North Vista 4E 2024 Prelim Paper 2 QP

[Turn over NORTH VISTA SECONDARY SCHOOL Preliminary Examination 2024 Secondary 4 Express/ 5 Normal Academic CANDIDATE NAME CLASS _________________________________________________________________________ MATHEMATICS 4052/02 Paper 2 20 August 2024 2 hours 15 minutes Candidates answer on the Question Paper. 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 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. Gives 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. The total of the marks for this paper is 90. This document consists of 23 printed pages. INDEX NUMBER For Examiner’s Use Category Question No. Accuracy Brackets Fractions Units Others Marks Deducted 90

2 Mathematical Formulae Compound Interest Total amount = nrP )1001( + Mensuration Curved surface area of a cone = rl Surface area of a sphere = 24 r Volume of a cone = hr 2 3 1 Volume of a sphere = 3 3 4 r Area of triangle ABC = Cabsin2 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 1 (a) Solve the inequality 5 3 2 13x−  −  . Answer ...…………………...……….. [2] (b) Solve these simultaneous equations. 1 52 2 3 13 xy xy += −= You must show your working. Answer x = ...…….… y = ……...…… [3]

4 1 (c) 3 41 rqp r += − (i) Find p when 7r = and 15q=− . Answer p = .…………………...…… [1] (ii) Rearrange the formula to make r the subject. Answer r = ...……..……...………….. [3]

5 [Turn over 1 (d) Solve 15 321 xx =+− . Answer x = ...….…… or ..….……... [3]

6 2 (a) The table shows the amount of ‘Food Waste Output’ and ‘Food Waste Recycled’ in Singapore from 2008 to 2010. Year 2008 2009 2010 Food Waste Output (*Tonnes) 565 000 605 000 640 000 Food Waste Recycled (*Tonnes) 65 000 75 000 99 000 *1 tonne = 1000 kg (i) Write the total amount of Food Waste Output from 2008 to 2010 in standard form. Answer ..…………...……….. tonnes [1] (ii) Given that the percentage increase in Food Waste Recycled from 2009 to 2010 is the same as the percentage increase from 2010 to 2011, calculate the amount of Food Waste Recycled in 2011. Answer ..…………...……….. tonnes [2] (iii) Per capita food waste is defined as the amount of Food Waste Output generated by each person. Given that the population in 2008 is 4.84 million, calculate the per capital food waste in kilograms per day. Answer ..………...……….. kg / day [2]

7 [Turn over 2 (a) (iv) It is given that The recycling rate is given by the formula Food Waste RecycledRecycling Rate = Food Waste Output . In 2007, 509 000 tonnes of food waste was disposed, and the recycling rate was 8.6%. Calculate the Food Waste Output in 2007. Answer ..…………...……….. tonnes [2] (b) A river of length 612 m is represented by 9 cm on Map A. (i) The actual perimeter of a lake is 1700 m. Find the perimeter of the lake on Map A. Answer …........…………...…… cm [2] (ii) The area of the lake on Map A is 36 cm2. Calculate the area of the lake on Map B which has a scale of 1: 5100. Answer …........………...…...… 2cm [2] Food Waste Output = Food Waste Disposed + Food Waste Recycled

8 3 A piece of wire of length 120 cm is cut into two parts. One part of the wire is bent to form a square of side x cm. The remaining part of the wire is bent to form a circle with radius, r cm. (a) Show that the radius of the circle, r is given by 60 2 x  − cm. Answer [2] (b) If the area of the square is equal to the area of the circle, form an equation in x and show that it reduces to ( ) 24 240 3600 0xx− − + = . Answer [2]

9 [Turn over 3 (c) Solve the equation ( ) 24 240 3600 0xx− − + = , giving your solutions correct to two decimal places. Answer x = …............... or …...……….. [4] (d) Explain why one of the solutions has to be rejected. Answer Reject ……………………because………………………………………… ……………………………………………………………………….………………….. ……………………………………………………………………….………………….. .……………………………………………………………………...……………..… [1]

10 4 (a) The heights of 12 students from Group A were recorded. The results are shown in the stem-and-leaf diagram. 15 0 2 16 1 2 4 6 8 17 1 1 3 4 18 0 Key: 15 0 means 150 cm (i) Find the mean height. Answer …........…………...…...… cm [1] (ii) Find the standard deviation of the heights. Answer …........…………...…...… cm [1] (iii) The mean height of students from Group B is 168 cm and the standard deviation of heights is 9.5 cm. Make a comment comparing the averages and a comment comparing the distribution of the heights of students from Group A and Group B. 1. ……………………………………………………………………………………… ...………………………………………………………………………………….……. ...………………………………………………………………………………….……. ...………………………………………………………………………………….……. 2. ………………………………………………………………………………………. ...………………………………………………………………………………….……. ...………………………………………………………………………………….…… ...………………………………………………………………………………….….. [2]