Algebra worksheet — GCSE Foundation

1.Work out the value of 3n − 2 when n = 1

2.Which expression is equivalent to 6x − (2x − 5)?

3.A caterer uses the formula C = 6p + 20 to work out the total cost, £C, of a buffet for p people, where £20 covers fixed costs. A customer is charged £92. Work out how many people, p, the buffet was for.

4.The graph of a straight line has equation y = 4x − 5. Beth says the y-intercept is 4. Work out the correct y-intercept.

5.Work out the value of a² − 2b when a = −3 and b = 4.

6.A geometric sequence starts at 3, and each term after that is found by multiplying the term before it by 2. Write down the first four terms.

7.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.

8.Grace says that 2(x + 1) and 2x + 2 always have the same value. Work out the value of both expressions when x = 3.

9.A runner's journey is shown on a distance-time graph: she runs 8 km in the first hour, rests for 30 minutes with no distance gained, then runs a further 4 km in the next 30 minutes. Work out her average speed for the whole journey, in kilometres per hour.

10.A rule turns each input x into an output y. The inputs are x = −1, 0, 1, 2 and the matching outputs are y = 5, 3, 1, −1. Work out the rule.

11.Which of these statements is an identity?

12.Expand 2(x + 12)

13.A statement contains an equals sign and one unknown letter, and it is only true for particular value(s) of that letter. What is this type of statement called?

14.Expand 4(2x − 3).

15.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?