Algebra worksheet — GCSE Foundation

1.Work out the values of x and y that satisfy both x + y = 10 and x − y = 4.

2.Make x the subject of the formula y = (x − 4)/5.

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

4.Which of these is an inequality?

5.A straight line has equation y = 2x − 7. Write down the coordinates of the point where the line crosses the y-axis.

6.The formula for converting a temperature in Fahrenheit, F, to Celsius, C, is C = 5(F − 32) ÷ 9. Work out C, to 1 decimal place, when F = 98.6.

7.The simultaneous equations 2x + 3y = 12 and x − y = 1 are given. Work out the value of y.

8.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

9.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.

10.A sequence has the position-to-term rule: the term is the square of the position number. Its first four terms are 1, 4, 9, 16. Work out the 10th term.

11.A speed-time graph for a car shows the speed increasing steadily from 5 m/s to 17 m/s over 6 seconds. Work out the acceleration of the car, in m/s².

12.Solve x² + 3x − 10 = 0.

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

14.Solve 3(2x − 1) = 27

15.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.