2023 Springfield 3G3 Mathematics (4052) (P2-QP)

[Turn Over SPRINGFIELD SECONDARY SCHOOL End-Of-Year Examination 2023 Sec 3 Express STUDENT NAME CLASS REGISTER NUMBER MATHEMATICS 4052/02 Paper 2 10 October 2023 2 hours 15 minutes Candidates answer on the question paper Additional Materials: graph paper READ THESE INSTRUCTIONS FIRST Write your class, 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, graphs or rough working. Do not use staples, paper clips, glue or correction fluid. Answer all the questions. 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 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  . The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 90. For Examiner’s Use Total /90 Do not turn over this question paper until you are told to do so. ______________________________________________________________________________________________________ This question paper consists of 21 printed pages.

2 Mathematical Formulae Compound Interest Total amount = n rP      + 1001 Mensuration Curved surface area of a cone = rl Surface area of a sphere = 4 2r Volume of a cone = hr 2 3 1 Volume of a sphere = 3 3 4 r Area of triangle ABC = Cabsin2 1 Arc length = rθ, where θ is in radians Sector area = 2 2 1 r , where θ 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 [Turn Over Answer all the questions 1 (a) By writing each number correct to 1 significant figure, estimate the value of 54.3 7.9 3.56  . Answer ................................... [2] (b) Given 310.65 10 10 a − =  , find the value of a. Answer ................................... [2] 2 (a) Given that 527 7 1 k− = , find the value of k. Answer k = ................................... [2] (b) Solve the inequality 3 5 15 2 22x x x−  −  + . Answer ................................... [3] (c) Represent your answer in part (b) on the number line given. [1] 0 2 4 6 8 10 12

4 3 (a) Alice uses all 320 one-centimetre cubes to make a décor, which is in the shape of a cuboid. The perimeter of the top of the cuboid is 26 cm. Given that each side of the cuboid has a length greater than 3 cm, find the height of the cuboid. Answer ................................... [3] (b) Given 534320 2 3 5=   . Find the smallest positive integer n such that 4320 n is a perfect cube. Answer n=................................... [1]

5 [Turn Over 4 The temperature at the base of Mt Everest is 5 C . The temperature at the top of Mt Everest is 11 C− . (a) Find the difference between the two temperatures. Answer ...................................oC [1] (b) Assuming that the temperature falls at a steady rate as height increases and the height of Mt Everest is 8850 m. At a particular point, the temperature is 0 C , how high is this point above the base of Mt Everest? Answer ................................... m [2] 5 (a) The length of a rectangle is increased by 10%. At the same time, its breadth is decreased by 18%. Find the percentage increase or decrease in its area. Answer ...................................% [3]

6 (b) Ken is returning to Singapore from Tokyo. He decided to book the following flight. Depart – Tokyo to Singapore From (time) To (time) Price (¥) Tokyo Singapore 32400 *Fares include airport tax and fuel surcharge. Add-ons: ¥6200 for 20 kg check-in baggage, meal, drink and snack. Ken decided to purchase the add-ons. He booked the flight using his credit card which requires him to pay a processing fee at 5% of the total fare. The exchange rate for the day was: 1 Singapore dollar (SGD) = 106.80 Japanese Yen (¥) Calculate the total amount of money Ken needs to pay in Singapore dollars. Answer $................................... [3]

7 [Turn Over 6 (a) A housewife planned to buy $30 worth of vegetables at x cents per kg. Write down an expression, in terms of x, for the number of kg she planned to buy. Answer ...................................kg [1] (b) She found that the price of vegetables had decreased by 6 cents per kg. Write down an expression in terms of x for the number of kg she can buy for $30 now. Answer ...................................kg [1] (c) Given that she actually bought 55 9 kg more than she had planned, form an equation in x and show that it reduces to 2 6 3240 0xx− − = . Answer [3] (d) Solve the quadratic equation 2 6 3240 0xx− − = and use your answer to find the number of kg of vegetables she bought after the price had decreased. Answer .................................kg [3]

8 7 The table below shows some values of x and the corresponding values of y, where 2 3yx x=+ . x 0.5 1 1.5 2 2.5 3 3.5 4 y 6.25 4 a 5.5 7.45 10 13.11 16.75 (a) Find the value of a. Answer a = ................................... [1] (b) On the grid on page 9, draw the graph of 2 3yx x=+ for 0.5 4x [3] (c) Using your graph, estimate the solution of the equation 2 39 x x=+ . Answer x = ................. , ................. [2] (d) By drawing a tangent, find the gradient of the curve at the point where x = 3. Answer ................................... [2] (e) A line of equation yk= , where k is a constant, is a tangent to the curve. Draw this tangent and find the value of k. [2]

9 [Turn Over 0.5 1 1.5 2 2.5 3 3.5 4 0 2 4 6 8 10 12 14 16 18 20 y x

10 8 A cylindrical pipe is partially submerged in water. The cross-section of the pipe is a circle of centre O and radius 17 cm, passing through A, D, C and E. ABCD is a major segment of the circle that is above the water level, angle ABD = 90o. (a) Show that angle AOB = 72.9o, correct to 1 decimal place. Answer [2] (b) Calculate the major arc length ADC. Answer ................................... cm [3] D 12 cm B A C O E