Algebra worksheet — GCSE Foundation

1.Which of these rules generates the sequence 6, 11, 16, 21, …?

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

3.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.

4.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

5.Expand and simplify 2(a + 6) − 2(a − 7)

6.For the equation 2x + 3 = 11, and the inequality 2x + 3 > 11, which statement correctly compares their solutions?

7.The solution to an inequality is n ≤ 5. Write down the largest integer value of n that satisfies this inequality.

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

9.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.

10.A ramp rises 3 m over a horizontal distance of 12 m. Work out the gradient of the ramp.

11.A number, w, satisfies the statement "three times w, minus 5, is at least 16". Which of these is the correct inequality for w?

12.Oliver has m stickers and gives 5 of them away. The number he has left is L = m − 5. Work out L when m = 8.

13.Work out the gradient of the straight line with equation 2x + y = 8.

14.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?

15.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?