Algebra worksheet — GCSE Foundation

1.p = 4. Work out the value of 2p³.

2.A company's profit is £500 in its first year. Each year after that, the profit is £300 more than the year before. Work out the profit in the company's 6th year.

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

4.Which expression means the same as a × a × a?

5.A plant is 4 cm tall in week 1. Each week after that, its height increases by 5 cm. Work out the first week in which the plant is taller than 30 cm.

6.The equation 3(2x − 1) = 4x + 9 is rearranged by expanding the brackets. Which of these is the correctly expanded equation?

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

8.A hall is set out in rows of chairs for an assembly. Row 1 has 50 chairs, row 2 has 45 chairs, row 3 has 40 chairs, and row 4 has 35 chairs, with each row after the first having 5 fewer chairs than the one before. Work out an expression, in terms of n, for the number of chairs in row n.

9.Which of these numbers is a cube number?

10.Work out the distance of the point (−6, 4) from the x-axis.

11.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

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

13.Work out the equation of the straight line through the points (−3, 4) and (1, −8).

14.Expand 2(x + 12)

15.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).