Algebra worksheet — GCSE Higher

1.A triangle has vertices at (1, 1), (1, 5) and (6, 1). Work out the area of the triangle.

2.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.

3.Work out the coordinates of the point halfway between (−9, −2) and (−1, −2).

4.Isla says that the lines y = 2x + 1 and y = −2x + 3 are parallel. Write down the statement that gives the correct answer for the correct reason.

5.The first four terms of a sequence are 2, 2√3, 6, 6√3, ... Work out the next term.

6.A box holds n pencils. A shop has 6 full boxes and 4 loose pencils. All of these pencils are shared equally between 2 classes. Write down the expression for the number of pencils each class receives.

7.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.

8.Write down the expression that means the same as m² × m × 3.

9.Factorise fully 12x² + 18x.

10.A plumber charges a call-out fee of £30 plus £25 per hour worked. Work out the total charge for a job that takes 3 hours.

11.A cuboid has a square base of side x metres and a height that is 3 m more than x. Its volume is 150 m³. This gives the equation x³ + 3x² − 150 = 0, which can be solved using the iterative formula xₙ₊₁ = ∛(150 − 3xₙ²). Taking x₀ = 4, work out x₂ correct to 2 decimal places.

12.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

13.Which expression is equivalent to 7x − 3(2x − 6)?

14.The diagram shows the graph of a function. Which equation could it represent?

15.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.