ACSI 2014 Y3 Core Mathematics Paper 2

Anglo - Chinese School (Independent) FINAL EXAMINATIONS 2014 YEAR 3 INTEGRATED PROGRAMME CORE MATHEMATICS PAPER 2 WEDNESDAY 8th October 2014 1 hour 30 minutes INSTRUCTIONS TO STUDENTS Do not open this examination paper until instructed to do so. A calculator is required for this paper. Answer all the questions on the answer sheets provided. At the end of the examination, fasten the answer sheets together. Unless otherwise stated in the question, all numerical answers must be given exactly or correct to three significant figures. Answers in degrees are to be given to one decimal place. INFORMATION FOR STUDENTS The maximum mark for this paper is 80. _____________________________________________________ This question paper consists of 5 printed pages. [Turn over

ACS(Independent)MathDept/Y3IPCoreMathPaper2/2014/FinalExamination 2 Full marks are not necessarily awarded for a correct answer with no working. Answers must be supported by working and/or explanations. Where an answer is incorrect, some marks may be given for correct method, provided this is shown by written working. You are therefore advised to show all working. Answer all the questions on the answer sheets provided. Please start each question on a new page. 1 [Maximum mark: 5] (a) Given that the equation 46 5 7  nn can be expressed as 02  rqnpn find the values of p, q and r. [3] (b) Solve for n. [2] 2 [Maximum mark: 7] (a) Solve the inequality 512 12  x . [3] (b) Find the range of values of x for which 5)32)(2(  xx . [4] 3 [Maximum mark: 9] (a) Solve the equation 112 415   xx eee , giving your answer correct to two decimal places where appropriate. [5] (b) (i) Sketch the graph of xy  3 , indicating the y-intercept clearly. [2] (ii) Insert on your sketch the additional graph required to obtain a graphical solution of the equation 2)3(3 xx . [2] 4 [Maximum mark: 8] The straight line 22yx cuts the curve 2 31xy at the points A and B. Find (i) the coordinates of A and B, [4] (ii) the equation of the perpendicular bisector of AB. [4]

ACS(Independent)MathDept/Y3IPCoreMathPaper2/2014/FinalExamination 3 5 [Maximum mark: 8] The diagram shows a rectangular sheet of metal measuring 15 cm by 12 cm. A square of side x cm is cut out from each corner and the metal sheet is used to make an open box with base ABCD and height x cm. (i) Express the length of the side AB and BC in terms of x. [2] (ii) If 60 cm3 of water is added into the box, the height of the water level will be 11 2 cm. Form an equation in x and show that it reduces to 070272 2  xx . [2] (iii) Solve the equation 070272 2  xx . Hence, find the capacity of the box. [4] 6 [Maximum mark: 12] (a) Express   1 12 1 12 2 2    xx as a single fraction. [3] (b) Solve the equations (i) xx 2log42log3  , [5] (ii)   3log21log323log 22 2 2  xx . [4]

ACS(Independent)MathDept/Y3IPCoreMathPaper2/2014/FinalExamination 4 7 [Maximum mark: 9] (a) Given that the line mxy  3 meets the curve 22 6 5y x x   , find the range of values of m. [4] (b) P is a point on the curve xy 1 and Q is a fixed point with coordinates  6,2 . The midpoint of PQ is (h, k). (i) If the x-coordinate of P is n, write down the coordinates of the midpoint of PQ in terms of n. [2] (ii) Hence, express k in terms of h. [3] 8 [Maximum mark: 12] (a) A triangle has sides 15, 41, and 52. What is its area? [5] (b) AB is a chord on the circle with centre O and C is a point on AB such that  60OCB . Given that OC = 6 cm and BC = 8 cm, find (i) OB, [3] (ii) AOC . [4]

ACS(Independent)MathDept/Y3IPCoreMathPaper2/2014/FinalExamination 5 9 [Maximum mark: 10] Answer the whole of Question 9 on a sheet of graph paper. The table shows experimental values of 2 variables, x and y. x 1 2 2.5 3 y 2.12 2.86 3.44 4.18 (i) It is known that x and y are connected by the equation 132  bxay . By plotting y2 against x3, obtain a straight line to represent the above data. [4] (ii) Use your graph to estimate the value of a and of b. [2] (iii) By drawing a suitable straight line, find the value of x and of y which satisfy the simultaneous equations ay2 – bx3 = 1 y2 – x3 = 1 [4] End of Paper Answer Key 1 a) 30,21,4  rqp b) n = 6.42 or -1.17 2 a) 122  x b) 2 1x or 1x 3 a) 85.1x 4 i) A (-5, -8) and B (-1, 0). ii) 0112  xy 5 i) AB = )215( x cm BC = )212( x cm iii) 140 cm³ 6 a) 2 12 2       x x b) i) 82 orx ii) 5.83 7 a) 8 15m b) i)       m mm 2 61,2 2 ii) )1(4 1112   h hk 8 a) 234 cm² b i) 7.21 cm ii)  9.13AOC 9 ii) 4 1a 8 1b iii) 82.1x 56.2y