Algebra worksheet — GCSE Higher

1.f(x) = x + 3 and g(x) = 2x. Work out fg(x).

2.A plumber charges a call-out fee plus an hourly rate. The total cost, y in pounds, of a job lasting x hours is given by y = 45x + 60. Work out the total cost of a job that lasts 3 hours.

3.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.

4.Work out the period of the graph of y = cos x, in degrees.

5.Point P has coordinates (2, −5). P is reflected in the x-axis to point Q. Write down the coordinates of Q.

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

7.A cup of tea cools after being made. Its temperature-time graph is a curve. Three tangents are drawn on the graph: at t = 2 minutes the tangent has gradient −8; at t = 10 minutes the tangent has gradient −3; at t = 20 minutes the tangent has gradient −0.5. Which of these statements about the tea's cooling is correct?

8.The simple interest, £I, earned on a savings account is given by the formula I = PRT/100, where P is the amount invested in pounds, R is the interest rate per year and T is the time in years. Rearrange the formula to make P the subject.

9.A Fibonacci-type sequence is defined by aₙ = aₙ₋₁ + aₙ₋₂ for n ≥ 3. Given that a₁ = 5 and a₃ = 17, work out a₂.

10.Solve the inequality 2(x − 1) ≤ 8.

11.A geometric sequence has first term 3 and common ratio √3. Work out the position of the first term of the sequence that exceeds 30.

12.The nth term of a sequence is n² + 3. Work out the first term of the sequence that is greater than 50.

13.Solve the simultaneous equations x + y = 1 and 2x + y = 5.

14.A regular hexagon has sides of length (x + 2) cm. Write down an expression, in terms of x, for the perimeter of the hexagon.

15.Solve x² − 6x = 0.