Greenridge Sec 2024 4NA MA Prelims P2-vetted

[Turn over This paper consists of 19 printed pages, including this cover page. GREENRIDGE SECONDARY SCHOOL 2024 PRELIMINARY EXAMINATION SECONDARY 4 NORMAL (ACADEMIC) CANDIDATE NAME CLASS - INDEX NUMBER MATHEMATICS SYLLABUS A 4045/02 Paper 2 6 August 2024 Setter: Mrs Goh-Kok Mei Leng 2 hours Candidates answer on the Question Paper. Additional Materials: Nil READ THESE INSTRUCTIONS FIRST Write your class, index number and name 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 the 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. For , use either your calculator value or 3.142. For Examiner’s Use Total 70

2 Mathematical Formulae Compound interest Total amount = n rP       1001 Mensuration Curved surface area of a cone = πrl Surface area of a sphere = 24πr Volume of a cone = 21 π3 rh Volume of a sphere = 34 π3 r Area of triangle ABC = Cab sin2 1 Arc length = r , where  is in radians Sector area = 2 2 1 r , where  is in radians Trigonometry C c B b A a sinsinsin  Abccba cos2222  Statistics Mean = f fx   Standard deviation = 22          f fx f fx

3 [Turn over Answer all the questions. 1 (a) Express 17 5 as a percentage. Answer …………...…………..… % [1] (b) Express 40.4% as a fraction in its simplest form. Answer …………...………….……... [1] (c) Simplify 3 2 3 6 32 5 8 20 x y x y . Answer …………...…………..…….. [2] (d) Simplify 225 4 6 15 x x   . Answer …………...………….……... [2]

4 2 (a) Write as a single fraction in its simplest form 51 64 xx  . Answer …………...…………..…….. [2] (b) Solve the equation 61 2 5 3x  . Answer …………...………………… [2] (c) It is given that 2 5ax b  . (i) Find the value of x when a = 5 and b = 2. Answer x = ……...………………… [2] (ii) Express a in terms of b and x. Answer …………...………………… [1]

5 [Turn over 3 A circle with centre O has a radius of 4 cm. A and B are points on the circumference of the circle. Given that  95AOB , calculate (a) the circumference of the circle, Answer …………...…………… cm [1] (b) the perimeter of the sector AOB, Answer …………...…………… cm [2] (c) the area of the minor sector AOB. Answer …………...…………… cm2 [2] O A B 95 4 cm

6 4 In the diagram, XYZ is a straight line, WX = 25 cm, WY = 17 cm and WZ = 15 cm. It is given that angle 90XZW . Calculate (a) the length of XY, Answer …………...…………… cm [2] (b) angle ZWY , Answer Angle ZWY = …………… [1] (c) angle YWX , Answer Angle YWX = …………… [2] (d) the area of triangle WXY. W 15 25 X Y Z 17

7 [Turn over Answer …………...…………… cm2 [1] 5 Kevin recorded the colour of cars that entered a carpark in an hour. The pie chart shows his results. (a) There were twice as many blue cars as red cars. Find the angle representing blue cars. Answer …………...………………… [2] (b) Given that there were 66 white cars, find the total number of cars in the survey. Answer …………...………………… [2] White 108° 54° Silver Others Blue Red

8 6 The graph shows the parking fees charged by a shopping mall. Find (a) the maximum number of minutes that the shopping mall offered free parking, Answer …………...……… minutes [1] (b) the duration a car is in the carpark if the parking cost is $6, Answer …………...………… hours [1] (c) the cost of parking if a person parks his car for 4.5 hours, Answer $ ………...………………… [1] (d) the least number of hours he has parked if the person has paid $9.00 for the parking. 10 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 No. of hours parked Cost of parking ($)

9 [Turn over Answer …………...………… hours [1] 7 (a) The scale of a map is 1 : 40 000. (i) The distance between two railway stations is 8 cm on a map. Find, in kilometres, the actual distance between the stations. Answer ………………….…….... km [2] (ii) A field has an area of 90 km2. Find the area of the field on the map in square centimetres. Answer ….…………................... cm2 [2]

10 7b (b) The point X is the point of intersection of the bisector of angle CAB and the perpendicular bisector of AC. (i) Measure angle ABC. Answer Angle ABC = .………….... [2] (ii) Construct the bisector of angle CAB and the perpendicular bisector of AC. Hence, label the point X. [3] (iii) Measure and write down the length of AX. Answer AX = ….………………...... [1] A B C