Algebra worksheet — GCSE Higher

1.n is an integer. Which of these expressions is always an even number?

2.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

3.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.

4.A gym charges a joining fee plus a monthly fee. Anna paid £100 in total after 3 months of membership. Ben paid £160 in total after 6 months of membership (same joining fee and monthly fee as Anna). Work out the monthly fee.

5.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.

6.The height, h metres, of a ball t seconds after a stopwatch is started follows h = (t − 1)(5 − t) for 1 ≤ t ≤ 5, where h = 0 means the ball is at ground level. Work out the two times at which the ball is at ground level.

7.Solve the inequality 5x − 3 > 2x + 9.

8.A colony of bacteria doubles in number every hour. At 9am there are 5 bacteria in the colony. Work out how many bacteria there will be at 12 noon.

9.Factorise fully 56x − 24

10.The discriminant of a quadratic equation is greater than zero. Which statement about the solutions of that equation is correct?

11.A quadratic graph y = ax² + bx + c has its turning point on the y-axis. Which statement about its roots must be true?

12.Factorise fully 5x + 5y − 5

13.The point (5, −12) lies on the circle x² + y² = 169, which has centre (0, 0). Work out the equation of the tangent to the circle at (5, −12), giving your answer in the form y = mx + c.

14.Two brothers have ages that add up to 30. The elder brother is 6 years older than the younger brother. Work out the age of the younger brother.

15.A student is asked whether the lines y = (2/5)x − 1 and 5y = −2x + 15 are perpendicular. The student answers: "Yes, because when I rearrange the second equation I get y = −(2/5)x + 3, and 2/5 times −2/5 is negative." Which of these is a correct comment on the student's reasoning?