Algebra worksheet — GCSE Foundation

1.A rectangle has length (2x + 5) cm and width (x − 2) cm. Work out an expression, in terms of x, for the perimeter of the rectangle. Give your answer in its simplest form.

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

3.A regular hexagon has sides of length (x + 2) cm. Write down an expression, in terms of x, for the perimeter of the hexagon.

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

5.An arithmetic sequence has first term 40 and common difference −6. Work out the 9th term of the sequence.

6.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.

7.Make x the subject of the formula y = 2x − 9.

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

9.Work out the coordinates of the reflection of (6, −3) in the y-axis.

10.The formula for the volume of a cuboid is V = lwh, where l is the length, w is the width and h is the height. Make h the subject of the formula.

11.Kai writes the expression 8 − 3x + 5x² and says it has three terms. Ryan says it only has two terms because a number on its own is not a term. Work out the correct number of terms in the expression.

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

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

14.Two numbers have a sum of 24. Their difference is 6. Work out the two numbers.

15.Solve the simultaneous equations 5x − 2y = 16 and 3x + 2y = 16. Work out the value of x.