Algebra worksheet — GCSE Higher

1.A line segment has one endpoint at (−6, 2) and its midpoint at (−1, 5). Work out the coordinates of the other endpoint.

2.A car accelerates uniformly from rest at 2.5 m/s² until it reaches a speed of 20 m/s, then travels at this constant speed for a further 30 seconds. Work out the total distance travelled.

3.Work out the equation of the straight line through the points (−2, 1) and (0, 7).

4.A Fibonacci-type sequence begins 3, 5, 8, 13, ... where each term after the second is the sum of the two terms before it. Work out the 7th term of the sequence.

5.A circle has equation x² + y² = 25. Does the point (3, 4) lie on this circle?

6.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.

7.Work out the gradient of the straight line with equation 3y = 12 − 6x.

8.A taxi fare, in pounds, for a journey of m miles is given by the formula F = 3 + 2.5m. A journey costs £15.50. Work out the distance travelled, m, by first rearranging the formula to make m the subject, then substituting F = 15.50.

9.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.

10.Simplify (x² − 9) ÷ (x² + 5x + 6).

11.f(x) = x + 2 and g(x) = x². Work out the value of x for which fg(x) = gf(x).

12.A student uses the iterative formula xₙ₊₁ = √(7xₙ + 3) to find an approximate solution of an equation. Work out which equation this iterative formula solves.

13.A line has equation y = −4x + 1. Work out the equation of the line perpendicular to it that passes through the point (0, 3).

14.The formula connecting speed, distance and time is v = s ÷ t. Work out v, in km/h, when s = 180 and t = 4.

15.The graph of y = f(x) has x-intercepts at x = −2 and x = 6 and crosses the y-axis at (0, −12). Work out the x-intercepts and the y-intercept of y = −f(x).