2024 CGS EM Prelim Paper 1 with Ans Key

Name: Register No.: Class: CRESCENT GIRLS’ SCHOOL SECONDARY FOUR PRELIMINARY EXAMINATION MATHEMATICS 4052/01 Paper 1 19 August 2024 2 hours 15 mins Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name and index number on all the work you hand in. Write in dark blue or black pen on both sides of the paper. 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. 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  . At the end of the examination, fasten all your work securely together. 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 90. This question paper consists of 20 printed pages. Question 1 2 3 4 5 6 7 8 9 10 11 12 Marks Question 13 14 15 16 17 18 19 20 21 22 23 24 Marks Table of Penalties Qn. No. Presentation –1 Accuracy/ Units –1 Parent’s/ Guardian’s Signature For Examiner’s Use 90

2 2024 Prelim S4 Mathematics P1 Mathematical Formulae Compound Interest Total amount = 1 100 n rP+ 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 1Area of triangle = sin 2ABC ab C Arc length = , where is in radiansr 21Sector area = , where is in radians2 r  Trigonometry sin sin sin a b c A B C== 2 2 2 2 cosa b c bc A= + − Statistics Mean = fx f   22 Standard Deviation = fx fx ff  −  

3 2024 Prelim S4 Mathematics P1 [Turn over Answer all the questions. 1 Calculate ( ) 3 2 3 1.75 2.03 3.85 135.7 − − . (a) Write down the first six digits on your calculator display. Answer ……………………… [1] (b) Write your answer in part (a) correct to 3 decimal places. Answer ……………………… [1] 2 The following items are to be packed into gift bags for distribution to an old folks’ home. 84 packets of cereals. 126 cans of baked beans. 168 packets of biscuits. The items are to be packed such that the contents in each gift bag are the same and there are no leftovers. Find (a) the maximum number of gift bags required, Answer ………………………... [2] (b) the list of contents in each gift bag. Answer ……………………………………………………………………………………… ……………………………………………………………………………………… [1]

4 2024 Prelim S4 Mathematics P1 3 In a concert, 1 3 of the audience were under the age of 20, 25% were over 50 and 2 3 of those over 50 were females. (a) Find the fraction of the whole audience that were between 20 and 50 inclusive. Answer ………………………... [1] (b) 100 of the audience were men above 50. Find the audience size. Answer ………………………... [2] 4 y is inversely proportional to 2.x If x is decreased by 60%, find the percentage increase in y . Answer ………………………..% [3]

5 2024 Prelim S4 Mathematics P1 [Turn over 5 Finance company A pays investors compound interest at 1.2% per annum, compounded every month. Finance company B pays investors simple interest at 1.5% per annum. Mr Tan intends to invest a certain sum for 5 years. He thinks he should invest in finance company A. Do you agree? Explain. Answer ……………………………………………………………………………………………. ……………………………………………………………………………………………. [3] 6 (a) A pair of shoes costs ( ) 2$ 3 7x − and a bag costs ( ) 2$ 2 3 5xx−+ . Find the total cost of three such pairs of shoes and five of the bags, in terms of x. Answer $ ………………………………………... [2] (b) Factorise 32 2 4 8p p p− − + completely. Answer ………………………………………... [2]

6 2024 Prelim S4 Mathematics P1 7 (a) Solve the inequalities 3 2 712 3 823 xxx +−  −  . Answer ………………………... [2] (b) {positive integers less than 17} { : 3 15} {factors of 20} A x x B  = =   = (i) List down the elements in the set AB . Answer …………….…………………… [1] (ii) Find ( )n A B  Answer .…………………… [1] 8 P is the point ( )6, 4−− and Q is the point ( ),xy . The gradient of the line PQ is 2 3 . Find the ratio of :xy in its simplest form. Answer …………… : …………… [2]

7 2024 Prelim S4 Mathematics P1 [Turn over 9 A map is drawn to a scale of 1 : 25 000. (a) The distance between two points on the map is 27.5 centimetres. Find the actual distance, in kilometres, between the two points. Answer ….…………………... km [1] (b) A farm has an area of 36 square centimetres on this map. Find the area of the farm, in square centimetres, on a second map which is drawn to a scale of 1 : 120 000. Answer ….…………………... cm2 [3]

8 2024 Prelim S4 Mathematics P1 10 The first four terms in a sequence of numbers are given below. 2 1 2 2 2 3 2 4 3 2 11 4 5 21 5 8 33 6 11 47 T T T T = + = = + = = + = = + = (a) Find 5T . Answer ….…………………... [1] (b) Show that the nth term of the sequence, nT , is given by 2 73nn++ . Answer [1] (c) Tn and Tn+1 are consecutive terms in the sequence. Find and simplify an expression, in terms of n, for 1 .nnTT+ − Answer ….…………………... [2] (d) Explain why two consecutive terms of the sequence cannot have a difference of 6. Answer ……………………………………………………………………………………… ……………………………………………………………………………………… [2]

9 2024 Prelim S4 Mathematics P1 [Turn over 11 (a) The number of sides of regular polygon A is triple that of another regular polygon B. The ratio of each interior angle of the polygon A to that of the polygon B is 4 : 3. (i) Find the number of sides of the polygon A. Answer ….…………………... [2] (ii) Hence, find the exterior angle of the polygon B. Answer ….…………………...  [1] (b) Explain briefly why each interior angle of a polygon cannot be 110 . ……………………………………………………………………………………… ……………………………………………………………………………………… [1]

10 2024 Prelim S4 Mathematics P1 12 Solve the simultaneous equations. 37 14 33 1 343 xy xy += − =− Answer x = ….………… , y = …..………... [3]