Algebra worksheet — GCSE Foundation

1.A graph has equation y = 3x + 2. Which word or phrase best describes its shape?

2.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.

3.Which of these equations is equivalent to 5x − 2 = 3x + 8?

4.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

5.Solve 5(x + 3) = 40

6.A candle is 30 cm tall and burns down at a steady rate of 1 cm per hour. Write down the function for the height of the candle y, in centimetres, after x hours.

7.Which expression is equivalent to 4(x − 2) + 10?

8.A colony of bacteria doubles in number every hour. At 9am there are 5 bacteria in the colony. Work out how many bacteria there will be at 12 noon.

9.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.

10.The formula for the circumference of a circle is C = 2πr, where r is the radius. Make r the subject of the formula.

11.Solve 2(x + 3) = 10

12.A graph has equation y = −2x² + 5. Which statement about its shape is correct?

13.A ramp rises 3 m over a horizontal distance of 12 m. Work out the gradient of the ramp.

14.Which of these equations is true for every value of x, making it an identity rather than an equation with just one solution?

15.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.