Algebra worksheet — GCSE Foundation

1.The first four terms of a sequence are 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.

2.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).

3.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.

4.y = x + 4. Work out the value of y when x = 3.

5.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).

6.The simple interest, £I, earned on a savings account is given by the formula I = PRT/100, where P is the amount invested in pounds, R is the interest rate per year and T is the time in years. Rearrange the formula to make P the subject.

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

8.a = 2 and b = 5. Work out the value of ab².

9.A cinema sells adult tickets for £10 and child tickets for £6. A family group buys 9 tickets in total, spending £74. Work out how many adult tickets were bought.

10.Factorise x² − 64.

11.Work out the gradient of the straight line with equation 2x + y = 8.

12.Factorise fully 56x − 24

13.Amelia's mother is three times as old as Amelia. Four years ago her mother was five times as old as Amelia was then. Work out Amelia's age now.

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

15.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.