Algebra worksheet — GCSE Foundation

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

2.The formula connecting speed, distance and time is v = s ÷ t. Work out v, in km/h, when s = 180 and t = 4.

3.Write down 0.2x with its coefficient written as a fraction in its simplest form.

4.A straight line has equation 4y = 12x + 20. Work out the gradient of the line.

5.There are 30 students in a Year 10 maths class. There are 2 more boys than girls. Work out the number of boys and the number of girls.

6.The first five cube numbers are 1, 8, 27, 64, 125. Write down the next cube number in the sequence.

7.To solve 5x − 4 = 2x + 8, Chloe's working is shown. Line 1: 5x − 4 = 2x + 8. Line 2: 3x − 4 = 8. Line 3: 3x = 4. Line 4: x = 4/3. Chloe has made a mistake in her working. Which line contains the mistake?

8.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

9.The formula for the perimeter of a square is P = 4s, where s is the side length. Make s the subject of the formula.

10.Solve 5(x + 3) = 40

11.Solve x² − 100 = 0.

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

13.A taxi fare in pounds is given by F = 2.50 + 1.20m, where m is the number of miles travelled. Sam takes a taxi for a journey of 6 miles. Work out the fare.

14.Work out the gradient of the straight line with equation 3y = 12 − 6x.

15.Solve the inequality 5 − x ≤ 2.