Beatty Sec EM 4E5N P1 2020 QP

1 SUBJECT : Mathematics LEVEL : Sec 4E/5N/4N PAPER : 4048/1 DURATION : 2 hours SETTER : Mr Lee Chau Loong DATE : 24 August 2020 CLASS : NAME : REG NO : Write your name, class and index number in the spaces on the top of this page. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all 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. You are expected to use a scientific calculator to evaluate explicit numerical expressions. 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, 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 number of marks for this paper is 80. _____________________________________________________________________________ This paper consists of 16 printed pages (including this cover page) [Turn over BEATTY SECONDARY SCHOOL PRELIMINARY EXAMINATION 2020 For Examiner’s Use 80 [Turn over O

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 Answer all the questions. 1 Solve the pair of simultaneous equations 2 3 4xy+= 42xy+ =− Answer x = ……………………… y = …………….……….. [3] 2 Solve the equation ( )3 2 1 8x x x− = − . Answer x = …………. or ………….. [2] 3 In a regular n-sided polygon, one interior angle : one exterior angle = 5 : 1. Find the value of n. Answer n = ………………. [2] [Turn over

4 4 (a) What is misleading with the survey collected below? Explain your answer. Answer : ……………………………………………….………...…………………… ………………………………………………………………………………………..... [1] (b) What is misleading with the graph shown below? Explain your answer. Answer : ……………………………………………….………...…………………… ………………………………………………………………………………………..... [1] Source: https://www.buzzfeednews.com/article/katienotopoulos/graphs-that-lied-to-us Question posed: What should cost less? A litre of petrol or a litre of milk? Yes 43% No 57%

5 5 Danny deposits $1000 in a bank that pays compound interest of r% per annum. At the end of 10 years, his money doubles. Calculate the value of r. Answer r = ………………….. [2] 6 (a) Factorise 3 10 5 6ap by apy b+ − − completely. Answer ……………………………. [2] (a) Factorise 22 9 22 xy− completely. Answer ……………………………. [2] 7 A map has a scale of 1 : 25000. A park on the map has an area of 30 cm2. Find the area of the park on another map with scale 2 cm : 3 km. Answer ………………………… cm2 [3] [Turn over

6 8 (a) When x is increased by a factor of 2, y decreases by a factor of 1 8 . State a possible equation relating x and y. Answer y = …………………… [1] (b) p varies directly with the square root of q. Given that p = 27 when q = 9, (i) find the equation relating p and q, Answer ………......................... [2] (ii) find the value of q when p = 81. Answer q = …....................... [1] 9 A rope 115 metres long was cut into 3 parts. Each part was then reduced by 15 metres each. The ratio of the three parts became 2 : 5 : 3. Express the original length of the longest part as a percentage of the whole rope. Answer ……..……………….. % [4]

7 10 (a) Write 2 21 3xx−+ in the form ( ) 2 a x b++ . Answer …………………..……………….. [2] (b) Hence solve 2 21 3xx−+ = 0. Leave your answer correct to 2 decimal places. Answer x = ……………… or ………..…….. [2] 11 The ages of customers visiting a cafe in the morning are summarised in the table below. Ages 0 10x 10 20x 20 30x 30 40x 40 50x 50 60x Frequency 6 15 23 14 8 6 (a) In which age group is the median found? Answer ……………………. [1] (b) Calculate an estimate of the mean and standard deviation. Answer mean = ……………… years old , SD = ……………...…. years old [2] [Turn over

8 12 (a) Shade 'PQ . Answer : [1] (b) Express the shaded region using set notation. Answer …………………….. [1] (c)   is an integer :1 50xx =   A= { prime numbers } B= { factors of 50 } From the list below, circle all the statements that are true. Answer: [2] 9 A , 1 AB , BA , ( )' 13n A B= , AB = , ( ) ( )n B n A 13 A cone is cut into three sections X, Y and Z, such that a : b : c = 1 : 1 : 1. The volume of Y is k times the volume of the original cone. Find the value of k. Answer k = ……………………. [2] P Q a b c X Y Z  

9 14 (a) Simplify 31 32 63q p p q −           . Answer ………………… [2] (b) Solve 23 10 1na a a a a   = . Answer n = ……….……….. [1] (c) Solve 8 64x = . Answer x = ……….……….. [1] 15 p , –13, r , s , t , 35, … (a) Each term of the sequence is found by adding a constant c to the previous term. Find the value of c, of p, of r, of s, and of t. Answer c = ……..…, p = ………., r = ….……, s = …………, t = ……….. [3] (b) Find an expression, in terms of n, for the general term of the sequence. Answer ….……….……….. [1] (c) How many terms in the sequence are between 10 and 100? Answer ….……….………. terms [1] 3 [Turn over

10 16 (a) On the given axes, sketch the graph of ( ) 2 31yx= − + . Answer : [2] (b) The graph of ( ) xy a b= crosses the y-axis at 600 and passes through 274, 18932   . Find the value of a and of b. Answer a = …………