Algebra worksheet — GCSE Higher

1.A train's distance-time graph shows it travelling 100 km at a steady speed in the first 1.5 hours, waiting at a signal for 0.25 hours, then travelling a further 47 km in 0.75 hours. Work out the average speed for the whole journey, correct to 1 decimal place.

2.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.

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

4.The point (9, 12) lies on the circle x² + y² = 225, which has centre (0, 0). The tangent to the circle at (9, 12) crosses the x-axis at the point P. Work out the x-coordinate of P.

5.f(x) = x³ − 3x² − 4. Work out the pair of consecutive integers between which the solution of f(x) = 0 lies.

6.Simplify (x² − 9) ÷ (x² + 5x + 6).

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

8.Work out the smallest positive value of x, in degrees, for which y = tan x is undefined.

9.A circle has centre (0, 0) and equation x² + y² = 100. A straight line is drawn from the origin through the point P(8, 9). Work out whether P lies inside, on, or outside the circle.

10.The nth term of a sequence is n² + 2n − 4. Work out the 7th term.

11.A circle has centre (0, 0) and equation x² + y² = 50. Work out the radius of the circle, giving your answer as a surd in its simplest form.

12.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.

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

14.The graph of y = 20/x is drawn for x > 0. As the value of x increases, what happens to the value of y?

15.The formula for the area of a trapezium is A = (a + b)h / 2, where a and b are the parallel side lengths and h is the height. Make h the subject of the formula.