Algebra worksheet — GCSE Foundation

1.The point (−4, 7) is moved 4 units to the right and 9 units down. Write down the coordinates of the point it reaches.

2.Matchsticks are laid out as a row of squares, with each new square sharing a side with the square before it. The first square uses 4 matchsticks and every extra square uses 3 more. Work out how many matchsticks a row of 4 squares uses.

3.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.

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

5.The diagram shows the graph of a quadratic function. Write down the values of x where the graph crosses the x-axis.

6.A line segment has one endpoint at (−6, 2) and its midpoint at (−1, 5). Work out the coordinates of the other endpoint.

7.Which expression is equivalent to 7x − 3(2x − 6)?

8.A rectangle has width x cm. Its length is 3 cm more than its width. The perimeter of the rectangle is 38 cm. Form an equation and solve it to find x.

9.A triangle has vertices at (1, 1), (1, 5) and (6, 1). Work out the area of the triangle.

10.A taxi fare, in pounds, for a journey of m miles is given by the formula F = 3 + 2.5m. A journey costs £15.50. Work out the distance travelled, m, by first rearranging the formula to make m the subject, then substituting F = 15.50.

11.Expand 2(x − 13)

12.A straight line passes through the points (0, 4) and (1, 9). Write down the gradient of the line.

13.Solve 5x + 2 = 17.

14.The formula for the perimeter of a rectangle is P = 2(l + w). One rectangle has l = 9 cm and w = 4 cm. A second rectangle has l = 6 cm and w = 5 cm. Work out how many cm greater the perimeter of the first rectangle is than the perimeter of the second.

15.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.