Math - Sec 2 - SA 2 - 2021 - Northbrooks Sec

1 0 NORTHBROOKS SECONDARY SCHOOL End-of-Year Examination 2021 Secondary 2 Express I CANDIDATE _NAME I CLASS MATHEMATICS Paper1 Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST REGISTER NUMBER Write your register number, name 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. 4052/01 7 October 2021 1 hour 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 rr, use either your calculator value or 3.142, unless the question requires the answer in terms of rr. 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 40. Q1 Q2 Setter: Wang Pei Fen FOR EXAMINER'S USE Q3 Q4 QS Q6 Q7 DO NOT TURN THE PAGE UNTIL YOU ARE TOLD TO DO SO. This document consists of 11 printed pages. Mathematical Formulae Partnerlnlearning 298 QB :~

Compound interest Mensuration Trigonometry Statistics 2 Total amount= P(l + ~) 11 100 Curved surface area of a cone = rcrl Surface area of a sphere =4rcr 2 1 1 ? Vo ume of a cone =-rcr-h 3 4 Volume of a sphere =-rcr 3 3 Area of triangle ABC= .!.ab sinC 2 Arc length= r0, where 0 is in radians Sector area= .!..,.2 0 , where 0 is in radians 2 a b C -----=-- sinA sinB sinC a2 = b2 + c2 - 2bc cos A '""fx Mean=-~- Lf Standard deviation = Partnerlnlearning 299

3 Answer all the questions . 1 Given that v = u + Ft , express t in tem1s of F, m, u and v. m 2 Factorise fully 4ax + 3b + 12bx + a . Partner! n Learning 300 Answer ............................... [3] Answer ... .... .... .................... [3]

3 y is directly proportional to x2. It is known thaty = 10 whenx = 5. Find (a) the value ofy whenx = 10, (b) 1 the values of x when y = 40 . 4 Answer y = ........................ [3] Answer x = ................ or x = ............... [3] Partnerlnlearning 301

5 4 Solve these simultaneous equations. 7c +4d = 2 8c + 5d = 1 Partnerlnlearning 302 Ans111er c == ••••••••.......•..•.•••.••••..••• d = ......... .. .... ..... ...... . [4]

5 D I I I I I I I 6 A ~lJition wit \ I \ I \ \ I \ \ ' \ \ I \ \ I \ \ I \ \ \ \ I \ I Diagram II Diagram I shows a quadrilateral ABCD, in which DA = AB = x cm and BC= CD= y cm. Angle ABC= angle CDA = 90°. (a) Show that the area of this quadrilateral is xy cm2• Answer (b) Area of this quadrilateral is 60 cm2. Express y in te1ms of x. [2] Answer ............. ...... ......... [1] Partnerlnlearning 303 BP-303

7 Five of these quadrilaterals are joined together to make the shape shown in Diagram II. (c) 120 Show that the outside perimeter, P cm of this shape is given by P = 1 Ox+ - . X Answer [2] (d) Given that P = 74, show that 5x 2 -31x+60 = 0 . Answer [2] (e) Solvetheequation 5x2 -37x+60=0 Answer x = ............ .... or x = ....... ...... .. [3] (f) Find the two possible values of y when P = 74. Answer y = ................ or y = ............... [2] Partnerlnlearning 304 BP-304

8 6 The diagram shows two lines , L1 and L2. (a) Write down the equation of L1. Answer ....... ...... .... ...... ..... ... [1] (b) Write down the coordinates of the point where L2 crosses the x-axis. Partnerlnlearning 305 Answer ( ............. , .... ........ ) [1]

(c) 9 (i) On the same axes, draw the graph of y = x. [l] (ii) Hence write down the value of k such that the point (k, k) lies on L2. Answer k= .. .. ...... ... ..... ...... . [l] Partnerlnlearning 306 BP-306

7 10 • • TuitI011 • • • • • • • • • wit r.···'•) c-·:• .. ·-• • • • .. ,) . . , • • • • • 0 1 2 3 4 5 The dot diagram shows the number of children living in 20 HDB flats. (a) Find the total number of children in these 20 HDB flats Answer .... .... ..... ... ...... ..... children [2] (b) Find the number of flats that have less than 3 ·children living in them. Answer ..................................... [I] (c) A flat is selected at random. Find the probability that the flat has at least 3 children living in it. Partnerlnlearning 307 Answer ..... .. ........ .. .. ........ [2] BP-307