Algebra worksheet — GCSE Foundation

1.Solve the simultaneous equations 3x + 2y = 16 and x + y = 7. Work out the value of y.

2.A rule turns each input x into an output y. The inputs are x = 0, 1, 2, 3 and the outputs are y = 4, 7, 10, 13. Work out the output when x = 5.

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

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

5.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?

6.Which expression is equivalent to 2(x + 6)?

7.The formula for the circumference of a circle is C = 2πr, where r is the radius. Make r the subject of the formula.

8.Priya has a budget of £50 for a school trip. The coach costs £14 and each student ticket costs £4. Using the inequality 14 + 4s ≤ 50, work out the greatest number of student tickets, s, she can buy.

9.A caterer uses the formula C = 6p + 20 to work out the total cost, £C, of a buffet for p people, where £20 covers fixed costs. A customer is charged £92. Work out how many people, p, the buffet was for.

10.Write down the expression that means the same as m × m × m × n.

11.A ball is thrown in the air. Its height, h metres, above the ground after t seconds is given in this table: when t = 0, h = 0; when t = 1, h = 15; when t = 2, h = 20; when t = 3, h = 15; when t = 4, h = 0. Use the table to find the two times, in seconds, at which the ball is at ground level.

12.Solve 3(2x − 1) = 27

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

14.Solve the simultaneous equations 2x + y = 7 and x + 2y = 8.

15.A table shows values of y = x² − x − 6 for x from −3 to 4: at x = −3, y = 6; x = −2, y = 0; x = −1, y = −4; x = 0, y = −6; x = 1, y = −6; x = 2, y = −4; x = 3, y = 0; x = 4, y = 6. Using the table, write down the two roots of x² − x − 6 = 0.