XMS SEC 4 AMATH 2022 WA1 QP

This document consists of 8 printed pages. [Turn over XINMIN SECONDARY SCHOOL SEKOLAH MENENGAH XINMIN Weighted Assessment 1 2022 CANDIDATE NAME CLASS INDEX NUMBER ADDITIONAL MATHEMATICS Secondary 4 Express Setter: Mr Johnson Chua Vetter: Mrs Loh Si Lan 4049 22 February 2022 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) 2 2 162yx x= − − , leaving your answer in positive index. [1] (b) 32 2 5 4 7 3x x xy x + − += , leaving your answer in positive index. [2] (c) ( ) 424 5 3yx=− [2]

4 2 (i) Differentiate 2 2 53 10 6 x x + − with respect to x. [2] (ii) Differentiate 42 2 53 10 6 x x  +  − with respect to x, leaving your answer in the form ( ) ( ) 2 2 53 53 m n kx x x + − where k, m and n are constants. [2]

5 [Turn over 3 The equation of a curve is 235y x x=+ . Find the gradient(s) of the curve at the point(s) where it crosses the line 6yx= . [5]

6 4 (i) By considering the general term, explain why the binomial expansion of 7 2 3 xx  + does not have a term independent of x. [3] (ii) Find the term independent of x in the expansion of ( ) 7 2 2 3 52xxx  +− . [3]

7 [Turn over 5 A tangent to a circle at the point ( )6,6− passes through the origin. The centre, C, of the circle lies on the line 4 3 40yx−= . (i) Show that the centre of the circle is ( )8, 4− . [4] (ii) Find the equation of the circle. [2]

8 (iii) Find the coordinates of the circle which is nearest to the y-axis. [2] (iv) Explain why the point ( )10,6.5P − lies outside the circle. [2] END OF PAPER

9 [Turn over Answer Key 1. (a) −2𝑥 + 32 𝑥3 (b) 5 + 7 𝑥2 − 6 𝑥3 (c) −96 × (5 − 3𝑥2)3 2 (i) −120𝑥 (10𝑥2−6)2 (ii) −15𝑥(5𝑥2+3) 3 (5𝑥2−3)5 3 3√5 4 (i) Since r = 14/3, which is not an integer, there is no term independent of x. (ii) – 1890 5 (i) (–8 , 4) (ii) (𝑥 + 8)2 + (𝑦 − 4)2 = 8 (iii) (−8 + √8, 4) (iv) Since the distance between P and centre of circle is longer than the length of radius, P lies outside the circle.