Anglican High 4048_02 AS

NAME: _______________________________ ( ) CLASS: 4 ( ) 9o MATHEMATICS 4048/02 Paper 2 31 August 2022 2 hours 30 minutes Candidates answer on the Question Paper and Graph Paper READ THESE INSTRUCTIONS FIRST Write your name, index number and class on all the work you hand in. Write in dark blue or black pen. You may use a HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all the 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. 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  , use either your calculator value or 3.142, unless the question requires the answer in terms of  . 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. ---------------------------------------------------------------------------------------------------------------------------- For Examiners’ Use Questions 1 2 3 4 5 6 7 Marks Questions 8 9 10 11 12 13 14 Marks Table of Penalties Units 100 Clarity/Logic Accuracy/Precision Parent’s Name and Signature: Date: This document consists of 23 printed pages and 1 blank page. SOLUTIONS S4

2 1 (a) Below are the first five terms of a sequence. 1 17 4 25 9 33 16 41 25 49 (i) Find the sixth term of the sequence. (ai) 36 12 57 19= B1 award mark even if student give 36 57 (ii) nT is the nth term of the sequence. Find an expression, in terms of n, for nT . (aii) 2 89 n nT n= + B2: 1 mark for each series. (iii) The kth term is 1. Find the value of k. (aiii) ( )( ) 2 2 89 8 9 0 9 1 0 9 or 1 (N.A.) kk kk kk kk =+ − − = − + = = =− M1 A1 (b) Ali invested $7500 in a saving account for 3 years. The rate of compound interest was fixed at r% per annum. At the end of 3 years, there was $8436.48 in his account. Find the value of r. b ( ) 3 3 3 $8436.48 $7500 1 100 $8436.481 100 $7500 $8436.481 100 $7500 1 1.04100 1.04 1 100 4 r r r r r r =+  += += += = −  = M1 M1 A1

3 2 The diagram shows a rhombus ABCD, with sides 5 units, and coordinates ( )2,0A − and ( )1, 4D . (a) Show that the equation of line BC is 3 4 12yx=− . (a) ( )( 2 5,0) 3,0BB− + = 40Gradient 1 ( 2) 4 3 −= −− = ( ) 4 3 403 3 4 4Equation of : 4 3 3 4 12 y x c c c BC y x yx =+ =+ =− =− =− M1: coordinates of B or C M1