Algebra worksheet — GCSE Higher

1.A student is asked to simplify (6x³ − 15x²)/(4x² − 10x) fully. Four attempts are shown below. Which one is correct?

2.Solve 5(x + 3) = 40

3.A sequence has nth term 3n + 4. Two terms are missing from the list of its first five terms: 7, 10, _, 16, _. Work out the missing 3rd and 5th terms added together.

4.Work out the value of m² + 3m when m = −2

5.The tangent to a curve at the point (6, 1) has gradient −3. Work out the y-coordinate of the point where this tangent crosses the y-axis.

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

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

8.A plumber charges a £40 call-out fee plus £25 for each hour worked. The total charge, £C, for a job lasting h hours is given by C = 40 + 25h. Work out the charge for a job lasting 3 hours, and name what kind of statement C = 40 + 25h is.

9.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.

10.The first five terms of a quadratic sequence are 4, 7, 12, 19, 28. Work out an expression, in terms of n, for the nth term.

11.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.

12.Line L has equation y = 3x − 2. Work out the gradient of a line perpendicular to L.

13.The graph of y = 20/x is drawn for x > 0. As the value of x increases, what happens to the value of y?

14.When a number is added to its square the result is 30. Work out the possible values of the number.

15.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.