Algebra worksheet — GCSE Foundation

1.Solve the inequality 3x − 1 ≤ 11.

2.Factorise fully 5x + 5y − 5

3.Make x the subject of the formula y = x + 7.

4.n = 3. Work out the value of (2n)².

5.A speed-time graph for a car shows the speed increasing steadily from 5 m/s to 17 m/s over 6 seconds. Work out the acceleration of the car, in m/s².

6.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.

7.Point P has coordinates (5, 2). Point P is rotated 180° about the origin to point Q. Write down the coordinates of Q.

8.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.

9.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.

10.An equation has exactly one value of x that makes it true, but an identity is true for every value of x. Which of these best explains why 3x + 5 = 20 is an equation rather than an identity?

11.A conversion graph shows that 5 miles is equivalent to 8 kilometres. Use this to work out how many kilometres are equivalent to 20 miles.

12.In which quadrant does the point (−3, 0.5) lie?

13.Solve (3x + 2)/5 = (x + 4)/3

14.A pattern is made from tiles. Pattern 1 has 7 tiles, pattern 2 has 11 tiles, pattern 3 has 15 tiles, and pattern 4 has 19 tiles, with each new pattern having 4 more tiles than the one before it. Work out an expression, in terms of n, for the number of tiles in pattern n.

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