Algebra worksheet — GCSE Foundation

1.Solve x² = 49.

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

3.A number machine multiplies its input by 3. The output is 15. Work out the input.

4.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.

5.Solve the simultaneous equations 3x + 2y = 16 and x + y = 7. Work out the value of y.

6.A straight line has equation y = 5x. Work out the value of y when x = 3.

7.The first five terms of a sequence are 6, 10, 14, 18, 22. Work out an expression, in terms of n, for the nth term.

8.Look at the statement 2x + 5 = 17. Considering whether it is an expression, an equation, a formula, or an identity, which classification is correct?

9.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).

10.A phone plan costs a fixed £15 per month plus 8p per minute of calls. In one month, Jamal's bill was £23.80. Form an equation using m for the number of minutes, and solve it to find how many minutes Jamal used that month.

11.A taxi charges a fixed fee of £3 plus £2 for every mile travelled. The journey is m miles. Write down an expression for the total cost, in pounds.

12.A box contains 6 chocolates. Write down an expression for the total number of chocolates in c boxes.

13.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.

14.Which expression is equivalent to 0.5(4x + 6) − x?

15.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.