2023 VS Prelim P2

This paper consists of 22 printed pages, including the cover page. [Turn over Class Register Number Name 4052/02 23/S4PR/EM/2 MATHEMATICS PAPER 2 Thursday 24 August 2023 2 hours 15 minutes VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHO OL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHO OL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHO OL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL VICTORIA SCHOOL PRELIMINARY EXAMINATION SECONDARY FOUR Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, class and register number 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 the 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. The omission of essential working will result in loss of marks. The total number of 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. Gives answers in degrees to one decimal place. For π, use either your calculator value or 3.142.

2 VICTORIA SCHOOL 23/S4PR/EM/2 Mathematical Formulae Compound interest Total amount = 1 100 nrP+ 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 = 1 sin2 ab C Arc length = r , where  is in radians Sector area = 21 2 r  , where  is in radians Trigonometry sin sin sin a b c A B C== 2 2 2 2 cosa b c bc A= + − Statistics Mean = fx f   Standard deviation = 22fx fx ff  −  

3 VICTORIA SCHOOL 23/S4PR/EM/2 1 (a) Given that 2 ,xys x x p− = + express p in terms of , and .s x y Answer p= ................................................ [2] (b) Solve these simultaneous equations. 3 2 4 5 4 3 0 xy xy −= − + = You must show your working. Answer x= ..................................................... y = ................................................ [3]

4 VICTORIA SCHOOL 23/S4PR/EM/2 (c) Write 2 3 1 3 p pp −+− as a single fraction in its simplest form. Answer ............................................................... [2] (d) Solve the equation 14 2.2 1 3xx +=−+ Answer x= .................. or x= ................. [3]

5 VICTORIA SCHOOL 23/S4PR/EM/2 2 (a) It is given that Adam’s monthly allowance is 130% of Bryan’s and Bryan’s monthly allowance is 80% of Charles’. (i) Find, in its simplest form, the ratio of Adam’s monthly allowance to Charles’. Answer .................................................... [2] (ii) If Adam’s monthly allowance is $110, find the total monthly allowance of the three boys. Answer $ .................................................... [2] (b) Dave’s family had dinner at a restaurant which gave a $10 discount and charges 10% service charge and 8% GST. The final amount they were charged on their bill was $68.50. Find the marked price of their dinner. Answer $...................................................... [3]

6 VICTORIA SCHOOL 23/S4PR/EM/2 (c) John bought a property for $550 000. He is required to make a down payment of 20% and simple interest of 1.5% per annum on the outstanding amount. This is followed by a series of monthly instalments over the next 30 years. (i) Calculate the simple interest paid over the next 30 years. Answer $ .................................................... [3] (ii) Calculate the value of each instalment. Answer $ .................................................... [2]

7 VICTORIA SCHOOL 23/S4PR/EM/2 [Question 3 is printed on the next page]

8 VICTORIA SCHOOL 23/S4PR/EM/2 3 (a) Complete the table of values for 104. 5yx x= − + + x 4.5− 4− 3− 1− 0 1 2 3 4 y 11.5 2 2− 2.5− 2− 1.33− 0.25 1.11 [1] (b) On the grid opposite, draw the graph of 104 5yx x= − + + for 4.5 4.x−   [3] (c) Using your graph, find the range of values of x for which 2y . Answer ....................................................... [1] (d) By drawing a tangent, find the gradient of the curve where 3.x=− Answer ....................................................... [2] (e) The equation 1027 5x x+= + can be solved by finding the points of intersection of the straight line y ax b=+ and the curve 104. 5yx x= − + + (i) Find the value of a and of b. Answer a = ..................................................... b= ................................................ [2] (ii) By drawing the line y ax b=+ , solve the equation 102 7 . 5x x+= + Answer x= ..................... or ..................... [3]

9 VICTORIA SCHOOL 23/S4PR/EM/2 12 10 8 6 4 2 0 5− 4− 3− 2− 1− 1 2 3 4 2− 4− x y

10 VICTORIA SCHOOL 23/S4PR/EM/2 4 (a) The heights of 80 pupils in School A were measured. The cumulative frequency curve below shows the distribution of their heights. (i) Use the curve to estimate (a) the median height, Answer ..................................................cm [1] (b) the interquartile range. Answer ..................................................cm [2] (ii) Pupils who are above a certain height will be selected to perform at the National Day Parade (NDP). The selection results revealed that 20% of the pupils were tall enough. Find the minimum height for a pupil to be selected. Answer ..................................................cm [2] 0 10 20 30 40 50 60 70 80 90 90 100 110 120 130 140 150 Height (cm) Cumulative Frequency