Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 7
107 practice questions
Topics covered
Practice questions
11–20 of 48 · Normal
Question 11
3 marks · Normal
Answer and see the solution →Solve the inequality .
Write your answer using inequalities.
Question 12
4 marks · Normal
Answer and see the solution →A number is chosen. The sum of the square of the number and 6 times the number is 40.
(a)[1 mark]Let the number be . Write a quadratic equation for this problem.
(b)[2 marks]Solve the equation to find the value(s) of .
(c)[1 mark]State the value(s) of that solve the original problem.
Question 13
4 marks · Normal
Answer and see the solution →Consider the quadratic equation , where is a constant.
Complete the following table by factorising the equation for each given value of , and listing the roots.
k Factorised form Roots 5 -7 Question 14
3 marks · Normal
Answer and see the solution →Solve the inequality .
Question 15
3 marks · Normal
Answer and see the solution →A rectangular field has a perimeter of 38 m. The length is 4 m less than twice the width. Form a quadratic equation for the width, , and solve the equation to find the width. Show your reasoning.
Question 16
2 marks · Normal
Answer and see the solution →A rectangular garden has an area of 96 m². The length of the garden is 4 metres longer than its width. Find the width of the garden.
Question 17
2 marks · Normal
Answer and see the solution →The table shows values of and for the graph of .
x y -4 2 Write down the value of when:
(a)[1 mark](i)
(b)[1 mark](ii)
Question 18
3 marks · Normal
Answer and see the solution →Write down the algebraic form of a cubic equation for a graph with a single turning point and which passes through the point (1, 0).
Give your answer in the form .
Question 19
3 marks · Normal
Answer and see the solution →The graph of is shown below.
Explain what happens to the value of as approaches zero from the positive side, and as becomes very large.
Question 20
4 marks · Normal
Answer and see the solution →A company's profit, thousand dollars, after years is given by for .
(a)[1 mark]Calculate the company's profit when .
(b)[1 mark]Determine whether the company makes a loss at .
(c)[2 marks]State how the graph of against helps you decide when the company will break even.