



Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
math a level paper pure edexcel
Typology: Essays (high school)
1 / 7
This page cannot be seen from the preview
Don't miss anything!




Answer the questions in the spaces provided – there may be more space than you need.
The marks for each question are shown in brackets – use this as a guide as to how much time to spend on each question.
6. Figure 1 shows a sketch of part of the graph y = f( x ) where Figure 1 (a) State the range of f. (1 mark) (b) Given that , where k is a constant has two distinct roots, state the possible values of k. **(7 marks)
7.** Show that f ( x ) can be written in the form , where A , B and C are constants to be found. (7 marks) ___________________________________________________________________________________
8. A ball is dropped from a height of 80 cm. After each bounce it rebounds to 70% of its previous maximum height. (a) Write a recurrence relation to model the maximum height in centimetres of the ball after each subsequent bounce. (2 marks) (b) Find the height to which the ball will rebound after the fifth bounce. (2 marks) (c) Find the total vertical distance travelled by the ball before it stops bouncing. (4 marks) (d) State one limitation with the model. **(1 mark)
9.** Solve in the range. Round your answer to 1 decimal place. **(4 marks)
10.** Use proof by contradiction to show that there is no greatest positive rational number. **(4 marks)
11.** The first three terms in the binomial expansion of are. (a) Find the values of a and b. (5 marks) (b) State the range of values of x for which the expansion is valid. (2 marks) (c) Find the value of c. (2 marks) ___________________________________________________________________________________
Figure 3 Figure 3 is a graph of the price of a stock during a 12-hour trading window. The equation of the curve is given above. (a) Show that the price reaches a local maximum in the interval. (5 marks) Figure 3 shows that the price reaches a local minimum between 9 and 11 hours after trading begins. (b) Using the Newton–Raphson procedure once and taking t 0 = 9.9 as a first approximation, find a second approximation of when the price reaches a local minimum. (6 marks)