Algebra worksheet — GCSE Foundation

1.A quadratic graph has equation y = (x − 4)². A student says this graph crosses the x-axis at two different points. Explain why the student is wrong.

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

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

4.y = x + 10. Work out the value of y when x = 0.

5.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.

6.Priya buys b balloons for a party. Each balloon costs 15p. Write down an expression for the total cost, in pence.

7.Point R has coordinates (3, −5). Point R is reflected in the line y = 2 to point S. Write down the coordinates of S.

8.Grace says that 2(x + 1) and 2x + 2 always have the same value. Work out the value of both expressions when x = 3.

9.A number machine adds 6 to its input. Work out the output when the input is −4.

10.Make x the subject of the formula y = 4x − 3.

11.A gym charges a reduced price for the first month of membership and a standard price for every month after that. The total cost is £5 for 1 month, £12 for 2 months, £19 for 3 months and £26 for 4 months. Work out an expression, in terms of n, for the total cost, in pounds, of n months of membership.

12.Which expression means 'add 3 to n, then multiply the result by 4'?

13.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?

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

15.The graph of W = 840 ÷ L shows how the width, W metres, of a rectangular field of area 840 m² depends on its length, L metres. Use the relationship to work out the width when the length is 35 m, and hence the perimeter of the field.