CHIJ SJC 4048 01 QP

[Turn over Index Number Class Name Calculator’s model CHIJ ST JOSEPH’S CONVENT PRELIMINARY EXAMINATION MATHEMATICS Paper 1 Secondary 4 Express / 4 Normal Academic (O level) / 5 Normal Academic 4048/01 Friday, 27 August 2021 2 hours Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your index number, class, name and calculator model in the spaces at 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. 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. Working in pencil will not be marked. The total of the marks for this paper is 80. 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. FOR EXAMINER’S USE 80 This document consists of 19 printed pages. Setter(s) : Mrs Lee Ann Gee O O

2 [Turn over Mathematical Formulae Compound interest Total amount = P nr )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 = , 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 = 2 2 )( f fx f fx  −  r  

3 [Turn over Answer all the questions. 1 Given that 1 264 n= , find n. For Examiner’s Use Answer n = ................................................................ [1] 2 List the integer values of x which satisfy the inequality 1243 − xx . Answer ................................................................ [3] 3 (i) Factorise completely 22 10xx+− . Answer ................................................................ [1] (ii) Hence, factorise completely 22(2 3) (2 3) 10yy− + − − . Write your answer as simply as possible. Answer ................................................................ [2]

4 [Turn over 4 (a) Find the prime factors of 1080, giving your answer in index form. For Examiner’s Use Answer ................................................................ [1] (b) Two integers, P and Q, can be written as products of prime factors. 3 21 5, . c c P a b Q a b + =   = The lowest common multiple (LCM) of P and Q is 1080. (i) Given that a < b, write down the values of a, b and c. Answer a = ..............., b =................., c =................................ [2] (ii) Find the highest common factor (HCF) of P and Q. Answer ................................................................ [1]

5 [Turn over 5 If a − b = −6, ab = 40, a > 0 and b > 0, evaluate For Examiner’s Use (i) (2a + 2b)2, Answer ......……………………………………… [2] (ii) (2a)2 − (2b)2. Answer ........…….………………………….…… [3]

6 [Turn over 6 The diagram shows a triangle with base AB and height AC. For Examiner’s Use The area of the triangle is increased by 125% when AB is reduced by 10% and AC is increased by x%. Find the value of x. Answer x = ……..........………………………… [3]

7 [Turn over 7 (i) A result of global warming is that the ice of some glaciers is melting. Twelve years after the ice disappears, tiny plants, called lichen, start to grow on the rocks. Each lichen grows approximately in the shape of a circle. The relationship between the diameter of this circle and the age of the lichen can be approximated with the formula, 7 12dt=− for t ≥ 12, where d represents the diameter of the lichen in millimetres, and t represents the number of years after the ice has disappeared. Calculate the diameter of the lichen, 16 years after the ice disappeared. For Examiner’s Use Answer ……………………………...mm [1] (ii) Anniston measured the diameter of some lichen and found it to be 35 millimetres. How many years ago did the ice disappear? Answer ....……………………..……years [2]

8 [Turn over 8 (a) A 15% profit is earned on the cost price of a television set if it is sold for $1426. Find For Examiner’s Use (i) the profit, Answer $………………………………………… [2] (ii) the cost price of the television set. Answer $………………………………………… [2] (b) Another television set with the same cost price is sold for $1007.50. Express the loss as a percentage of the cost price of the television set. Answer …………………………………………% [2]

9 [Turn over 9 (a) y is proportional to mx . Write down the value of m when For Examiner’s Use (i) y hours is the time taken to travel a distance x km at a constant speed, Answer m = ………………………………………… [1] (ii) y cm2 is the area of a circle of radius x cm. Answer m = ………………………………………… [1] (b) The force, F, between two particles is inversely proportional to the square of the distance between them. The force is 54 units when the distance between the particles is r metres. Find the force when the distance is 3r metres. Answer …………………………………………units [2] 10 (a) Use set notation to describe the shaded region. Answer ……………………………….........…… [1] (b) ℰ = {x: x is an integer, 1 ≤ x ≤ 20}. The Venn diagram shows the elements of  and two sets, R and S. Use one of the symbols below to complete each statement.      (i) RS ……....… S . [1] (ii) { 19,20} ……....… S . [1] (iii) 3 ……....… R . [1] B 15 9 18 S 20 17 19 5 7 10 11 13 14 16 ℰ R 3 6 1 2 4 8 12 ℰ

10 [Turn over 11 In 2019, the average height of both young males and young females in a certain country is represented in this graph. For Examiner’s Use (a) Since 2001, the average height of 20-year-old females has increased by 2.3 cm, to 170.6 cm. What was the average height of a 20-year-old female in 2001? Answer ……………………………….........……cm [1] (b) Explain how the graph shows that on average the growth rate for girls slows down after 12 years of age. Answer ..................................................................................................................................... ..................................................................................................................................... ........................................................................