Algebra worksheet — GCSE Foundation

1.Which of these is an expression?

2.The formula for the circumference of a circle is C = 2πr, where r is the radius. Make r the subject of the formula.

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

4.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.

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

6.A cinema sells adult tickets and child tickets. On one evening, 40 tickets are sold in total. There are 8 more adult tickets sold than child tickets. Work out the number of child tickets sold.

7.Which of these numbers is a cube number?

8.A rectangle has width x cm. Its length is 3 cm more than its width. The perimeter of the rectangle is 38 cm. Form an equation and solve it to find x.

9.Solve the inequality 2(x − 1) ≤ 8.

10.Solve 3(2x − 1) = 27

11.A phone company works out a monthly bill, £B, using the formula B = 18 + 0.05t, where £18 is the fixed monthly charge and t is the number of extra text messages sent beyond the free allowance, each charged at 5p. Farida's bill for one month is £24.50. Work out the number of extra text messages, t, she sent.

12.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?

13.A rectangle has length k cm and width 5 cm less than its length. Write down an expression for the width of the rectangle, in cm.

14.Solve 3x − 1 = 8

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