2024 DHS Y5 H2 Math Promo Practice Paper 2 (QP)

© DHS 2024 Name: Index Number: Class: DUNMAN HIGH SCHOOL Promotional Examination Practice Paper 2 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 Promotional Examination Practice Paper 2 1 The selling price of a desktop monitor, keyboard and mouse is $317.90 in total. During the Great Electronics Sale, two companies, A and B, offered the following discounts to their customers. Company Discounts given for each item Total price after the discount Desktop monitor Keyboard Mouse A 10% 15% 10% $282.66 B 5% 25% 20% $283.72 (a) Find the selling prices of a desktop monitor, keyboard and mouse. [3] (b) Kim works at Company B and the e mployees from Company B are offered a further 2% discount on the original price of the mouse. Explain if this additional discount will make it more attractive for Kim to purchase all the three items from her own company than from Company A. [1] 2 Given that 0,x solve the inequality 2 ,xax − where a is constant such that 3.a [4] 3 The diagram shows the curve ( )f 1 .yx=− The curve has a maximum point at ( 1,5)− and two asymptotes 2x=− and 1.y= On separate diagrams, sketch the graphs of (a) f ( ),yx= [2] (b) g'( ), where g( ) f (1 ).y x x x= = − [2] y O x y = 1 x = –2 (−1, 5) 

3 DHS 2024 Year 5 H2 Mathematics Promotional Examination Practice Paper 2 4 A curve C has parametric equations 3 2 3, , . 1 3 yt t xt = + =  (a) Find d d y x in terms of t. Explain why C has no stationary points. [2] (b) Sketch C, indicating clearly the equation of the asymptote if any. [2] 5 It is given that e 2 e .yx=+ (a) Show that 22 2 d d d