Algebra worksheet — GCSE Higher

1.A water tank empties according to y = −5x + 200, where y is the number of litres left after x minutes. Work out the coordinates of the point where this graph crosses the x-axis.

2.The nth term of a geometric sequence is given by aₙ = 3 × 2ⁿ⁻¹. Work out the position of the first term that is greater than 1,000.

3.A student attempts to prove that the sum of any three consecutive integers is a multiple of 3. Line 1: Let the three consecutive integers be n, n + 1 and n + 2. Line 2: Their sum is n + (n + 1) + (n + 2) = 3n + 2. Line 3: 3n + 2 leaves a remainder of 2 when divided by 3, so it is not a multiple of 3. Line 4: So the sum of three consecutive integers is not always a multiple of 3. Which line contains the FIRST error?

4.The cost, in pounds, of hiring a van for d days is given by the formula C = 25 + 18d. A customer's hire cost £133. Work out how many days, d, they hired the van for, by first rearranging the formula to make d the subject.

5.By completing the square, find the turning point of the curve y = x² + 6x + 2.

6.Solve x² − x − 12 = 0.

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

8.Simplify (x² − 9) ÷ (x² + 5x + 6).

9.A student is proving that (n + 1)² − n² is always an odd number. Which of these correctly completes the first line of algebra?

10.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.

11.The simple interest, £I, earned on a savings account is given by the formula I = PRT/100, where P is the amount invested in pounds, R is the interest rate per year and T is the time in years. Rearrange the formula to make P the subject.

12.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.

13.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?

14.Expand and simplify (2x − 1)(x + 5)(x − 2). Write down the coefficient of x in your answer.

15.A scout leader is 44 years old and one of the scouts is 16 years old. Work out how many years it will be until the leader is exactly twice as old as the scout.