2022 NHHS Sec 2 EOY Math

This paper consists of 8 printed pages. Page 1 of 8 END OF YEAR EXAMINATION 2022 Subject : Mathematics (Part 1) Level : Secondary Two Express Date : 11 October 2022 Duration : 1 hour READ THESE INSTRUCTIONS FIRST Write your name, index number and class on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue, correction fluid or correction tape. Answer all questions. If working is needed for any question, it must be shown with the answer. Omission of essential working will result in loss of marks. The use of an approved scientific calculator is expected, where appropriate. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For , use either your calculator value or 3.142, unless the question requires the answer in terms of . The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 40. Class Index Number Name FOR MARKER’S USE ONLY Question Number Maximum Mark Mark 1 6 2 5 3 3 4 6 5 6 6 4 7 6 8 4 Total Mark 40 NAN HUA HIGH SCHOOL

Nan Hua High School End of Year Examination 2022 Mathematics _________________________________________________________________________ Page 2 of 8 Answer all the questions. 1 (a) Expand and simplify 2(11 3) (3 5)(7 )xxx   . Answer …………….…….…… [2] (b) Factorise completely (i) 291 0 0x, Answer …………….…….…… [2] (ii) 41 0 85wy x wx y . Answer …………….…….…… [2]

Nan Hua High School End of Year Examination 2022 Mathematics _________________________________________________________________________ Page 3 of 8 2 (a) Solve the inequality 10 2 45 m. Answer …………….…….…… [2] (b) Represent your solution on the number line below. [2] (c) If m is an integer, write down the largest possible value of m that satisfies the inequality. Answer …………….…….…… [1] 3 The mass, M grams, of a metal ball is directly proportional to the cube of its radius, R centimeters. The mass of a metal ball is 264 g when the radius is 2 cm. Find the mass of the metal ball, in kilograms, when its radius is 6 cm. Answer …………….………kg [3]

Nan Hua High School End of Year Examination 2022 Mathematics _________________________________________________________________________ Page 4 of 8 4 (a) Express 2 5 67 3 3 1 x xx x   as a single fraction in its simplest form. Answer …………….…….…… [3] (b) Solve the equation 31 0 925 5 2mm . Answer …………….…….…… [3]

Nan Hua High School End of Year Examination 2022 Mathematics _________________________________________________________________________ Page 5 of 8 5 A map has a scale of 1 cm to 0.5 km. (a) Express the scale of the map in the form 1 : n, where n is an integer. Answer …………….…….……. [1] (b) The length of a path is 720 m. Find its corresponding length on the map. Answer …………….…….… cm [2] (c) An advertisement on a new residential development makes the following claim: (1 hectare = 0.01 km2) Given that the plot of land is represented by 0.22 cm2 on the map, comment on whether the claim is correct. Explain your answer with appropriate working. Answer ……….…….……………………………………………………......…… ………………………………………………………………….………... [3] Find your dream home here on the sprawling plot of land that spans a total area of 6 hectares!

Nan Hua High School End of Year Examination 2022 Mathematics _________________________________________________________________________ Page 6 of 8 6 (a) Make d the subject of the formula 2 7 3 dc dc . Answer …………….…….…… [3] (b) Find the value of d when c = 1. Answer d = ……….…….…… [1]

Nan Hua High School End of Year Examination 2022 Mathematics _________________________________________________________________________ Page 7 of 8 7 20 boys took part in a survey. The number of coins each boy had in his wallet was recorded. Number of coins 1 2 3 4 5 6 Number of boys 2 4 6 x 2y 1 (a) Show that x + 2y = 7. [1] (b) The mean of the distribution is 3.3. Show that 2x + 5y = 16. [2] (c) Hence, find the value of x and of y. Answer x = ..…… , y = ...….… [3]

Nan Hua High School End of Year Examination 2022 Mathematics _________________________________________________________________________ Page 8 of 8 8 In the diagram, PQR is a straight line, ∆PQS  ∆PTS, and triangle PRS is similar to triangle PST. Given that PS = 8 cm, PT = 5.6 cm, angle PQS = 114o and angle SPT= 27o, calculate (a) angle PSR, Answer Angle PSR = ………… [2] (b) the length of PR. Answer PR = …….…….… cm [2] End of Part I S Q R P T

Nan Hua High School End of Year Examination 2022 Mathematics _________________________________________________________________________ Page 9 of 8 Answers 1. (a) 234 2 9xx (b)(i) (3 10)(3 10)xx (ii) (2 )(4 5)xy w 2. (a) 28 ( o r 8 . 4 )5mm  (b) (c) 9 3. 6 cm 4. (a) 11 15 (3 1)(2 3) x xx   (b) 1 9m 5. (a) 1 : 50000 (b) 1.44 cm (c) Actual land area of 0.055 km2 = 0.055 0.01 = 5.5 hectares Since the actual land area is less than 6 hectares, the claim in the advertisement is incorrect. 6. (a) 3 2 3 7 cd c (b) 1 2d 7. (c) x = 3, y = 2 8. (a) PSR = 114o (b) 311.4 cm (3 s.f.) [or 11 cm]7PR 11 10 9 8 7 8.4

This paper consists of 13 printed pages. Page 1 of 13 END OF YEAR EXAMINATION 2022 Subject : Mathematics (Part 2) Level : Secondary Two Express Date : 11 October 2022 Duration : 1 hour 30 minutes READ THESE INSTRUCTIONS FIRST Write your name, index number and class on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue, correction fluid or correction tape. Answer all questions. If working is needed for any question, it must be shown with the answer. Omission of essential working will result in loss of marks. The use of an approved scientific calculator is expected, where appropriate. If the degree of accuracy is not specified in the question, and if the answer is not exact, give the answer to three significant figures. Give answers in degrees to one decimal place. For , use either your calculator value or 3.142, unless the question requires the answer in terms of . The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 60. Class Index Number Name FOR MARKER’S USE ONLY Question Number Maximum Mark Mark 1 7 2 5 3 7 4 4 5 7 6 6 7 9 8 5 9 10 Total Mark 60 NAN HUA HIGH SCHOOL