END OF TERM 3 MATHEMATICS EXAM ACADEMIC YEAR 2020/2021 STAGE 9 Date: 11/06/2021 INSTRUCTIONS - Answer all questions. - Use a black or dark blue pen. - Write your name in the box at the top of the page. - Write your answer to each question in the space provided. - Do not use an erasable pen or correction fluid - You should use a calculator where appropriate. - You must show all necessary working clearly; no marks will be given for unsupported answers from a calculator. INFORMATION The total mark for this paper is 100. The number of marks for each question or part question is shown in brackets [ ]. The maximum time is Two hours (2h). 2 Q1. a. Mount Everest is the highest mountain in the world. The summit is 8848 metres above sea level. Round this number to 1 significant figure (1 s. f.) [2] b. [3] c. Work out 𝟑𝟖−𝟕 𝟐+𝟓 Give your answer to 2 decimal places [3] 3 Q2. [2] [3] 4 Q3. a. [3] b. Factorise and simplify: i. ii. 𝑥 2 −5𝑥 𝑥 2 −3𝑥−10 𝑛2 −100 𝑛+10 [4] [2] 5 1 3 Q4. a. Without using a calculator, find the value of: 27 + 1 1 − 4 2 + 100 [4] 2 b. By using a calculator, find the value of 83 Q5. Simplify a. ( 4𝑥 8 𝑦 3 ) c. 3 [3] 2𝑥 5 𝑦 2 𝟑𝒙−𝟒 × b. 𝟐 𝒙+𝟏 + [1] 𝟑 𝒙+𝟐 𝟐 𝟑 𝟏 𝒙𝟐 [3] [3] 6 Q6. A company sells regular size boxes of washing powder. They decide to make a large size box by increasing the dimensions in the ratio 5 : 4. a. Calculate the measurements of the large box. b. Find i. the volume of a regular box ii. the volume of large box [3] [2] [2] c. Write down and simplify the ratio volume of large box : volume of regular box [2] 7 Q7. a. [3] b. [2] c. [3] Q8. a. Find the gradient and y intercept for the function 2𝑦 = 5 − 3𝑥 [3] 8 b. [3] c. Find the equation of a straight line which is perpendicular to 𝑦 + 𝑥 = −1 and passes through the point (0,3). [3] 9 Q9. a. Solve the following equation: 23𝑥−1 = 32 b. [3] [3] 10 10. A bottling machine fills 500 bottles in 15 minutes. How many bottles will it fill 1 in 1 ℎ𝑜𝑢𝑟𝑠 ( 𝑖. 𝑒 90 𝑚𝑖𝑛𝑢𝑡𝑒𝑠)? 2 [3] 11. A factory produces cars in red, blue, white and green in the ratio 7: 5: 3: 1. Out of a production of 48 000 cars, how many are white? [3] Q12 a. Find the equation of a straight line which is parallel to the line 𝑦 = −4𝑥 + 7 and passes through the point (0, 2). [3] 11 b. Find the midpoint and length of the line segment joining (12, 4) and (4, -2). Midpoint: …………………………………. [3] Length: ………………………………… [3] 13. [4] 12 14. [4] 15. Convert 𝟎. 𝟔𝟖𝟔𝟖𝟔𝟖 … to a fraction. [4] 13 16. [3] End.