[FMS] [2023] 4E EM 4052 Prelims P1 QP

NAME: ____________________________ ( ) CLASS: _______ MATHEMATICS 4052/01 Paper 1 Date: 22 August 2023 Duration: 2 hours 15 minutes Candidates answer on the Question Paper. ___________________________________________________________________ READ THESE INSTRUCTIONS FIRST Write your name, index number and class on all the work you hand in. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all the questions. The number of marks is given in brackets [ ] at the end of each question or part question. 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 total of the marks for this paper is 90. 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. For Examiner’s Use Table of Penalties Question Number 90 Presentation  1  2 Parent’s / Guardian’s Signature Rounding off  1 Setters: Ms Shamsiah and Mr Kua KT This question paper consists of 23 printed pages.  FAIRFIELD METHODIST SCHOOL (SECONDARY) PRELIMINARY EXAMINATION 2023 SECONDARY 4 EXPRESS / 5 NORMAL (ACADEMIC)

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2023 2 Mathematics Paper 1 Mathematical Formulae Compound interest Total amount = P Mensuration Curved surface area of a cone = Surface area of a sphere = Volume of a cone = Volume of a sphere = Area of a triangle ABC = Arc length = , where is in radians Sector area = , where is in radians Trigonometry Statistics Mean = Standard deviation = n r      + 1001 rl 24 r hr 2 3 1 3 3 4 r Cabsin2 1 r  2 2 1 r  C c B b A a sinsinsin == Abccba cos2222 −+=   f fx 22       −     f fx f fx

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2023 3 Mathematics Paper 1 Answer all the questions. 1 (a) Express 540 as a product of its prime factors. Answer ……………………………………… [1] (b) The number is a perfect cube. m and n are prime numbers. Find the value of m and the value of n. Answer m = ………………………………… n = ………………………………… [1] 2 (a) Calculate . Write your answer correct to 5 significant figures. Answer ……………………………………… [1] (b) Write your answer to part (a) in standard form. Answer ……………………………………… [1]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2023 4 Mathematics Paper 1 3 The first four terms of a sequence are 13, 17, 21, 25. (a) Write down the 7th term of the sequence. Answer ……………………………………… [1] (b) Write down an expression for the nth term of the sequence. Answer ……………………………………… [1] (c) Explain why 318 is not a term of this sequence. Answer …………………………………………………………………………………………… ……………………………………………………………………………………….. [1] 4 The pie chart below shows the age groups (in years) of 240 adults who took part in a triathlon. (a) Find the value of x. Answer x = …………………………… [1] (b) Calculate the number of adults aged 41 to 50 years old who took part in the triathlon. Answer ………………………… adults [1] 21 to 30 31 to 40 41 to 50 51 to 60 Over 60 72° 75° 69° 2x ° x °

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2023 5 Mathematics Paper 1 5 L is a line with a negative gradient and it has positive x- and y-intercepts. The value of y-intercept is five times the value of x-intercept. Given that the x-intercept is , find the equation of L. Answer ………………………………… [3] 6 An empty fuel tank is filled using a cylindrical pipe with diameter 8 cm. Fuel flows along this pipe at a rate of 2 metres per second. It takes 24 minutes to fill the tank. Calculate the capacity of the tank. Give your answer in litres. Answer ………………………………… l [3] 2 5

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2023 6 Mathematics Paper 1 7 (a) Simplify ( ) 3 4 481x − . Answer ………………………………… [2] (b) Solve 1 1 5 432 2 8 x= . Answer x = …………………….……… [2]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2023 7 Mathematics Paper 1 8 (a) {integers : 2 24}xx =   {multiples of 3} {prime numbers} P Q = = List the elements in (i) P, Answer …………………………………………………………… [1] (ii) (P Q)’. Answer …………………………………………………………… [1] (b) The Venn diagram below shows the elements of and three sets A, B and C. (i) Circle the correct statement(s) from the list below. n(A) = 3 A B = {1, 13} [2] (ii) Find the value of n[ ]. Answer ………………………………… [1] 7 9 11 A B C 2 4 8 5 3 6 10 12 13 1

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2023 8 Mathematics Paper 1 9 Simplify . Answer ………………………………… [3] 10 Ching and Lex each have a savings account. The ratio Ching’s savings : Lex’s savings = 3 : 5. They each spent $60 from their savings. The new ratio Ching’s savings : Lex’s savings = 4 : 7. Find the total amount of money Ching and Lex have in their accounts now. Answer $ ………………………………… [4]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2023 9 Mathematics Paper 1 11 (a) Solve cos cos65x=−  , where 0 180 .x   Answer x = .………………………….… ○ [1] (b) The area of a triangle PQR is 15 cm2, PQ = 10 cm and PR = 6 cm. Find the possible values of QPR . Answer QPR = …………○ or …………○ [3] 12 Given that A = 46 02   − and B = 2 01 k  − , find (a) A2, Answer ………………………………… [1] (b) the value of k if A = 2B. Answer k = ………….………………… [1]

NAME: ____________________________ ( ) CLASS: _______ FMS(S) Sec 4 Express / 5 Normal (Academic) Preliminary Examination 2023 10 Mathematics Paper 1 13 The sales of the IMic and Lovono laptops , in dollars, made by PC Enterprise in the years 2021 and 2022 are summarised below. (a) Represent the information in a 2 × 2 matrix S. Answer S = ………………..……………… [1] (b) Evaluate the matrix R = ( 1 1 ) S. Answer ………………………………… [1] (c) State what each element in matrix R represents. Answer ………………………………………………………………………………… ………………………………………………………………………………………. [1] Sales Year IMic Lovono 2021 34 000 20 100 2022 14 500 30 000