Algebra worksheet — GCSE Foundation

1.A rectangular photo has length (x + 3) cm and width x cm. Its area is 40 cm². Work out the value of x.

2.A straight line has equation y = 5x. Work out the value of y when x = 3.

3.Line C passes through (0, 0) and (4, 2). Line D passes through (0, 0) and (2, 2). Write down which of the two lines is the steeper.

4.Solve 2x² − 32 = 0.

5.Which of these values of x is a solution of x² + 2x − 15 = 0?

6.Oliver has m stickers and gives 5 of them away. The number he has left is L = m − 5. Work out L when m = 8.

7.The nth term of a sequence is n² + 3. Work out the first term of the sequence that is greater than 50.

8.Look at the statement 2x + 5 = 17. Considering whether it is an expression, an equation, a formula, or an identity, which classification is correct?

9.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.

10.Water is poured into a container at a constant rate. A graph of the depth of the water, in cm, against the time since pouring began, in minutes, is a straight line through the origin, and it passes through the point (3, 12). Use the graph to work out the depth of the water after 7 minutes.

11.On a map, where each grid unit represents 1 km, Ravi's house is at (−3, 4) and the library is at (6, 4). Work out the distance between Ravi's house and the library.

12.Solve x² + 7x = 0.

13.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.

14.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.

15.Make x the subject of the formula y = x/2 − 5.