Math - Sec2 - SA2 - 2023 - Bedok South Sec

127 BEDOK SOUTH SECONDARY SCHOOL END-OF-YEAR EXAMINATION 2023 CANDIDATE NAME CLASS MATHEMATICS PAPER 1 Candidates answer on the Question Booklet. READ THESE INSTRUCTIONS FIRST INDEX NUMBER Write your class, index number and name on all the work you hand in. Write in dark blue or black ink on both sides of the paper. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all questions. 2EXP 4052/01 9 October 2023 1 hour 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 in the space below the question . Omission of essential working will result in loss of marks. The total of the marks for this paper is 40. The use of an approved scientific calculator is NOT ALLOWED. Examiner's Use ... Penaltv Question No. Units Presentation Sub-Total Total . . Mark -1 /-2 ~

2 Answer all the questions. 1 Expand and simplify (3x+ )(2 -x)-3(.x-1). Answer ...... ... .... ..... .... ... .... .... [2] 2 Factorise completely x 2 + 7 x - 7xy- 49y. Answer ............... .... .... ........ .. [2] 3 Factorise completely (p + 3)2 -(2q-l)" using special products of algebraic expressions. Answer ....... .. ..... ............... ... ....... ... .... .. [2] 4 . . . . . ' 2p-1 4p 1 -4p+1 Express as a smgle fract10n m 1ts s1mples··: form--+-----2 2p-4 Answer ...... ... .... ... .... .. ........... [2] 128

5 3 2 5 Express as a single fraction in its simplest form --- --., . a+ 1 4a +., Answer .... .... ..... ...... .. ...... .. .... [2] 6 The diagram shows two right angled triangles , ABD and BCD. 129 AB = 17 cm, AD= 8 cm, BC= 12 cm, BD = 15 cm and CD= 9 cm. A B 12 Find, in fractions in its simplest form, the values of (a) sinL.BDC, (b) tan LABD . D 9 C Answer ............ .... ... ............ .. [I J Answer ... ......... ........ ...... ... .... [1]

'130 4 7 The following table shows some values of a and b. a 6 4 3 b 3 8 15 Detennine whether a is inversely proportional to the square root of b + 1. Ans·wer ..... ... ... .. ..... .... ............ ... ... .. ..... ... ... .... ...... ... ... ....... ........... ...... ....... .... ... [2] 8 pis directly proportional to the square of q. The sum of the values of p when q = 2 and q = 3 is 26. Find p when q = 4. Answer ... .... ....... ..... .. .. .... ... ... [3]

9 131 s rr11itio11 The test marks of a group of students are shown in the stem-anct-le~diagram. 0 2 3 5 7 9 I x 4 5 8 3 8 Key: 1 I 5 means 15 vVit (a) Find the value of x if the median score is 12.5. Answer ... ....... .... .... ...... ..... ... . [1] (b) ~ of the students scored more than v. Find the value ofJ;. s - Answer .... ... ....................... .. . [l] (c) Explain why the mean may not be an appropriate average to use to summarise the scores of the students. Answer ..... .......... ..... ..... ..... .... .. ... ..... .. ..... ... ......... ................ ....... ....... ....... [l] BP-127

6 10 Wendy bought 20 boxes of strawberries at S6 each. She later threw away x boxes which were spoilt and sold the remaining boxes at $8 each . 132 (a) Write down an expression in term.s of x to represent the amount Wendy received from selling the stra vberries and show that it simplifies to 160-Sx . Ans,ver [ l] (b) By fonning and solving an inequality, fi nd the maximum number of spoilt boxes if Wendy did not make a loss. Answer ...... ............... .. .......... [3]

BP-129 7 11 In the diagram, triangle ABC is congruent to triangle EFD. L.BAC=89°, LDFE=61°, BC= 8 cm, CD= 4 cm,DE= 7 cm and£F=4 cm. E A · uition B 8 D Calculate (a) LBCD, Answer .. ...... ...... ... ... .... .. .. ..... [2] (b) AF. Ans11·er ................................. [3] 133

8 12 The shorter side of a rectangle is x cm. 134 Tuition perim_et = ' v . 'T .. X area= 35 cm 2 X (a) Write down an expression in terms of x to represent the length of the longer side of the rectangle , given that the area c,f the rectangle is 3 5 cm2. Answer ... ... ... ... .. .. ..... ..... ... .... [l] (b) Write do\vn an expression in term; of x to represent the length of the longer side of the rectangle , given that the perimeter of the rectangle is 24 cm. Show that it simplifies to ( 12 - x) cm. Annver ( c) Equate the two expressions of the length of the longer side of the rectangle from parts (a) and (b) and show that it ~implifies to x2 --12x +35 = 0 Answer [l ] BP-130

-----~··· -- ---- - --- --- 135 9 (d) Solve the equation x2 - l 2x + 35 = 0 . Find the lengths of the shorter and longer sides of the rectangle. Answer: Length of shorter side = ...... ............. ....... ...... . Length of longer side= .. ...... ..... ................ ... . [3] BP-131

10 13 Let x be the tens digit and y be the ones digit of a two-diigit number, represented as I Ox+ y. '136 (a) The number is equal to 4 times the sum of its digits. Write down an equation in x and y to represent this infonnation and show that it simplifies to 2.x - y = 0. Ans,ver [I] (b) The number formed y reversing its digits , represented as I Oy + x, is 9 more than the original number. Write down an equation in x and y to represent this infonnation and show that it simplifies to x-y = -1 . Answe r ( c) Solve these two equations to find the tvi!o-digit number. [l] Answer ... .. ... .... ......... .. .......... [3] End of Paper