Algebra worksheet — GCSE Higher

1.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.

2.An exponential graph y = A × rˣ passes through the points (0, 8) and (2, 18). Work out the value of r, correct to 2 decimal places.

3.A candidate solves the inequality x² > 9 and writes: "x² > 9, so x > 3." Which of these is a correct comment on the candidate's work?

4.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.

5.Solve 4(x − 3) = 2x + 6.

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

7.Solve (3x + 2)/5 = (x + 4)/3

8.A curve has equation y = x³ − 4x. Work out the coordinates of the point where the curve crosses the y-axis.

9.Solve 3x + 14 = 8x − 6

10.A rule turns each input x into an output y. The inputs are x = −1, 0, 1, 2 and the matching outputs are y = 5, 3, 1, −1. Work out the rule.

11.A rule turns each input x into an output y. The inputs are x = 0, 1, 2, 3 and the outputs are y = 4, 7, 10, 13. Work out the output when x = 5.

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

13.Which of these pairs of lines are perpendicular to each other?

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

15.A company's weekly profit, P thousand pounds, when it makes x thousand items is modelled by P = x² − 8x + 12, for x ≥ 0. Work out the values of x for which the company makes a loss.