Algebra worksheet — GCSE Higher

1.A caterer uses the formula C = 6p + 20 to work out the total cost, £C, of a buffet for p people, where £20 covers fixed costs. A customer is charged £92. Work out how many people, p, the buffet was for.

2.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).

3.Work out the gradient of the straight line with equation y = (2x/5) − 3.

4.y = 5 − 2x. Work out the value of x when y = 11.

5.A number, w, satisfies the statement "three times w, minus 5, is at least 16". Which of these is the correct inequality for w?

6.A taxi charges a £3 fixed fee plus £2 for each mile travelled. Write an expression, in pounds, for the total cost of a journey of n miles.

7.The point (9, 40) lies on the circle x² + y² = 1681, which has centre (0, 0). Work out the equation of the tangent to the circle at (9, 40), giving your answer in the form ax + by = c.

8.Solve the simultaneous equations y = 3 − x and x² + y² = 9, giving both pairs of solutions.

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.Work out the value of 3x² − 4x when x = −2.

11.(2x + 3)(x + a) ≡ 2x² + 11x + 12 is an identity. Work out the value of a.

12.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.

13.The simultaneous equations kx + 2y = 4 and 3x + y = 5 have no solution. Work out the value of k.

14.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.

15.Solve the inequality 2(x − 1) ≤ 8.