Algebra worksheet — GCSE Foundation

1.Which expression is equivalent to 6x − (2x − 5)?

2.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.

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

4.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

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

6.The perimeter, P, of a rectangle with length l and width w is calculated using P = 2l + 2w. What kind of mathematical statement is P = 2l + 2w?

7.Work out the equation of the straight line that passes through (−2, 3) and (4, −9).

8.A plant is 4 cm tall in week 1. Each week after that, its height increases by 5 cm. Work out the first week in which the plant is taller than 30 cm.

9.A box contains 6 chocolates. Write down an expression for the total number of chocolates in c boxes.

10.The formula connecting speed, distance and time is v = s ÷ t. Work out v, in km/h, when s = 180 and t = 4.

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

12.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?

13.Solve the simultaneous equations 4x + 3y = 25 and 4x − y = 1. Work out the value of y.

14.The cost, in pounds, of hiring a van for d days is given by the formula C = 25 + 18d. A customer's hire cost £133. Work out how many days, d, they hired the van for, by first rearranging the formula to make d the subject.

15.A pizza shop charges a fixed delivery fee of £3, plus £9 for each pizza ordered. Write down the function for the total cost y, in pounds, of ordering x pizzas.