2022 STC Math Prelims P1 Ans

CANDIDATE NAME CLASS INDEX NUMBER MATHEMATICS 4048/1 Paper 1 29 August 2022 2 hours Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, class 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 paper clips, highlighters, 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. Calculators should be used 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 answers in terms of . The number of marks is given in brackets [ ] at the end of each question or part question. The total marks for this paper is 80. This document consists of 21 printed pages. CHIJ ST. THERESA’S CONVENT PRELIMINARY EXAMINATION 2022 SECONDARY 4 EXPRESS / 5 NORMAL (ACADEMIC)

CHIJ ST. THERESA’S CONVENT SECONDARY FOUR EXPRESS / FIVE NORMAL(ACADEMIC) 2022 PRELIMINARY EXAMINATION MATHEMATICS PAPER 1 2 Compound interest Total amount = P 1 100 n r+ Mensuration Curved surface area of a cone = rlπ Surface area of a sphere = 2π4 r Volume of a cone = hr 2π3 1 Volume of a sphere = 3π3 4 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== a2 = b2 + c2 − 2bc cos A Statistics Mean = fx f   Standard deviation = 22fx fx ff  −  

CHIJ ST. THERESA’S CONVENT SECONDARY FOUR EXPRESS / FIVE NORMAL(ACADEMIC) 2022 PRELIMINARY EXAMINATION MATHEMATICS PAPER 1 3 Answer all the questions. 1 Simplify ( ) ( )2 5 3 3 2a b a b+ − − . Answer …………………………… [2] 2 Factorise completely (a) 22 5 3xx+− , Answer …………………………… [1] (b) 3 6 2ax ay x y+ − − . Answer …………………………… [2] ( ) ( )2 5 3 3 2 10 6 3 6 7 12 a b a b a b a b ab + − − = + − + =+ [M1 – correct expansion] [A1] ( )( ) 22 5 3 2 1 3 xx xx +− = − + [B1] ( ) ( ) ( )( ) 3 6 2 3 2 2 2 3 1 ax ay x y a x y x y x y a + − − = + − + = + − [A1] [M1]

CHIJ ST. THERESA’S CONVENT SECONDARY FOUR EXPRESS / FIVE NORMAL(ACADEMIC) 2022 PRELIMINARY EXAMINATION MATHEMATICS PAPER 1 4 3 If Abigail sells a bicycle for $270, she would make a loss of 25%. How much must she sell the bicycle for to make a profit of 40%? Answer $ …………………………… [2] 4 Cerra changed S$500 to US dollars in January at a rate of S$1 = USD 0.753. In October, she changed the US dollars back to Singapore dollars at a rate of S$1 = USD 0.722. Find the difference in the amount of Singapore dollars she received. Give your answer correct to the nearest cent. Answer S$ …………………………… [2] 75% of the cost price = $270 270140% of the cost price = 140%75% $ 504  = [A1] [M1] S$1 USD 0.753 0.753S$500 500 USD 376.501 Since USD 0.721 S$1, 1 USD 376.50 376.500.721 S$521.47 Hence, difference = 521.47 500 S$21.47 =  =  = =  =  = −= [A1] [M1]

CHIJ ST. THERESA’S CONVENT SECONDARY FOUR EXPRESS / FIVE NORMAL(ACADEMIC) 2022 PRELIMINARY EXAMINATION MATHEMATICS PAPER 1 5 5 The graph shows the total number of fraudulent insurance claims received by a company in each of the years from 2019 to 2021. (a) State one misleading feature of the graph. Answer…………………………………………………………………………………….. …………………………………………………………………………………………….. …………………………………………………………………………………………….. ……………………………………………………………………………………….. [1] (b) Explain how this feature affects the reader’s interpretation of the graph. Answer…………………………………………………………………………………….. …………………………………………………………………………………………….. …………………………………………………………………………………………….. …………………………………………………………………………………………….. ……………………………………………………………………………………….. [1] Year 2019 2020 2021 900 1000 1100 800 Number of fraudulent insurance claims Rapid increase in fraudulent insurance claims The vertical axis of the graph does not start from zero. (Accept other plausible answers) [B1] The reader might think that there is a sudden spike/significant increase in the number of fraudulent insurance claims in the year 2021. (Accept other plausible answers) [B1]

CHIJ ST. THERESA’S CONVENT SECONDARY FOUR EXPRESS / FIVE NORMAL(ACADEMIC) 2022 PRELIMINARY EXAMINATION MATHEMATICS PAPER 1 6 6 (a) Solve the equation 25 132 xx −−= . Answer …………………………… [2] (b) It is given that 225 2qp=− . (i) Find q when 3p=− . Answer …………………………… [1] (ii) Rearrange the formula to make p the subject. Answer p = …………………………… [2] ( ) 25 132 2 3 2 5 6 2 6 15 6 49 12 4 xx xx xx x x −−= − − = − + = − =− = [M1 – Getting rid of the denominator correctly] [A1] ( ) 2 25 2 3 7q= − − = [B1] 2 2 2 25 2 2 25 25 2 25 2 qp pq qp qp =− =− −= − = [M1 – Isolating p correctly] [A1]

CHIJ ST. THERESA’S CONVENT SECONDARY FOUR EXPRESS / FIVE NORMAL(ACADEMIC) 2022 PRELIMINARY EXAMINATION MATHEMATICS PAPER 1 7 7 Given that 7xy−= and 18xy= , find the values of 22xy− . Answer ……………… or ………..…… [4] ( ) ( ) ( ) ( ) ( ) ( )( ) ( ) ( ) 2 22 22 2 22 22 7 49 2 49 49 2 49 2 18 85 2 85 2 18 121 11 or 11 11 7 or 11 7 77 or 77 xy xy x xy y x y xy x y x xy y xy x y x y x y −=  − = − + =  + = + =+ = + = + + = + =  + = −  − = + − =− =− [M1] [A1 for both answers] [A1, A1]

CHIJ ST. THERESA’S CONVENT SECONDARY FOUR EXPRESS / FIVE NORMAL(ACADEMIC) 2022 PRELIMINARY EXAMINATION MATHEMATICS PAPER 1 8 8 (a) On the Venn diagram, shade the region which represents ' AB . [1] (b) Write down the sets represented by the shaded region. Answer …………………………… [1] 9 The diagram shows a regular octagon, ABCDEFGH, and three sides, PH, HG and GQ, of a second regular polygon. Angle PHA = 81. Find the number of sides in the second regular polygon. Answer …………………………… [3] A B C D E F G H P Q 81 A B B A 'BA [B1] [B1] ( ) ( ) o o o o o o o o o o o oo o o 8 2 180 8 135 360 135 81 144 (Angles at a pt) 2 180 144 180 360 144 36 360 360 1036 AHG PHG n n nn n n −= =  = − − = − = −= =  = = [M1] [M1] [A1]

CHIJ ST. THERESA’S CONVENT SECONDARY FOUR EXPRESS / FIVE NORMAL(ACADEMIC) 2022 PRELIMINARY EXAMINATION MATHEMATICS PAPER 1 9 10 (a) Simplify 33 2 6 14 5 15 x xy y  . Answer …………………………… [2] (b) 9999 11114 4444 k = + + + Without the use of a calculator, find the value of k. Answer …………………………… [2] 11 The values of seven numbers are ( )3x− , ( )3x+ , ( )4x− , ( )7x+ , ( )4x+ , ( )3x− , ( )2x+ . Find the value of x if the sum of the mode and the median of the numbers is 17. Answer …………………………… [2] 3 3 3