SASS 2023 Prelim 4E5N 4052 Math Paper 2 (with Ans Key)

MATHS7015SLL © SAS 2023 [Turn over Index Subject TG Class Number Candidate Name _______________________________ ST ANDREW’S SECONDARY SCHOOL PRELIMINARY EXAMINATION 2023 SECONDARY 4 EXPRESS / 5 NORMAL (ACADEMIC) MATHEMATICS 4052/02 Paper 2 TUESDAY 15 AUGUST 2023 2 hours 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, subject TG, class and index number in the spaces at the top of this page. 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. The number of marks is given in brackets [ ] at the end of each question or part question. 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 total of the marks for this paper is 90. 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. This question paper consists of 22 printed pages. ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCH OOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL

2 Mathematical Formulae Compound interest Total amount = n rP      + 1001 Mensuration Curved surface area of a cone = πrl Surface area of a sphere = 4πr2 Volume of a cone = 3 1 πr2h Volume of a sphere = 3 4 πr3 Area of triangle ABC = ab2 1 sin C 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 == bccba 2222 −+= cos A Statistics Mean = f fx   Standard deviation = 22        −  f fx f fx

3 [Turn over Answer all the questions. 1 (a) Simplify 1 8 4 1216 x y −   . Answer ............................................... [2] (b) Simplify 22 15 10 6 4 94 ax bx ay by ab + − − − . Answer ............................................... [3] (c) 1 33 ba b −=+ + Express b in terms of a. Answer b = ........................................ [3]

4 (d) Solve the equation 2 7 9 0xx− + = by completing the square. Leave your answers correct to 3 decimal places. Answer x = ................. or .................. [3]

5 [Turn over 2 (a) Ruth bought a refrigerator selling at $2300. She chose to pay for the item by monthly instalments over 2 years. A simple interest of 1.5% per annum was charged on the price of the refrigerator. Calculate the amount Ruth needed to pay each month. Give your answer correct to the nearest cent. Answer $ ............................................ [3]

6 (b) Ruth changed Singapore dollars ($) $800 into Malaysian Ringgit (RM) for her holiday trip. The exchange rate was $1 = RM 3.16. She spent RM 2250 and then changed the remaining money back into Singapore dollars upon return from her trip. How many dollars did she receive on her return? Give your answer correct to the nearest dollar. Answer $ ............................................ [3]

7 [Turn over (c) Ruth invested $P in an account. The account had a compound interest rate of 1.8% per annum compounded quarterly. After 2 years, the money had earned total interest of $675.68. Calculate the value of P. Answer P = ........................................ [3]

8 3 (a) (i) The sum of the first n terms of a sequence is given by 2pn qn+ . The sum of the first 2 terms is 26. The sum of the first 4 terms is 76. Form and solve the two simultaneous equations to find the value of p and the value of q. Answer p = ......................................... q = ........................................ [3] (ii) Hence, find the 90th term of this sequence. Answer ............................................... [2]

9 [Turn over (b) The first four diagrams in a sequence are shown below. (i) In Diagram 2, there are 5 dots and 6 lines. Find the number of dots and the number of lines in Diagram 8. Answer Dots = ....................................... Lines = ...................................... [1] (ii) Find an expression, in terms of n, for the number of dots in Diagram n. Answer ............................................... [1] (iii) Explain, with calculations, whether it is possible to have a diagram that is made up of 97 dots and 150 lines in this sequence. .............................................................................................................................. .............................................................................................................................. [3]

10 4 (a) P, Q, R, S and T are points on the circumference of a circle, centre O. Angle PSQ = 32° and O lies on TQ. PS intersects TQ at Y, PS is parallel to QR and QR = RS. (i) Prove that triangle TYS is similar to triangle PYQ. Give a reason for each statement you make. [2] (ii) Find angle TPS. Give a reason for each step of your working. Answer Angle TPS = ......................... [4] Y NOT TO SCALE