Pearson Edexcel Centre umber Candidate umber Level 3 GCE …

1 Centre NumberCandidate NumberWrite your name hereSurnameOther namesTotal MarksPaper Reference*P58346A0148*P58346A 2018 Pearson Education over Candidates may use any calculator allowed by the regulations of the Joint Council for Qualifications. Calculators must not have the facility for symbolic algebra manipulation, differentiation and integration, or have retrievable mathematical formulae stored in 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.

2 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. Answers should be given to three significant figures unless otherwise A booklet Mathematical Formulae and Statistical Tables is provided. There are 15 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 Read each question carefully before you start to answer it.

3 Try to answer every question. Check your answers if you have time at the SubsidiaryPaper 1: Pure MathematicsWednesday 16 May 2018 MorningTime: 2 hours8MA0/01 You must have:Mathematical Formulae and Statistical Tables, calculatorPearson Edexcel Level 3 GCE2*P58346A0248* DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREAA nswer ALL questions. Write your answers in the spaces Find23613xxx + d giving your answer in its simplest form.

4 (4)_____3*P58346A0348*Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREAQ uestion 1 continued_____(Total for Question 1 is 4 marks)4*P58346A0448* DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA2. (i) Show that x 2 8x + 17 > 0 for all real values of x(3) (ii) If I add 3 to a number and square the sum, the result is greater than the square of the original number.

5 State, giving a reason, if the above statement is always true, sometimes true or never true.(2)_____5*P58346A0548*Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREAQ uestion 2 continued_____(Total for Question 2 is 5 marks)6*P58346A0648* DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA3. Given that the point A has position vector 4i 5j and the point B has position vector 5i 2j, (a) find the vector AB ,(2) (b) find AB.

6 Give your answer as a simplified surd.(2)_____7*P58346A0748*Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREAQ uestion 3 continued_____(Total for Question 3 is 4 marks)8*P58346A0848* DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA4. The line l1 has equation 4y 3x = 10 The line l2 passes through the points (5, 1) and ( 1, 8).

7 Determine, giving full reasons for your answer, whether lines l1 and l2 are parallel, perpendicular or neither.(4)_____9*P58346A0948*Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREAQ uestion 4 continued_____(Total for Question 4 is 4 marks)10*P58346A01048* DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA5. A student s attempt to solve the equation 2 log2 x log2 x = 3 is shown below.

8 2 log2 x log2 x = 3 2 log2 xx = 3 using the subtraction law for logs 2 log2 x() = 3 simplifying log2 x = 3 using the power law for logs x = 32 = 9 using the definition of a log (a) Identify two errors made by this student, giving a brief explanation of each.(2) (b) Write out the correct solution.(3)_____11*P58346A01148*Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREAQ uestion 5 continued_____(Total for Question 5 is 5 marks)12*P58346A01248* DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS = 100 (x 9)2 Figure 1 A company makes a particular type of children s toy.

9 The annual profit made by the company is modelled by the equationP = 100 (x 9)2 where P is the profit measured in thousands of pounds and x is the selling price of the toy in pounds. A sketch of P against x is shown in Figure 1. Using the model, (a) explain why 15 is not a sensible selling price for the toy.(2) Given that the company made an annual profit of more than 80 000 (b) find, according to the model, the least possible selling price for the toy.(3) The company wishes to maximise its annual profit. State, according to the model, (c) (i) the maximum possible annual profit, (ii) the selling price of the toy that maximises the annual profit.

10 (2)_____13*P58346A01348*Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREAQ uestion 6 continued_____14*P58346A01448* DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREAQ uestion 6 continued_____15*P58346A01548*Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN