2024 4NA ahmad Ibrahim paper 1

1 This document consists of 17 printed pages. [Turn over AISS PRELIM/4045/01/2024 AHMAD IBRAHIM SECONDARY SCHOOL GCE N-LEVEL PRELIMINARY EXAMINATION 2024 SECONDARY 4 NORMAL (ACADEMIC) Name: Class: Register No.: MATHEMATICS SYLLABUS A Paper 1 Candidates answer on the Question Paper. 4045/01 30 July 2024 2 hours 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, glue or correction fluid. Answer all questions. The number of marks is given in brackers [ ] 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. For , use either your calculator value or 3.142. For Examiner’s Use / 70

2 AISS PRELIM/4045/01/2024 [Turn Over Mathematical Formulae Compound Interest Total amount = n rP    + 1001 Mensuration Curved surface area of a cone = πrl Surface area of a sphere = 4πr2 Volume of a cone = 3 1 πr2h Volume of a sphere = 3 4 πr3 Area of triangle ABC = 2 1 ab sin C Arc length = rθ, where θ is in radians Sector area = 2 1 r2θ, where θ is in radians Trigonometry C c B b A a sinsinsin == a2 = b2 + c2 − 2bc cos A Statistics Mean = f fx   Standard deviation = 22        −  f fx f fx

3 AISS PRELIM/4045/01/2024 [Turn over Answer all the questions. 1 Calculate 0.7 4.9 2 5.8 3 + − , leaving your answer to 4 significant figures. Answer .…………………………. [1] 2 Write these numbers in order of size, starting with the smallest. 21 50 , 2 30.25 , 0.412, 0.16 , 39% Answer ……… , ……… , ……… , ……… , ……… [2] 3 Find the largest integer satisfying 3x < –22.5. Answer ………………………....... [2]

4 AISS PRELIM/4045/01/2024 [Turn Over 4 (a) Steven makes a candy salad. He uses gummy bears, candy corn and jellybeans in the ratio 7 : 3 : 5 respectively. He uses 1.4 kg of jellybeans. How much gummy bears does he use? Answer ……………………….. kg [1] (b) Irene makes a candy salad using fruit pastilles, mints and liquorice. The ratio of fruit pastilles : mints is 2 : 3. The ratio of mints : liquorice is 4 : 9. Find the ratio of fruit pastilles : mints : liquorice. Answer ………. : ……… : ……… [1] 5 y is inversely proportional to the square of x. Given that y = 15 when x = 3, find y when x = 5. Answer ………………………… [2]

5 AISS PRELIM/4045/01/2024 [Turn over 6 Simplify (a) 2483xx , Answer ………………….............. [1] (b) ( ) 2 6 327y Answer …………………............... [1] 7 Given that 12 32 8 a− = , find a. Answer ….……………………….. [2]

6 AISS PRELIM/4045/01/2024 [Turn Over 8 Daniel has a bag of marbles. 3 10 of the marbles are red. 40% of the remaining marbles are orange. The other 21 marbles are yellow. How many marbles are there in the bag? Answer …………………………... [2] 9 The graphs of y = x – 5 and 3x + 4y = 29 meet at point P. Find the coordinates of point P. Answer (…………... , …………..) [3]

7 AISS PRELIM/4045/01/2024 [Turn over 10 Solve 5(x – 4) = 6 – (2 – x). Answer x = ……………………… [2] 11 Simplify 2 2 41 6 13 5 y yy − −+ . Answer ………………………….. [3]

8 AISS PRELIM/4045/01/2024 [Turn Over 12 The scale of a map is given as 1 : 50 000. (a) A road on the map is 19 cm long. Find the actual length of the road in kilometres. Answer ………………………. km [1] (b) A farm has an area of 35 km2. Find the area of the farm on the map in square centimetres. Answer ……………………… cm2 [2]

9 AISS PRELIM/4045/01/2024 [Turn over 13 The diagram shows an equilateral triangle of side 10 cm and three identical sectors. Calculate the shaded area. Answer ……………………… cm2 [3] 14 Bhutia invested $5000 in an account paying compound interest at r% per year. After 3 years, she earned an interest of $800. Calculate the value of r. Answer ………………………….. [3]

10 AISS PRELIM/4045/01/2024 [Turn Over 15 The expression x2 – 18x + 19 can be written in the form (x – 9)2 + n. (a) Find the value of n. Answer n = …………………….... [1] (b) Hence solve x2 – 18x + 19 = 0. Answer x = ……… or x = ………. [2] 16 13 1 2 bca bc += + (a) Calculate a when b = 1.5 and c = –1.2. Answer a = ……………………… [1] (b) Rearrange the equation to make b the subject. Answer b = ……………………… [2]