2024 GSS 4E Math Prelim Paper 1 FINAL

This paper consists of 22 printed pages, including this cover page. GREENRIDGE SECONDARY SCHOOL 2024 PRELIMINARY EXAMINATION SECONDARY 4 EXPRESS / 5 NORMAL (ACADEMIC) CANDIDATE NAME CLASS - INDEX NUMBER MATHEMATICS 4052/01 Paper 1 22 August 2024 Setter: Mr Chin Zhi Hao 2 hours 15 minutes Candidates answer on the Question Paper. Additional Materials: Nil READ THESE INSTRUCTIONS FIRST Write your class, index number and name 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 or correction fluid. 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 of the marks for this paper is 90. For Examiner’s Use Total 90

2 Mathematical Formulae Compound interest Total amount = n rP       1001 Mensuration Curved surface area of a cone = πrl Surface area of a sphere = 24πr Volume of a cone = 21 π3 rh Volume of a sphere = 34 π3 r Area of triangle ABC = Cab sin2 1 Arc length = r , where  is in radians Sector area = 2 2 1 r , where  is in radians Trigonometry C c B b A a sinsinsin  Abccba cos2222  Statistics Mean = f fx   Standard deviation = 22          f fx f fx

3 [Turn over Answer all the questions. 1 (a) Calculate . Answer …………………………… [1] (b) An item costs $24 when rounded off to the nearest dollar. What is the maximum possible price of the item? Answer $.….………...……………… [1] 2 (a) Given that 912 = 27x, find x. Answer x = ………………………… [2] (b) The number of people owning cars in a country increased by p% every year, from 5000 in the year 2020, to 6500 in the year 2024. Find the value of p. Answer p = ………………………… [2] 3 2123 3 25.01

4 3 School students were surveyed on their favourite brand of drink. The results are represented in the pie chart below. Brand B Brand C 9% 39% Brand A 41% Brand D 21% (a) State one error in the pie chart above. Answer ……………………………………………………………………………… ……………………………………………………………………………… ……………………………………………………………………………… [1] (b) State one way to correct the error stated in part (a). Answer ……………………………………………………………………………… ……………………………………………………………………………… ……………………………………………………………………………… [1] 4 Factorise 6x2 – x – 2. Answer ……………………………... [2]

5 [Turn over 5 Write 23 2 2 1xx  as a single fraction in its simplest form. Answer ……………………………... [2] 6 Six positive integers have a mean of 15, a median of 15 and a mode of 16. The range of these numbers is 7. Find the six numbers. Answer …..… …..… …..… …..… …..… …..… [2] 7 Solve the inequality 2 3 5 45 xx  . Answer ……………………………... [2]

6 8 (a) Convert 40o into radians. Leave your answers in terms of  . Answer …………………….… radians [1] (b) Convert 23 km/h into m/s. Answer ………………………….. m/s [1] 9 Calculate the total surface area of a solid hemisphere with radius 6 cm. Answer …………………….…….. cm2 [2]

7 [Turn over 10 2 bccb a  Rearrange the formula to make b the subject. Answer b = ………………………… [3] 11 Triangle ABC is such that AB = 16 cm, BC = 63 cm, AC = 65 cm. Do points A, B and C lie on the circumference of a circle? Explain with working. Answer ……………………………………………………….…………………………… ……………………………………………………….…………………………… ……………………………………………………….…………………………… [3]

8 12 (a) Factorise a2b4 – ab2. Answer …………………………… [1] (b) Expand and simplify (3x + 2)2 + 4x(2 – x). Answer …………………………… [3] 13 (a) Find the area of a regular hexagon with each side 7 cm. Answer .………...……………… cm2 [2] (b) Find the interior angle of a regular 15-sided polygon. Answer .………...…………………... [1]

9 [Turn over 14 (a) y is directly proportional to 3 x . Find the percentage increase of y when x increases by 700%. Answer ……………………………. % [2] (b) 6 men took 50 hours to paint a mural wall. How long does it take for 4 men to paint the same wall? Answer ………………………. hours [2]

10 15 A bag contains some green counters, some orange counters and some yellow counters. The probability of picking a green counter at random is 0.2. The probability of picking an orange counter at random is 0.1 more than the probability of choosing a yellow counter at random. (a) Show that the probability of picking a yellow counter at random is 0.35. Answer [1] (b) If there are 14 yellow counters, how many counters are there altogether? Answer …………………… counters [2] (c) If 3 orange counters are removed, what is the new probability of picking a yellow counter at random? Answer …………………………… [1]