Algebra worksheet — GCSE Foundation

1.Expand 2(x + 12)

2.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.

3.A rectangle is x cm wide and twice as long as it is wide, so its area A cm² is given by A = 2x². Work out A when x = 3.

4.Work out the value of 2(x + 2) when x = −5

5.Simplify k + k + k + k + k.

6.A currency conversion graph shows that £4 is equivalent to 5 US dollars. Use this to work out how many US dollars are equivalent to £24.

7.A ribbon of length L metres is cut into 5 equal pieces, and then 3 metres is removed from one piece. Write down an expression, in metres, for the length of that piece after 3 metres is removed.

8.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

9.The formula for the profit, £P, made on an item is P = S − C, where S is the selling price and C is the cost price. Make S the subject of the formula.

10.The graph of y = 24/x is drawn for x > 0. Work out the value of y when x = 6.

11.Write down the y-intercept of the line with equation y = 3x + 8.

12.A printer starts a job with 480 sheets of paper loaded and prints at a steady rate. The number of sheets left, S, after t minutes is given by S = 480 − 24t. Work out how many minutes it takes for the paper to run out completely.

13.x = 5. Work out the value of 3x² − 4.

14.Explain why the equation 4x + 3 = 4x + 10 has no solution for x.

15.Write down the coefficient of p in the expression 7 − 4p + 9q.