NASS 2026 MA-O S4&5 Prelim P2 (QP)

Name: .............................................................. Register no: ........... Class: ........... NGEE ANN SECONDARY SCHOOL O PRELIMINARY EXAMINATION MATHEMATICS 4052/02 Paper 2 26 August 2026 2 hours 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. The number of marks is given in brackets [ ] at the end of each question or part question. If working is needed for any question it must be shown with the answer. Omission of essential working will result in loss of marks. The total of the marks for this paper is 90. The use of an approved scientific calculator is expected, where appropriate. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For , use either your calculator value or 3.142. For Examiner’s Use Total /90 Checked by student: ………………………………. Date: ………………… This document consists of 21 printed pages and 1 blank page.

2 NAS/2026/Prelim/MA-O/P2 Mathematical Formulae Compound interest Total amount = 1 100 n rP    Mensuration Curved surface area of a cone = πrl Surface area of a sphere = 24πr Volume of a cone = 21 π3 r h Volume of a sphere = 34 π3 r Area of a triangle ABC = Cab sin2 1 Arc length = r , where  is in radians Sector area = 21 2 r  , where  is in radians Trigonometry C c B b A a sinsinsin  2 2 2 2 cosa b c bc A   Statistics Mean = f fx   Standard deviation = 22fx fx f f        

3 NAS/2026/Prelim/MA-O/P2 Answer all the questions. 1 Points A, B and C are on horizontal ground. AB = 418 m and AC = 680 m. B is on a bearing of 312 from A. C is due west of A. (a) Show that BC = 463.3 m, correct to one decimal place. Answer [2] North B A C 418 680

4 NAS/2026/Prelim/MA-O/P2 (b) A surveyor is standing at point A and operates a drone hovering vertically above point C. The surveyor’s eye level is 1.74 m above the ground. The angle of elevation of the drone from the surveyor’s eye level is 16.5 . Estimate the height of the drone above the ground at point C. Give your answer to one decimal place. Answer ……………………………m [2] (c) The surveyor receives the following instructions. Maintaining the same height above the ground, navigate the drone to a point T within triangle ABC such that T is equidistant from points B and C, and is also equidistant from the lines AC and BC. Using geometrical constructions, locate and label point T on the diagram on the previous page. [3]

5 NAS/2026/Prelim/MA-O/P2 (d) The surveyor receives further clarification about the location of T. T is on a bearing of x from C. CT = y m. By calculation, find the values of x and y. Do not obtain your answers by measurement from the diagram. Answer x = …………………………… y = …………………………… [5]

6 NAS/2026/Prelim/MA-O/P2 2 (a) (i) Solve the inequality 8 5 3 12x    . Answer ……………………………… [2] (ii) Represent your answer to part (a)(i) on this number line. [1] (b) Simplify   1 4 4 1 525 5 p pqq     . Answer ……………………………… [2] (c) Evaluate   2 17 6 7 7 r r r   . Answer ……………………………… [2] 5 4 3 2 1 0 2 3 4 5 x 1

7 NAS/2026/Prelim/MA-O/P2 (d) Write as a single fraction in its simplest form 2 2 3 5 8 2 4 4 3 a b a b a ab b    . Answer ……………………………… [3]

8 NAS/2026/Prelim/MA-O/P2 3 (a) (i) Complete the table of values for 2 120100y x  . x 2 1 1 2 3 4 5 6 y 20 20 70 86.7 92.5 95.2 96.7 [1] (ii) On the grid, draw the graph of 2 120100y x  for 2 6 x   . [3] 10 20 30 40 50 60 70 80 90 100 y x 0 1 2 3 4 5 6 1 2 10 20 30 40 50 60

9 NAS/2026/Prelim/MA-O/P2 (iii) By drawing a tangent, estimate the gradient of the curve at 3.5x . Answer ……………………………… [2] (b) Carl has two types of power banks, Power Bank A and Power Bank B, for charging his mobile phone. (i) Using Power Bank A, the battery percentage, y%, of Carl’s mobile phone after x hours of charging is given by the function 2 120100y x  , 2x . What does your answer to part (a)(iii) tell you about Power Bank A? ……………………………………………………………………………... ……………………………………………………………………………... [1] (ii) The solutions to the equation 3 2 5 12 0x x   represent the charging durations for which Power Bank A and Power Bank B charge Carl’s phone to the same battery percentage. Carl has only 4 hours to charge his mobile phone. By drawing a suitable straight line on the grid, determine whether Carl should use Power Bank A or Power Bank B. Answer [4]

10 NAS/2026/Prelim/MA-O/P2 4 (a) 3 1PQ       and 91 32QR        . Explain why the points P, Q and R are collinear. …………………………………………………………………………………….. …………………………………………………………………………………….. ……………………………………………………………………………….......... [2] (b) The coordinates of Q are  0, 1 . Show that P lies on the x-axis. Answer [2]