Algebra worksheet — GCSE Higher

1.f(x) = 2x − 1. Work out ff(x).

2.A walker's distance-time graph is described as follows: she walks 3 km in the first 15 minutes at a steady speed, rests for 10 minutes, then walks a further 3 km in the next 20 minutes, also at a steady speed. Work out her speed, in km/h, during the first 15 minutes.

3.A cafe sells coffees at £c each and pastries at £p each. Three coffees and two pastries cost £9.60. Two coffees and two pastries cost £7.60. Work out the price of one coffee.

4.The point A(−6, 8) lies on the circle x² + y² = 100, whose centre is the origin O. The tangent to the circle at A crosses the y-axis at the point B. Work out the length of OB.

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

6.Solve the inequality x² ≥ 16, giving your answer using set notation.

7.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.

8.A company's profit is £500 in its first year. Each year after that, the profit is £300 more than the year before. Work out the profit in the company's 6th year.

9.Solve the inequality x² + 6x + 9 > 0.

10.The nth term of a sequence is 4n + 2. A term in the sequence has value 30. Work out its position, n, in the sequence.

11.A circle has centre (0, 0) and equation x² + y² = 100. Work out which one of these points lies on the circle.

12.Factorise 3x² + 10x − 8.

13.Solve the simultaneous equations 5x − 2y = 16 and 3x + 2y = 16. Work out the value of x.

14.Simplify fully: (x + 2)/(3x) × 6x²/(x² − 4)

15.Describe the single transformation that maps the graph of y = x² onto the graph of y = x² + 3.