*P66785A0152* Turn over Candidate s urname O t h er names Total M a rks C entre N umber C a ndidate N umber Please check the examination details below before entering your candidate information P66785A ©2020 Pearson Education Ltd. 1/1/1/1/1/ You must have: Mathematical Formulae and Statistical Tables (Green), calculator Candidates may use any calculator allowed by Pearson regulations. Calculators must not have the facility for symbolic algebra manipulation, differentiation and integration, or have retrievable mathematical formulae stored in them. Instructions • Use black ink or ball-point pen. • If pencil is used for diagrams/sketches/graphs it must be dark (HB or B). • Fill in the boxes at the top of this page with your name, centre number and candidate number. • Answer all questions and ensure that your answers to parts of questions are clearly labelled. • Answer the questions in the spaces provided – there may be more space than you need • You should show sufficient working to make your methods clear. Answers without working may not gain full credit. • Inexact answers should be given to three significant figures unless otherwise stated. Information • A booklet ‘Mathematical Formulae and Statistical Tables’ is provided. • There are 16 questions in this question paper. The total mark for this paper is 100. • The marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question Advice • Read each question carefully before you start to answer it. • Try to answer every question. • Check your answers if you have time at the end. Mathematics Advanced Paper 1: Pure Mathematics 1 Paper Reference 9MA0/01 Morning (Time: 2 hours) Pearson Edexcel Level 3 GCE Wednesday 7 October 2020 *P66785A0252* 2 1. (a) Find the first four terms, in ascending powers of x , of the binomial expansion of 1 8 1 2 + ( ) x giving each term in simplest form. (3) (b) Explain how you could use x = 1 32 in the expansion to find an approximation for 5 There is no need to carry out the calculation. 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_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ *P66785A0352* Turn over 3 Question 1 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 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By taking logarithms of both sides, solve the equation 4 3 p −1 = 5 210 giving the value of p to one decimal place. 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Relative to a fixed origin O ● point A has position vector 2 i + 5 j − 6 k ● point B has position vector 3 i − 3 j − 4 k ● point C has position vector 2 i − 16 j + 4 k (a) Find AB → (2) (b) Show that quadrilateral OABC is a trapezium, giving reasons for your answer. 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The function f is defined by f ( x ) = 3 7 2 x x − − x , x ≠ 2 (a) Find f −1 (7) (2) (b) Show that ff ( x ) = ax b x + − 3 where a and b are integers to be found. 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A car has six forward gears. The fastest speed of the car ● in 1 st gear is 28 km h –1 ● in 6 th gear is 115 km h –1 Given that the fastest speed of the car in successive gears is modelled by an arithmetic sequence , (a) find the fastest speed of the car in 3 rd gear. (3) Given that the fastest speed of the car in successive gears is modelled by a geometric sequence , (b) find the fastest speed of the car in 5 th gear. 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_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ *P66785A01152* Turn over 11 Question 5 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 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_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ (Total for Question 5 is 6 marks) *P66785A01252* 12 6. (a) Express sin x + 2 cos x in the form R sin ( x + α ) where R and α are constants, R > 0 and 0 < α < 2 π Give the exact value of R and give the value of α in radians to 3 decimal places. (3) The temperature, θ °C , inside a room on a given day is modelled by the equation θ = 5 + sin 3 12 − πt + 2 cos 3 12 − πt 0 t < 24 where t is the number of hours after midnight. Using the equation of the model and your answer to part (a), (b) deduce the maximum temperature of the room during this day, (1) (c) find the time of day when the maximum temperature occurs, giving your answer to the nearest minute. 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_____________________________________________________________________________________ *P66785A01452* 14 Question 6 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 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_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ *P66785A01552* Turn over 15 Question 6 continued _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ 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