Algebra worksheet — GCSE Foundation

1.Which of these points lies in the first quadrant?

2.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.

3.Grace has t books. Noah has 1 book fewer than Grace. Write down an expression for the number of books Noah has.

4.The cost, in pounds, of hiring a van for d days is given by the formula C = 25 + 18d. A customer's hire cost £133. Work out how many days, d, they hired the van for, by first rearranging the formula to make d the subject.

5.Solve 2x − 2 = 2

6.Work out the value of n² − n when n = −3

7.A number machine multiplies its input by 2 and then subtracts 5. Work out the output when the input is 6.

8.Solve the inequality 5x − 3 > 2x + 9.

9.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

10.A triangle has vertices at (1, 1), (1, 5) and (6, 1). Work out the area of the triangle.

11.A charity's fundraising total, T pounds, over d days follows T = (d − 3)(30 − d) for 3 ≤ d ≤ 30, where T = 0 marks the start and end of the campaign. Work out how many days the campaign runs for, from start to end.

12.There are 50 adults on a coach to the Lake District. Every adult is either a man or a woman. There are 10 more men than women. Work out the number of men.

13.A rectangle has width x cm. Its length is 3 cm more than its width. The perimeter of the rectangle is 38 cm. Form an equation and solve it to find x.

14.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.

15.y = 3x − 2. Work out the value of y when x = 4.