Algebra worksheet — GCSE Foundation

1.A number machine multiplies its input by 5. Work out the output when the input is −1.

2.Noah says that y = 3 is the solution of the equation y + 10 = 12. Noah is wrong. Work out the correct value of y.

3.Solve x² = 81.

4.The formula for converting a distance in miles, m, to kilometres, k, is k = 8m ÷ 5. Work out k when m = 10.

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

6.The point C is 6 units to the right of the origin and 0 units up. Write down the coordinates of C.

7.Which of these values of x is a solution of x² + 2x − 15 = 0?

8.Work out the value of 3x² − 4x when x = −2.

9.A Fibonacci-type sequence begins 3, 5, 8, 13, ... where each term after the second is the sum of the two terms before it. Work out the 7th term of the sequence.

10.Yusuf has £40 saved and adds £6 each week. His sister Aisha has £10 saved and adds £11 each week. After how many weeks will they have saved the same amount?

11.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.

12.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.

13.Factorise fully 5x + 5y − 5

14.A straight line has equation 4y = 12x + 20. Work out the gradient of the line.

15.Write down the expression that means 5 more than half of n.