2024 NJC Paper 1 H2 Math Prelim (Qn Paper)

* © NJC 2024 NATIONAL JUNIOR COLLEGE SENIOR HIGH 2 Higher 2 NAME CLASS 2ma2 REGISTRATION NUMBER MATHEMATICS 9758/01 Preliminary Examination 09 September 2024 Paper 1 3 hours Candidates answer on the Question Paper. Additional Materials: List of Formulae (MF26) READ THESE INSTRUCTIONS FIRST Write your name, class and registration number in the boxes above. Please write clearly and use capital letters. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use paper clips, glue or correction fluid. Answer all the questions. Write your answers in the spaces provided in the question paper. 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 graphing and/or scientific calculator is expected, where appropriate. All relevant working, statements and reasons must be shown in order to obtain full credit for your solution. You are reminded of the need for clear presentation in your answers. Up to 2 marks may be deducted for improper presentation. The number of marks is given in the brackets [ ] at the end of each question or part question. The total number of marks for this paper is 100. Question Number Marks Possible Marks Obtained 1 4 2 4 3 5 4 7 5 8 6 8 7 8 8 9 9 10 10 11 11 12 12 14 Presentation Deduction – 1 / – 2 TOTAL 100 This document consists of 7 printed pages.

2 © NJC 2024 1 A circular sector has radius r cm and angle  radians. This sector has area A cm2 and fixed perimeter k cm. (i) Show that d 2.d2 Ak rr =− [2] (ii) Given that r is increasing at a constant rate of 1cm s ,10 k − find in terms of k, the rate at which A is changing when the arc length of the sector is equal to the radius. [2] 2 Two of the roots of the equation 32 0z az bz c+ + + = are 2i π33e − and –2. Given further that a, b and c are integer constants, find the values of a, b and c. [4] 3 Do not use a calculator to solve this question. (i) Solve the inequality 2 6 1.45 x xx − +− [3] (ii) Hence solve the inequality 2 2 6 1.45 xx xx − +− [2] 4 Relative to the origin O, points A, B and C have position vectors a, b and c respectively, where a, b and c are non-zero vectors that are not parallel to one another. The points A, B and C are not collinear. A point of trisection is a point that divides a line segment internally in the ratio 1: 2 or 2 :1. Suppose another two points D and E are points of trisection of line segments AB and AC respectively and both points are nearer to A than to B and C respectively. The lines BE and CD meet at point F. (i) Show that t he vector equations of the lines BE and CD can be expressed a