Algebra worksheet — GCSE Foundation

1.The simultaneous equations x = 2 and x + y = 9 are given. Work out the value of y.

2.Solve the inequality 5 − x ≤ 2.

3.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.

4.Make c the subject of the formula k = 6c.

5.Solve x − 4 = −9

6.Which of these is an inequality?

7.Which of these is a formula, rather than an expression, an equation, or an identity?

8.p = 4. Work out the value of 2p³.

9.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.

10.Which of these quadratic graphs does NOT cross the x-axis at all?

11.The point (−4, 7) is moved 4 units to the right and 9 units down. Write down the coordinates of the point it reaches.

12.A taxi firm charges a fixed fee of £3.50 plus £2.20 per mile. Work out the total cost of a journey of 6 miles.

13.Which expression is equivalent to 2(x + 6)?

14.Solve 2x + 7 = x + 13

15.A geometric sequence starts at 4, and each term after that is found by multiplying the term before it by 3. Write down the first four terms of the sequence.