Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 7
107 practice questions
Topics covered
Practice questions
21–30 of 107
Question 21
2 marks · Easy
Answer and see the solution →The solutions to the quadratic inequality are required.
Write down the values of that satisfy the inequality.
Question 22
3 marks · Easy
Answer and see the solution →A rectangular swimming pool is 4 m longer than it is wide. Its area is 60 m².
(a)[1 mark]Let the width be metres. Write a quadratic equation to represent the area.
(b)[2 marks]Solve your equation to find the width of the swimming pool.
Question 23
3 marks · Easy
Answer and see the solution →The following table shows three different quadratic equations. For each equation, state the number of real solutions.
Table of quadratic equations Equation Number of real solutions x^2 - 9 = 0 x^2 + 2x + 5 = 0 x^2 - 4x + 4 = 0 Question 24
1 mark · Easy
Answer and see the solution →A ball is thrown and its height (in metres) t seconds after being thrown is given by .
At what time does the ball hit the ground again?
Question 25
2 marks · Easy
Answer and see the solution →Solve the inequality and write your answer as an inequality.
Question 26
2 marks · Normal
Answer and see the solution →Solve the quadratic equation by factorisation.
Question 27
3 marks · Normal
Answer and see the solution →A rectangular garden has a length that is 2 m greater than its width. The area of the garden is 48 m^2.
(a)[1 mark]Form a quadratic equation for the width of the garden, .
(b)[2 marks]Solve the equation to find the width of the garden.
Question 28
3 marks · Normal
Answer and see the solution →Solve the inequality .
Write your answer using inequalities.
Question 29
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 30
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