Algebra worksheet — GCSE Higher

1.Work out the gradient of the straight line with equation 2x + y = 8.

2.The formula for converting a temperature from degrees Celsius, C, to degrees Fahrenheit, F, is F = 1.8C + 32. Work out F when C = 20, and identify what kind of mathematical statement F = 1.8C + 32 is.

3.Simplify 5a/6 − a/3

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.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

6.The nth term of a sequence is n² + 3. Work out the first term of the sequence that is greater than 50.

7.Make x the subject of the formula y = 4(x − 6).

8.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.

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 line y = 2x + 7 and the circle x² + y² = 4 are given. By finding the discriminant of the resulting quadratic, without solving it fully, work out how many points the line and the circle intersect at.

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

12.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.

13.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

14.Solve x² + 3x − 10 = 0.

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