Algebra worksheet — GCSE Higher

1.Work out the value of 3x² − 4x when x = −2.

2.The first five terms of a quadratic sequence are −1, 4, 13, 26, 43. Work out an expression, in terms of n, for the nth term.

3.Solve 5(x + 3) = 40

4.Which expression means 'triple c, then add double d'?

5.The point (9, 40) lies on the circle x² + y² = 1681, which has centre (0, 0). Work out the equation of the tangent to the circle at (9, 40), giving your answer in the form ax + by = c.

6.Factorise fully 12x² + 18x.

7.A car's speed, in m/s, during a journey is: 0 at t = 0 s, 8 at t = 4 s, and 8 (constant) from t = 4 s to t = 10 s, increasing at a constant rate between t = 0 and t = 4. Estimate the total distance the car travels, using the areas of a triangle and a rectangle.

8.Solve 3x + 14 = 8x − 6

9.A delivery van's distance-time graph shows the following: it travels 9 km in the first 15 minutes at a steady speed, stops for 45 minutes to unload, then travels a further 21 km in the next 30 minutes, also at a steady speed. Work out the average speed, in km/h, for the whole journey.

10.Two numbers have a sum of 24. Their difference is 6. Work out the two numbers.

11.A tank already contains some water and is then filled at a constant rate. After 2 minutes it contains 50 litres in total; after 7 minutes it contains 150 litres in total. Work out the rate at which water is added, in litres per minute.

12.n = 3. Work out the value of (2n)².

13.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.

14.A rectangular garden has length (x + 7) m and width (x − 7) m. Work out an expression for the area of the garden, giving your answer in its simplest form.

15.Four sequences are shown below. Sequence P: 3, 6, 12, 24, … Sequence Q: 1, 4, 9, 16, … Sequence R: 2, 4, 8, 14, … Sequence S: 5, 10, 15, 20, … Work out which of the sequences P, Q, R and S is geometric.