Algebra worksheet — GCSE Foundation

1.A square tile has an area of 144 cm². Work out the side length of the tile.

2.A cinema sells adult tickets and child tickets. On one evening, 40 tickets are sold in total. There are 8 more adult tickets sold than child tickets. Work out the number of child tickets sold.

3.In which quadrant does the point (−3, 0.5) lie?

4.Work out the value of 5a + 2 when a = 3

5.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.

6.A taxi fare, in pounds, for a journey of m miles is given by the formula F = 3 + 2.5m. A journey costs £15.50. Work out the distance travelled, m, by first rearranging the formula to make m the subject, then substituting F = 15.50.

7.The point A lies on the x-axis. Which statement about A must be true?

8.A point lies on the y-axis. What can be said about the x-coordinate of that point?

9.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.

10.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.

11.A charity's fundraising total, T pounds, over d days follows T = (d − 3)(30 − d) for 3 ≤ d ≤ 30, where T = 0 marks the start and end of the campaign. Work out how many days the campaign runs for, from start to end.

12.Write down the expression that means the same as 3 × y × y.

13.A ferry's distance-time graph is a straight line from (0 minutes, 0 km) to (25 minutes, 15 km). Work out the ferry's speed in kilometres per hour.

14.n = 3. Work out the value of (2n)².

15.A straight line passes through the points (0, 4) and (1, 9). Write down the gradient of the line.