Algebra worksheet — GCSE Foundation

1.Write down the gradient of the line with equation y = −x + 3.

2.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.

3.A sequence begins at 7. Each term after the first is found by adding 6 to the term before it. Work out the 6th term of the sequence.

4.The formula for the perimeter of a rectangle is P = 2(l + w). One rectangle has l = 9 cm and w = 4 cm. A second rectangle has l = 6 cm and w = 5 cm. Work out how many cm greater the perimeter of the first rectangle is than the perimeter of the second.

5.Which expression means 'triple c, then add double d'?

6.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?

7.A sequence starts at 2. Each term after that is found using the rule "double the previous term, then add 1". Work out the 4th term of the sequence.

8.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.

9.The solution set of an inequality is x ≥ 7. Write down the value that does NOT satisfy this inequality.

10.Solve the inequality 5 − x ≤ 2.

11.Yuki is y years old. Her brother is 4 years younger than Yuki. Write down an expression, in terms of y, for the brother's age in 5 years' time.

12.Six years ago Harry was three times as old as his brother Leo. Harry is now 24 years old. Work out Leo's age now.

13.The graph of P = 480 ÷ V shows how the pressure, P pascals, of a gas depends on its volume, V cm³, at constant temperature. Use the relationship to work out the volume when the pressure is 32 pascals, and then work out by how much the volume increases when the pressure drops to 24 pascals.

14.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.

15.The point A lies on the x-axis. Which statement about A must be true?