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 .................................................