Algebra worksheet — GCSE Foundation

1.To solve 5x − 4 = 2x + 8, Chloe's working is shown. Line 1: 5x − 4 = 2x + 8. Line 2: 3x − 4 = 8. Line 3: 3x = 4. Line 4: x = 4/3. Chloe has made a mistake in her working. Which line contains the mistake?

2.Write down the number of terms in the expression 4x² − 7x + 3.

3.Sophie's mother is 34 years old. In x years' time she will be 50 years old. Work out the value of x.

4.Solve x/4 + 1 = 3

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

6.Write down the expression that means the same as p + p + p + q.

7.Which of these is a factor of 15x + 20?

8.A car passes the 15 km marker on a road and passes the 195 km marker 3 hours later. Work out the gradient of the distance-time graph, that is the rate of change of distance with time.

9.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.

10.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).

11.n = 3. Work out the value of (2n)².

12.To rearrange the formula y = 3x − 8 to make x the subject, Priya writes: 'Add 8 to both sides to get y + 8 = 3x, then divide both sides by 3 to get x = y + 8 ÷ 3.' Work out the correct expression for x.

13.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

14.The point A lies on the x-axis. Which statement about A must be true?

15.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.