2024 DHS Y5 H2 Math Promo Practice Paper 1 (QP)

Name: Index Number: Class: DUNMAN HIGH SCHOOL Promotional Examination Practice Paper 1 Year 5 MATHEMATICS (Higher 2) 9758/01 3 hours Additional Materials: List of Formulae (MF27) READ THESE INSTRUCTIONS FIRST Write your Name, Index Number and Class on all the work you hand in. Write in dark blue or black pen on both sides of the paper. 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. Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. You are expected to use an approved graphing calculator. Unsupported answers from a graphing calculator are allowed unless a question specifically states otherwise. Where unsupported answers from a graphing calculator are not allowed in a question, you are required to present the mathematical steps using mathematical notations and not calculator commands. You are reminded of the need for clear presentation in your answers. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question.

2 DHS 2024 Year 5 H2 Mathematics Practice Paper 1 1 A café sells three types of cake: banana, chocolate and walnut. The café gives 12% discount on total cost to any customer who buys more than 12 cakes. The number of each type of cake bought by Alice, Betty and Charlotte, together with the total amount paid, are shown in the following table. Banana Chocolate Walnut Amount paid ($) Alice 5 3 2 52 Betty 3 4 5 68 Charlotte 4 8 2 66 Determine the original selling price of each type of cake. [3] 2 A curve C undergoes, in succession, the following transformations. A: Translation of 4 units in the negative y-direction. B: Stretching parallel to the x-axis by a factor of 2. C: Reflection in the x-axis. The equation of the resulting curve is 2 4.4 xy=+ Determine the equation of the original curve C before the transformations were carried out. [3] 3 The graph of f ( )yx= has a maximum turning point at (2,3) and passes through the origin. The lines 1x=− and 2y= are asymptotes to the graph, as shown in the diagram below. (a) State the range of values of x for which the graph of 1 f ( )y x= is increasing. [1] (b) Sketch the graph of f '( ),yx= showing clearly the axial intercepts and the asymptotes. [3] x y (2,3) O

3 DHS 2024 Year 5 H2 Mathematics Practice Paper 1 4 The function f is defined by 2 4f : , . xxx x +  (a) Give a reason why f does not have an inverse. [1] (b) The domain is now restricted to 0 2.x Find 1f ( )x− and state its domain, showing your working clearly. [4] 5 A curve C has equation 2 1 , 2 y bx bx = − where b < 0.