Algebra worksheet — GCSE Foundation

1.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.

2.Write down the gradient of the line with equation y = 6 + 4x.

3.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.

4.The diagram shows a straight line passing through the origin, drawn on a numbered grid. Which of these points lies on the line?

5.A cycle route is 84 km long. Freya sets off along it at a steady 14 km/h. Write down the function for the distance y, in kilometres, that is still to be cycled after x hours.

6.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.

7.There are 50 adults on a coach to the Lake District. Every adult is either a man or a woman. There are 10 more men than women. Work out the number of men.

9.The formula for the volume of a cuboid is V = lwh, where l is the length, w is the width and h is the height. Make h the subject of the formula.

10.Work out the value of 5a + 2 when a = 3

11.Solve 3(2x − 1) = 27

12.A straight line has equation y = 4x + 3. A second line is parallel to the first line and passes through the point (0, −5). Work out the equation of the second line.

13.The point A is at (5, −3). In which quadrant does A lie?

14.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.

15.A ramp rises 3 m over a horizontal distance of 12 m. Work out the gradient of the ramp.