CAT HIGH 2025 EMATH PRELIM P2 QP

1 Name: Index Number: Class: CATHOLIC HIGH SCHOOL 2025 Preliminary Examination Secondary 4 (O-Level Programme) Mathematics 4052/02 Paper 2 27 Aug 2025 2 hours 15 minutes Booklet A Additional material: Question Booklet B READ THESE INSTRUCTIONS FIRST Write your name, index number and class on all the work you hand in. Write in dark blue or black pen. You may use a soft pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all questions in the space provided. 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 ofπ . The number of marks is given in brackets [ ] at the end of each question or part question. The total mark for this paper is 90. For examiners’ use ____________________________________________________________________________________________ This booklet consists of 12 printed pages 40 A

2 Mathematical Formulae Compound interest Total amount = Mensuration Curved surface area of a cone = Surface area of a sphere = Volume of a cone = Volume of a sphere = Area of triangle ABC = Arc length = , where is in radians Sector area = , where is in radians Trigonometry Statistics Mean = Standard deviation = nrP      + 1001 l r π 2 4rπ h r 3 1 2π 3 3 4 rπ C b asin 2 1 θr θ θ2 2 1 r θ C c B b A a sin sin sin = = A c b c b a cos 2 2 2 2− + = ∑ ∑ f x f 22      − ∑ ∑ ∑ ∑ f x f f x f

3 1 Every evening Juline and Evangeline play a game of tic-tac-toe. When they play against each other, Juline has a 2 5 chance of winning and Evangeline has a 1 6 chance of winning. Find, as a fraction in its simplest form, the probability that (i) Juline will win on both Monday and Tuesday next week. Answer ……………………………..…..… [1] (ii) Juline will win on either Wednesday or Thursday next week but not on both days. Answer …………………………………………[2] (iii) it will be a draw on Friday next week. Answer …………………………………………[2]

4 2(a)(i) On the Venn diagram, shade the region which represents ''( ).PQ [1] (ii) Use set notation to describe the shaded region. Answer ………..……………………[1] P Q F K ξ

5 2(b) { }integers : 20 50xxξ = ≤≤ A = { perfect square } B = { prime numbers } C = { multiples of 7} (i) List the elements in 'AC∩ . Answer ………………………………………….[1] (ii) Find the value of n ()BC∩ . Answer ………………………………………….[1] (iii) A number, p, is chosen at random from the set (B U C). Find the probability that pA∈ . Answer ………………………………………….[2]

6 3. O is the centre of the circle ABCDE. XY is a tangent to the circle at E and EC intersects BD at F. OZ is a straight line that passes through A and is parallel to XY. The lines CB produced and EA produced meet at W. 71BCE∠= ° and 64OBC∠= ° . (a) Complete the following statements. (i) BDE∠ = ………………………………………….° because ……….……………………………………….[2] (ii) AOE∠ = ……………………………………………..° because …………………………………….…………[2] X Y A B C E D O F Z W

7 Find (b) BOE∠ , Answer BOE∠ =………………………………...° [1] (c) OCE∠ , Answer OCE∠ =………………………………………...° [1] (d) ABW∠ . Answer ABW∠ =………………………………………° [2]

8 4. In the diagram, a lighthouse is at O. Four ships, A, B, C and D are positioned around it with OA = 3 km , OB = 5 km, OC = 8 km and OD = 6 km. The bearing of A from O is 027° and the bearing of B from O is 103°. Ship D lies due west of O and Ship C lies due south of D. (a) Calculate the distance between Ship A and Ship B. Answer …………………………………km [3] A B O N D C 3 5 6 8

9 (b) The keeper of the lighthouse is standing on top of the lighthouse, which is 20 m tall. Calculate the angle of depression, from where he is standing to Ship A. Answer ……………………………………. ° [2] (c) Calculate the bearing of Ship C from O. Answer ………………………………………° [2]

10 (d) A speedboat travels directly from Ship A to Ship B. Calculate the shortest distance between the speedboat and the lighthouse during its journey. Answer ……………………………… km [2] (e) It is suggested that Ships A, B and the lighthouse at O form a right-angled triangle. Showing your working clearly, determine whether this is true. Answer [2]