Algebra worksheet — GCSE Foundation

1.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).

2.Solve x² − x − 12 = 0.

3.Solve 2x − 2 = 2

4.A quadratic curve has a minimum turning point at (3, −4). Which of these statements about the curve must be true?

5.Write down the expression that means the same as (x + 7) ÷ 4.

6.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

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

8.A pattern is made from tiles. Pattern 1 uses 4 tiles, pattern 2 uses 7 tiles, pattern 3 uses 10 tiles and pattern 4 uses 13 tiles, with each pattern using 3 more tiles than the one before. Work out an expression, in terms of n, for the number of tiles used in pattern n.

9.Work out the value of 2x² when x = −3

10.Which of these is an inequality?

11.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.

12.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.

13.Make p the subject of the formula n = p/3.

14.Which of these statements is an identity?

15.Which expression means 'add 3 to n, then multiply the result by 4'?