PHSS Final EM DA 2023 QP + Solutions

1 NAME: ( ) CLASS: TEACHING GROUP: MARKS /100 PEI HWA SECONDARY SCHOOL Diagnostic Assessment 2023 Secondary Four Express / Five Normal (Academic) MATHEMATICS 4052 21 June 2023 2 hours 30 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your class, teaching group, index number and name 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 questions. The number of marks is given in the 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 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. Give answers in degrees to one decimal place. For , use either your calculator value or 3.142, unless the question requires the answer in terms of . This question paper consists of 20 printed pages. For Examiner’s Use Category Question No. Correction tape Pencil written Arrows Units Others

2 Mathematical Formulae Compound Interest Total amount = 1 100 n rP+ Mensuration Curved surface area of a cone = rl Surface area of a sphere = 24 r Volume of a cone = hr 2 3 1 Volume of a sphere = 3 3 4 r Area of triangle ABC = Cabsin2 1 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 == Abccba cos2222 −+= Statistics Mean = f fx   Standard Deviation = 22        −  f fx f fx

3 Answer all the questions. 1 (a) Simplify 2 6 3 2 8x y −   , leaving your answer in positive indices. Answer .………..……………… [2] (b) Given that 2x = 5, find the value of 48xx− + . Answer .………..……………… [2] 2 The following chart shows the sales of a company over the years. State one aspect of the graph that may be misleading and explain how this may lead to a misinterpretation of the graph. ……………………………………………………………………………………............... ……………………………………………………………………………………............... ……………………………………………………………………………………............... [2]

4 3 x is decreased by 50% and then increased by 40%. Find the percentage decrease in x from its original value. Answer .………..………………% [2] 4 Write as a single fraction in its simplest form ( ) 2 35 1 1 x x x +− − . Answer .………..……………… [3] 5 Ther