Algebra worksheet — GCSE Higher

1.The simultaneous equations kx + 2y = 4 and 3x + y = 5 have no solution. Work out the value of k.

2.Two numbers have a sum of 24. Their difference is 6. Work out the two numbers.

3.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.

4.The graph of y = cos x is transformed onto the graph of y = cos(x − 90°). State the direction of the translation and which standard graph the image is.

5.A straight line has equation 4y = 12x + 20. Work out the gradient of the line.

6.Which of these statements is an identity?

7.Work out the value of a² − 2b when a = −3 and b = 4.

8.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.

9.A taxi charges a £3 fixed fee plus £2 for each mile travelled. Write an expression, in pounds, for the total cost of a journey of n miles.

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

11.Which expression means 'y squared, multiplied by 3'?

12.A straight line has equation y = 4 − 3x. Work out the gradient of the line.

13.The function f(x) = x² for all real values of x has no inverse function, but g(x) = x² for x ≥ 0 does have one. Which statement correctly explains this?

14.The solution set of a quadratic inequality is {x : x ≤ −3} ∪ {x : x ≥ 5}. Which of these inequalities has this solution set?

15.A geometric sequence begins 80, 40, 20, 10, ... Work out the next term in the sequence.