Algebra worksheet — GCSE Foundation

1.Tom is asked to classify the statement 5(2x − 3) = 10x − 15. Which statement about it is correct?

2.A sequence has the position-to-term rule 5n − 2, where n is the position number. Which of these is a term in the sequence?

3.A car's speed-time graph shows the following: its speed increases steadily from 0 m/s to 20 m/s over the first 10 seconds, then stays constant at 20 m/s for the next 15 seconds. Work out the total distance travelled in the first 25 seconds.

4.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.

5.Simplify 2b − 1 + 2b − 4 + 2b

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

7.Expand 4(2x − 3).

8.The solution set of x ≥ −1 is drawn on a number line. Which description of that number line is correct?

9.A recipe gives the cooking time, in minutes, for a chicken as T = 40m + 20, where m is the mass in kg. A chicken has a mass of 1.8 kg. Work out the cooking time in hours and minutes.

10.A currency conversion graph shows that £4 is equivalent to 5 US dollars. Use this to work out how many US dollars are equivalent to £24.

11.A gym charges a reduced price for the first month of membership and a standard price for every month after that. The total cost is £5 for 1 month, £12 for 2 months, £19 for 3 months and £26 for 4 months. Work out an expression, in terms of n, for the total cost, in pounds, of n months of membership.

12.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?

13.The formula y = x² + 1 gives y in terms of x. Work out the value of y when x = −2.

14.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x

15.A geometric sequence has first term 5, and each term after that is 3 times the term before it. Work out the first term of the sequence that is greater than 1000.