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Head to savemyexams.co.uk for more awesome resources Functions and Sequences Difficulty: Hard Question Paper 1 Level A Level only Subject Maths - Pure Exam Board Edexcel Topic Functions and Sequences Sub-Topic Difficulty Hard Booklet Question Paper 1 Time allowed: 54 minutes Score: /45 Percentage: /100 Grade Boundaries: 1 A* A B C D E U >76% 61% 52% 42% 33% 23% <23% Question 1 2 Head to savemyexams.co.uk for more awesome resources Head to savemyexams.co.uk for more awesome resources (Total 13 marks) 3 Question 2 Head to savemyexams.co.uk for more awesome resources The function f is defined by k is a positive constant. (a) State the range of f. (1) (b) Find f –1 and state its domain. (3) The function g is defined by x>0 (c) Solve the equation g(x) + g(x2) + g(x3) = 6 giving your answer in its simplest form. 4 (4) Head to savemyexams.co.uk for more awesome resources (d) Find fg(x), giving your answer in its simplest form. (2) (e) Find, in terms of the constant k, the solution of the equation fg(x) = 2k2 (2) (Total 12 marks) 5 Question 3 Head to savemyexams.co.uk for more awesome resources A sequence a1, a2, a3, ... is defined by a1 = k, an+1 = 2an – 7, n ≥ 1, where k is a constant. (a) Write down an expression for a2 in terms of k. (b) Show that a3 = 4k – 21. (1) (2) 4 Given that ∑ ar = 43 , r=1 (c) find the value of k. (4) (Total 7 marks) 6 Question 4 Head to savemyexams.co.uk for more awesome resources Jacob is making some patterns out of squares. The first 3 patterns in the sequence are shown in Figure 2. Figure 2 (a) Find an expression, in terms of n, for the number of squares required to make pattern n. (2 marks) Jacob uses a total of 948 squares in constructing the first k patterns. (b) Show that . (2 marks) (Total 4 marks) 7 Question 5 Head to savemyexams.co.uk for more awesome resources At the beginning of each month Kath places £100 into a bank account to save for a family holiday. Each subsequent month she increases her payments by 5%. Assuming the bank account does not pay interest, find (a) the amount of money in the account after 9 months. (3 marks) Month n is the first month in which there is more than £6000 in the account. (b) Show that 8 (4 marks) Head to savemyexams.co.uk for more awesome resources Maggie begins saving at the same time as Kath. She initially places £50 into the same account and plans to increase her payments by a constant amount each month. (c) Given that she would like to reach a total of £6000 in 29 months, by how much should Maggie increase her payments each month? (2 marks) (Total 9 marks) 9