XMS SEC 4 AMATH 2023 WA1 QP

This document consists of 9 printed pages and 1 blank page. [Turn over XINMIN SECONDARY SCHOOL SEKOLAH MENENGAH XINMIN Weighted Assessment 1 2023 CANDIDATE NAME CLASS INDEX NUMBER ADDITIONAL MATHEMATICS Secondary 4 Express Setter: Mr Johnson Chua Vetter: Ms Vanessa Chia 4049 22 February 2023 45 minutes Candidates answer on the Question Paper READ THESE INSTRUCTIONS FIRST Write your name, register number and class in the spaces at the top of this page. 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 questions. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. The use of an approved scientific calculator is expected, where appropriate. 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. You are reminded of the need for clear presentation in your answers. At the end of the paper, fasten all your work securely together. 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 30. Errors Qn No. Errors Qn No. Accuracy Simplification Brackets Units Geometry Marks Awarded Presentation Marks Penalised For Examiner’s Use 30 Parent’s/Guardian’s Signature:

2 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation Binomial expansion , where n is a positive integer and 2. TRIGONOMETRY Identities Formulae for ,02 =++ cbxax a acbbx 2 42 −−= ( ) nrrnnnnn bbar nbanbanaba ++     ++     +     +=+ −−− ......21 221 ( ) ( ) ( ) ! 1...1 ! ! ! r rnnn rnr n r n +−−=−=      1cossin 22 =+ AA AA 22 tan1sec += AA 22 cot1cosec += ( ) BABABA sincoscossinsin = ( ) BABABA sinsincoscoscos = ( ) BA BABA tantan1 tantantan  = AAA cossin22sin = AAAAA 2222 sin211cos2sincos2cos −=−=−= A AA 2tan1 tan22tan −= ABC C c B b A a sinsinsin == Abccba cos2222 −+= Abc sin2 1=

3 [Turn over Answer all the questions. 1 Differentiate each function with respect to x. (a) 324 3 1y x x x= − + − [1] (b) ( ) 22 2 21 21 x y x − = − , leaving your answer in the form 221kx x − , where k is a constant. [2] 2 A curve has the equation ( ) 2 5y px=− . The gradient of the curve at (2, )q is 4− . Find the value(s) of p and q given that p > q. [4]

4 3 (a) Find the first three terms, in ascending powers of x, in the expansion of ( ) 82 px− . [2] (b) When ( ) ( ) 2 81 2 2x px−− is expanded as far as the term in 2x , the result is 2q rx+ . Find the value of p, q and r. [4]

5 [Turn over TURN OVER FOR QUESTION 4

6 4 (a) Write down the general term in the binomial expansion of 14 3 13x x  + . [1] (b) Write down the power of x in this general term. [1] (c) Explain why the term in 4 1 x does not exist in the expansion of 14 3 13x x  + . [2]

7 [Turn over (d) Find the middle term in the expansion of 14 3 13x x  + . [2]

8 5 The equation of a circle, C1, with centre A, is 22 6 4 27x y x y+ − + = . (a) Show that coordinates of A is (3, 2)− and that radius of C1 is 40 units. [3] (b) The highest point on circle, C1, is P. Find the equation of the tangent to circle, C1, at P. [1] (c) Explain why the point ( 3,8)Q − lies outside the circle, C1. [2]

9 [Turn over (d) A second circle, C2, passes through the points A and Q. Given that the line 3 2 7yx−= passes through the centre of C2, find the equation of C2. [5] END OF PAPER

10 BLANK PAGE Answer Key 1 (a) 212 6 1xx−+ (b) 26 2 1xx − 2 2, 1pq= =− 3 (a) 22256 1024 1792 ...px p x− + + (b) 1, 256, 1280p q r=− = =− 4 (a) 14 14 414 3 rrxr −−  (b) 14 4 r− (c) Since 9 2r = , which is not an integer, 4 1 x term does not exist. (d) 14 7505784 x 5 (b) 2 40y=− + (c) Length of : 136CQ units Since length of CQ is longer than the length of radius, Q lies outside the circle. (d) 22( 10) ( 9) 170xy− + − =