Algebra worksheet — GCSE Higher

1.Work out the value of (x − 4)/2 + 3 when x = 10

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

3.Six years ago Harry was three times as old as his brother Leo. Harry is now 24 years old. Work out Leo's age now.

4.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x

5.Factorise fully 56x − 24

6.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

7.Line L has equation y = 3x − 2. Work out the gradient of a line perpendicular to L.

8.A taxi fare in pounds is given by F = 2.50 + 1.20m, where m is the number of miles travelled. Sam takes a taxi for a journey of 6 miles. Work out the fare.

9.A rule turns each input x into an output y. The inputs are x = 1, 2, 3, 4 and the matching outputs are y = −5, −3, −1 and one missing value. Work out the missing value of y.

10.A rectangle is x cm wide and twice as long as it is wide, so its area A cm² is given by A = 2x². Work out A when x = 3.

11.A tank already contains some water and is then filled at a constant rate. After 2 minutes it contains 50 litres in total; after 7 minutes it contains 150 litres in total. Work out the rate at which water is added, in litres per minute.

12.A straight line passes through the points (2, 5) and (4, 11). Work out the gradient of the line.

13.Work out the value of a² − 2b when a = −3 and b = 4.

14.Work out the gradient of the straight line with equation y = (2x/5) − 3.

15.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).