Algebra worksheet — GCSE Foundation

1.Which of these is an equation, rather than an expression, a formula or an identity?

2.Make x the subject of the formula y = 4x − 3.

3.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.

4.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.

5.Which of these numbers is a cube number?

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

7.The diagram shows the graph of a straight line, drawn on a grid numbered from −5 to 5 on both axes. Which equation could represent the line?

8.The mean of four numbers is 12.5. Three of the numbers are 8, 15 and 19. Form an equation using n for the fourth number, and solve it to find n.

9.A formula is F = 4s. A pupil says that when s = 5 the value of F is 9, because they added 4 and 5 instead of multiplying. Work out the correct value of F when s = 5.

10.The point (−4, 7) is moved 4 units to the right and 9 units down. Write down the coordinates of the point it reaches.

11.Solve the simultaneous equations x + y = 1 and 2x + y = 5.

12.a = 2 and b = 5. Work out the value of ab².

13.Solve 5x − 9 = 16

14.Rosie is asked whether 4(x + 3) = 4x + 12 is an equation or an identity. Which statement is correct? Give a reason for your answer.

15.A table shows values of y = x² − x − 6 for x from −3 to 4: at x = −3, y = 6; x = −2, y = 0; x = −1, y = −4; x = 0, y = −6; x = 1, y = −6; x = 2, y = −4; x = 3, y = 0; x = 4, y = 6. Using the table, write down the two roots of x² − x − 6 = 0.