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Pearson Edexcel Level 3
GCE Mathematics
Advanced Subsidiary
Paper 1 : Pure
Monday 27 May 2019
Time: 1 hour 4 5 minutes
Paper Reference(s)
8MA0/0 1
You must have:
Mathematical Formulae and Statistical Tables, calculator
Candidates may use any calculator permitted by Pearson regulations. Calculators must not have the facility for algebraic 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).
- 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 paper. The total mark is 87.
- 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.
- If you change your mind about an answer, cross it out and put your new answer and any working underneath.
The line L 1 has equation 4 𝑥 + 2 𝑦 − 3 = 0 (a) Find the gradient of L 1. (1) The line L 2 is perpendicular to L 1 and passes through the point (2, 5). (b) Find the equation of L 2 in the form y = mx + c , where m and c are constants. (3)
_______________________________________________________Total for Q1 is 4 marks
= −𝑥
2 𝑥^3
, 𝑥 ≠ 0 Given that 𝑦 = 7 at 𝑥 = 1 , find 𝑦 in terms of 𝑥, giving each term in its simplest form. (6)
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______________________________________________________ Total for Q 3 is 6 marks
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___________________________________________________Total for Q 4 is 5 marks
A curve has equation 𝑦 = (^) √𝑥 +
(a) Find, in simplest form 𝑑𝑦 𝑑𝑥
(b) Hence find the range of values of 𝑥 for which the curve is increasing (2) ___________________________________________________________________________
Prove by first principles that 𝑑 𝑑𝑥 (𝑥^2 ) (^) = 2 𝑥 (3)
_______________________________________________________Total for Q 6 is 3 marks
The curve C has equation 𝑦 =
𝑥^2
Where k is a constant. (a) Sketch C in the space below, stating the horizontal asymptote (3) The line 𝑙 has equation 𝑦 = − 2 𝑥 + 5 (b) Show that the x coordinate of any point of intersection of 𝑙 with C is given by a solution of the equation 𝑘 − 3 𝑥^2 + 2 𝑥^3 = 0 (2)
(a) Find the first 3 terms, in ascending powers of x, of the binomial expansion of ( 3 +
5 ( 3 ) (b) Explain how you could use your expansion to estimate the value of 2. 965. You do not need to perform this calculation ( 2 )
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___________________________________________________ Total for Q 8 is 5 marks
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_______________________________________________________ Total for Q 9 is 6 marks
A circle C has equation 𝑥^2 + 𝑦^2 + 6 𝑥 − 4 𝑦 + 5 = 0 (a) Find (i) The coordinates of the centre of C, (ii) The exact radius of C leaving your answer as simply as possible (3) The straight line, with equation 𝑥 = 𝑘, where 𝑘is a constant, intersects C at 2 distinct points. (b) Find the range of possible values for 𝑘. (2)
𝑓(𝑥) = 𝑥^3 + 𝑥^2 − 8 𝑥 − 12
(a) Prove that (𝑥 − 3 ) is a factor of 𝑓(𝑥). ( 2 ) (b) Hence, using algebra, show that the equation 𝑓(𝑥) = 0 has only 2 distinct roots. (3) Figure B shows a sketch of part of the curve 𝑦 = 𝑓(𝑥). (c) Deduce, giving reasons for your answer, the number of real roots of the equation 2 𝑥^3 + 2 𝑥^2 − 16 𝑥 − 50 = 0 (3) Given that 𝑘 is a constant and the curve with equation 𝑦 = 𝑓(𝑘𝑥) passes through (1,0), (d) Find the two possible values of 𝑘 (2)
𝑥 Figure B 𝑦 = 𝑓(𝑥) 𝑦
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