SASS 2023 Prelim 4E5N 4052 Math Paper 1 (with Ans Key)

MATHS7015SLL © SAS 2023 [Turn over Index Subject TG Class Number Candidate Name _______________________________ ST ANDREW’S SECONDARY SCHOOL PRELIMINARY EXAMINATION 2023 SECONDARY 4 EXPRESS / 5 NORMAL (ACADEMIC) MATHEMATICS 4052/01 Paper 1 MONDAY 7 AUGUST 2023 2 hours 15 minutes Candidates answer on the Question Paper. READ THESE INSTRUCTIONS FIRST Write your name, subject TG, class and index number in the spaces at the top of this page. 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. 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 90. 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 question paper consists of 21 printed pages. ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST AND REW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCH OOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL ST ANDREW’S SCHOOL

2 Mathematical Formulae Compound interest Total amount = n rP      + 1001 Mensuration Curved surface area of a cone = πrl Surface area of a sphere = 4πr2 Volume of a cone = 3 1 πr2h Volume of a sphere = 3 4 πr3 Area of triangle ABC = ab2 1 sin C Arc length = r , where  is in radians Sector area = 2 2 1 r , where  is in radians Trigonometry C c B b A a sinsinsin == bccba 2222 −+= cos A Statistics Mean = f fx   Standard deviation = 22        −  f fx f fx

[Turn over 3 Answer all the questions. 1 The number 899 899 when corrected to m significant figures is 900 000. State the largest possible value of m. Answer m = ....................................... [1] ________________________________________________________________________________ 2 (a) A range of values for x is represented on the number line below. Write down the inequalities that represent this range of values for x. Answer ............................................... [1] (b) Solve the inequality 14 12 3xx+  + . Answer ............................................... [1] ________________________________________________________________________________ 3 Expand and simplify 3[ 2( 5 )]u w u−− . Answer ............................................... [2] ________________________________________________________________________________ 2− 0 1 2 3 4 5 1− x

4 4 The graph shows the total number of wild elephants in a national park in Thailand at the end of each of the given years. (a) State one misleading feature of the graph. ........................................................................................................................................ ........................................................................................................................................ [1] (b) Explain how this feature affects the reader’s interpretation of the graph. ........................................................................................................................................ ........................................................................................................................................ [1] ________________________________________________________________________________ 5 Solve 2 2 2 13 3 3 81x x x x −+ + = . Answer x = ........................................ [2] ________________________________________________________________________________ 200 210 220 230 240 250 2015 2016 2017 2018 2019 2020 2021 2022 Number of wild elephants Y ear Rapid fall in the number of wild elephants

[Turn over 5 6 Write as a single fraction in its simplest form 2 52 (2 3) 2 3 x xx −++ . Answer ............................................... [2] ________________________________________________________________________________ 7 (a) Factorise completely 23 4 4xx−− . Answer ............................................... [1] (b) Hence, factorise completely 23(2 3) 4(2 3) 4yy− − − − . Write your answer as simply as possible. Answer ............................................... [2] ________________________________________________________________________________

6 8 The Earth is 81.5 10 kilometres from the Sun. (a) A terametre is 1012 metres. Find the distance of the Earth from the Sun in terametres. Answer ............................. terametres [1] (b) Mercury is 75.81 10 kilometres from the Sun. How much nearer is the Sun to Mercury than to the Earth? Give your answer in standard form. Answer ......................................... km [2] ________________________________________________________________________________ 9 The scale of a map is 1 : 500 000. (a) Two towns are 23 km apart. Calculate the distance between the two towns, in centimetres, on the map. Answer ......................................... cm [1] (b) A lake is represented by an area of 250 cm2 on the map. Calculate the actual area of the lake in square kilometres. Answer ........................................ km2 [2] ________________________________________________________________________________

[Turn over 7 10 The probability that Danny follows a study timetable each day is 0.6. Find the probability that Danny (a) follows the timetable for 2 consecutive days, Answer ............................................... [1] (b) follows the timetable only for 1 day out of 2 consecutive days. Answer ............................................... [2] ________________________________________________________________________________ 11 (a) Write down all the possible subsets of {0, 3}. Answer .................................................................. [1] (b) The Venn diagram shows the sets P, Q and R. (i) Find n( 'P  R). Answer ............................................... [1] (ii) k  P Write down all the possible values of k. Answer k = ........................................................... [1] _________________________________