Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Chapter
Algebra 7
18 practice questions
Practice questions
11–18 of 18
Question 11
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 12
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 13
3 marks · Normal
Answer and see the solution →Solve the inequality .
Question 14
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 15
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 16
2 marks · Hard
Answer and see the solution →A rectangular plot has an area of 77 m². The length of the plot is 6 metres shorter than twice its width. Let the width of the plot be metres.
Write down a quadratic equation in for this situation and solve the equation to find the width of the plot.
Question 17
4 marks · Hard
Answer and see the solution →Solve the quadratic equation by completing the square. Give your answers in surd form.
Question 18
4 marks · Hard
Answer and see the solution →A factory machines a rectangular sheet so that its length is 5 cm more than its width. The area of the sheet is 84 cm².
Let the width of the sheet be cm.
Form a quadratic equation for , solve it, and explain which solution is suitable for this context.