Algebra worksheet — GCSE Foundation

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

2.A point has coordinates (−6, 9). Work out the sum of the x-coordinate and the y-coordinate.

3.To rearrange y = 2x − 5 to make x the subject, Sam writes: 'Add 5 to both sides to get y + 5 = 2x, then divide both sides by 2 to get x = (y + 5)/2.' Which statement about Sam's method is correct?

4.Which of these statements is an identity?

5.Work out the value of 3x² − 4x when x = −2.

6.y = x + 10. Work out the value of y when x = 0.

7.Jack is x years old. His brother Kwame is 3 years older than Jack. Write down an expression for Kwame's age.

8.The diagram shows the graph of a quadratic function. Write down the values of x where the graph crosses the x-axis.

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

10.Simplify 5a/6 − a/3

11.Water is poured into a container at a constant rate. A graph of the depth of the water, in cm, against the time since pouring began, in minutes, is a straight line through the origin, and it passes through the point (3, 12). Use the graph to work out the depth of the water after 7 minutes.

12.Ethan is 10 years old and his father is 40 years old. Work out how many years ago Ethan's father was seven times as old as Ethan.

13.Priya has a budget of £50 for a school trip. The coach costs £14 and each student ticket costs £4. Using the inequality 14 + 4s ≤ 50, work out the greatest number of student tickets, s, she can buy.

14.a = 2 and b = 5. Work out the value of a²b.

15.Expand and simplify 2(a + 6) − 2(a − 7)