Algebra worksheet — GCSE Foundation

1.A cycle route is 84 km long. Freya sets off along it at a steady 14 km/h. Write down the function for the distance y, in kilometres, that is still to be cycled after x hours.

2.Solve the inequality 2(x − 1) ≤ 8.

3.ABCD is a parallelogram. A has coordinates (−3, 1), B has coordinates (2, 1) and C has coordinates (4, 4). Work out the coordinates of D.

4.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.

5.Solve x² − 5x + 6 = 0 by factorising.

6.Which of these is a term, rather than a whole expression, an equation, or a formula?

7.A conversion graph shows that 5 miles is equivalent to 8 kilometres. Use this to work out how many kilometres are equivalent to 20 miles.

8.Amelia's mother is three times as old as Amelia. Four years ago her mother was five times as old as Amelia was then. Work out Amelia's age now.

9.A model rocket's height is given by h = −5t² + 20t, where h is in metres and t is in seconds. A student says the graph of h against t is n-shaped. Which statement gives the correct verdict on the SHAPE and the reason that settles it from the equation?

10.x = 5. Work out the value of 3x² − 4.

11.The perimeter, P, of a rectangle with length l and width w is calculated using P = 2l + 2w. What kind of mathematical statement is P = 2l + 2w?

12.Write down the first four terms of the sequence with nth term 6n − 5.

13.Which of these quadratic graphs does NOT cross the x-axis at all?

14.In a sequence, each term is half the term before it. The sequence begins 100, 50, 25. Write down the next term.

15.Work out the value of 3a − 2b when a = 5 and b = 4