Algebra worksheet — GCSE Higher

1.Ben writes n + 4 ≤ 9. Which statement describes what Ben has written? Give a reason for your answer.

2.A water butt holds 200 litres and is being drained at a steady 8 litres per minute. Write down the function for the amount of water y, in litres, left after x minutes.

3.Factorise 6x² − 7x − 3.

4.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.

5.Which of these pairs of lines are perpendicular to each other?

6.The equation x³ = 6x + 20 can be solved using the iterative formula xₙ₊₁ = ∛(6xₙ + 20). Taking x₀ = 3, x₁ = 3.3620 correct to 4 decimal places. Using the full unrounded value of x₁, work out x₂ correct to 3 decimal places.

7.Tom buys 2 notebooks and 6 pencils on Monday, priced at p pence each for a notebook and q pence each for a pencil. On Tuesday he buys 3 more notebooks and 1 more pencil. Write a simplified expression, in pence, for the total amount Tom has spent on notebooks and pencils.

8.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) + 5 crosses the y-axis.

9.The iterative formula xₙ₊₁ = xₙ³ − 2 is used repeatedly, starting from x₀ = 2. Which of these describes what happens to the sequence of values as n increases?

10.The nth term of a sequence is n² + 2n − 4. Work out the 7th term.

11.Solve the inequality 9 − 2x ≥ 1.

12.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

13.A gym charges a reduced price for the first month of membership and a standard price for every month after that. The total cost is £5 for 1 month, £12 for 2 months, £19 for 3 months and £26 for 4 months. Work out an expression, in terms of n, for the total cost, in pounds, of n months of membership.

14.Factorise x² − 64.

15.A graph has equation y = x² − 6x + 5. A student says its turning point has x-coordinate 6, because that's the coefficient of x. Which statement corrects the student's mistake?