Algebra worksheet — GCSE Foundation

1.Isla says that the lines y = 2x + 1 and y = −2x + 3 are parallel. Write down the statement that gives the correct answer for the correct reason.

2.Solve x² − 6x = 0.

3.The simultaneous equations y = 3 and 4x − y = 9 are given. Work out the value of x.

4.Which expression means the same as a × a × a?

5.Solve the simultaneous equations 5x − 2y = 16 and 3x + 2y = 16. Work out the value of x.

6.The point P has coordinates (0, 12). Write down the axis that P lies on and the y-coordinate of P.

7.n = 3. Work out the value of (2n)².

8.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.

9.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.

10.Write down the number of terms in the expression 4x² − 7x + 3.

11.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.

12.Make x the subject of the formula y = x + 7.

13.Expand 7(a + 8)

14.A student says 4(2x − 3) is equivalent to 8x − 3. Which statement gives the correct verdict and reason?

15.A quadratic graph has roots at x = −3 and x = 5, and it crosses the y-axis at (0, −15). Work out the equation of the curve in the form y = (x − a)(x − b).