Greendale 2021 Prelim Sec4E AMATHP1

Name:___________________________________ ( ) Class: Sec This document consists of 19 printed pages including this cover page. Greendale Secondary School 2021 GREENDALE SECONDARY SCHOOL Preliminary Examination 2021 Additional Mathematics 4049/01 Paper 1 31 August 2021 Secondary 4 Express 2 hours 15 minutes Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your index number and name 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 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. At the end of the examination, 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 90. Question Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q1 0 Q11 Q12 i,ii iii i,ii iii,i v Marks 90

Greendale Secondary School 2 Secondary 4 Express Preliminary Examination 2021 Additional Mathematics Paper 1 No of additional booklets/ writing paper used No of additional graph paper used Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation , Binomial expansion , where n is a positive integer and 2. TRIGONOMETRY Identities Formulae for ABC Area of  =

Greendale Secondary School 3 Secondary 4 Express Preliminary Examination 2021 Additional Mathematics Paper 1 Answer all the questions. 1 The curve has a stationary point. (i) Find the x-coordinate of the stationary point. [3] (ii) Find . [2] (iii) Determine the nature of the stationary point. [1]

Greendale Secondary School 4 Secondary 4 Express Preliminary Examination 2021 Additional Mathematics Paper 1 2 Water is poured into an inverted cone. The radius of its circular base is 3x cm and its vertical height is cm. (i) Express the volume of the cone in terms of x. [2] (ii) If the water is poured into the container at a constant rate of , calculate the rate of change of x when . [4]

Greendale Secondary School 5 Secondary 4 Express Preliminary Examination 2021 Additional Mathematics Paper 1 3 The equation of the curve is given by , where c is a constant. (i) Find the range of values of c such that . [3] (ii) Given that , find the values of m such that is a tangent to the curve. [3]

Greendale Secondary School 6 Secondary 4 Express Preliminary Examination 2021 Additional Mathematics Paper 1 4 It is given that and that . (a) Find, in terms of x, (i) [2] (ii) [1] (b) Hence, write down, in terms of n and x, . [1] (c) Show that is always positive, for all values of n. [2]

Greendale Secondary School 7 Secondary 4 Express Preliminary Examination 2021 Additional Mathematics Paper 1

Greendale Secondary School 8 Secondary 4 Express Preliminary Examination 2021 Additional Mathematics Paper 1 5 Do not use a calculator for this whole question. It is given that A and B are angles in the same quadrant such that and . (a) Find the values of (i) , [3] (ii) . [2] (b) Use your answers in (a) to deduce which quadrant the angle must lie in. Explain your answer. [2]

Greendale Secondary School 9 Secondary 4 Express Preliminary Examination 2021 Additional Mathematics Paper 1 6 (i) Express , in the form of , where p and q are constants to be found. [4] (ii) Solve . [3]

Greendale Secondary School 10 Secondary 4 Express Preliminary Examination 2021 Additional Mathematics Paper 1 7 It is given that where a and b are positive integers and . (i) The graph passes through . Show that the smallest possible value of b is 4 and find the value of a. [2] (ii) Sketch the graph . [3] (iii) Find the exact value of the gradient of the tangent at . [2]