SGSS 4N Prelim 2023 P2

Mathematical Formulae Compound Interest Total amount = 1 100 n rP + Mensuration Curved surface area of a cone = rl Surface area of a sphere = 24πr Volume of a cone = 21 π3 rh Volume of a sphere = 34 π3 r Area of triangle ABC = 1 sin2 ab C Arc length = r, where  is in radians Sector area = 21 2 r  , where  is in radians Trigonometry sin sin sin a b c A B C== 2 2 2 2 cosa b c bc A= + − Statistics Mean = fx f   Standard deviation = 22fx fx ff  − 

2 SGSS/MathP2/4NA4NT(OOS)/Prelim/2023 Section A (62 marks) Answer all the questions in this section. 1 Calculate (a) 2 321 733 −  + , Answer .................................................. [1] (b) 3 47.53 3.25 2.712 4.3 − −+ . Answer .................................................. [1] 2 The table below records the score when a fair die is tossed 25 times. Score 1 2 3 4 5 6 Frequency 5 3 4 6 4 3 (a) Calculate the mean score. Answer .................................................. [1] (b) If these results were represented by a pie chart, calculate the angle for the sector representing a score of 4. Answer ................................................ º [2]

3 [Turn over SGSS/MathP2/4NA4NT(OOS)/Prelim/2023 3 Written as the product of its prime factors, 322520 2 3 5 7.=    (a) Write 2160 as the product of its prime factors. Show your working clearly. Answer .................................................. [2] (b) (i) Find the highest common factor (HCF) of 2160 and 2520. Answer .................................................. [1] (ii) Find the smallest positive integer of k such that 2520k is a perfect square. Answer k = ........................................... [1]

4 SGSS/MathP2/4NA4NT(OOS)/Prelim/2023 (a) Simplify 3 2 1 .45 xx +− Answer .................................................. [2] (b) Simplify 637 49 .2 10 xx  Answer .................................................. [2] 4

5 [Turn over SGSS/MathP2/4NA4NT(OOS)/Prelim/2023 5 Ali has a fair coin and an ordinary fair 6-sided die. He tosses the coin and throws the die. If he gets a tail and a three, he records the outcome as (T, 3). (a) List all Ali’s possible outcomes. Answer [2] (b) Find the probability that Ali gets (i) a head and a number more than 2, Answer .................................................. [1] (ii) a tail and a prime number. Answer .................................................. [1] 6 (a) The quantities a and b are in the ratio 8 : 6. The quantities b and c are in the ratio 9 : 3. Write the ratio a : b : c in its simplest form. Answer ............... : ............... : .............. [2] (b) (i) Solve the inequality 5 26.x Answer .................................................. [1] (ii) Write down the largest integer value x, satisfying 5 26.x Answer x = ........................................... [1]

6 SGSS/MathP2/4NA4NT(OOS)/Prelim/2023 7 (a) Write the following numbers in standard form. (i) 203000 Answer .................................................. [1] (ii) 0.0001894 Answer .................................................. [1] (b) (5.3×10a) × (2.5×10b) = k × 10n, where 1≤ k <10. (i) Find the value of k. Answer k = ........................................... [1] (ii) Write down an expression for n in terms of a and b. Answer n = .......................................... [1]

7 [Turn over SGSS/MathP2/4NA4NT(OOS)/Prelim/2023 8 (a) In triangle FGH, FG = 6 cm, GH = 7 cm and angle FGH = 55º. Calculate the length of FH. Answer FH = ................................... cm [3] (b) The diagram shows a triangle PQR. PQ = 6.3 cm, PR = 8.1 cm, QR = 12.2 cm and angle QPR = 100º. Calculate angle PQR. Answer Angle PQR = ........................ º [3] F G 6 7 H 55º Q P 6.3 8.1 12.2 100º R

8 SGSS/MathP2/4NA4NT(OOS)/Prelim/2023 9 (a) This year, Mr Cheng earns $12 420. This is 3.5% more than he earned last year. Calculate the amount Mr Cheng earned last year. Answer $ ............................................... [2] (b) John deposited $1000 in a bank. At the end of 2 years, he received an interest of $50. Calculate the rate of simple interest given by the bank. Answer .............................................. % [2] (c) Sam deposited $25 000 in a bank which pays out 3.7% compound interest per annum. Calculate the interest he will receive after 5 years.

9 [Turn over SGSS/MathP2/4NA4NT(OOS)/Prelim/2023 Answer $ ............................................... [2] 10 The table of values below is for the curve 2 4y x x= + + . x 4− 3− 2− 1− 0 1 2 3 y 16 10 6 p 4 6 10 16 (a) Find the value of p. Answer p = ........................................... [1] (b) On the grid, draw the graph of 2 4y x x= + + for 4 3.x−   _ _ _ _ _ _ || | | y x 14 12 10 0 1 2 _16 8 | _ 1– 2 4 6 | | 32–– 4 3– [2] [2]

10 SGSS/MathP2/4NA4NT(OOS)/Prelim/2023 (c) Use your graph to find (i) the coordinates of the minimum point, Answer (...................... , ......................) [1] (ii) the value of y when 2.5.x=− Answer y = ............................................ [1] (d) By drawing a tangent, find the gradient of the curve 2 4y x x= + + when x = 1. Answer .................................................. [2]