Algebra worksheet — GCSE Higher

1.Matchsticks are laid out as a row of squares, with each new square sharing a side with the square before it. The first square uses 4 matchsticks and every extra square uses 3 more. Work out how many matchsticks a row of 4 squares uses.

2.A rule turns each input x into an output y. An input of 1 gives an output of 1, an input of 2 gives an output of 4 and an input of 3 gives an output of 9. Work out the rule.

3.A plumber charges a £35 call-out fee plus £20 for each hour worked, h. On a certain job the total charge was £115. Work out how many hours the plumber worked.

4.Solve 4(x − 3) = 2x + 6.

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

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

7.On a distance-time graph, a horizontal line segment shows a period when the graph's gradient is 0. What does this tell you about the journey during that time?

8.A theatre's front row has 18 seats. Each row behind has 4 more seats than the row in front. Which row has exactly 62 seats?

9.The graph of y = f(x) passes through the point (0, 4). Work out the y-coordinate of the point where the graph of y = f(x) − 6 crosses the y-axis.

10.Solve 2(x + 3) = 10

11.Solve the inequality 3x − 1 ≤ 11.

12.A triangle has vertices at (1, 1), (1, 5) and (6, 1). Work out the area of the triangle.

13.The diagram shows the graph of a quadratic function. Which equation could it represent?

14.The tangent to a curve at the point (5, 2) is the line y = mx + c. This tangent crosses the y-axis at (0, −8). Work out the gradient, m, of the tangent.

15.The equation x² − 6x + k = 0 has exactly one solution. Work out the value of k.