Algebra worksheet — GCSE Higher

1.Work out the gradient of the straight line with equation 2x + y = 8.

2.A water tank is a cuboid with a square base of side x metres and height (x + 1) metres. Its volume is 10 m³. This gives x³ + x² − 10 = 0, which can be solved using the iterative formula xₙ₊₁ = ∛(10 − xₙ²). Taking x₀ = 2, so that x₁ is the value found after the formula has been used once, work out x₃ correct to 3 decimal places.

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

4.Make x the subject of the formula y = x/2 − 5.

5.The braking distance of a car, in metres, is estimated using the formula d = 0.4v² + 6, where v is the speed in mph. A car travelling at 35 mph brakes. Work out the estimated braking distance.

6.The equation x² − 4x + k = 0 has two different real solutions. Work out the range of values of k.

7.Expand and simplify (2x − 1)(x + 5)(x − 2). Write down the coefficient of x in your answer.

8.Rosie is asked whether 4(x + 3) = 4x + 12 is an equation or an identity. Which statement is correct? Give a reason for your answer.

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

10.The formula for converting a temperature from degrees Celsius, C, to degrees Fahrenheit, F, is F = 1.8C + 32. Work out F when C = 20, and identify what kind of mathematical statement F = 1.8C + 32 is.

11.Line L has equation y = 2x + 3. Work out the equation of the line perpendicular to L that passes through the point (4, 1), giving your answer in the form x + 2y = c.

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

13.Expand and simplify 2(a + 6) − 2(a − 7)

14.Factorise 3x² + 10x − 8.

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