2022 CGS Sec 2 EOY Math

Name: Register No.: Class: CRESCENT GIRLS’ SCHOOL SECONDARY TWO END OF YEAR EXAMINATION 2022 MATHEMATICS 4052 11 October 2022 2 hours Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, register number and class on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use 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. 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 π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. At the end of the examination, submit the whole Question Paper. 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. This question paper consists of 20 printed pages. Question 1 2 3 4 5 6 7 8 9 Marks Question 10 11 12 13 14 15 16 17 18 Marks Table of Penalties Qn. No. Presentation –1 Significant Figures/ Units –1 Parent’s/ Guardian’s Signature For Examiner’s Use 80

2 Crescent Girls’ School 2022 EOY S2 Math Mathematical Formulae Mensuration Curved surface area of a cone = rl 2Surface area of a sphere = 4 r 21Volume of a cone = 3 rh 34Volume of a sphere = 3 r Statistics Mean = fx f  

3 Crescent Girls’ School 2022 EOY S2 Math [Turn over Answer all the questions on the question paper. 1 Expand and simplify ( )( ) 23 4 5 4 3p p p− − + . Answer …………………………….. [2] 2 Factorise 35 21 10 6ad bd ac bc− + − completely. Answer …………………………….. [2] 3 (i) Solve 73 176 x−+ − . Answer …............…................... [2] (ii) Hence, given that x is a prime number, state the greatest possible value of x . Answer x = …........................ [1]

4 Crescent Girls’ School 2022 EOY S2 Math 4 Tracy has $50. A shop sells a pack of eggs for $x each and a carton of milk for $y each. If Tracy buys 2 packs of eggs and 5 cartons of milk, she will receive $0.10 in change. If she buys 5 packs of eggs and 2 cartons of milk, she will be short of $6.50. Find the price of each item. Answer Price of one pack of eggs = $…………………………….. Price of one carton of milk = $…………………………….. [4]

5 Crescent Girls’ School 2022 EOY S2 Math [Turn over 5 (i) Factorise 223 48ab− completely. Answer …............…................... [1] (ii) Hence, or otherwise, find the values of a and b if 223 48 51ab−= Answer a = …………………………….. b = …………………………….. [2]

6 Crescent Girls’ School 2022 EOY S2 Math 6 (a) Shannon has a picture measur ing 70 cm by 100 cm. She puts the picture in a frame that gives it a border of uniform width x cm on all four sides. (i) If the combined area of the picture and the border is 8800 cm 2, form an equation in terms of x , and show that it reduces to 2 85 450 0xx+ − = . [2] (ii) Hence, find the width of the border. Answer …………………………… cm [2] (b) Explain why 25 3 0x += has no real solutions. Answer ……………………………………………………………………….. ………………………………………………………………………………… ………………………………………………………………………………… ………………………………………………………………………………… [1]

7 Crescent Girls’ School 2022 EOY S2 Math [Turn over 7 (i) Express 2 47 3 2 8 2 x x x x −− − − as a single fraction in its simplest form. Answer …….........……................ [3] (ii) Hence, or otherwise, solve 2 47 03 2 8 2 x x x x −=− − − . Answer x= …….........……................ [2] (iii) For 2 47 3 2 8 2 xy x x x=− − − − , explain why 2x and 4 3x− . Answer ………………………………………………………………………... ………………………………………………………………………………… ………………………………………………………………………………… ………………………………………………………………………………… [1]

8 Crescent Girls’ School 2022 EOY S2 Math 8 It is given that 2T is inversely proportional to 3r . When 5T = , 2r= . (a) Find an equation connecting T and r . Answer …….........……................ [2] (b) Find the values of T when 4r= . Answer T = ……........... or …….................. [2] 9 Two variables, p and q are connected by an equation. The table below shows some values of p and q. Explain why p is not directly proportional to q. p 3 7 11 13 19 q 7 15 23 27 39 Answer [2]

9 Crescent Girls’ School 2022 EOY S2 Math [Turn over 10 In the figure below, BDFG is a parallelogram, AE // BD // GF, ABC and CDEF are straight lines. The length of CD = DE = EF = 6 cm. (a) (i) Name the quadrilateral that is congruent to quadrilateral BHED. Answer Quadrilateral ……................. [1] (ii) Name the quadrilateral that is congruent to quadrilateral BHID. Answer Quadrilateral ……................. [1] (b) Name the triangle that is similar to triangle BAH and triangle CBD. Answer Triangle ……................. [1] (c) Given that GF = 10 cm, find the length of AE. Answer …….........……................ cm [2] F G B D C A H I E

10 Crescent Girls’ School 2022 EOY S2 Math 11 Flag buntings are to be hung as decoration between two rows of st alls at a carnival. Figure 1 shows a picture of the flag bunting s. Figure 2 shows the top view of the stalls with the flag buntings. The 3 strings of flag buntings are equally spaced out along the row of stalls and are parallel to one another. (a) It is given that the two rows of stalls are 3.2 metres apart and the length of each row is 7.5 m. Assuming the flag buntings are put up taut without any slack, calculate the total length of flag buntings required for decoration. Answer …….........……................ m [2] (b) Alice has to hang the flag buntings from the top edge of the support pillars of the two rows of stalls. She uses a ladder of length 2. 9 metres to complete this task. When the ladder leans against the top edge of the support pillars, it forms an angle of 58 with the flat ground. Find the height of the flag buntings above the ground. Answer …….........……................ m [2] Legend Flag buntings R o w 1 R o w 2 3.2 m 7.5 m Figure 1 Figure 2