1 霹雳怡保培南独立中学 SM POI LAM (SUWA) IPOH FINAL EXAMINATION 2023 MATHEMATICS PAPER 2 DATE : 7 NOVEMBER 2023 (TUESDAY) TIME : 0830-1000 (1 HOUR 30 MINUTES) NAME：______________________ REG NO : _________________ CLASS： J1YI, J1LI, J1AI, J1XIN, J1HE, J1PIN Candidates answer on the Question Paper. INSTRUCTIONS l Answer all questions. l Use a black or dark blue pen. You may use an HB pencil for any diagrams or graphs. l Write your name, register number and class on all the work you hand in. l Write your answer to each question in the space provided. l Do not use an erasable pen or correction fluid. l You are allowed to use a calculator. l You must show all necessary working clearly. l Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question. l For p, use either your calculator value or 3.142. INFORMATION l The total mark for this paper is 50. l The number of marks for each question or part question is shown in brackets [ ]. This paper consists of 4 pages, including this cover page. Prepared by ： ………..…………….. (Mr. Pua Yong Cheng) Checked by： ……………………….. (Mr. Ong Eik Hooi) Do Not Turn This Page Until You Are Told To Do So
2 1. During the children’s day celebration, a school distributed 825 cakes, 495 sweets and 660 biscuits equally to the students of the school. (a) Find the largest possible number of students in the school that day. [3] (b) Find the largest number of cakes, sweets and biscuits received by each student. [2] 2. Use a calculator to evaluate each of the following, leaving your answer correct to 3 decimal places. (a) !3.21 − 8 ! " ( × (−9.81) − (−6 # $ )% [2] (b) (−35)& ÷ [−12 − 12 ' %# − 8.99%3] × [−2.3 ÷ (−)] [2] 3. By writing each value to 1 significant figure, estimate the value of 2".!%×'.#' *'.* . Show your working. [2] 4. The perimeter of a rectangle is (5 + 12 − 10) cm. The length of the rectangle is (4 + 3 − 3) cm. (a) Find an expression, in terms of x and y, for the breadth of the rectangle. [2] (b) It is given that x = 7 and y = 2. Find the area of the rectangle. [2] 5. Consider the pattern: 1 2 + 1 3 = 3 + 2 2 × 3 = 5 6 1 3 + 1 4 = 4 + 3 3 × 4 = 7 12 1 4 + 1 5 = 5 + 4 4 × 5 = 9 20 1 5 + 1 6 = 6 + 5 5 × 6 = 11 30 ⋮ 1 + 1 34 = 34 + × 34 = (a) Write down the 5th line in the pattern. [1] (b) Find the values of k, p and q. [3] (c) Find the value of # '+ + # '!. [1]
3 6. The marked price, inclusive of GST of a laptop is $3849.40 before a sale. During the sale, the laptop is offered at a 15% discount. The first 100 customers will be given an additional 10%off the discounted price. (a) Find the price of laptop excluding GST before the sale. [1] (b) Find the price paid by Jasper who is the 101st customer [2] (c) Find the price paid by Amber who is the 99th customer, giving your answer correct to the nearest cent. [2] 7. Danise received some money from her mother. He divides the money between shopping, education and savings in the ratio 4 : 7 : 5 respectively. (a) If he saved $2000, calculate the total amount of money he received from her mother. [1] (b) He invests all his savings into an investment plan that pays simple interest at a rate of 3% per annum for 5 years. Calculate the total amount that he will receive at the end of 5 years. [2] 8. On a particular day, the exchange rate between Australian dollars (A$) and Singapore dollars (S$) was S$1 = A$0.93. (a) Suzanne exchanged A$360 into Singapore dollars. Calculate how many Singapore dollars she received. Leave your answer correct to the nearest dollar. [1] (b) On the same day, the exchange rate between Singapore dollars and US dollars (US$) was US$1 = S$1.42. Michelle exchanged A$1400 into US dollars. Calculate how many US dollars she received. Leave your answer correct to the nearest dollar. [2] 9. The perimeter of the semicircle ABC is equal to the perimeter of the parallelogram DEFG. The diameter of the semicircle is 2x cm, DE = ( − 1)cm and DG = ( + 13) cm. (a) Form an equation in x and solve it to find the value of x. [2] (b) Given also that the area of the semicircle is 132cm2 more than the area of the parallelogram, find the length of DH. [Take = %% $ .] [3]
4 10. In each of the following figures, PQ // RS. Find the value of x in each figure. (a) [2] (b) [2] 11. Answer the whole of this question on a sheet of graph paper. The table below shows some values of x and the corresponding values of where = −2 − 3. x −3 −1 1 3 y 3 −5 (a) Find the values of a and b. [1] (b) Using a scale of 2 cm to represent 1 unit on the x-axis for −3 ≤ ≤ 3. Using a scale of 1 cm to represent 1 unit on the y-axis for −10 ≤ ≤ 3. On your axes, draw and label the graph of = −2 − 3. [3] (c) Write down the gradient and y-intercept of the line. [2] (d) From your graph, find (i) the value of y when x = 2, [1] (ii) the value of x when y = −4. [1] (e) Draw and label the graph of x = 1.5 on the same axes. Hence, write down the coordinates of the point where the graphs = −2 − 3 and x =1.5 meet. [2] End of papers