2022 FMSS Prelim P1

NAME: ____________________________ ( ) CLASS: _______ FAIRFIELD METHODIST SCHOOL (SECONDARY) PRELIMINARY EXAMINATION 2022 SECONDARY 4 EXPRESS / 5 NORMAL (ACADEMIC) MATHEMATICS 4048/01 Paper 1 Date: 23 August 2022 Duration: 2 hours 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 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 of the marks for this paper is 80. For Examiner’s Use Table of Penalties Question Number 80 Presentation € 1 € 2 Parent’s / Guardian’s Signature Rounding off € 1

Name: _________________________ ( ) Class: ______________________ FMS(S) Sec 4 N(A) Preliminary Examination 2009 2 Mathematics Paper 1 Setters: Mr Alester Tan This question paper consists of 20 printed pages.

Name: __________________________________ ( ) Class: __________ FMS(S) Sec 4 Exp/Sec 5 N(A) Preliminary Examination 2022 3 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 =

Name: __________________________________ ( ) Class: __________ FMS(S) Sec 4 Exp/Sec 5 N(A) Preliminary Examination 2022 4 Mathematics Paper 1 Answer all the questions. 1 Vivien invested $2500 in a bank at a simple interest rate of 3% per annum. The total value of the investment in the bank after a few years is $2912.50. Calculate the number of years in which she has invested in the bank. Answer ……………………………years [2] ____________________________________________________________________________ 2 In the triangle, PR = 19.5 cm, RQ = 12.2 cm and angle PRQ = 90o. Calculate PQ. Answer PQ = ….……………………cm [2] ____________________________________________________________________________ 3 A train travels 120 km in 1 hour 45 minutes. During the first 30 minutes, the train travels at an average speed of 96 km/h. Calculate the average speed of the train during the last 1 hour 15 minutes. Answer …………………………… km/h [2] P Q R 19.5 12.2

Name: __________________________________ ( ) Class: __________ FMS(S) Sec 4 Exp/Sec 5 N(A) Preliminary Examination 2022 5 Mathematics Paper 1 4 A bag contains balls of equal sizes of which 12 are blue, 6 are yellow and the rest are white. The probability of drawing a blue ball from the box is . (a) Find the total number of white balls in the bag. Answer ……………………… white balls [1] (b) Find the number of yellow balls that should be added to the bag so that the probability of drawing a yellow ball is . Answer ………………… yellow balls [1] ____________________________________________________________________________

Name: __________________________________ ( ) Class: __________ FMS(S) Sec 4 Exp/Sec 5 N(A) Preliminary Examination 2022 6 Mathematics Paper 1 5 Write as a single fraction in its simplest form . Answer ………………………………… [2] ____________________________________________________________________________ 6 (a) Five positive consecutive integers have a mean of 19. The largest integer is x. Find the value of x. Answer x = …………………………… [1] (b) A set of data is listed as and where p is an integer, and . Trevor says that is not the median. Explain, with mathematical reasoning, why he is correct. Answer …………………………………………………………………………………… …………………………………………………………………………………… …………………………………………………………………………………… …………………………………………………………………………………[2]

Name: __________________________________ ( ) Class: __________ FMS(S) Sec 4 Exp/Sec 5 N(A) Preliminary Examination 2022 7 Mathematics Paper 1 7 The dimension of a wooden cuboid is 3 cm by 2 cm by 2 cm. It takes 6174 of such wooden cuboids to form a cube. Find the length of the cube. Answer ..…………………………… cm [2] ____________________________________________________________________________ 8 Travis wanted to buy a particular pair of sneakers in 2020 but he waited until 2021 when its price was reduced by 13.2%. In 2020, the cost of the pair of sneakers was $510. Calculate the cost of the sneakers in 2021. Answer $………………………………… [2]

Name: __________________________________ ( ) Class: __________ FMS(S) Sec 4 Exp/Sec 5 N(A) Preliminary Examination 2022 8 Mathematics Paper 1 9 (a) Solve Answer x = ……………………………… [1] (b) Simplify . Answer …...……………………………… [2] ____________________________________________________________________________ 10 The table below shows the favourite drinks of a group of students. A pie chart is to be drawn to show this information. Calculate the angle of each sector of the pie chart. Write your answers in the table. Favourite drink Number of students Sector angle Fruit juice Soft drink Coffee represents 6 students. [3]

Name: __________________________________ ( ) Class: __________ FMS(S) Sec 4 Exp/Sec 5 N(A) Preliminary Examination 2022 9 Mathematics Paper 1 11 An interior angle of a regular hexagon is 5 times the size of the exterior angle of another n-sided regular polygon. Find the value of n. Answer n = ……………………………… [3] ____________________________________________________________________________ 12 (a) On the Venn Diagram shown in the answer space, shade the set . Answer [1] (b) 𝜉 = {x: x is an integer and x 1} P = {x: x is a prime number} Q = {x: x is a perfect square} R = {x: x is an integer ending in 2} (i) Find . Answer ………………………………. [1] (ii) Find . Answer ………………………………. [1]

Name: __________________________________ ( ) Class: __________ FMS(S) Sec 4 Exp/Sec 5 N(A) Preliminary Examination 2022 10 Mathematics Paper 1 13 The figure shows a container with a height of 40 cm and a width of 15 cm. The other dimensions are as shown. The container was initially empty and it takes 35 seconds to fill the container at a constant rate. (a) Find the time taken for the water level to reach 10 cm. Answer ………………………………s [1] (b) On the grid below, sketch the graph of the height of the water level (d cm) against time (t seconds) for the container. [2] 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 2.2 15 cm 15 cm 30 cm 10cm Height (d cm) Time (t seconds)