PLMGS 4E 5NA Math P1 Prelim 2017 FINAL

Name: ___________________________ ( ) Class: _______ Centre Number S Index Number MATHEMATICS 4048/01 Paper 1 16 August 2017 Candidates answer on the Question Paper. 2 hours READ THESE INSTRUCTIONS FIRST Write your Centre number, index number, name and class on all the work you hand in. Write in dark blue or black pen. You may use a HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all questions. If working is needed for any question, it must be shown with the answer. Omission of essential working will result in a loss of marks. 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 . 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. The total of the marks for this paper is 80. This paper consists of 17 pages, including this cover page. Paya Lebar Methodist Girls’ School (Secondary) Preliminary Examination 2017 Secondary 4 Express / 5 Normal Academic Calculator Model: (if applicable) For Examiner’s Use 80 My Target is:

2 [Turn over Mathematical Formulae Compound interest Total amount = n rP       1001 Mensuration Curved surface area of a cone = rl Surface area of a sphere = 4r2 Volume of a cone = 3 1 r2h Volume of a sphere = 3 4 r3 Area of triangle ABC = 2 1 ab sin C Arc length = r, where  is in radians Sector area = 2 1 r2, where  is in radians Trigonometry C c B b A a sinsinsin  a2 = b2 + c2 – 2bc cos A Statistics Mean = f fx   Standard deviation = 22          f fx f fx

3 [Turn over Answer all the questions. For Examiner’s Use 1 (a) Simplify ).5(2)3(3  xyx Answer [1] (b) Factorise .36)12( 2x Answer [1] 2 Factorise completely .10142115 aybybxax  Answer [2] 3 (a) On the Venn diagram, shade the region that represents A  B. [1] (b)  = {x : x is a positive integer} P = {x: x  3} Q = {x:  1 < 2x  3  9} List the elements in P  Q. Answer [1]  A B

4 [Turn over 4 n is a positive integer. For Examiner’s Use Show that, for all n, )516()34( 22  nn is divisible by 4. Answer [2] 5 The volume of a rectangular prism is 288 cm3. The height of the prism is 9 cm. The length of the rectangular base is twice its width. Find the length of the rectangular base of the prism. Answer cm [2] 6 In triangle XYZ, angle XYZ = 52. XY = 17.4 cm and XZ = 13.8 cm. Find the two possible sizes of angle XZY. Answer  or  [2]

5 [Turn over 7 The diagram shows a pyramid of height 45 cm. For Examiner’s Use The volume of the liquid in the pyramid is two-third the volume of the pyramid. Calculate the depth, h centimetres, of the liquid. Give your answer correct to 2 decimal places. Answer h = [2] 8 Jim draws this graph to show the mass of food waste for the last four years. State one feature of the graph that may be misleading and explain how this may lead to a misinterpretation of the graph. Answer [2] h 45 2015 1100 2013 2014 2016 Mass in thousand (kg) Huge Reduction in Food Waste

6 [Turn over 9 Write as a single fraction in its simplest form .21 2 472 3 2 xxx  For Examiner’s Use Answer [2] 10 O is the centre of the circle passing through A, B, C and D. Angle DOC = 100 and angle ABC = 70. Find (a) angle DAC, Answer  [1] (b) angle ADO, Answer  [1] (c) angle ACO. Answer  [2] B C O 100 70 A D

7 [Turn over 11 (a) Express 21215 xx in the form .)( 2 qpx  For Examiner’s Use Answer [1] (b) Hence write down the minimum value of .1215 2xx Answer [1] (c) Write down the equation of the line of symmetry of the graph of .1215 2xxy  Answer [1] 12 The formula to estimate the pressure under sea at different depths below the sea level is given as ,100941001.1 5 dP  where P is the pressure in Newton per square metre, and d is the depth, in metres, below the sea level. (a) A scuba diver experienced a pressure of 51022.2  N/m2 when under the sea. Use this formula to estimate the depth of the diver below the sea level. Answer m [1] (b) Two scuba divers are at different depths below the sea level. The difference in pressure at their two depths is 5105.3  N/m2. Estimate the difference between the depths of the two divers. Answer m [2]

8 [Turn over 13 In Singapore, Lim pays $567.40 for 10 grams of gold. For Examiner’s Use On a visit to Los Angeles, he paid 1275.10 US dollars for 1 ounce of gold. 1 US dollar = 1.382 Singapore dollars. 1 ounce of gold = 31.10 grams of gold. Is gold cheaper in Singapore or Los Angeles? You must show your calculations. Answer [3] 14 The diagram shows a rectangle and a square. The sides are horizontal and vertical. The length of the rectangle is the same as the side of the square. The width of the rectangle is half of the side of the square. Point A has coordinates (14, 16) and B has coordinates (30, 8). Find the coordinates of C. Answer C ( , ) [2] C C B(30, 8) O y x A(14, 16)

9 [Turn over 15 For Examiner’s Use The shape APDQA is formed by two intersecting circles. The radii of the circles, centres B and C, are 6 cm and 5 cm respectively. At each of the points of intersection P and Q, the radius of one of the circle is perpendicular to the radius of the other. Calculate (a) angle PCQ, Answer  [1] (b) the perimeter of APDQA, Answer cm [2] (c) the area of APDQA. Answer cm2 [3] A B Q P D C 6 cm 5 cm

10 [Turn over 16