Beatty Prelim 4NA P1 2024

[Turn over BEATTY SECONDARY SCHOOL PRELIMINARY EXAMINATION 2024 SECONDARY FOUR NORMAL (ACADEMIC) CANDIDATE NAME CLASS REGISTER NUMBER MATHEMATICS (SYLLABUS A) 4045/01 Paper 1 1 August 2024 Setter: 2 hours Candidates answer on the Question Paper Additional Materials: Nil READ THESE INSTRUCTIONS FIRST Write your name, class and register 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 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 with the answer. Omission of essential working will result in loss of marks. The total of the 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. For Examiner’s Use This document consists of 15 printed pages and 1 blank page.

2 Mathematical Formulae Compound Interest Total amount = Mensuration Curved surface area of a cone = Surface area of a sphere = Volume of a cone = Volume of a sphere = Area of triangle ABC = Arc length = , where θ is in radians Sector area = , where θ is in radians Trigonometry Statistics Mean = Standard Deviation = nrP )1001( + rl 24 r hr 2 3 1 3 3 4 r Cabsin2 1 r 2 2 1 r C c B b A a sinsinsin == Abccba cos2222 −+= f fx   22        −  f fx f fx

3 [Turn over 1 5 4  3.9 2 30.5 − 5 7 3 Write these numbers in order of size, starting with the smallest. Answer ………., ………., ……….., ………, ……. [2] smallest 2 Find the smallest integer satisfying 5 3 9x− . Answer …..…………...……... [2] 3 (a) Express 1 km : 240 m as a ratio in its simplest form. Answer ………… : …............ [1] (b) A barrister mixes type A tea and type B tea in the ratio of 2 : 5 to get a special blend of tea. How much type B tea are there in 21 kg of the special blend? Answer …………….......... kg [1]

4 4 Jamal is paid a fixed rate for the first 36 hours he works in a week. For any extra hours, he is paid an overtime rate. The following graph shows how much he is being paid based on his working hours. (a) In a particular week, he worked for 25 hours. How much is he paid? Answer $ ……………............. [1] (b) The company that employed Jamal claims that its rate of overtime pay is 2.5 times the normal pay rate. Is the claim correct? Explain your answer. Answer [2]

5 [Turn over 5 (a) Express 756 as a product of its prime factors. Answer ………………............ [1] (b) Find the highest common factor of 756 and 3 2 32 3 5 . Answer ………………............ [1] (c) Write down the smallest positive integer of n, where 756n is a perfect square. Answer ………………............ [1] 6 It is given that GHI and XYZ are similar. Find (a) angle YXZ, Answer Angle YXZ = ..................... [1] (b) the length of GH. Answer …………….......... cm [2]

6 7 Draw a reduction of the given trapezium using a scale factor of 2 3 . [2] 8 One of the angles of a triangle measures x. Given that 4sin 7x = , find the two possible values of x. Answer x = ………… or …….….. [2] 9 The first four terms of a sequence are 11, 8, 5 and 2. (a) Write down the next two terms in the sequence. Answer ………….., …………. [1] (b) Find an expression for the nth term in the sequence. Answer ……………................. [1] (c) Is −45 a term of this sequence? Explain your answer. Answer [2]

7 [Turn over 10 The following stem-and-leaf diagram shows the weight distribution of 18 students in kg. Stem Leaf 4 5 7 9 5 1 5 7 7 7 8 6 0 1 4 5 8 7 1 1 3 6 Key: 4 | 5 means 45 kg (a) State the modal weight. Answer ………………....... kg [1] (b) Find the median of the distribution. Answer ………………....... kg [1] (c) Find the interquartile range of the distribution. Answer ………………....... kg [2] 11 (a) Convert 50 m/s to km/h. Answer ………............... km/h [1] (b) A lorry travels at x km/h and completes its journey in 1 hour 15 minutes. Find the speed of the lorry, in terms of x, if it is required to complete the same journey in 45 minutes. Answer ………............... km/h [2]

8 12 It is given that 22 3 mnp q −= . (a) Find p when 2m=− , 3n=− and 5q= . Answer ……………….……… [1] (b) Rearrange the formula to make n the subject. Answer n = ..………………… [2] 13 The quadrilateral has one line of symmetry, marked as a dotted line in the diagram. (a) Write down the value of x. Answer x = …………....…… [1] (b) Calculate y. Answer y = …………....…… [2]

9 [Turn over 14 May invested $4800 in a company, which pays a simple interest of 5% per annum. Find the number of years it will take for her to receive an interest of $2280 on her investment. Answer ………….......... years [2] 15 22 4 10 2 5 6 5 6 a b x x x x x x −+=− − + − + Find a and b. Answer a = ………...…........... b = ………...…........... [3]

10 16 X is the intersection of the angle bisector of angle QRP and the perpendicular bisector of QR. (a) By using construction, find and label X. [3] (b) Measure the longest possible distance of X from a vertex of the triangle PQR. Answer ………...…........... cm [1] 17 (a) June exchanges 500 Singapore dollars (S$) for 555 Australian dollars (AUD). Complete the exchange rate. Answer S$1 = ............... AUD [1] Q P R