[Presbyterian High] [2023] 4E EM 4052 Prelims P1_MS

4052/01/4E Preliminary Examination/2023 PRESBYTERIAN HIGH SCHOOL MATHEMATICS 4052/01 PAPER 1 14 August 2023 Monday 2 hours 15 minutes MARK SCHEME

2 Presbyterian High School 4052/01/4E Prelim/2023 Answer all the questions. 1 Solve 7 18 3 .x x  7 18 3 4 18 9 --- B12 x x x x     2 (a) Calculate 3 2 26.18 4.52 0.4 . Write your answer correct to 5 significant figures. 8593.4 --- B1 (b) Write your answer to part (a) in standard form. 38.5934 10 --- B1 3 (a) Express 784 as a product of prime factors. 2 784 2 392 2 196 2 98 7 49 7 7 1 (b) It is given that a and b are prime numbers. Find the smallest values of a and b such that 784 a b is a perfect cube.   4 2 7784 2 7 7 and 2 --- B1, B12 a a bb       4 Expand and simplify   5 1w w  .    2 2 5 1 5 5 --- M1: at least 2 correctly expand ed terms 4 5 --- A1 w w w w w w w          4 2784 2 7 --- B1 

3 Presbyterian High School 4052/01/4E Prelim/2023 5 The bar graph below shows the results of a survey conducted on the service quality of a hotel. Service quality of a hotel (a) Find the percentage of respondents who answered ‘Strongly Satisfied’ and ‘Satisfied’. 18 27 100%18 27 20 10 5 56.25% --- B1       (b) Suggest the use of another statistical diagram to represent the results of the survey conducted, that can show the relative size of a part in relation to the whole. Pie Chart --- B1 6 Find the largest integer that satisfies 2 3 4.y  2 3 4 2 7 7 B1: seen this answer2 y y y     The largest integer is 3. ---- B1 Number of respondents 0 10 20 30 Satisfied Strongly Satisfied Somewhat Satisfied Unsatisfied Strongly Unsatisfied Responses

4 Presbyterian High School 4052/01/4E Prelim/2023 7 P is directly proportional to 3.Q When 2, 64Q P  . When the value of Q is halved, the value of P changes by a factor of m. Find the value of m.   3 3 3 3 3 3 When 2 and 64 64 2 ---- M1: attempt to fin d the proportionality constant by substitution 8 8 18 82 8new P k Q Q P k k P Q QP Q Q                    Hence the factor m is 1 .8 --- A1 8 The diagram shows a quadrilateral playground ABCD. A circular fence is constructed around the playground such that the vertices, A, B, C and D of the playground touch the circumference of the fence. (a) Construct the perpendicular bisector of AB. [1] (b) Con