ANDSS AM2024WA2

This document consists of 9 printed pages. Setter: Mr Azmi O ANDERSON SECONDARY SCHOOL Weighted Assessment 2 2024 Secondary Three Express CANDIDATE NAME: CLASS: / INDEX NUMBER: ADDITIONAL MATHEMATICS 4049 29 April 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.

WA2 3E Add Maths 2024 2 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation 2 0ax bx c+ + = , a acbbx 2 42 −−=

WA2 3E Add Maths 2024 3 1 Find the range of values of k for which 2( 3) 4k x x k+ − + is always positive for all real values of x. [4]

WA2 3E Add Maths 2024 4 2 (a) The equation of a polynomial is given by ( ) 3f 9 10x x x= − − . Factorise ( )f x completely. [3] (b) Hence solve the equation ( )f0 x = . [2]

WA2 3E Add Maths 2024 5 3 A triangle has an area of ( )3 75+ cm2. Its perpendicular height is given to be ( )2 108 4− cm. Find the length of its base leaving your answer in the form 3 cmab m  + where a, b and m are integers. [4]

WA2 3E Add Maths 2024 6 4 (a) Solve the equation 3 11 2xx−= . [3]

WA2 3E Add Maths 2024 7 (b) Given that 15 12 5+ can be expressed in the form 5ab+ , where a and b are rational numbers, show that 2 2 36 5 15bb += . [4]

WA2 3E Add Maths 2024 8 5 The line y x k=− is a tangent to the curve 22 39xy+= . Find the possible values of k. [4]

WA2 3E Add Maths 2024 9 6 The function ( ) 32f 3 5x x ax x b= + − + , where a and b are constants, has a factor of 32x− and leaves a remainder of 40− when it is divided by 2x+ . (a) Find the value of a and of b. [5] (b) Hence find the remainder when ( )f x is divided by 4x+ . [1] End of Paper