Algebra worksheet — GCSE Higher

1.Explain why the equation 4x + 3 = 4x + 10 has no solution for x.

2.A straight line passes through the points (−1, 2) and (3, 14). Work out the equation of the line.

3.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

4.A plumber charges a call-out fee of £30 plus £25 for each hour worked. The total bill for a job was £130. Work out how many hours the plumber worked.

5.A candle is 30 cm tall and burns down at a steady rate of 1 cm per hour. Write down the function for the height of the candle y, in centimetres, after x hours.

6.The solution set of an inequality is described as: x is less than −3, or x is greater than or equal to 1. Write this solution set using set notation.

7.A speed-time graph shows a constant speed of 15 m/s for 20 seconds. Work out the distance travelled, using the area under the graph.

8.A taxi firm charges a fixed fee of £3.50 plus £2.20 per mile. Work out the total cost of a journey of 6 miles.

9.The area of a triangle is given by the formula A = bh/2, where b is the base and h is the height. Make h the subject of the formula.

10.Solve 2x + 7 = x + 13

11.A square patio of side length n slabs is surrounded by a single border of square paving slabs of the same size. For a patio with side length n, the total number of slabs used for the patio and its border together is 9 when n = 1, 16 when n = 2, 25 when n = 3, and 36 when n = 4. Work out an expression, in terms of n, for the total number of slabs.

12.Solve the inequality 3x − 1 ≤ 11.

13.Expand and simplify (x − 3)²

14.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?

15.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.