Sec 1 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 1 MATH EOY 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 [Numbers] Consider the following set of numbers. 29, √5, 3𝜋 2 , 1, 0. 2̇ 3̇ , 73, √16, 9 Write down all (a) the irrational number(s), (b) the prime number(s), (c) the perfect square(s), [1] [1] [1] 2 [Approximation & Estimation] Express (a) 10.0945 correct to 2 decimal places. (b) 20 947 correct to 3 significant figures. (c) Estimate the value of 12.46−√9.23 1.01+3.84 by writing each number correct to 1 significant figure. Show your working clearly. [1] [1] [2] 3 [HCF & LCM] (a) Find the highest common factor of 1428 and 2660. (b) Find the lowest common multiple of 26 × 32 × 515 and 25 × 33 × 7. Leave your answer in index notation form. (c) Using prime factorisation, find √2304. Show your working clearly. (d) Find the smallest integer value of k where 168𝑘 is a perfect square. [1] [1] [2] [2] 4 [Number Operations] Evaluate the following without using calculator. Show your working clearly. (a) 2 − (−3) − 5 × 5 ÷ (10 − 15)2 (b) 3 3 5 + (−2) − ( 2 3 + 5 6) ÷ 1 1 6 [2] [3] 5 [Algebra] (a)(i) Given that 𝑎 = 5, 𝑏 = −3, 𝑐 = −1, find the value of 𝑎𝑐2 − 4𝑏2. (ii) Given that 𝑑 = − 1 3 , 𝑒 = 5 7 , 𝑓 = 3 8, find the value of de−5f def . (b) Expand the following algebraic expressions. (i) −5(2𝑏 − 7 5). (c) Factorise the following completely. (i) 2𝑎 − 14𝑎2𝑏 + 22𝑎𝑏2 (d) Express 2(𝑥+3) 5 − 3(𝑥−2) 4 as a single fraction in its simplest form. [1] [1] [1] [1] [3]

Page 3 Paradigm Specialising in O Level Mathematics Paradigm Secondary Math Department 6 [Number Patterns] (a) Fill in the next two terms of the number sequences. (i) −3, −1, 1, 3, 5, ___, ___, … (ii) −6, −10, −18, −34, −66, ___, ___, … (b) The diagram below shows the first three figures of a sequence of chopsticks. (i) Find the number of chopsticks used in Figure 4. (ii) Find an expression for the nth term. (iii) Hence, find the number of chopsticks used in the 200th term. [1] [1] [1] [1] [1] 7 [Percentage] (a) Find 66 2 3 % of m if m is 78. (b) Find n if 160% of n is 280. (c) On a menu, the marked price of meal is $𝑥. Tommy was given a 17% discount from the marked price. After that, a 10% service charge was charged to his bill. Finally, a 7% Goods and Services Tax (GST) was charged to his bill. Find the amount he paid for his meal in terms of x. [1] [1] [2] 8 The table below shows the prices of three packs of batteries sold at a supermarket. Pack A Pack B Pack C Number of batteries in each pack 16 10 12 Price of each pack/$ 15.90 12.60 14.90 Which pack of batteries has the best value for money? Show your working clearly. [2] 9 [Speed] To celebrate Singapore’s 55th. Holly ran 33 km in 250 minutes, rested for 1 4 hour and ran 22 km in 2 hours. Find her average speed in kilometres per hour. [2]

Page 4 Paradigm Specialising in O Level Mathematics Paradigm Secondary Math Department 10 [Polygon] (a) Four of the exterior angles of an octagon (eight-sided polygon) are 52° each. The remaining exterior angles are equal. Find the value of one of the remaining exterior angles. (b) Each interior angle of a regular polygon is 120°. How many sides does the polygon have? [2] [2] 11 [Angle] In the diagram given below, 𝐴𝐵𝐶 and 𝐷𝐸𝐹 are parallel lines, and 𝐸𝐵𝑇 and 𝐹𝐶𝑇 are straight lines. ∠𝐷𝐸𝐵 = 105°, ∠𝐸𝐶𝐹 = 95° and ∠𝐶𝐹𝐺 = 130°. Find the values of a, of b, of c and of d. State your reasons clearly [4] 12 [Perimeter and Area of Composite Figures] In the figure given below, 𝐴𝐶𝐸𝐹 is a trapezium, 𝐵𝐶𝐷𝐻 is a parallelogram, 𝐸𝐺𝐹 is a semicircle and 𝐴𝐶 is parallel to 𝐹𝐸. It is given that 𝐴𝐵 = 19 cm, 𝐵𝐶 = 7 cm, 𝐷𝐸 = 10 cm, 𝐸𝐹 = 12 cm, 𝐴𝐹 = 13 cm, 𝐵𝐻 = 5 cm, 𝐴𝑋 = 12 cm and 𝐶𝑌 = 4 cm. Find (a) the perimeter of the shaded figure, (b) the area of the shaded figure. [2] [4]

Page 5 Paradigm Specialising in O Level Mathematics Paradigm Secondary Math Department 13 [Mensuration] The diagram shows a concrete slab of length 48 cm, width 20 cm and height 20 cm with a cylindrical hollow section of diameter 12 cm. Find (a) he volume of the concrete slab. (b) the total surface area of the concrete slab. [3] [3] 14 [Linear Graph] A class of students in Paradigm wants to sell cupcakes for fund raising. The profit, $ y for selling x cupcakes is given by 𝑦 = 3𝑥 − 50, for 0 ≤ 𝑥 ≤ 60. The table shows some values of x and its corresponding values of y. (a) Find the values of p and of q. (b) On the graph paper opposite, using a scale of 2 cm to represent 10 cupcakes on the x-axis and 2 cm to represent $20 on the y-axis, draw the graph of 𝑦 = 3𝑥 − 50, for 0 ≤ 𝑥 ≤ 60. (c) Use your graph to find (i) the profit made when 45 cupcakes are sold. (ii) the number of cupcakes that must be sold to make a profit of $126. (d) State the gradient of the graph and explain what the gradient represents. (e) How many cupcakes must the students sell before they could start making a profit? 𝑥 0 10 30 50 60 𝑦 −50 𝑝 40 100 𝑞 [2] [3] [2] [2] [2] [2]

Page 6 Paradigm Specialising in O Level Mathematics Paradigm Secondary Math Department 15 [Statistics] The pictogram shows the number of people visiting a public library in a week. (a) 250 people visited the library on Sunday. Complete the pictogram to represent this data. (b) Find the ratio of the number of people who visited the library during the weekdays to the number of people who visited the library during the weekends. (c) Ashley claims that a line graph is a better representation of the data. Explain why she made such a claim. [1] [2] [1]

Page 7 Paradigm Specialising in O Level Mathematics Paradigm Secondary Math Department Answer Key 1 (a) √5, 3𝜋 2 (b) 29 (c) √16, 1, 9 2 (a) 10.09 (b) 20 900 (c) 10−√9 1+4 = 1.4 or 1 2 5 3 (a) 1428 = 2 × 2 × 3 × 7 × 17 2660 − 2 × 2 × 5 × 7 × 19 HCF of 1428 and 2660 2 × 2 × 7 = 28 (b) Lowest common multiple of 26 × 32 × 515 and 25 × 33 × 7 26 × 32 × 515 × 7 Reject: non-index notation answer (c) 2304 = 28 × 32 √2304 √28 × 32 24 × 3 = 48 (d) 168 = 23 × 3 × 7 168𝑘 = 24 × 32 × 72 𝑘 = 2 × 3 × 7 𝑘 = 42 4 (a) 2 + 3 − 25 ÷ (−5)2 2 + 3 − 25 ÷ 25 5 − 1 = 4 (b) 18 5 − 2 ( 4 6 + 5 6) ÷ ( 7 6) 18 5 − 2 − 9 6 ÷ 7 6 18 5 − 2