NASS 2025 EMATH PRELIM P2 QP

Name: .............................................................. Register no: ........... Class: ........... NGEE ANN SECONDARY SCHOOL O PRELIMINARY EXAMINATION MATHEMATICS 4052/02 Paper 2 29 August 2025 2 hour 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, register number and class 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. 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. For Examiner’s Use Total /90 Checked by student: ………………………………. Date: ………………… This document consists of 28 printed pages.

2 NAS/2025/Prelim/MA-O/P2 Mathematical Formulae Compound Interest Total amount = 1 100 n rP+ Mensuration Curved surface area of a cone = rlπ Surface area of a sphere = 2π4 r Volume of a cone = h r2π3 1 Volume of a sphere = 3π3 4 r Area of triangle ABC = 1 sin2 ab C Arc length = rθ , where θ is in radians Sector area = 21 2 r θ , where θ is in radians Trigonometry sin sin sin abc ABC= = 2 22 2 cosa b c bc A=+− Statistics Mean = fx f ∑ ∑ Standard deviation = 22fx fx ff  − ∑∑ ∑∑

3 NAS/2025/Prelim/MA-O/P2 Answer all the questions. 1 (a) 23( ) 1hybx b += − (i) Find h when 5b= , 2x= and 0y= . Answer h = …………………………………. [2] (ii) Rearrange the formula to make b the subject. Answer b = …………………………………. [3]

4 NAS/2025/Prelim/MA-O/P2 (b) Solve these simultaneous equations. 6 3 16 9 2 11 xy xy −= += Answer x = …………………………………. y = …………………………………. [3]

5 NAS/2025/Prelim/MA-O/P2 (c) Solve 2 19 3 2 72 53 3 x xx x + +=−− − . Give your solutions correct to two decimal places. Answer x = …….…….…… or x = ……..……….. [3]

6 NAS/2025/Prelim/MA-O/P2 2 (a) Complete the table of values for 52y x= + . [1] x – 3 – 2 – 1 1 1.5 2 3 y 0.3 – 0.5 – 3 7 4.5 3.7 (b) On the grid opposite, draw the graph of 52y x= + for 3 3.x−≤ ≤ [3] (c) The equation 52 tx+= has no solution for 33 x−≤ ≤ . Given that atb<< , use your graph to find the possible values of a and b. (d) By drawing a tangent, find the gradient of the curve at =x 2. Answer ……………………………………. [2] Answer a = ….……..… b = ……...…..…. [2]

7 NAS/2025/Prelim/MA-O/P2 x 2 y – 1 – 1 – 2 – 2 – 3 – 3 1 1 2 3 3 4 5 6 7 0

8 NAS/2025/Prelim/MA-O/P2 (e) The points of intersection of the line 45yx= − and the curve give the solutions of the equation 2 20 0Ax Bx−+= . Find the value of A and B. Answer A = …………………………………. B = …………………………………. [2]

9 NAS/2025/Prelim/MA-O/P2 3 The front wheel of a tricycle has a circumference of x cm. The two rear wheels of the tricycle each has a circumference of 50 cm lesser than the front wheel. The tricycle travels 15 m. (a) Write down an expression, in terms of x, for the number of revolutions that the front wheel makes. Answer ………………………………………. [1] (b) Write down an expression, in terms of x, for the number of revolutions that each rear wheel makes. Answer ………………………………………. [1] (c) Each rear wheel makes 2.5 more revolutions than the front wheel. Form an equation, in terms of x, and show that it simplifies to 2 50 30000 0xx−− = . [2]

10 NAS/2025/Prelim/MA-O/P2 (d) Solve the equation 2 50 30000 0xx−− = . Answer x = ………………or x = …………………. [3] (e) Find the diameter of the front wheel of the tricycle. Answer ……………………………………cm [1]