2023 GSS 3E EOY Math Express P1

[Turn over This paper consists of 20 printed pages, including this cover page. GREENRIDGE SECONDARY SCHOOL 2023 END-OF-YEAR EXAMINATION SECONDARY 3 EXPRESS CANDIDATE NAME CLASS - INDEX NUMBER MATHEMATICS 4052/01 Paper 1 3 October 2023 Setter: Mr Lim Yeun Chen 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 Write these numbers in order of size, starting from largest. 3 158 −7.8 14%6 53 Answer ………… , …………, …………, ………… [2] 2 Aden needs a loan of $99 800 to buy a new car. Bank ABC charges a simple interest of 2.58% per annum. If Aden plans to take a five year loan, what is the total amount he has to pay for the loan? Answer $ …………………………… [2] 3 By rounding off each number to 1 significant figure, estimate 46 0.07035 22.34 3.1 4.45   . Show your workings clearly. Answer ……………………………… [2]

4 4 (a) Change 330 degrees to radians. Answer ………………………… rad [1] (b) Change 5 8  radians to degrees. Answer …………………………… ° [1] 5 A is the point (3, 6) and B is the point (8, n). The length of the line segment AB is 34 . Find the possible values of n. Answer n = ………… or ………… [3]

5 [Turn over 6 The sine of an angle is 0.6231. Give two possible values for the angle. Answer ……………° or ……………° [2] 7 Given that 177 49 p  , find the value of p. Answer p = ………………………… [2] 8 Janelle invests $6850 in a bank that pays compound interest at a rate of 3.13% per annum. Find the total interest she will earn from the investment after 7 years. Give your answer correct to the nearest cent. Answer $ …………………………… [3]

6 9 2 2y x 2 2yx 1y x 3yx 5xy 3yx Write down a possible equation for each of the sketch graphs below. In each case select one of the equations from the box above. (a) Answer ……………………………… [1] (b) Answer ……………………………… [1] (c) Answer ……………………………… [1] x y x y x y O O O

7 [Turn over 10 If 5x is a solution of the equation 22 9 0x x a   , find the other solution of the equation. Answer x = ………………………… [3] 11 (a) Solve the inequality 2 15 19x . Answer ……………………………… [1] (b) Randy says there are a total of 8 prime numbers which satisfy the inequality 2 15 19x . Explain whether Randy’s claim is correct. Answer ………………………………………………………………………………………… ………………………………………………………………………………………… ………………………………………………………………………………………… [2]

8 12 In the right-angled triangle below, angle BAC = 90, AC = 16 cm, BC = 20 cm. AB is produced to P and AC is produced to Q. (a) Express cos x as a fraction, in its simplest form. Answer ……………………………… [1] (b) Calculate angle ABC. Answer ……………………………..° [2] A B C P Q 20 cm 16 cm x

9 [Turn over 13 Simplify (a) 2 0 3 66( )a b a  , Answer ……………………………… [2] (b) 1 15 3 125 a    . Answer ……………………………… [2]

10 14 In the diagram, AS = 12 cm, BS = 3 cm and AR = 9 cm. Show that triangle ABC is congruent to triangle ARS. Give a reason for each statement you made. Answer ……………………………………………………………………………………………….. ……………………………………………………………………………………………….. ……………………………………………………………………………………………….. [3] 15 Given that 22 23xy and 17xy  , find the value of   2 33xy without solving for values of x and y. Answer ……………………………… [2] 12 cm 3 cm 9 cm A B C T S R