Algebra worksheet — GCSE Higher

1.The first four terms of a sequence are 2, 6, 10, 14. Priya says the nth term is 4n. Work out the correct expression for the nth term.

2.A straight line has equation 4y = 12x + 20. Work out the gradient of the line.

3.A circle has equation x² + y² = 25. Does the point (3, 4) lie on this circle?

4.Solve 3x + 14 = 8x − 6

5.The curve y = x² − 3x. Use the chord between x = 1 and x = 4 to estimate the gradient of the curve at x = 2.5.

6.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.

7.p = 4. Work out the value of 2p³.

8.Solve the inequality 2(3x − 1) ≥ 4x + 8.

9.Harry is 14 years old and Mia is 8 years old. Will Harry ever be exactly twice as old as Mia? Give a reason for your answer.

10.A hall is set out in rows of chairs for an assembly. Row 1 has 50 chairs, row 2 has 45 chairs, row 3 has 40 chairs, and row 4 has 35 chairs, with each row after the first having 5 fewer chairs than the one before. Work out an expression, in terms of n, for the number of chairs in row n.

11.The graph of y = f(x) has a minimum turning point at (4, −5). The graph of y = f(x) + a has a minimum turning point whose minimum VALUE is 2. Work out the value of a, and state the coordinates of the minimum turning point of y = f(x) + a.

12.The graph of y = f(x) has a maximum turning point at (5, 8). Which of these correctly gives the corresponding turning point on the graph of y = −f(x + 1), and its type?

13.There are 30 students in a Year 10 maths class. There are 2 more boys than girls. Work out the number of boys and the number of girls.

14.A rectangular vegetable plot has an area of 30 m² and its length is 4 m greater than its width, x metres. This gives x² + 4x − 30 = 0, which can be solved using the iterative formula xₙ₊₁ = √(30 − 4xₙ). The starting value is x₀ = 3, so x₁ is the value after the formula has been used once. Work out x₃, and use it to find an estimate for the length of the plot, giving your answer correct to 1 decimal place.

15.f(x) = (x + 1)/2. Find f⁻¹(x).