Algebra worksheet — GCSE Foundation

1.Write down the expression that means the same as m × m × m × n.

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

3.Which expression means 'triple c, then add double d'?

4.The volume of a cuboid is given by the formula V = lwh. Work out V, in cm³, when l = 2, w = 3 and h = 6.

5.The graph of t = 240 ÷ s shows how the time, t hours, taken for a car journey of 240 miles depends on its average speed, s mph. Use the relationship to work out the time taken when the average speed is 48 mph.

6.A point has coordinates (x, y). In which two quadrants is the product x × y positive?

7.The point D has coordinates (3, −8). Write down the distance of D from the y-axis.

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

9.Simplify p + p + p.

10.A gardener charges a fixed fee of £15 plus £8 for each hour worked. The total charge, £T, for a job lasting h hours is given by T = 15 + 8h. Work out the charge for a job lasting 4 hours, and identify what kind of statement T = 15 + 8h is.

11.A ball is thrown in the air. Its height, h metres, above the ground after t seconds is given in this table: when t = 0, h = 0; when t = 1, h = 15; when t = 2, h = 20; when t = 3, h = 15; when t = 4, h = 0. Use the table to find the two times, in seconds, at which the ball is at ground level.

12.A taxi charges a £3 fixed fee plus £2 for each mile travelled. Write an expression, in pounds, for the total cost of a journey of n miles.

13.Work out the gradient of the straight line with equation 3y = 12 − 6x.

14.Which of these values of x is a solution of x² + 2x − 15 = 0?

15.The formula connecting speed, distance and time is v = s ÷ t. Work out v, in km/h, when s = 180 and t = 4.