Outram Sec 4E5N Maths P1 Prelim 2022

1 Subject : Mathematics Level (Stream) : Secondary Four Express & Five Normal Academic Paper : 1 (4048) Date : 29 August 2022 Duration : 2 hours Marks : 80 READ THESE INSTRUCTIONS FIRST Write your name, class and index number 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, highlighters, glue or correction fluid. Answer all questions on the Question Paper. 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 . The number of marks is given in brackets [ ] at the end of each question or part question. 80 This document consists of 21 printed pages, including this cover page. Setter: MR AJMAL KHAN OUTRAM SECONDARY SCHOOL PRELIMINARY EXAMINATION 2022 Class Index No Name: __________________________________________________

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 = n rP       1001 rl 24 r hr 2 3 1 3 3 4 r Cabsin2 1 r  2 2 1 r  C c B b A a sinsinsin  Abccba cos2222    f fx 22            f fx f fx

3 Answer all the questions. 1 The shape above is formed by stacking 6 congruent rectangular boxes. Each rectangle box has a length of 20cm and breadth of 10cm. Find the perimeter of the shape. Answer: ……………………cm [2] ___________________________________________________________________________________________ 2 (a) 4 boys take 12 hours to completely paint 3 rooms. How long would it take 12 boys to completely paint 3 rooms? Answer: ……………………hours [1] (b) A girl takes 8 hours to paint 1 room. How long would it take for a boy and a girl to paint completely 1 room together? Answer: ……………………hours [2]

4 3 (a) Javed sold a watch for $900. He made a profit of 80% of the cost price. Calculate the cost price. Answer ………………………….[2] _______________________________________________________________________________________ (b) Ching Boi borrowed a sum of money from XYZ Bank, which charges 2.75% per annum, compounded quarterly. At the end of the first year, he needs to pay an interest charge of $78.50. Find the original sum of money Ching Boi borrowed, giving your answer correct to the nearest cent. Answer …………………………[2]

5 4 (a) Shade the region representing [2] (i) A ∪ B′ , (ii) (A′ ∪ B)′ . (b) 𝜀 = {integers: 4 ≤ x < 20} A = {factors of 30} B = {multiples of 4} (i) List the elements in 𝐴 ∩ 𝐵. Answer ……………………………… [1] (ii) Find 𝑛(𝐴 ∪ 𝐵). Answer ……………………………… [1] A B A B A

6 5 The first four terms in a sequence is given as such 𝑇1 = 30 + 3 𝑇2 = 31 + 5 𝑇3 = 32 + 7 𝑇4 = 33 + 9 (a) Find the value of T5. Answer …………………………… [1] (b) Find, an expression, in terms of n, for Tn. Answer …………………………….. [2]

7 6 (a) Simplify 2(7 5) 11x . Answer ……………………………………... [1] (b) Factorise 10 5a ab . Answer ……………………………………... [1] 7 Factorise completely 4 3 20 15px qx py qy   . Answer ……………………………………... [2] 8 The area of triangle ABC is 47.9 cm2. AB = 17.5 cm and BC = 11.6 cm. Find the two possible sizes of angle ABC. Answer …………………….or……………... [2]

8 9 (a) Express 676 as a product of its prime factors. Answer …………………………………... [2] (b) Given that 676n is a perfect cube, find the smallest possible integer value of n. Answer n = …………………………...…… [2] [2]

9 10 Two cards are drawn at random one at a time with replacement from a pack of 10 cards, numbered 1 to 10. Find the probability that the two numbers on the cards drawn are (a) both even, Answer …………………………….…… [2] (b) multiples of 2 but not multiples of 4. Answer …………………………………... [2]

10 11 The data below shows the marks scored by 10 students in a Mathematics test. 24, 28, 82, 38, 45, 46, 54, 58, 80, 64. Find the (a) median, (b) interquartile range. 12 In a regular polygon, the ratio interior angle: exterior angle = 5:1 Calculate the number of sides of the polygon. Answer………………………… [2] Answer …………………………. [2] Answer………………………….. [3]