Sec 3 A Math EOY Mock Exam Paper

Page 1 Paradigm Specialising in O Level Mathematics Paradigm Secondary Math Department Name: School: Target Grade: MOCK EOY PAPER 2025 SECONDARY 3 AMATH READ THESE INSTRUCTIONS FIRST INSTRUCTIONS TO CANDIDATES 1. Find a nice comfortable spot without distraction. 2. Be fully focused for the whole duration of the test. 3. Speed is KING. Finish the paper as soon as possible then return-back to Check Your Answers. 4. As you are checking your answers, always find ways to VALIDATE your answer. 5. Avoid looking through line by line as usually you will not be able to see your Blind Spot. 6. If there is no alternative method, cover your answer and REDO the question. 7. Give non-exact answers to 3 significant figures, or 1 decimal place for angles in degree, or 2 decimal place for $$$, unless a different level of accuracy is specified in the question. Wish you guys all the best in this test. You can do it. I believe in you. Team Paradigm PARADIGM [Turn Over]

Page 2 Paradigm Specialising in O Level Mathematics Paradigm Secondary Math Department 1 [Simultaneous Equation] Find the coordinates of the points of intersection of the curve 𝑥ଶ−𝑥𝑦+𝑦ଶ = 16 and the line 2𝑥−3𝑦=4. [5] 2 [Complete The Square] A dolphin jumps out of the water during a dolphin show. The height, 𝑦 𝑚, of the dolphin is given by 𝑦 = −4.5𝑡ଶ+ 9𝑡 , where 𝑡 is the time in seconds after the dolphin jumps out of the water. (i) Express 𝑦 = −4.5𝑡ଶ+ 9𝑡 in the form 𝑦 = 𝑎(𝑡 − ℎ)ଶ+ 𝑘 . (ii) How long did it take the dolphin to reach the maximum height and what is the maximum height? (iii) Find the range of values of t where the height of the dolphin is at least 3.375 m. [2] [2] [2] [4] 3 [Nature of Roots] (a) Find the largest integer k for which the line 𝑦 = 2𝑥 + 𝑘 intersects the curve 𝑥ଶ+ 2𝑦ଶ = 8 at two distinct points. (b) Show and explain why there are no values of 𝑚 for which the curve 𝑦=(𝑚−5)𝑥ଶ+2𝑚𝑥+(𝑚+3) is always positive. [5] [4] 4 [Surds] A cylinder has volume ൫√45 + √3൯ cm3. If the base area of the cylinder is ൫√45 + √3൯ cm3, find the height of the cylinder. Give your answer in the form 𝑎+𝑏√15 , where a, b and are rational numbers. [3] 5 [Exponential] Solve the equation 2𝑒ଶ௫=7+15𝑒ଶ௫ giving your answer correct to 1 significant figure. [4] 6 [Exponential] Explain why7௡ାଵ−4(7௡)−ଵ ଻(7௡) is an even number for all positive values of 𝑛. [3] 7 [Exponential Word Problem] The mass, m grams, of a radioactive substance remaining, t days after being measured is given by 𝑚 = 10𝑒ି଴.଴ଵ௧+ 0.2 . (a) Find the initial mass. (b) Sketch the graph 𝑚 = 10𝑒ି଴.଴ଵ௧+ 0.2 𝑓𝑜𝑟 𝑡 ≥ 0. (c) Find the least number of days it takes before the amount of substance is reduced to 5% of its initial mass. (d) Explain why the mass of the radioactive substanc