North Vista 4E EM Prelim P1 2024 QP

[Turn over NORTH VISTA SECONDARY SCHOOL Preliminary Examination 2024 Secondary 4 Express/ 5 Normal Academic CANDIDATE NAME CLASS _________________________________________________________________________ MATHEMATICS 4052/01 Paper 1 19 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 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 90. 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. This document consists of 20 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 = 1 100 nrP+ Mensuration Curved surface area of a cone = πrl Surface area of a sphere = 24 r Volume of a cone = 21 π3 rh Volume of a sphere = 34 π3 r Area of triangle ABC = Cabsin2 1 Arc length = rθ, where θ is in radians Sector area = 21 2 r  , where θ is in radians Trigonometry C c B b A a sinsinsin == 2 2 2 2 cosa b c bc A= + − Statistics Mean =   f fx Standard deviation = 22fx fx ff −  

3 [Turn over Answer all the questions. 1 Calculate 3 13.5 14.04 0.31 15.625 + −+ , giving your answer correct to one significant figure. Answer ……………………………... [1] 2 Alex buys a shirt at a price of £14.75. Paul buys a shirt at a price of $21.99. The exchange rate is $1 = £0.73. Calculate how much more Paul pays than Alex. Answer …...…….……………………... [2] 3 (a) Simplify 3 4 25(3 5 ) . Give your answer in the form 35ab . Answer …...…….……………………... [1] (b) 100 972 4 2 2 k−  = Use laws of indices to find the value of k. Show your working. Answer k = …………..………………... [2]

4 4 (a) A number p has exactly 12 factors. Two of the factors are 4 and 15. Find the value of p. Answer p = …………………………... [1] (b) (i) Express 525 as the product of its prime factors. Answer ………….…………………… [1] (ii) The LCM of 15, x and 35 is 525. Find two possible values of x between 15 and 100. Answer x = …………. , …………… [2] 5 Jessica invests $4540 at a rate of r % per year compound interest. At the end of 10 years, she has earned $1328.54 in interest. Calculate the value of r. Answer r = ……...…………………… [3]

5 [Turn over 6 Ayden claims that a regular polygon can be formed with the ratio interior angle to exterior angle = 5: 4. Explain why Ayden is wrong. ……………………………………………………………...……………………………… ……………………………………………………………...……………………………… ……………………………………………………………...……………………………… [2] 7 The expression 2 17x ax++ can be written in the form 2( 6)xb−+ . (a) Find the value of a and of b. Answer a = ………………………….. b = ………………………….. [2] (b) Explain why when x = 6, the expression 2 17x ax++ has its minimum value. ……………………………………………………………...………………………. ……………………………………………………………...………………………. [1] 8 A shopkeeper makes a loss of 24% when he sells an article for $136. Calculate the selling price of the article in order for the shopkeeper to make a profit of 40%. Answer $………………...……………. [2]

6 9 A bag contains some yellow and blue balls. The ratio of the yellow balls to the blue balls is 1 : 4. 5 yellow balls are removed from the bag and 10 blue balls are added to the bag. The new ratio of yellow balls to blue balls is 1 : 6. Find the original number of yellow balls in the bag. Answer …..……………………….…… [3] 10 It is given ( 4,2)P − , (2,10)Q and ( 4, 5)R −− . (a) Write down the equation of the line PR. Answer ………………………………... [1] (b) The line 5 10y mx+= has the same gradient as QR. Find the value of m. Answer m = …………………………... [2]

7 [Turn over 11 Each term in this sequence is found by subtracting the same number from the previous term. 78, a, b, c, 42, ……… (a) Find the values of a, b and c. Answer a = ……………………………. b = ……………………………. c = ……………………………. [2] (b) Write down an expression, in terms of n for the nth term. Answer …..……………………….…… [1] (c) Write an inequality in n and solve it to find the first negative term of this sequence. Answer …..……………………….…… [2] 12 (a) Write down the set represented by the shaded region. Answer …..……………………….…… [1] ε

8 12 (b) ε = {integer x : 1 15x } A = {perfect squares} B = {prime numbers} (i) Find n ()AB ' . Answer …..……………………….…… [1] (ii) List the elements in AB ' . Answer …..……………………….…… [1] (iii) Given that ()C A B ' and n(C) > 0, list the elements in one possible set of C. Answer …..…………………………… [1] 13 Sketch the graph of y = (4 – x)(2 + x). State clearly the coordinates of the points where the graph crosses the axes and the turning point on the curve. O [3] y x

9 [Turn over 14 The diagram shows the marks obtained, out of 100, by 160 local students in a Mathematics test. The cumulative frequency curve shows the distribution of the marks. (a) Use the curve to find (i) the median mark, Answer ………………………………... [1] (ii) the interquartile range of the distribution. Answer ………………………………... [2] (b) A group of 160 foreign students took the same test and had the same median as the group of local students but a higher interquartile range. Describe how the cumulative frequency curve for the group of foreign students may differ from the curve for the group of local students. ……………………………………………………………...……...……………….. ……………………………………………………...……………...……………...… [1] 140 160 Marks Cumulative Frequency Frequency 50 60 70 80 90 20 40 60 80 100 120 40 0 100

10 15 Write as a single fraction in its simplest form 2 43 9 81 xx x x +−+ − . Answer …………………………...…… [2] 16 (a) Expand and simplify (2 3 )(7 5 )x y x y+− . Answer …………………………...…… [2] (b) Factorise completely. (i) 3 3 3x y xy−