Algebra worksheet — GCSE Higher

1.Which of these is an identity?

2.A triangle has vertices at (1, 1), (1, 5) and (6, 1). Work out the area of the triangle.

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

4.Line C passes through (0, 0) and (4, 2). Line D passes through (0, 0) and (2, 2). Write down which of the two lines is the steeper.

5.Make x the subject of the formula y = x/2 − 5.

6.A hall is set out in rows of chairs for an assembly. Row 1 has 50 chairs, row 2 has 45 chairs, row 3 has 40 chairs, and row 4 has 35 chairs, with each row after the first having 5 fewer chairs than the one before. Work out an expression, in terms of n, for the number of chairs in row n.

7.A circle has centre (0, 0) and equation x² + y² = 50. Work out the radius of the circle, giving your answer as a surd in its simplest form.

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

9.A taxi fare, in pounds, for a journey of m miles is given by the formula F = 3 + 2.5m. A journey costs £15.50. Work out the distance travelled, m, by first rearranging the formula to make m the subject, then substituting F = 15.50.

10.Work out the gradient of a line that is perpendicular to the line with equation 2x + 3y = 6.

11.Work out the value of a² − 2b when a = −3 and b = 4.

12.A company's weekly profit, P thousand pounds, when it makes x thousand items is modelled by P = x² − 8x + 12, for x ≥ 0. Work out the values of x for which the company makes a loss.

13.The graph of y = f(x) has a minimum turning point at (3, −5), crosses the x-axis at x = 1, and crosses the y-axis at (0, −2). Exactly one of these statements about the graph of y = −f(x + 2) is true. Which statement is true?

14.Work out the smallest positive value of x, in degrees, for which y = tan x is undefined.

15.The point (−4, 3) lies on the circle x² + y² = 25, which has centre (0, 0). Work out the equation of the tangent to the circle at (−4, 3), giving your answer in the form y = mx + c.