Algebra worksheet — GCSE Foundation

1.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.

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

3.A straight line has gradient −3 and passes through the point (0, 1). Work out the value of y when x = 2.

4.Work out the value of 5y + 9 when y = 0

5.A square has sides of length y cm. Write down an expression for the perimeter of the square.

6.Which expression is equivalent to 3(2x − 5) + 4x?

7.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.

8.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.

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

10.Make x the subject of the formula y = x + 7.

11.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.

12.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.

13.A sequence has the position-to-term rule: the term is the square of the position number. Its first four terms are 1, 4, 9, 16. Work out the 10th term.

14.Which expression means 'triple c, then add double d'?

15.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.