Algebra worksheet — GCSE Foundation

1.Solve x² − 100 = 0.

2.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.

3.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.

4.A ball's height, h metres, t seconds after being thrown follows h = (t − 1)(9 − t). Given that the ball is at ground level at t = 1 and t = 9, work out at what time t the ball reaches its maximum height, using symmetry.

5.Point P has coordinates (5, 2). Point P is rotated 180° about the origin to point Q. Write down the coordinates of Q.

6.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.

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

8.A ramp rises 3 m over a horizontal distance of 12 m. Work out the gradient of the ramp.

9.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.

10.Solve 2x² = 18.

11.Harry will spend at most £150 on a party. The cake costs £60 and each helium balloon costs £3. Solve an inequality to find all the possible numbers of balloons, x, that he can buy.

12.A square has sides of length y cm. Write down an expression for the perimeter of the square.

13.Which expression means 'triple c, then add double d'?

14.Solve the inequality x − 10 < −3.

15.A geometric sequence starts at 3, and each term after that is found by multiplying the term before it by 2. Write down the first four terms.