Algebra worksheet — GCSE Foundation

1.The diagram shows the graph of a quadratic function. Which equation could it represent?

2.A lift has a weight limit: it must carry no more than 630 kg. Let w be the total weight, in kg, carried by the lift. Which inequality describes this?

3.A cinema sells adult tickets for £10 and child tickets for £6. A family group buys 9 tickets in total, spending £74. Work out how many adult tickets were bought.

4.A rectangle has length (2x + 5) cm and width (x − 2) cm. Work out an expression, in terms of x, for the perimeter of the rectangle. Give your answer in its simplest form.

5.The formula for the volume of a cuboid is V = lwh, where l is the length, w is the width and h is the height. Make h the subject of the formula.

6.A rectangular garden has width w metres and length (w + 3) metres. A gardener writes its perimeter as 2w + 3. Which statement corrects the gardener's mistake?

7.Amelia is buying books. Each book costs £5 and she has at most £30 to spend. Write down an inequality for x, the number of books she can buy.

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

9.Expand 2(x + 12)

10.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

11.Work out the gradient of the straight line with equation y = (2x/5) − 3.

12.A vertical line passes through the point (4, 7). Write down the equation of this line.

13.The simple interest, £I, earned on a savings account is given by the formula I = PRT/100, where P is the amount invested in pounds, R is the interest rate per year and T is the time in years. Rearrange the formula to make P the subject.

14.A sequence has the position-to-term rule 5n − 2, where n is the position number. Which of these is a term in the sequence?

15.The graph of y = x² − 2x − 8 takes these values: when x = −2, y = 0; when x = −1, y = −5; when x = 0, y = −8; when x = 3, y = −5; when x = 4, y = 0. Use these values to write down the two solutions of x² − 2x − 8 = 0.