Sec 2 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 2 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 [Simultaneous Equation] Solve the simultaneous equations. 𝑥 3 − 3𝑦 4 = 2 4𝑥 + 3𝑦 = 16 [3] 2 [Linear Graph The diagram shows a line segment 𝐴𝐵. (a) Find the gradient of the line 𝐴𝐵. (b) State the equation of the line that is parallel to the y-axis and passes through the point A. (c) Draw and label a line 𝑙1 that has a zero gradient and a y-intercept of −4. [1] [1] [1] 3 [Expansion] (a) Simplify 𝑥2 − (𝑥 − 1)2 + (𝑥 − 2)2 − (𝑥 − 3)2. (b) Hence, find the value of 20202 − 20192 + 20182 − 20172. [2] [2] 4 [Factorisation]Factorise fully (a) 8𝑥2 − 2, (b) 15𝑎2 − 5𝑎𝑏 + 2𝑏 − 6𝑎. [2] [2] 5 [Changing Subject Formula] Make x the subject of the formula. 𝑦 = √ 4𝑥 𝑝𝑥−1 6 [Algebraic Fraction] (a) Simplify 5𝑎2𝑏 7𝑐 ÷ 15𝑏2𝑎 4𝑐3 . (b) Express 3𝑦 (𝑦−2)2 + 3 4−2𝑦 as a single fraction in its simplest form. [2] [3]

Page 3 Paradigm Specialising in O Level Mathematics Paradigm Secondary Math Department 7 [Quadratic Equation] (a) Solve 2𝑥2 + 15𝑥 − 8 = 0. (b) Hence, solve the equation 2(𝑝 − 1)2 + 15(𝑝 − 1) − 8 = 0. [2] [2] 8 [Quadratic Equation - Application] Rio cycled for 30 km at a constant speed of x km/h. He then ran for the remaining 8 km at a constant speed of (𝑥 − 15) km/h. (a) Write down an expression, in terms of x, for the time in hours that Rio cycled. (b) Write down an expression, in terms of x, for the time in hours that Rio ran. (c) Given that the total time taken for the whole training is 2 hours, form an equation in x and show that it reduces to 𝑥2 − 34𝑥 + 225 = 0. (d) Solve the equation 𝑥2 − 34𝑥 + 225 = 0. (e) Explain why one of the solutions in (d) is not a possible solution. (f) Find the time taken, in hours and minutes that Rio cycled. [1] [1] [3] [2] [1] [1] 9 [Quadratic Equation - Sketching] The curve 𝑦 = 3 + 2𝑥 − 𝑥2 cuts the x-axis at two points 𝐴 and 𝐵, and the y-axis at 𝐶. Find (i) the coordinates of 𝐴 and 𝐶, (ii) the equation of the line of symmetry. [2] [1]

Page 4 Paradigm Specialising in O Level Mathematics Paradigm Secondary Math Department 10 [Coordinate Geometry] The variables of x and y are connected by the equation 𝑦 = −𝑥2 + 14𝑥 − 24. Some corresponding values of x and y are given in the table below. 𝑥 0 1 2 4 6 8 10 12 𝑦 −24 −11 0 16 24 𝑝 16 0 (a) Calculate the value of p. (b) On the grid opposite, draw the graph of 𝑦 = −𝑥2 + 14𝑥 − 24 for 0 ≤ 𝑥 ≤ 12. (c) State the equation of the line of symmetry for 𝑦 = −𝑥2 + 14𝑥 − 24. (d) From the graph, find the value of y when 𝑥 = 1.5. (e) By drawing a tangent, find the gradient of the curve at the point (6, 24). (f)(i) On the same axes, draw the graph of 𝑦 = 2𝑥 − 4 for 0 ≤ 𝑥 ≤ 12. (ii) Write down the x-coordinates of the points where this line intersects the curve. [1] [3] [1] [1] [2] [2] [1] 11 [Direct Proportion] P is directly proportional to the square of r and 𝑃 = 200 when 𝑟 = 5. (a) Express the P in terms of r. (b) When r is increased by 300% , find the percentage increase in P. [3] 12 [Maps and Scale] The scale of a map is 1: 80 000. (a) The length of a river is 5400 m. Find the length, in centimetres, of the river on this map (b) The area of a town on the map is 105 cm2. Find the actual area, in square kilometres, of the town. [2] [2] 13 [Congruent & Similar Triangle] The diagram below, which is not drawn to scale, shows 𝑃𝑄 is parallel to 𝑆𝑇. It is given that 𝑃𝑄 = 18 cm, 𝑆𝑇 = 11 cm, 𝑇𝑄 = 𝑥 cm and 𝑅𝑇 = (𝑥 + 2) cm. (a) State a triangle that is similar to ∆𝑆𝑅𝑇. (b) Hence, find the value of 𝑥. [1] [2]

Page 5 Paradigm Specialising in O Level Mathematics Paradigm Secondary Math Department 14 [Pythagoras Theorem and Trigonometry] The diagram shows a field ABCD. Q is on AB such that DQ is perpendicular to AB. 𝐷𝑄 = 58 m, 𝐷𝐵 = 71 m, angle 𝐷𝐴𝑄 = 64°, angle 𝐷𝐵𝐶 = 90° and angle 𝐵𝐶𝐷 = 25°. Calculate (a) QB, (b) AB, (c) the shortest distance from B to DC. [2] [2] [2] 15 [Statistics] The stem-and-leaf diagram shows the test results of a class of students. 0 1 2 3 4 2 8 3 5 7 8 1 2 4 4 4 8 0 5 5 Key: 1⃒8 means 18 marks Find (a) (i) the modal mark, (ii) the median mark. (b) Is the mean or median, a better representation of the subject ability of the class? Explain your answer. (c) A new student joined the class and took the same test. The new mean mark for the class is 30. Find the mark of the new student who joined the class. [1] [1] [1] [1]

Page 6 Paradigm Specialising in O Level Mathematics Paradigm Secondary Math Department Answer Key 1 𝑦 = − 2 3 𝑥 = 4 1 2 2 (a) Gradient of the line 𝐴𝐵 = −2 (b) 𝑥 = −3 (c) 3 𝑥2 − (𝑥2 − 2𝑥 + 1) + 𝑥2 − 4𝑥 + 4 − (𝑥2 − 6𝑥 + 9) = 2𝑥 − 1 − 4𝑥 + 4 + 6𝑥 − 9 = 4𝑥 − 6 or (𝑥 − 𝑥 + 1)(𝑥 + 𝑥 − 1) + (𝑥 − 2 − 𝑥 + 3)(𝑥 − 1 + 𝑥 − 3) = 2𝑥 − 1 + 2𝑥 − 5 = 4𝑥 − 6 4(2020) − 6 = 8074 4 (a) 2(2𝑥 − 1)(2𝑥 + 1) (b) (5𝑎 − 2)(3𝑎 − 𝑏) 5 𝑥 = 𝑦2 𝑝𝑦2 − 4 𝑦2 = 4𝑥 𝑝𝑥 − 1 𝑝𝑥𝑦2 − 𝑦2 = 4𝑥 𝑝𝑥𝑦2 − 4𝑥 = 𝑦2 𝑥(𝑝𝑦2 − 4) = 𝑦2 𝑥 = 𝑦2 𝑝𝑦2 − 4 6 (a) 4𝑎𝑐2 21𝑏 (b) 3𝑦+6 2(𝑦−2)2

Page 7 Paradigm Specialising in O Level Mathematics Paradigm Secondary Math Department 7 (a) 𝑥 = 1 2 or 𝑥 = −8 (b) 𝑝 = 1 1 2 or 𝑝 = −7 8 (a) 30 𝑥 ℎ (b) 8 𝑥−15 ℎ (c) 30 𝑥 + 8 𝑥−15 = 2 30(−15)+8𝑥 𝑥(𝑥−15) = 2 30𝑥−450+8𝑥 𝑥(𝑥−15) = 2 30−450 𝑥(𝑥−15) = 2 38𝑥 − 450 = 2𝑥2 − 30𝑥 2𝑥2 − 30𝑥 − 38𝑥 + 450 = 0 2𝑥2 − 68𝑥 + 450 = 0 𝑥2 − 34𝑥 + 225 = 0 (d) 𝑥 = 25 or 𝑥 = 9 (e) When 𝑥 = 9, 9 − 15 = −6 hence the running speed will be negative which is not possible. Therefore, 𝑥 = 9 is not a possible solution. (f) Time taken by Rio cycle = 1 hour and 2 minutes 9 (a)(i) 𝐴(−1,0); 𝐶(0,3) (ii) 𝑥 = 1 10 (a) 𝑝 = 24 (b) Graph Drawn (c) 𝑥 = 7 (d) 𝑦 = −511 (e) Gradient = 2 11 32 (f)(i) refer to graph (ii) 𝑥 = 2 and 𝑥 = 10 11 (a) 𝑃 = 8𝑟2 𝑃 = 𝑘𝑟2 𝑃 = 8𝑟2 (b) Percentage increase = 1500% 𝑃𝑛𝑒𝑤 = 8(4𝑟)2 = 16𝑉 Percentage increase = 16𝑃−𝑃 𝑃 × 100 = 1500%

Page 8 Paradigm Specialising in O Level Mathematics Paradigm Secondary Math Department 12 (a) Lengths of river on the map = 6.75 cm (b) Actual area of the town is 67.2 km2 13 (a) ∆𝑃𝑅𝑄 𝑥+2 2𝑥+2 = 11 18 18(𝑥 + 2) = 11(2𝑥 + 2) 18𝑥 + 36 = 22𝑥 + 22 4𝑥 = 14 𝑥 = 3.5 14 (a) 41.0 m 𝑄𝐵 = √712