Algebra worksheet — GCSE Foundation

1.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.

2.Solve the inequality 9 − 2x ≥ 1.

3.A pattern is made from tiles. Pattern 1 has 7 tiles, pattern 2 has 11 tiles, pattern 3 has 15 tiles, and pattern 4 has 19 tiles, with each new pattern having 4 more tiles than the one before it. Work out an expression, in terms of n, for the number of tiles in pattern n.

4.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.

5.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.

6.A point has coordinates (−6, 9). Work out the sum of the x-coordinate and the y-coordinate.

7.x = 5. Work out the value of 3x² − 4.

8.Point A has coordinates (4, −5). Point B has coordinates (4, 3). Work out the distance between A and B.

9.Work out the coordinates of the reflection of (6, −3) in the y-axis.

10.Rosie is asked whether 4(x + 3) = 4x + 12 is an equation or an identity. Which statement is correct? Give a reason for your answer.

11.Given that (x − 4)(x + 9) = 0, write down the two solutions of x.

12.a = 2 and b = 5. Work out the value of a²b.

13.The first five square numbers are 1, 4, 9, 16, 25. Write down the next square number in the sequence.

14.Make x the subject of the formula y = 2x − 9.

15.A number, w, satisfies the statement "three times w, minus 5, is at least 16". Which of these is the correct inequality for w?