Mock E Math Paper

Mock Preliminary Examination 2024 NAME: __________________________________________________________________________ CLASS: ___________ REGISTER NUMBER: ( ) MATHEMATICS 4048/01 PAPER 1 14 August 2024 Secondary 4 Express 2 hours Additional Materials: Nil READ THESE INSTRUCTIONS FIRST Write your name, registration 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 the 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 𝜋, use either your calculator value or 3.142, unless the question requires the answer in terms of 𝜋. 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 80. This document consists of 16 printed pages

Answer all the questions 1 Sally and Ken both have a total of $550 in the ratio of 3 : 8. How much does Ken have? Answer $...…………………...……. [2] _________________________________________________________________________ 2 Solve 𝑥 4 + 5 = 8. Answer.….…………………...……. [1] _________________________________________________________________________ 3 John walks to school. He leaves home at 6.00 am and reaches his school at 7.15 am. The distance of the school from his house is 1200 m. Calculate his walking speed in km/h. Answer……….……………... km/h [2] _________________________________________________________________________ 4 The prime factorisation of two integers, M and N are shown below. M = 𝑝8 × 𝑞4 × 𝑟6 N = 𝑝𝑥+1 × 𝑞4 × 𝑟2𝑦−1 (a) Explain why M is a perfect square? Answer …………………………………………………………………………… …………………………………………………………………………........... [1] (b) The HCF of M and N is 𝑝5 × 𝑞4 × 𝑟3. Find the values of x and y. Answer x =.….….…, y =….….…. [2] _________________________________________________________________________ [Turn over

5 (a) Simplify and expand (2x + 4) (3x – 7). Answer.….…………………...……. [2] (b) Simplify 2𝑎3𝑏7𝑐 8𝑎−2𝑏−3. Answer.….…………………...……. [2] _________________________________________________________________________ 6 Show that (2𝑛 + 3)2 − 5 is a multiple of 2 for all integer values of n. Answer [2] _________________________________________________________________________ 7 (a) Express 𝑥2 − 6𝑥 + 5 in the form of (𝑥 − 𝑎)2 + 𝑏. Answer.….…………………...……. [1] (b) Hence, solve 𝑥2 − 6𝑥 + 5 = 0. Answer.….……… or ………...…... [1] _________________________________________________________________________ [Turn over

8 In the diagram, AB = 5.1 cm, BC = 7.3 cm and AC = 6.2 cm. Find the area of triangle ABC. Answer.….…………………...……. [4] _________________________________________________________________________ [Turn over

9 Three identical pentagons are shown below to form a regular n-sided polygon. How many more such pentagons to completely form the regular polygon? Answer.….…………………...……. [3] _________________________________________________________________________ 10 The average length of a string of hair is 2.64 × 10−5 m. The average length of a bacteria is 0.00000192 m. (a) Express the average length of a bacteria in standard form. Answer.….…………………...… m [1] (b) Find the difference in their lengths of a hair and a bacteria. Express your answer in standard form. Answer.….…………………...… m [2] _________________________________________________________________________ [Turn over

11 (a) Express 2 𝑥+2 − 𝑥−3 𝑥2−4 as a single fraction. Answer.….…………………...……. [3] (b) (i) Factorise 𝑥2 + 6𝑥 + 9 completely. Answer.….…………………...……. [2] (ii) Hence, solve 2𝑥 𝑥+3 − 𝑥−3 𝑥2+6𝑥+9 = 0. Answer.….…………………...……. [5] _________________________________________________________________________ [Turn over

12 Janet collects stamps. 3 8 of her stamps are from Australia. 35% of the remaining stamps are from Malaysia. The rest are from Singapore. She has 195 Singapore stamps. How many Australia stamps does she collect? Answer.….…………………...……. [3] _________________________________________________________________________ 13 (a) Convert 73 degree into radian. Answer……………………...… rad [2] (b) Given that sin 𝜃 = 4 5 , find the two possible angles of 𝜃. Answer 𝜃=.………. or ………... [2] _________________________________________________________________________ [Turn over

14 A tablet is sold at $1450 after a discount of 20%. (a) Find the marked price of the tablet. Answer $…….…………...……. [1] (b) A customer bought the tablet at the discounted price, and he paid for it using a hire purchase scheme according to the following terms: a down-payment of 60% and the remaining to be paid in monthly instalments over 16 months at a simple interest rate of x% per annum. Given that the total interest he paid is $34.80, find x. Answer $………….……...……. [2] _________________________________________________________________________ 15 In the diagram, PQRS is a quadrilateral and QST is a straight line. (a) Explain why a circle can be drawn with points P, Q, R and S? Answer …………………………………………………………………………… …………………………………………………………………………........... [1] (b) Find angle RST. Answer.……….…………...……° [1] _________________________________________________________________________ [Turn over

16 Jacob draws the infographic below to show the trend of the number of trash generated in 2013 and 2023 in his country. Jacob claims that the amount of trash generated in 2023 is thrice of that in 2013. State one aspect of the infographic that may be misleading and explain why Jacob’s claim is wrong. Answer ………………………………………………………………………………… …………………………………………………………………………………………. …………………………………………………………………………………………. ………………………………………………………………………….................... [2] _________________________________________________________________________ 17 Solve 25𝑥−1 = 35𝑥−1. Answer x =.………………...……. [2] _________________________________________________________________________ [Turn over