Algebra worksheet — GCSE Foundation

1.Sophie's mother is 34 years old. In x years' time she will be 50 years old. Work out the value of x.

2.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.

3.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.

4.The mean of four numbers is 12.5. Three of the numbers are 8, 15 and 19. Form an equation using n for the fourth number, and solve it to find n.

5.A gym charges a joining fee plus a monthly fee. Anna paid £100 in total after 3 months of membership. Ben paid £160 in total after 6 months of membership (same joining fee and monthly fee as Anna). Work out the monthly fee.

6.A straight line has gradient 3 and passes through the point (1, 4). Work out the equation of the line.

7.The graph of y = mx + 6 passes through the point (−2, 0). Work out the value of m.

8.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.

9.Make x the subject of the formula y = 2x − 9.

10.Solve 2x² = 18.

11.Which of these is an expression?

12.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.

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

14.A point has coordinates (−6, 9). Work out the sum of the x-coordinate and the y-coordinate.

15.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.