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.