NBSS EM Prelim P1 2024 v2 QP

NAVAL BASE SECONDARY SCHOOL PRELIMINARY EXAMINATION 2024 O Name __________________________________ ( ) Class ___________ MATHEMATICS 4052/01 Paper 1 21 August 2024 Candidates answer on the Question Paper 2 hours 15 minutes 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. 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 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 π , use either your calculator value or 3.142, unless the question requires the answer in  . 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 90. Item For examiner’s use Presentation Accuracy Units Total Parent’s Signature __________________________________________________________________________ This paper consists of 24 printed pages. [Turn over

[Turn over 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 a triangle ABC = Arc length = , where is in radians Sector area = , where is in radians Trigonometry Statistics Mean = Standard deviation = 22        −  f fx f fx n rP      + 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

[Turn over 3 Answer all the questions. 1 Calculate 24 6.5613.5 0.37− . Answer ….………….….…………….. [1] 2 Simplify (a) 2534xy . Answer ….………….….…………….. [1] (b) 3(2 1) 5x−− . Answer ….………….….…………….. [1] 3 Factorise completely 322 13 6x x x−+ . Answer ….………….….…………….. [2]

[Turn over 4 4 The sine of an angle is 0.6 , find the two possible values for angle. Answer x = .………..…  or x = .……………  [2] 5 A class of 12 boys and 8 girls took a test. The girl’s marks were 3, 6, 7, 8, 9, 9, 10 and 10. (a) Find the mean mark for the girls. Answer ….………….….…………mark [1] (b) The mean mark for the boys were 8.0. Find the mean mark for the whole class. Answer ….………….….……….…mark [2]

[Turn over 5 6 (a) The number 12250 p q is a perfect cube. p and q are prime numbers. Find p and q. Answer p = .………….….…………….. q = ………………………….[3] (b) x is a number between 700 and 800. The highest common factor of x and 12 250 is 250. Find the smallest possible value of x. Answer x = ..………….….…………….. [1]

[Turn over 6 7 Given that 281 9 27xx= , find x. Answer ….………….….…………….. [2] 8 Raj has 120 one-centimetre cubes. He arranges all of the cubes into a cuboid. The perimeter of the top of the cuboid is 20 cm. Each side of the cuboid has a length greater than 3 cm. Find the height of the cuboid. Answer ….………….….……………. cm [2]

[Turn over 7 9 2 LT g= Rearrange the formula to make g the subject. Answer g =.………….….…………….. [3]

[Turn over 8 10 In the scale drawing, R is the centre of a rock bed, A is a ship and B is a port. The line AB shows the ship’s course. (a) Measure the bearing of B from A. Answer ….………….….…………… [1] (b) The rock bed covers a 25 km radius. If the ship were to stay on course, state the distance at which the ship will first hit the rock bed. Answer ….………….….…………km [2] B A R North Scale: 1 cm to 5 km

[Turn over 9 11 The table below shows the amount of time spent playing online games by a group of children in one particular week. Time (h hours) Frequency 02 h 4 24 h 9 46 h 15 68 h 13 8 10h 7 10 12h 2 (a) (i) Calculate an estimate of the mean time spent playing online games that week. Answer ….………….….………hours [1] (ii) Explain why this is only an estimate of the mean time these children spent playing online games that week. Answer ….………….….……………………………………..……………..……….. [1] (b) Calculate an estimate of the standard deviation of the time spent playing online games that week. Answer ….………….….………hours [2]

[Turn over 10 12 Solve the simultaneous equations. 242 3 19 4 xy xy −= =+ You must show your working. Answer x = ……….….………………… y = ………………………… [3]