Sec 3 E 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 E MATH 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 [Algebra] (a) Simplify 2𝑦2−3𝑦−5 𝑦2−1 . (b) 𝑏 = √ 4+5𝑎 3𝑎−11 Make a the subject of the formula. (c) (i) Express 𝑥2 + 6𝑥 − 11 in the form (𝑥 + 𝑏)2 + 𝑐, where b and c are constants. (ii) Hence, solve the equation 𝑥2 + 6𝑥 − 11 = 0. [3] [3] [2] [2] 2 [Quadratic Equation] A road up a mountain is 18 km long. Paul followed this road at an average speed of x km/h. (i) Write down an expression, in terms of x, for the number of hours he took to walk up the mountain. (ii) Paul came down the mountain by a different road. The length of this road was 25 km. His average speed coming down the mountain was 2 km/h greater than his average speed going up the mountain. Write down an expression, in terms of x, for the number of hours he took to walk down. (iii) It took Paul 1.5 hours less to come down than to go up. Write down an equation in x, and show that it simplifies to 3𝑥2 + 20𝑥 − 72 = 0. (iv) Solve the equation 3𝑥2 + 20𝑥 − 72 = 0, giving both answers to 2 decimal places. (v) Calculate, correct to the nearest minute, the total time Paul took to go up and come down the mountain. [1] [1] [3] [3] [2] 3 [Indices] (a) Simplify (5𝑥)3 × (9𝑦4)−1 2, leaving your answer in positive index notation. (b) Solve 62𝑦×36 6 1 3 = 216𝑦. [3] [3] 4 [Standard Form] (a) Sound travels at 1234.8 km/h. Express the speed of sound in metres per second, giving your answer in standard form. (b) Mercury is 6.58 × 107 kilometres from the Sun and the Pluto is 5.914 billion kilometres from the Sun. How much further from the Sun is Pluto than Mercury? [2] [2]

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