Algebra worksheet — GCSE Foundation

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

2.Solve the inequality 5 − x ≤ 2.

3.Which of these equations gives a graph shaped like a U, symmetrical about a vertical line?

4.The formula for the perimeter of a rectangle is P = 2(l + w). One rectangle has l = 9 cm and w = 4 cm. A second rectangle has l = 6 cm and w = 5 cm. Work out how many cm greater the perimeter of the first rectangle is than the perimeter of the second.

5.Which of these equations describes a vertical line?

6.Solve x² = 81.

7.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.

8.A distance-time graph shows a car travelling at a constant speed, covering 90 km in 2 hours. Work out the car's speed in km/h.

9.The first four terms of a sequence are 11, 18, 25, 32. Ravi thinks the nth term is 7n. Work out the correct expression for the nth term.

10.A rule multiplies the input by a fixed number and then adds a fixed number. An input of 1 gives an output of 5, and an input of 3 gives an output of 11. Work out the rule, writing the input as x and the output as y.

11.A printer starts a job with 480 sheets of paper loaded and prints at a steady rate. The number of sheets left, S, after t minutes is given by S = 480 − 24t. Work out how many minutes it takes for the paper to run out completely.

12.Solve 2(x + 3) = 10

13.The formula connecting distance (d), speed (s) and time (t) is d = st. Make s the subject of the formula.

14.A rectangle has length k cm and width 5 cm less than its length. Write down an expression for the width of the rectangle, in cm.

15.Which expression means 'add 3 to n, then multiply the result by 4'?