𝑦. A nswer ……….……………………………. [2] ___________________________________________________________________________ [Turn over

10 12 Simplify the following expressions. (a) 7𝑏𝑏2 35𝑎𝑎𝑏𝑏, Answer ……….……………………………. [1] (b) 2𝑎𝑎 3𝑏𝑏𝑏𝑏 ÷ 4𝑎𝑎2𝑏𝑏 𝑎𝑎𝑏𝑏𝑏𝑏2 . Answer ……….……………………………. [1] ___________________________________________________________________________ 13 Solve 2𝑥𝑥+2 3𝑥𝑥+1 = 4𝑥𝑥 Answer x = ……..….…… or ………..……. [3] ___________________________________________________________________________