Algebra worksheet — GCSE Foundation

1.Solve x² − x − 12 = 0.

2.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.

3.Write down the expression that means the same as m² × m × 3.

4.Make m the subject of the formula w = m − 8.

5.Expand 2(x + 12)

6.Work out the equation of the straight line that passes through (−2, 3) and (4, −9).

7.Write down the expression that means the same as (x + 7) ÷ 4.

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

9.Two numbers have a sum of 45. The larger number is 9 more than the smaller number. Form an equation using n for the smaller number, and solve it to find the larger number.

10.Kai writes the expression 8 − 3x + 5x² and says it has three terms. Ryan says it only has two terms because a number on its own is not a term. Work out the correct number of terms in the expression.

11.Work out the equation of the straight line through the points (−3, 4) and (1, −8).

12.The perimeter, P, of a rectangle with length l and width w is calculated using P = 2l + 2w. What kind of mathematical statement is P = 2l + 2w?

13.Make a the subject of the formula b = 20 − a.

14.y = x + 10. Work out the value of y when x = 0.

15.Here are the first five terms of an arithmetic sequence: 2, 5, 8, 11, 14. Work out the 8th term.