Pearson Edexcel International GCSE (9–1) · MATHEMATICS A · Unit
Unit 5
104 practice questions
Topics covered
Practice questions
11–20 of 48 · Normal
Question 11
4 marks · Normal
Answer and see the solution →A rectangle has length and width .
Rectangle with a square cut out A square of side cm is cut out of it.
(a)[1 mark]Write, in simplest form, an expression for the area of the original rectangle.
(b)[1 mark]Write an expression for the shaded area after removing the square.
(c)[2 marks]If the shaded area is , find the value of .
Question 12
2 marks · Normal
Answer and see the solution →Factorise fully:
Question 13
2 marks · Normal
Answer and see the solution →Write down the solution set for the inequality .
Question 14
2 marks · Normal
Answer and see the solution →Rearrange the formula to make the subject:
Question 15
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 16
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 17
2 marks · Normal
Answer and see the solution →Find the gradient of the straight line passing through the points (2, 7) and (6, 3).
Question 18
4 marks · Normal
Answer and see the solution →The line l has equation .
(a)[1 mark]Write down the gradient of l.
(b)[1 mark]Find the gradient of a line perpendicular to l.
(c)[2 marks]Find the equation of a line perpendicular to l that passes through the point (2, 1), giving your answer in the form .
Question 19
2 marks · Normal
Answer and see the solution →Find the mid-point of the line joining the points A(3, -4) and B(-5, 6).
Question 20
3 marks · Normal
Answer and see the solution →Copy and complete the table of values for for , then write the coordinates of the minimum point.
Table of values for \( y = x^2 - 2x + 1 \) x -1 0 1 2 3 y