Methodist Girls School Paper 1

Class Index Number Name : __________________________________________ This question paper consists of 22 printed pages and 2 blank pages. METHODIST GIRLS’ SCHOOL Founded in 1887 PRELIMINARY EXAMINATION 2022 Secondary 4 Tuesday MATHEMATICS 4048/01 2 August 2022 Paper 1 2 hours Candidates answer on the Question Paper. INSTRUCTIONS TO CANDIDATES Write your class, name and index number in the spaces at the top of this page. 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. Ans wer all the 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 numbe r 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. 80 www.KiasuExamPaper.com 555

Page 2 of 24 __________________________________________________________________________________ Methodist Girls’ School Mathematics Paper 1 Sec 4 Preliminary Examination 2022 Mathematical Formulae Compound Interest Total amount = Mensuration Curved surface area of a cone = Surface area of a sphere = 4 Volume of a cone = Volume of a sphere = Area of a triangle = absin C Arc length = rθ , where θ is in radians Sector area = , where θ is in radians Trigonometry a 2 = b 2 + c 2 – 2bc cos A Statistics Mean = Standard deviation = ( ) 100 r 1+ n P rlπ 2rπ h r2 3 1π 3 3 4 rπ 2 1 θ2 2 1 r C c B b A a sin sin sin = = ∑ ∑ f fx 22         − ∑ ∑ ∑ ∑ f fx f fx www.KiasuExamPaper.com 556

Page 3 of 24 __________________________________________________________________________________ Methodist Girls’ School Mathematics Paper 1 Sec 4 Preliminary Examination 2022 1. Arrange the following numbers from the smallest to the largest. 2 , 4 , 2.3 , 227% , 173 π • −− Answer ………………………………..………………………. [1] 2. The marked price of a washing machine in a shop is $m. During the Great Singapore Sale, it was sold at a discount of d %. (a) Express the selling price as a single fraction in terms of m and d. Answer $ …..……..…………… [1] (b) The shopkeeper made a profit of 25% from the sale of the washing machine. Express the cost price as a single fraction in terms of m and d. Answer $ …..………..………… [1] 3. Factorise completely 224 3 12px k kx p−+ − . Answer ………… ……….. … … ………………… [3] www.KiasuExamPaper.com 557

Page 4 of 24 __________________________________________________________________________________ Methodist Girls’ School Mathematics Paper 1 Sec 4 Preliminary Examination 2022 4. Solve 42 1 146 xx−− −= . Answer x = ……………………… [2] 5. (a) Given that p = 24 × 32 × 11 and q = 2 × 32 × 5 × 11. Find the greatest integer that divides p and q exactly. Answer …………………………… [1] (b) A number has exactly nine factors. Two of the factors are 12 and 18. List all the factors of the number. Answer ………………………………………………………… ………… [2] www.KiasuExamPaper.com 558

Page 5 of 24 __________________________________________________________________________________ Methodist Girls’ School Mathematics Paper 1 Sec 4 Preliminary Examination 2022 6. ε = {all real numbers} A = {all prime numbers} B = {all rational numbers} C = {all integers} D = {all negative numbers} E = {1, 2, 3, 4, 5, 6, 7} (a) List all the elements contained in the set AE∩ . Answer ……………………………………… [1] (b) Explain why ' CB φ∩= . Answer …………………………………………………………………………………… …………………………………………………………………………………………….. …………………………………………………………………………………………….. ……………………….......................................................................................................... ………………………………………………………………………………………… [1] (c) Which of the following statement(s) is/are correct? Statement 1: CB⊂ Statement 2: AC A∪= Statement 3: AD φ∩= Statement 4: CD φ∩= Answer Statement(s) number ……………….…………….is/are correct [2] www.KiasuExamPaper.com 559

Page 6 of 24 __________________________________________________________________________________ Methodist Girls’ School Mathematics Paper 1 Sec 4 Preliminary Examination 2022 7. Given that 2 3 25 hk hw − = , express h in terms of k and w. Answer ……………….…….…………… [3] 8. Given that n is a positive integer, explain whether 22(7 3) 4n+− is divisible by 7. Show your working clearly. Answer [2] www.KiasuExamPaper.com 560

Page 7 of 24 __________________________________________________________________________________ Methodist Girls’ School Mathematics Paper 1 Sec 4 Preliminary Examination 2022 9. The chart below shows the monthly sales of an electrical company from January to June in 2022. (a) State one feature of the graph that may be misleading. Answer ………………………………………………………………………………… ………………………………………………………………………………………… [1] (b) Explain how this may lead to a misinterpretation of the graph. Answer …………………………………………………………………………………. …………………………………………………………………………………………… …………………………………………………………………………………………… …………………………………………………………………………………………… ………………………………………………………………………………………… [1] 150 175 200 Sales ($ in thousands) Month January April May June February March 0 www.KiasuExamPaper.com 561

Page 8 of 24 __________________________________________________________________________________ Methodist Girls’ School Mathematics Paper 1 Sec 4 Preliminary Examination 2022 10. In the diagram, the line L cuts the y-axis at A (0, 15) and the x-axis at B (h, 0). Given that tan θ = 5 2 , where θ is the angle made by the line L and the horizontal x-axis, find (a) the value of h, Answer h = …………………… [1] (b) the equation of the line L. Answer …………….…………… [1] (c) The coordinates of point C is (−6 , 21). Calculate the length of AC. Answer …………….…… units [2] (d) ABCD is a trapezium. Find the coordinates of a possible point D. Answer ( ……… , .…….. ) [1] y O L B (h, 0) θ x A (0, 15) www.KiasuExamPaper.com 562

Page 9 of 24 __________________________________________________________________________________ Methodist Girls’ School Mathematics Paper 1 Sec 4 Preliminary Examination 2022 11. (a) Solve the inequality ( )15 3 5 72 xx−≤ + <+ . Answer …………….…………… [3] (b) Illustrate the solutions of the inequality on a number line clearly. Answer [1] (c)