ANDSS SEC3AM2024WA1_ANSWER

This document consists of 6 printed pages. Setter: Mr Aaron Wong O ANDERSON SECONDARY SCHOOL Weighted Assessment 1 2024 Secondary Three Express CANDIDATE NAME: CLASS: / INDEX NUMBER: ADDITIONAL MATHEMATICS 4049 29 February 2024 45 minutes Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your name, class and index number 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 paper clips, highlighters, glue or correction fluid/tape. Answer all the 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. You are reminded of the need for clear presentation in your answers. 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.

WA1 3E Add Maths 2024 2 1 (i) Express 2 213 x x−− in the form 2()a x h k−+ , where a, h and k are constants. [3] 1(i) ( ) ( ) ( ) ( ) 2 2 2 2 2 2 2 2 12 1 ( 6 ) 133 1 6 3 3 13 1 3 9 13 1 3 3 13 1 343 x x x x xx x x x − − = − − = − + − − = − − − = − − − = − − M1 for factorizing 1 3 M1 A1 (ii) Hence find the minimum value of 2 213 x x−− and the value of x at which the minimum occurs. [2] 1(ii) Minimum value = 4− Value of x which minimum occurs = 3 B1 B1 (iii) Sketch the curve 2 213 xyx= − − . [2] 1(iii) B1 – Correct shape B1 – Turning point and y- intercept stated O y x (3, −4) −0.464 6.46 −1

WA1 3E Add Maths 2024 3 2 Find the values of k for which the equation 2( 1) 2 2k x kx k+ − = − has real roots. [4] 2 2 2 ( 1) 2 2 ( 1) 2 2 0 k x kx k k x kx k + − = − + − + − = Since the equation has real roots, discriminant 0 . ( ) ( )( ) 2 22 22 2 4 1 2 0 4 4( 2) 0 4 4 4 8 0 4 8 0 48 2 k k k k k k k k k k k k − − + −  − − −  − + +  + − − M1 – Simplify quadratic equation M1 – correct discriminant 0 M1 – finding linear inequality A1 – range of k 3 The equation of a curve is 22 (4 ) 2y x k x k= + − − , where k is a constant. (a) Show that the line 7 18yx=− is a tangent to the curve when 5k = and find the coordinates of the point of intersection. [3] 3(a) When 5k = , 22 10 _____(1)y x x= − − 7 18 _____(2)yx=− Substitute (1) into (2): 2 2 2 2 2 10 7 18 2 8 8 0 4 4 0 ( 2) 0 2 x x x xx xx x x − − = − − + = − + = −= = Since there is only one solution of x, 7 18yx=− is tangent to the curve. OR Di