Algebra worksheet — GCSE Foundation

1.A square has vertices at (−2, 3), (−2, −3) and (4, −3). Write down the coordinates of the fourth vertex.

2.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?

3.Aisha saves money each week. In week 1 she has saved £15 in total, in week 2 she has saved £23 in total, in week 3 she has saved £31 in total and in week 4 she has saved £39 in total, with the total increasing by the same amount each week. Work out an expression, in terms of n, for the total amount she has saved, in pounds, after week n.

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

5.p = 4. Work out the value of 2p³.

6.A square has sides of length y cm. Write down an expression for the perimeter of the square.

7.Solve 2(x + 3) = 10

8.Which of these statements is an identity?

9.Write down the number of terms in the expression 4x² − 7x + 3.

10.Solve x² + 3x − 10 = 0.

11.Solve the inequality x − 10 < −3.

12.Work out the value of 2(x + 2) when x = −5

13.A water butt holds 200 litres and is being drained at a steady 8 litres per minute. Write down the function for the amount of water y, in litres, left after x minutes.

14.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

15.Which expression is equivalent to 5x − (x + 3)?