Algebra worksheet — GCSE Foundation

1.Grace has t books. Noah has 1 book fewer than Grace. Write down an expression for the number of books Noah has.

2.Which of these is a formula?

3.Which of these equations describes a vertical line?

4.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.

5.The graph of y = x² + 2x − 15 crosses the x-axis at two points. By factorising, work out the x-coordinates of these two points.

6.The first four terms of a sequence are 4, 6, 8, 10. Work out an expression, in terms of n, for the nth term.

7.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

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

9.Expand 7(a + 8)

10.A distance-time graph shows a car travelling at a constant speed, covering 90 km in 2 hours. Work out the car's speed in km/h.

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

12.How many turning points does the graph of y = x² − 7x + 10 have?

13.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.

14.In a shop a shirt costs £x and a pair of trousers costs £(2x + 30). Together the two items cost at least £150. Work out the lowest possible price of the shirt.

15.A sequence has the position-to-term rule: the term is the position number multiplied by itself. Its first five terms are 1, 4, 9, 16, 25. Work out the 8th term.