Algebra worksheet — GCSE Foundation

1.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.

2.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.

3.A square has vertices at (−2, 3), (−2, −3) and (4, −3). Write down the coordinates of the fourth vertex.

4.Simplify p + p + p.

5.a = 2 and b = 5. Work out the value of a²b.

6.Two numbers have a sum of 45. The larger number is 9 more than the smaller number. Form an equation using n for the smaller number, and solve it to find the larger number.

7.A number machine adds 6 to its input. Work out the output when the input is −4.

8.Jack is x years old. His brother Kwame is 3 years older than Jack. Write down an expression for Kwame's age.

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

10.y = 3x − 2. Work out the value of y when x = 4.

11.A statement contains an equals sign and one unknown letter, and it is only true for particular value(s) of that letter. What is this type of statement called?

12.A gym charges a joining fee plus a monthly fee. Anna paid £100 in total after 3 months of membership. Ben paid £160 in total after 6 months of membership (same joining fee and monthly fee as Anna). Work out the monthly fee.

13.Solve 4x² − 9 = 0.

14.A quadratic curve has a root at x = −2 and its turning point has x-coordinate 3. Work out the curve's other root, using the symmetry of the graph.

15.The first four terms of a sequence are 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.