EDEXCEL GCSE MATHS · HIGHER TIER
Exam Practice: More Graphs
More graphs · Graphs · Lesson 8 of 8 · 10 marks · 25 minutes
Name Date
Answer all questions. Show your working. The calculator is allowed where the question says so.
Question 1 NON-CALCULATOR · HIGHER [3 marks]
The graph of y = ab^x passes through the points (0, 3) and (2, 12). Find the value of a and the value of b.
Question 2 CALCULATOR · HIGHER [2 marks]
A car is bought for £15 000. Its value after t years is V = 15 000 × 0.88^t. (a) By what percentage does the value fall each year? (b) Work out the value after 3 years.
Question 3 NON-CALCULATOR · HIGHER [3 marks]
(a) Write down the radius of the circle x² + y² = 25. (b) Show that the point (3, −4) lies on the circle. (c) Write down the equation of the circle with centre (0, 0) and radius 6.
Question 4 CALCULATOR · HIGHER [2 marks]
One solution of cos x = 0.5 is x = 60°. Find the other solution between 0° and 360°.
Answers
Check your answer only once you have written one.
Question 1 [3 marks]
3 = ab⁰ = a, so a = 3. 12 = 3b², b² = 4, b = 2.
▸ a = 3 B1
▸ 12 = 3b² M1
▸ b = 2 A1
Question 2 [2 marks]
(a) 12% (b) 15 000 × 0.88³ = £10 222.08
▸ (a) 12% B1
▸ (b) £10 222.08 B1
Question 3 [3 marks]
(a) 5 (b) 3² + (−4)² = 9 + 16 = 25, so yes. (c) x² + y² = 36
▸ (a) 5 B1
▸ (b) 9 + 16 = 25 shown B1
▸ (c) x² + y² = 36 B1
Question 4 [2 marks]
The cosine graph is symmetrical about x = 180°, so x = 360 − 60 = 300°.
▸ Using symmetry, e.g. 360 − 60 M1
▸ 300° A1