EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Cubic and Reciprocal Graphs
Cubic and reciprocal graphs · Graphs · Lesson 7 of 8 · 9 marks · 20 minutes
Name Date
Answer all questions. Show your working. All questions are non-calculator.
Question 1 NON-CALCULATOR [2 marks]
Complete the table of values for y = x³ − 4x for x = −3, −2, −1, 0, 1, 2, 3.
Question 2 NON-CALCULATOR [2 marks]
Here are four graphs, A, B, C and D. Match each equation to its graph: y = 3 − 2x, y = x² − 1, y = x³, y = 5/x.
Question 3 NON-CALCULATOR [3 marks]
(a) Complete the table of values for y = 12/x for x = 1, 2, 3, 4, 6, 12. (b) Explain why the graph of y = 12/x never crosses the y-axis.
Question 4 NON-CALCULATOR [2 marks]
Write down the three values of x where the graph of y = x³ − 4x crosses the x-axis. Show how you know.
Answers
Check your answer only once you have written one.
Question 1 [2 marks]
y = −15, 0, 3, 0, −3, 0, 15
▸ At least 4 correct values B1
▸ All 7 correct B1
Question 2 [2 marks]
y = 3 − 2x - C. y = x² − 1 - A. y = x³ - D. y = 5/x - B.
▸ 2 correct matches B1
▸ All 4 correct B1
Question 3 [3 marks]
(a) 12, 6, 4, 3, 2, 1 (b) On the y-axis x = 0, and you cannot divide 12 by 0, so there is no point with x = 0.
▸ (a) At least 4 correct B1
▸ (a) All correct B1
▸ (b) Division by 0 is impossible, or x cannot be 0 C1
Question 4 [2 marks]
x³ − 4x = x(x² − 4) = x(x − 2)(x + 2). So x = 0, 2 or −2. (Or: the table gives y = 0 at these values.)
▸ A correct method, e.g. factorising or a table M1
▸ −2, 0 and 2 A1