Algebra worksheet — GCSE Higher

1.Write y = x² + 12x + 40 in the form (x + a)² + b, and hence write down the minimum value of y.

2.Meera writes the statement 3(x + 4) = 3x + 12. Which of these correctly describes what she has written, with a reason?

3.A phone plan costs a fixed £15 per month plus 8p per minute of calls. In one month, Jamal's bill was £23.80. Form an equation using m for the number of minutes, and solve it to find how many minutes Jamal used that month.

4.A straight line has equation y = 4 − 3x. Work out the gradient of the line.

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

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

7.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.

8.A rule turns each input x into an output y. An input of 1 gives an output of 1, an input of 2 gives an output of 4 and an input of 3 gives an output of 9. Work out the rule.

9.The equation x² − 6x + k = 0 has exactly one solution. Work out the value of k.

10.Work out the value of 2(x + 2) when x = −5

11.A sequence is defined by aₙ = aₙ₋₁ + aₙ₋₂ for n ≥ 3. Given that a₃ = 11 and a₅ = 29, work out a₁.

12.The nth term of a sequence is 4n + 2. A term in the sequence has value 30. Work out its position, n, in the sequence.

13.A circle has centre (0, 0) and radius 9. Work out the equation of the circle.

14.Factorise x² − 3x − 10.

15.A water butt holds 200 litres and is being drained at a steady 8 litres per minute. Write down the function for the amount of water y, in litres, left after x minutes.