MSHS 2026 Prelim AM P1 (for sharing)

This document consists of 19 printed pages and 1 blank page. [Turn over For Examiners’ Use Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 / 5 / 6 / 7 / 5 / 6 / 7 / 8 / 4 / 7 Q10 Q11 Q12 Q13 SUBTOTAL / 9 / 8 / 10 / 8 Statement Presentation Units Rounding Off Class/ Index Number Centre Number/ ‘O’ Level Index Number Name / / MARIS STELLA HIGH SCHOOL PRELIMINARY EXAMINATION SECONDARY FOUR ADDITIONAL MATHEMATICS 4049/1 Paper 1 20 August 2026 Candidates answer on the Question Paper. 2 hours 15 minutes READ THESE INSTRUCTIONS FIRST Write your class, 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. The number of marks is given in brackets [ ] at the end of each question or part question. The total of the marks for this paper is 90. 90

2 Mathematical Formulae 1. ALGEBRA Quadratic Equation For the equation ax2 + bx + c = 0, x = a acbb 2 42 −− Binomial expansion (a + b)n = an +       1 n an − 1b +       2 n an − 2b2 + ... +       r n an − r br + ... + bn, where n is a positive integer and       r n = ! !( )! n r n r− = ! )1)...(1( r rnnn +−− 2. TRIGONOMETRY Identities sin2 A + cos2 A = 1 sec2 A = 1 + tan2 A cosec2 A = 1 + cot2 A sin(A  B) = sin A cos B  cos A sin B cos(A  B) = cos A cos B  sin A sin B tan(A  B) = BA BA tantan1 tantan   sin 2 2sin cosA A A= 2 2 2 2cos 2 cos sin 2cos 1 1 2sinA A A A A= − = − = − 2 2 tantan 2 1 tan AA A= − Formulae for ABC A a sin = B b sin = C c sin 2 2 2 2 cosa b c bc A= + − 1 sin2 bc A=

3 1 A sum of $500 is invested in an account that pays compound interest at a rate of 6% per year. The interest is compounded annually. The investment is withdrawn in the year when the total interest exceeds $300. Find the least number of years the money must be invested before it is withdrawn. [5] [It is given that for compound interest, total amount 1 100 n rP=+  ]

4 2 Find the set of values of the constant m for which the curve 2 43y mx x m= + + + is completely above the line 4 12.yx=+ [6]

5 3 (a) Differentiate ln xy x= with respect to x. [3] (b) Hence find e 21 ln dx xx− . [4]

6 4 Express 2 2 2 7 5 23 xx xx −− −− in partial fractions. [5]

7 5 (a) Show that the x-coordinate of the stationary point on the curve 2 3 31 343y x x= − + is 3 72 . [4] (b) Determine the nature of this stationary point. [2]

8 6 The force, F Newtons, acting on a moving vehicle depends on its speed, s m/s and can be modelled by the formula kF As= , where A and k are constants. The table below shows corresponding values of s and F. (a) Explain how a straight line graph can be drawn to represent the formula and draw the graph on the grid on page 9. [4] (b) Use your graph to estimate the values of A and k. [3] s 2 4 6 8 10 F 6 22 50 80 150

9

10 7 (a) Find, in ascending powers of x, the first four terms in the expansion of 6 1 3 bx − , where b is a constant. Simplify the coefficients in your expansion. [4] (b) Given that the expansion of 6 2 3 3 11 3 bxxx   + + −     has no constant term, find the possible values of b. [4]