Algebra worksheet — GCSE Foundation

1.Expand 2(x + 12)

2.The mean of four numbers is 12.5. Three of the numbers are 8, 15 and 19. Form an equation using n for the fourth number, and solve it to find n.

3.Which of these is an identity?

4.Solve (3x + 2)/5 = (x + 4)/3

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

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

7.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.

8.A straight line has gradient 3 and passes through the point (1, 4). Work out the equation of the line.

9.a = 3 and b = 5. Work out the value of a²b.

10.Solve x² − 5x + 6 = 0 by factorising.

11.A fundraising chain letter starts with 3 people taking part in round 1. Each following round has 4 times as many people taking part as the round before. Work out the number of people taking part in round 4.

12.The simple interest, £I, earned on a savings account is given by the formula I = PRT/100, where P is the amount invested in pounds, R is the interest rate per year and T is the time in years. Rearrange the formula to make P the subject.

13.A company's profit is £500 in its first year. Each year after that, the profit is £300 more than the year before. Work out the profit in the company's 6th year.

14.Solve 2x + 7 = x + 13

15.Solve 5x + 2 = 17.