Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Chapter
Algebra 5
18 practice questions
Practice questions
11–18 of 18
Question 11
2 marks · Normal
Answer and see the solution →Factorise fully:
Question 12
2 marks · Normal
Answer and see the solution →Write down the solution set for the inequality .
Question 13
2 marks · Normal
Answer and see the solution →Rearrange the formula to make the subject:
Question 14
4 marks · Normal
Answer and see the solution →Solve the simultaneous equations:
(a)[2 marks]Substitute y into the second equation and simplify to a quadratic in x.
(b)[2 marks]Solve the quadratic equation to find the possible values of x.
Question 15
5 marks · Normal
Answer and see the solution →A rectangle has a length of (x+7) cm and a width of x cm. The area of the rectangle is 120 cm².
(a)[2 marks]Write an equation for the area in terms of x and expand the brackets.
(b)[1 mark]Rearrange your equation to the form ax² + bx + c = 0.
(c)[2 marks]Solve the equation for x.
Question 16
4 marks · Hard
Answer and see the solution →Solve the equation by factorising, and write down all possible values of as exact values.
Question 17
5 marks · Hard
Answer and see the solution →A garden is to be designed with a rectangular lawn of width m and length m. A path of uniform width m is built all around the lawn. The total area (lawn plus path) is m.
(a)[1 mark]Show that .
(b)[4 marks]Given that the width of the path, , is 2 m, form and solve a quadratic equation to find the dimensions of the lawn.
Question 18
4 marks · Hard
Answer and see the solution →Rearrange the formula to make the subject, expressing your answer in terms of . Show the necessary algebraic steps.