Bendemeer 2024 4NA Prelim P2 Question Paper

CANDIDATE NAME CLASS INDEX NUMBER . This document consists of 22 printed pages. MATHEMATICS (SYLLABUS A) 4045/02 Paper 2 5 August 2024 2 Hours Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, register number on all the work you hand in. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. The use of an approved scientific calculator is expected, where appropriate. Section A Answer all the questions. Section B Answer one 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 70. 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. For𝜋, use either your calculator value or 3.142. BENDEMEER SECONDARY SCHOOL 2024 PRELIMINARY EXAMINATION SECONDARY FOUR NORMAL (ACADEMIC) FOR ASSESSMENT USE 70

2 4045 Paper 2/ Sec Four NA / Prelim Exam / BDMS 2024 Mathematical Formulae Compound interest Total amount = 𝑃 (1 + 𝑟 100) 𝑛 Mensuration Curved Surface area of a cone = 𝜋𝑟𝑙 Surface area of a sphere = 4𝜋𝑟2 Volume of a cone = 1 3 𝜋𝑟2ℎ Volume of a sphere = 4 3 𝜋𝑟3 Area of triangle ABC = 1 2 𝑎𝑏sin C Arc length = rθ, where θ is in radians Sector area = 1 2 𝑟2𝜃, where θ is in radians Trigonometry 𝑎 𝑠𝑖𝑛 𝐴 = 𝑏 𝑠𝑖𝑛 𝐵 = 𝑐 𝑠𝑖𝑛 𝐶 𝑎2 = 𝑏2 + 𝑐2 − 2𝑏𝑐 𝑐𝑜𝑠 𝐴 Statistics 𝑀𝑒𝑎𝑛 = ∑𝑓𝑥 ∑𝑓 Standard deviation = √∑𝑓𝑥2 ∑𝑓 − ( ∑𝑓𝑥 ∑𝑓 ) 2

3 4045 Paper 2/ Sec Four NA / Prelim Exam / BDMS 2024 [TURN OVER Section A (62 Marks) Answer all the questions in this section. 1 (a) Calculate ( 4 5) −1 2 − √5 1 2. Answer ………………………… [1] (b) By writing each number correct to 1 significant figure, estimate the value of √9.103×284 13 . Answer ………………………… [1] 2 (a) (i) Find p. Answer p = ………………………° [1] (ii) Find q. Answer q = ………………………° [1] (b) Given that sin 𝑥 ° = 0.5 and 𝑥° is an obtuse angle, find 𝑥°. Answer …………………………….° [1]

4 4045 Paper 2/ Sec Four NA / Prelim Exam / BDMS 2024 3 Solve the simultaneous equations. 5𝑥 − 3𝑦 = 11 3𝑥 − 𝑦 = 9 Answer x = ………………………… y = ………………………… [3]

5 4045 Paper 2/ Sec Four NA / Prelim Exam / BDMS 2024 [TURN OVER 4 Faris owns a furniture shop. (a) The cost of a sofa was $1200. He made a profit of 25% on the cost price when he sold it. Find the selling price. Answer $………………………… [2] (b) He sold a cupboard at $188 with a loss of 10%. How much was the cost of the cupboard? Answer $………………………… [2]

6 4045 Paper 2/ Sec Four NA / Prelim Exam / BDMS 2024 5 (a) Write these numbers in order of size, starting with the smallest. 43 40 4 1 3 4−3 Answer …………, …………., …………, ………… smallest largest [1] (b) Write 𝑎2×𝑎1 𝑎−2 as a single power of a. Answer …………………………… [1] (c) Simplify 7𝑝5 × 2𝑝−1 2. Answer …………………………… [1]

7 4045 Paper 2/ Sec Four NA / Prelim Exam / BDMS 2024 [TURN OVER 6 It is given that y is inversely proportional to the square of x. When x = 1, y = 64. Find the value(s) of x when y = 25. Answer x = ………………………… [3] 7 ABCD is a parallelogram in which angle DAB = 67° and angle DCE = 23°. Given that BE is perpendicular to CB, find (a) angle BCE, Answer …………………………° [1] (b) angle CEB, Answer …………………………° [1] (c) angle EDC. Answer …………………………° [1]

8 4045 Paper 2/ Sec Four NA / Prelim Exam / BDMS 2024 8 The diagram shows a triangle ABC and a circle with centre A. The points B and D lie on the circumference of the circle. The radius of the circle is 8 cm. The length of the line AC is 17 cm. The area of triangle ABC is 44 cm2. . (a) Calculate the area of sector ABD. Answer ……………………………cm2 [4] (b) Calculate major arc length ABD if the reflex angle BAD is 5.6 rad. Answer ……………………………cm [1]

9 4045 Paper 2/ Sec Four NA / Prelim Exam / BDMS 2024 [TURN OVER 9 (a) Simplify 2𝑥 − 3(𝑥 − 4). Answer …………………………… [1] (b) Solve 8 𝑥+1 = 3𝑥 − 5 , leave your answer in 2 decimal places. Answer x = ……………or …………… [4]

10 4045 Paper 2/ Sec Four NA / Prelim Exam / BDMS 2024 10 In the diagram below, XYZ is a straight line. XZ is 5 times YZ. AY = 12 cm, WZ = 15 cm and sin 𝑎 ° = 3 5 . (a) Find XZ. Answer XZ = ……………………cm [1] (b) Show that YZ is 5 cm. Hence find the exact value of cos 𝑏°. Answer …………………………… [2] (c) Find the length AZ. Answer ……………………………cm [1]