CGS 2025 EMATH PRELIM P1 MS

Name: Solution Register No.: Class: CRESCENT GIRLS’ SCHOOL SECONDARY FOUR PRELIMINARY EXAMINATION MATHEMATICS 4052/01 Paper 1 21 August 2025 2 hours 15 mins 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 an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all the questions. 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 with the answer. Omission of essential working will result in loss of marks. The total of the marks for this paper is 90. 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 𝜋𝜋, use either your calculator value or 3.142. This question paper consists of 21 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 2025 Prelim S4 Mathematics P1 Mathematical Formulae Compound Interest Total amount = 1 100 n rP+ Mensuration Curved surface area of a cone = rlπ 2Surface area of a sphere = 4 rπ 21Volume of a cone = 3 rhπ 34Volume of a sphere = 3 rπ 1Area of triangle = sin 2ABC ab C Arc length = , where is in radiansrθθ 21Sector area = , where is in radians2 r θθ Trigonometry sin sin sin abc ABC= = 222 2 cosa b c bc A=+− Statistics Mean = fx f ∑ ∑ 22 Standard Deviation = fx fx ff  − ∑∑ ∑∑

3 2025 Prelim S4 Mathematics P1 [Turn over Answer all the questions. 1 Alex puts aside $8000 in an investment fund which offers compounded interest quarterly at an interest rate of 2% per annum. Calculate the total value of his investment at the end of 3.5 years. 4 3.5 2 4Total amount 8000(1 ) 100 $8578.57 ×= + = Answer $ ……………………… [2] 2 In the quadrilateral ABCD, BC = 5.25 cm, AC = 4.32 cm. Angle 90ADC = ° . Angle 35ACD= ° . (a) Calculate AD. sin35 4.32 2.4779 2.48 cm AD AD °= = = Answer ……………………… cm [1] (b) Given that the area of triangle 23.18 cmABC = , find the obtuse angle ACB. ( )( ) ( )( ) 1Area = sin2 13.18 4.32 5.25 s in 2 sin 0.28042 163.7 AC BC ACB ACB ACB ACB ∠ = ∠ ∠= ∠=° Answer ……….……………… … [2] 3 The density of gold is 19.32 g/cm3. A B C D 5.25 cm 4.32 cm

4 2025 Prelim S4 Mathematics P1 The mass of a gold bracelet is 37.51 g. (a) By rounding these numbers correct to 2 significant figures, find an estimate of the volume of the gold bracelet. Show the numbers you use. 3 3819 volume volume 2 cm ≈ = Answer ………………………. 3cm [2] (b) Without doing any further calculation, explain why the actual volume of the gold bracelet is less than the answer to part (a). The mass is rounded up to a larger value The density is rounded down to a smaller value Volume is found by dividing a larger mass by a smaller density The actual volume is less than the estimated volume ……………………………………………………………………………………… ……………………………………………………………………………………… [1] 4 A box contains 10 blue water bottles, 7 green water bottles and 5 red water bottles. (a) Two water bottles are drawn from the box. In the first draw, a water bottle is randomly drawn from the box with no replacement. What is the probability that a green bottle will be drawn on the second draw? ( in 2 draw)=P(non-green followed by green) + P(green followed by green) 15 7 7 6= 22 21 22 21 7 22 ndP green ×+× = Answer ……………………….. [2] (b) How many red water bottles should be added into the bag such that the probability of drawing a red water bottle on the first draw is 2 3 ? Let the number of red water bottles to be added be x. 52 22 3 3 15 44 2 29 x x xx x + =+ +=+ = Answer ……………………….. [2]

5 2025 Prelim S4 Mathematics P1 [Turn over 5 Express ( ) ( )2 12 22 32 xxx − −−− as a single fraction in its simplest form. ( ) ( ) ( )( ) ( ) ( ) ( )( ) ( )( ) ( )( ) 2 12 12 2 21 2 22 32 1 22 1 21 2 14 2 21 2 14 21 2 x xx xxx x xx x xx x xx −= −− +− −−− −+= +− −−= +− −−= +− Answer ……………………………………... [3] 6 Five positive integers have a mean of 18, a median of 14 and a mode of 33. Given that the two smallest integers are prime numbers, find the five numbers. Let the 2 smallest numbers be a and b. 14 33 33 18 5 10 ab ab ++ + + = × += Therefore, 3, 7ab= = . The five numbers are 3, 7, 14, 33, 33. Answer ……… , ……… , ……… , ……… , ………... [2]

6 2025 Prelim S4 Mathematics P1 7 In 2023, the revenue of a company was 12% more than in 2022. In 2024, it was 30% less than in 2023. (a) Given that p represents the revenue of the company in 2022, express the revenue in 2023 in terms of p. 1.12 p Answer ………………………... [1] (b) Ben said that in 2024, the revenue of the company was 33.6% less than in 2022. Do you agree? You must show your calculations. ( )Revenue in 2024 = 0.7 1.12 0.784 0.784Percentage change = 100% 21.6% Percentage decrease = 21.6% p p p p = − × =− I do not agree as there is only a drop of 21.6% in revenue between 2024 and 2022 instead of 33.6%. ……………………………………………………………………………………… …………………………………………………………………………………….... ……………………………………………………………………………………… [2] 8 (a) Solve 32 01 31xx−=−− . 32 1 31 3(3 1) 2(1 ) 9 3 2 2 11 5 5 11 xx xx xx x x =−− −= − −=− = = Answer x= …………………… [2] (b) Simplify 2 2 4 25 6 13 5 x xx − −− . ( ) ( )( ) ( ) 2 2 2 5 (2 5)4 25 6 13 5 2 5 3 1 (2 5) 31 xxx xx x x x x +−− =−− − + += + Answer ………..…………………… [2]

7 2025 Prelim S4 Mathematics P1 [Turn over 9 The ratio of exterior angle : interior angle of a regular polygon is 1 : 9. Calculate (a) the number of sides of the polygon, 180Exterior 10 18 360No. of sides = 18 20 °∠= = ° ° ° = Answer ….…………………... [2] (b) the sum of the interior angles of the polygon. ( )Sum of interior angles = 180 20 2 = 3240 °− ° Answer ….………………….. [1] 10 (a) Write down the set represented by the following shaded region. ε ( )' ( ' ) or ' A BC AB C∩∩ ∪ ∩ Answer ….…………..……………... [1] (b) Given that = {x : x is an integer, }, and its subsets A, B and C are A = { x : x is a factor of 16} B = {x : x is a prime number} C = {x : 91 x−≥ } (i) List the elements in the set AB∩ . A = {1, 2, 4, 8} B = {2, 3, 5, 7, 11} {2} AB∩= Answer …..………..…………………... [1] (ii) Find ( ' )nB C ∪ . ' { 1, 4, 6,8,9,10,12} { 1, 2.....8} ( ' ) 11 B C nB C = = ∪= Answer ……..……………... [1] (iii) Explain clearly if AC⊂ . A B C

8 2025 Prelim S4 Mathematics P1 A = {1, 2, 4, 8} { 1, 2.....8}C = All elements in Set A are elements in Set C AC≠ Therefore AC⊂