Algebra worksheet — GCSE Higher

1.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.

2.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.

3.Which expression is equivalent to 0.5(4x + 6) − x?

4.The formula y = x² + 1 gives y in terms of x. Work out the value of y when x = −2.

5.A parcel delivery company's cost graph shows the following: the cost is a flat £5 for parcels weighing up to 2 kg, and then rises by £2 for each additional kg above 2 kg. Use the graph to work out the weight of a parcel that costs £17.

6.The area of a triangle is given by the formula A = bh/2, where b is the base and h is the height. Make h the subject of the formula.

7.Solve x² − 100 = 0.

8.A phone plan costs a fixed £15 per month plus 8p per minute of calls. In one month, Jamal's bill was £23.80. Form an equation using m for the number of minutes, and solve it to find how many minutes Jamal used that month.

9.A bacteria colony doubles every 4 hours and its size is recorded only every 4 hours. The recorded population 20 hours after the start is 9,600. After how many hours did the recorded population first exceed 1,000?

10.The first five terms of a quadratic sequence are 6, 11, 18, 27, 38. Work out an expression, in terms of n, for the nth term.

11.A square has vertices at (−2, 3), (−2, −3) and (4, −3). Write down the coordinates of the fourth vertex.

12.Solve 3x + 14 = 8x − 6

13.Factorise fully 5x + 5y − 5

14.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.

15.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.