Algebra worksheet — GCSE Foundation

1.A square tile has an area of 144 cm². Work out the side length of the tile.

2.Solve the simultaneous equations x + y = 15 and x − y = 3. Work out the value of x.

3.A number machine adds 1 to its input. Isla says that an input of 5 gives an output of 6. Which statement is correct?

4.A table shows y = x² − 6x + 5 at these points (x, y): (0, 5), (1, 0), (2, −3), (3, −4), (4, −3), (5, 0), (6, 5). Using the symmetry shown, write down the x-coordinate of the turning point.

5.For the graph of y = 1/x, where x cannot be zero, which of these statements is correct?

6.Write down the expression that means the same as p + p + p + q.

7.y = 5x − 1. Work out the value of y when x = 3.

8.Expand 4(2x − 3).

9.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?

10.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.

11.Which expression is equivalent to 6x − (2x − 5)?

12.A sequence has the position-to-term rule n² − 3, where n is the position number. Work out the difference between the 6th term and the 5th term.

13.The area of a circle is given by the formula A = πr², where r is the radius. Rearrange the formula to make r the subject.

14.The point C is 6 units to the right of the origin and 0 units up. Write down the coordinates of C.

15.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.