Algebra worksheet — GCSE Foundation

1.A table shows y = x² − 6x + 5 at these points (x, y): (0, 5), (1, 0), (2, −3), (3, −4), (4, −3), (5, 0), (6, 5). Using the symmetry shown, write down the x-coordinate of the turning point.

2.A line segment has one endpoint at (−6, 2) and its midpoint at (−1, 5). Work out the coordinates of the other endpoint.

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

4.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

5.Simplify k + k + k + k + k.

6.A cafe sells coffees at £c each and pastries at £p each. Three coffees and two pastries cost £9.60. Two coffees and two pastries cost £7.60. Work out the price of one coffee.

7.Given that (x + 2)(x − 7) = 0, write down the two solutions of x.

8.Noah says that y = 3 is the solution of the equation y + 10 = 12. Noah is wrong. Work out the correct value of y.

9.Work out the equation of the straight line through the points (−3, 4) and (1, −8).

10.Which of these equations describes a vertical line?

11.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.

12.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.

13.Solve the simultaneous equations x + y = 1 and 2x + y = 5.

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

15.A vertical line passes through the point (4, 7). Write down the equation of this line.