Algebra worksheet — GCSE Higher

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

2.The tangent to a curve at the point (5, 2) is the line y = mx + c. This tangent crosses the y-axis at (0, −8). Work out the gradient, m, of the tangent.

3.Expand and simplify (x + 1)(x + 2)(x + 3).

4.Line L has equation y = 2x + 3. Work out the equation of the line perpendicular to L that passes through the point (4, 1), giving your answer in the form x + 2y = c.

5.A candidate solves the inequality x² > 9 and writes: "x² > 9, so x > 3." Which of these is a correct comment on the candidate's work?

6.A ball is thrown in the air. Its height, h metres, above the ground after t seconds is given in this table: when t = 0, h = 0; when t = 1, h = 15; when t = 2, h = 20; when t = 3, h = 15; when t = 4, h = 0. Use the table to find the two times, in seconds, at which the ball is at ground level.

7.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.

8.x = 5. Work out the value of 3x² − 4.

9.The perimeter, P, of a rectangle with length l and width w is calculated using P = 2l + 2w. What kind of mathematical statement is P = 2l + 2w?

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

11.Describe a sequence of two transformations that maps the graph of y = cos x onto the graph of y = cos(x + 90°) − 2.

12.A geometric sequence begins 162, 54, 18, 6, ... Work out the next term in the sequence.

13.Factorise 6x² − 7x − 3.

14.A geometric sequence has first term 4 and common ratio √2. Work out the sum of the first three terms of the sequence, giving your answer in the form a + b√2.

15.A circle has centre (0, 0) and passes through the point (5, 12). Work out the equation of the circle.