Crest Sec 4NA Prelim Question Paper 1

CREST SECONDARY SCHOOL SECONDARY FOUR PRELIMINARY EXAMINATION NA Name: ( ) Class: MATHEMATICS (SYLLABUS A) Paper 1 Candidates answer on the Question Paper. 4045/01 Wednesday 14 August 2024 2 hours READ THESE INSTRUCTIONS FIRST Write your class, index number and name 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. 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 in the space below the question. Omission of essential working will result in loss of marks. The total number of marks for this paper is 70. 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 15 printed pages and 1 blank page. Setter: Ms Liew Jia Meng [Turn over For Examiner’s use 70

2 Mathematical Formulae Compound Interest Total amount = nrP      + 1001 Measurement Curved surface area of a cone = rl Surface area of a sphere = 24 r Volume of a cone = 21 3 rh Volume of a sphere = 34 3 r Area of triangle ABC = Cabsin2 1 Arc length r= , where  is in radians Sector area = 21 2 r  , where  is in radians Trigonometry sin sin sin a b c A B C== 2 2 2 2 cosa b c bc A= + − Statistic Mean = fx f   Standard deviation = 22f x f x ff  −  

3 Answer all questions. 1 Write 0.002195 (a) correct to 3 significant figures, Answer ……….………………… [1] (b) in standard form. Answer ……….………………… [1] 2 Given that 52 32 2 x= , find x. Answer x = ….………………… [2] 3 Find the largest integer y satisfying 3 15y− . Answer y = ….………………… [2] [Turn over

4 4 The diagram shows the sketch of 2y ax bx c= + + . (a) State the value of a. Answer a = ….………………… [1] (b) Write down the equation of the line of symmetry. Answer ……….………………… [1] 5 In a sale, the price of a 10 kg sack of rice is reduced from $35.90 to $29.90. Calculate the percentage decrease. Answer ……….……………… % [2] 6 Find the length of the straight line joining (0, 6) and (4, – 2). Answer ……….………… units [2] y x O – 0.5 1

5 7 (a) Express 3780 in index notation. Answer ……….………………… [1] (b) Hence, find the smallest value of m such that 3780m is a perfect cube. Answer ……….………………… [1] 8 Three trains leave the depot every 3, 5 and 9 minutes respectively. Given that the three trains left the depot at 07 30 at the same time, find the next time that they will leave the depot together again. Answer ……….………………… [2] [Turn over

6 9 Solve these simultaneous equations. 5 2 19 33 xy xy −= + =− Show your working. Answer x = ….………………… y = ….………………… [3] 10 The diagram shows the speed-time graph of a car for part of a journey. It moves at a constant speed of 70 km/h for a duration of 0.5 hour before accelerating to 90 km/h in the next t hours. Give that the distance travelled is 51 km, find the total time taken for this part of the journey. Answer ……….………… hours [3] 0.5 90 70 Speed (km/h) Time (hours)

7 11 A map is drawn to a scale of 1 : 35 000. (a) Two schools are 20 cm apart on the map. Find the actual distance between the two schools, in kilometres. Answer ……….…………… km [1] (b) A town has an area of 2.1 km2. Find the area of the town on the map. Answer ……….…………… cm2 [2] 12 Solve 75 132 x xx − =+− . Answer x = ….………………… [3] [Turn over

8 13 In a science experiment, the growth rate R of a bacteria is inversely proportional to the square of the concentration of nutrient C. (a) Given that R = 10 units when C = 0.5 units, write a formula for R in terms of C. Answer R = ….………………… [2] (b) Find C when R = 40. Answer C = ….………………… [1] 14 Elliot invested a sum of money in a bank that paid compound interest at 6% per annum. At the end of 2 years, he had a total of $1685.40. What was his initial sum of investment? Answer $ ……………………… [3]

9 15 From the top of a cliff standing at 350 m high, Ted observes two boats, A and B whose angles of depression are 60  and 42  respectively. Find the distance between the two boats. Answer ……………………… m [3] 16 The diagram shows part of an 8-sided regular polygon. Calculate (a) angle PQR , Answer ……….………………… [1] (b) angle QPR , Answer ……….………………… [1] (c) the exterior angle of the polygon. Answer ……….………………… [1] [Turn over 350 m A B 42 60 P Q R S

10 17 The ages of the members in a country club, in years, are shown in the stem-and-leaf diagram below. 2 1 1 2 4 3 0 3 3 4 5 4 0 2 5 6 5 0 1 3 3 3 9 6 1 Key: 2 | 1 represents 21 years old (a) How many members are there? Answer ……….………………… [1] (b) Calculate the percentage of the members who are at least 50 years old. Answer ……….……………… % [1] (c) In the club, members who are under the age of 40 are categorised under the Junior membership. Find the probability of members who are not under the Junior membership. Answer ……….………………… [1]