CGS math eoy sec 1

Name: Register No.: Class: CRESCENT GIRLS’ SCHOOL SECONDARY ONE END OF YEAR EXAMINATION 2023 MATHEMATICS 4052 09 October 2023 2 hours Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, register number and class on all the work you hand in. Write in dark blue or black pen. You may use a pencil for any diagrams or graphs. Do not use paper clips, 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. Calculators should be used 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 π, use either your calculator value or 3.142, unless the question requires the answer in terms of π. At the end of the examination, submit the whole Question Paper. 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 80. This question paper consists of 20 printed pages. Question 1 2 3 4 5 6 7 8 9 10 11 Marks Question 12 13 14 15 16 17 18 19 20 21 22 Marks Table of Penalties Qn. No. Presentation –1 Units / Accuracy –1 Parent’s/ Guardian’s Signature For Examiner’s Use 80

2 Crescent Girls’ School 2023 EOY S1 Math Answer all the questions on the question paper. 1 Written as a product of its prime factors, 2023 = 7 × 172. (i) Explain why 2023 is not a perfect square. Answer …………………………………………………………………………………… …………………………………………………………………………………… …………………………………………………………………………………… [1] (ii) 2023× p q is a perfect cube greater than 1, where p and q are positive integers. Find the values of p and q that give the smallest possible value of 2023× p q . Answer p = …………………………… q = …………………………… [2]

3 Crescent Girls’ School 2023 EOY S1 Math [Turn over 2 It is given that a and b are two numbers, both greater than 40 and a < b. They have a highest common factor of 21 and a lowest common multiple of 1050. Find the value of a and b. Answer a = …………………………… b = …………………………… [3] 3 Arrange the following numbers in increasing order. ( ) 2470 22090.47, , , 0.4999 10000−−  Answer …………… , …………… , …………… , …………… [2] 4 Use a calculator to evaluate 3 3 16 7 5 17 2 12  − . Answer …………………………… [1]

4 Crescent Girls’ School 2023 EOY S1 Math 5 State the number of significant figures in 0.0030650. Answer …………………………… [1] 6 A lorry travels at an average speed of 68.7 km/h for 1.5 hours. (a) By rounding these numbers correct to 1 significant figure, find an estimate of the distance travelled by the lorry. Answer …………………………… km [1] (b) Without doing any further calculation, explain why the actual distance is less than the answer to part (a). Answer …………………………………………………………………………………… …………………………………………………………………………………… [1]

5 Crescent Girls’ School 2023 EOY S1 Math [Turn over 7 Expand and simplify ( )3 5 13 3p qpq− − +− . Answer …………………………… [2] 8 Factorize completely 3 18ab a−− . Answer …………………………… [2] 9 Write 312 6 xy −+ as a single fraction in simplest form. Answer …………………………… [2]

6 Crescent Girls’ School 2023 EOY S1 Math 10 Given that 23 32 xy z x yx y +− =+ , (i) find the value of z when 1x= and 4y= , Answer z = …………………………… [3] (ii) explain why if 1x= , then y cannot be −3 Answer …………………………………………………………………………………… …………………………………………………………………………………… …………………………………………………………………………………… [1]

7 Crescent Girls’ School 2023 EOY S1 Math [Turn over 11 A two-digit positive number is such that the tens digit is twice as large as the ones digit. (i) By letting the ones digit be x , express the tens digit of the number in terms of x . Answer …………………………… [1] (ii) Hence, express the two-digit positive number in terms of x . Answer …………………………… [1] (iii) Given that the sum of the original number and the number obtained when the digits are reversed is 99, form an equation in x and find the original number. Answer …………………………… [3]

8 Crescent Girls’ School 2023 EOY S1 Math 12 Amos earns $x every month. He deposits 25% of his monthly earnings into a savings account, and 20% of his monthly earnings into an investment account. He gives 1 11 of the remaining amount to his parents for household expenditure and spends the rest of the money on his personal monthly expenses. (a) Given that Amos’ personal monthly expenditure is $3250, set up an equation in x and show that the value of x is 6500. Answer [2] (b) (i) Calculate the amount of money Amos deposits monthly into the savings account. Answer $ …………………………… [1]

9 Crescent Girls’ School 2023 EOY S1 Math [Turn over (ii) After saving for 1 year, Amos transferred the amount of money in his savings account into a fixed deposit account that pays a simple interest of 3.2 % per annum. Calculate the amount of interest Amos will receive if he puts the money in the fixed deposit account for 3 years. Answer $ …………………………… [2] 13 The diagram below shows two lines l1 and l2. (a) Find the gradient of l1. Answer gradient of l1 = ……………………… [1] (b) Explain why the gradient of l2 is undefined. Answer …………………………………………………………………………………… …………………………………………………………………………………… [1] y x 20 40 −20 20 0 l1 l2

10 Crescent Girls’ School 2023 EOY S1 Math 14 A special thermometer known as a helium gas thermometer uses the pressure of helium gas to measure the temperature of the surroundings. The relationship between the temperature of the surroundings ( T ) in degrees Celsius (°C) and the pressure of the helium gas ( P ) in Pascals (Pa) is given by the equation 8 OP TP= + , where OP is a constant to be determined. The table below shows various values of T and the corresponding values of P . T (°C) 25 50 100 P (Pa) 2400 2600 3000 (a) By using a scale of 2 cm to represent 20 °C on the horizontal axis, and 2 cm to represent 500 Pa on the vertical axis, draw the graph for P (Pa) against T (°C) for 0 100T≤≤ on the grid on page 11. [3] (b) (i) Using your graph, state the value of OP . Answer OP = …………………………….. [1] (ii) Explain the significance of the value of OP in relation to the helium gas. Answer ……………………………………………………………………………. ……………………………………………………………………………. [1] (c) Using your answer from part (b)(i), determine the value of T when 0P= . Answer T = …………………………….. [1]