Algebra worksheet — GCSE Higher

1.A curve has equation y = x³ − 4x. Work out the coordinates of the point where the curve crosses the y-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.There are 50 adults on a coach to the Lake District. Every adult is either a man or a woman. There are 10 more men than women. Work out the number of men.

4.Solve the inequality 3x + 6 ≤ 0.

5.Find the common ratio of the geometric sequence 5, 5√2, 10, 10√2, ... Give your answer in surd form.

6.The first four terms of a sequence are 11, 18, 25, 32. Ravi thinks the nth term is 7n. Work out the correct expression for the nth term.

7.Which of these rules generates the sequence 6, 11, 16, 21, …?

8.A circle has centre (0, 0) and radius 9. Work out the equation of the circle.

9.A circle has equation x² + y² = 49. Work out the coordinates of the point(s) on the circle where the tangent is horizontal.

10.Factorise x² − 64.

11.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.

12.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.

13.A student says 4(2x − 3) is equivalent to 8x − 3. Which statement gives the correct verdict and reason?

14.Describe a sequence of two transformations that maps the graph of y = x² onto the graph of y = −(x − 5)².

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.