Algebra worksheet — GCSE Higher

1.Solve the simultaneous equations 2x + y = 7 and x − y = 2.

2.The first term of an arithmetic sequence is 5, and each term after that increases by 6. Work out the 8th term of the sequence.

3.A lift has a weight limit: it must carry no more than 630 kg. Let w be the total weight, in kg, carried by the lift. Which inequality describes this?

4.Two numbers have a sum of 45. The larger number is 9 more than the smaller number. Form an equation using n for the smaller number, and solve it to find the larger number.

5.Simplify (x² − 9) ÷ (x² + 5x + 6).

6.Write down the expression that means the same as (x + 7) ÷ 4.

7.Yusuf has £40 saved and adds £6 each week. His sister Aisha has £10 saved and adds £11 each week. After how many weeks will they have saved the same amount?

8.Which expression is equivalent to 3(2x − 5) + 4x?

9.Which of these quadratic graphs does NOT cross the x-axis at all?

10.The graph of y = f(x) has roots at x = −1 and x = 4, and crosses the y-axis at (0, −8). Which statement about the graph of y = f(x − 3) is correct?

11.Simplify 5a/6 − a/3

12.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.

13.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.

14.To rearrange y = 2x − 5 to make x the subject, Sam writes: 'Add 5 to both sides to get y + 5 = 2x, then divide both sides by 2 to get x = (y + 5)/2.' Which statement about Sam's method is correct?

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