Algebra worksheet — GCSE Foundation

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

2.A park is drawn on a grid in which 1 unit represents 1 km. The car park is at the point (0, 0) and the lake is at the point (3, 5). Work out the direct distance, in km, from the car park to the lake, giving your answer to 1 decimal place.

3.Which expression is equivalent to 4(x − 2) + 10?

4.Solve x² − 6x = 0.

5.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.

6.Look at the statement 2x + 5 = 17. Considering whether it is an expression, an equation, a formula, or an identity, which classification is correct?

7.Leo is three times as old as his brother. His brother is x years old. Write down an expression for Leo's age.

8.A rule turns each input x into an output y. The inputs are x = 0, 1, 2, 3 and the outputs are y = 4, 7, 10, 13. Work out the output when x = 5.

9.Which of these equations is equivalent to 5x − 2 = 3x + 8?

10.In the expression 5x² − 3x + 7, which of these is a single term of the expression?

11.The nth term of a sequence is 3n + 2. Work out the 4th term of the sequence.

12.Solve x² = 49.

13.A straight line has equation y = 2x − 7. Write down the coordinates of the point where the line crosses the y-axis.

14.An arithmetic sequence has first term 40 and common difference −6. Work out the 9th term of the sequence.

15.A straight line passes through the points (2, 5) and (4, 11). Work out the gradient of the line.