2023 Beatty Sec 4NA Math P1 QP

[Turn over BEATTY SECONDARY SCHOOL PRELIMINARY EXAMINATION 2023 SECONDARY FOUR NORMAL (ACADEMIC) CANDIDATE NAME CLASS REGISTER NUMBER MATHEMATICS (SYLLABUS A) 4045/01 Paper 1 2 August 2023 Setter: Click or tap here to enter text. 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 80. 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 19 printed pages and 1 blank pages.

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  3 5 14 6 17 25 Write these numbers in order of size, starting with the smallest. Answer ………., ………., ……….., ………, ……. [2] 2 The cost of a laptop bag had decreased from $250 to $189. Calculate the decrease as a percentage of the original cost. Answer ….. …………...….. % [2] 3 (a) Express 250 g: 3 kg as a ratio in its simplest form. Answer ………… : … ............ [1] (b) Owen had a ribbon of length k metres. He cut it into two parts in the ratio x : y, where y < x. Express the length of the longer ribbon, in terms of x, y and k for the length of the longer ribbon. Answer ………… …… ............ [1] 63%

4 4 Find the value of the obtuse angle x, when (a) sin x = 0.813, Answer ……………….... ......° [1] (b) cos x = −0.57. Answer ……………….... ......° [1] 5 y is inversely proportional to the square root of x. Given that y = 1.5 when x = 16, find an expression for y in terms of x. Answer ……………….... ........ [2] 6 Calculate the length of the line joining the points (3, −1) and (−2, 5). Answer …………….... ... units [2]

5 [Turn over 7 Draw an enlargement of this given quadrilateral using a scale factor of 1.5. [2] 8 (a) Find the largest integer satisfying 6 15y  . Answer ……………................. [2] (b) Expand and simplify (3 5)(7 2)x x  . Answer ……………................. [2]

6 9 The diagram shows three sides AB, BC and CD of a regular n-sided polygon with ∠ܥܦܤ= 18°. (a) Find the interior angle of the polygon. Answer ……………... ....... ° [1] (b) Calculate the number of sides of the polygon. Answer ……………... ............. [2] 10 (a) 16 3 na a a  Find the value of n. Answer n = ………... ............. [2] (b) 3x + 3x + 3x = 1 Find the value of x. Answer x =…………... .......... [2] A B C D 18°

7 [Turn over 11 In triangle ABC, AC = 17 cm, BC = 15 cm and 90ABC   . (a) Find the length of AB. Answer ……………… .… .. cm [2] (b) Find, as a fraction in its simplest form, tan CAB . Answer ……………………… [1] 12 (a) Factorise completely 2 26 15x y xy . Answer ………………....… … [1] A B C D 17 15

8 Write 2 1 4 9 3x x   as a single fraction in its simplest form. Answer ……………….... ........ [2] 13 The first four terms of a sequence are 22, 18, 14 and 10. (a) Write down the first negative term of the sequence. Answer ……………….... ........ [1] (b) Find an expression for the nth term of the sequence. Answer ……………….... ........ [1] (c) The nth term of another sequence is 8n − 2. Is 278 a term in this sequence? Explain your answer. Answer ………………………………………………………………………………………….. ………………………………………………………………………………………….. ………………………………………………………………………………………….. [2] (b)

9 [Turn over 14 A circle has centre O and radius 6 cm. The sector OABC has angle AOC =150°. Find the perimeter of the major sector OADC. Give your answer in the form p q  . Answer ……… ...….... ....... cm [3] 15 A parallelogram ABDE and a triangle BCD are joined as shown. EDC is a straight line. Ryan says that triangle BCD is an isosceles triangle. Is he correct? Show your workings clearly. Answer ………………………………………………………………………………………………. ………………………………………………………………………………………………. ……………………………………………………………………………………………… [3] O 6 A B C DE 120° 50° A B C 150° D

10 16 The diagram shows a spinner with six numbered sectors. Each time the pointer is spun, it is equally likely to stop on any of the sectors. The spinner is spun once. Find the probability that it stops on (a) an odd number, Answer ……… ...….... ............. [1] (b) a prime number, Answer ……… ...….... ............. [1] (c) a factor of 6. Answer ……… ...….... ............. [1] 2