Algebra worksheet — GCSE Higher

1.Solve 2x² = 18.

2.An arithmetic sequence has first term 40 and common difference −6. Work out the 9th term of the sequence.

3.Expand and simplify (x + 1)(x + 2)(x + 3).

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

5.A car park charges by the hour. Parking for 1 hour costs £5, 2 hours costs £9, 3 hours costs £13 and 4 hours costs £17, with the cost increasing by the same amount for each extra hour. Work out an expression, in terms of n, for the cost, in pounds, of parking for n hours.

6.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.

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

8.The point (3, 4) lies on the circle x² + y² = 25, which has centre (0, 0). Work out the gradient of the tangent to the circle at (3, 4).

9.A rectangular lawn is 4 m longer than it is wide. Its area is 96 m². Work out the length of the lawn.

10.Expand and simplify (x − 3)²

11.A quadratic graph has equation y = (x − 4)². A student says this graph crosses the x-axis at two different points. Explain why the student is wrong.

12.Work out the value of 4p² − 3 when p = 2.5

13.A circle has centre (0, 0) and passes through the point (12, 35). Work out the equation of the circle.

14.A geometric sequence has first term 5, and each term after that is 3 times the term before it. Work out the first term of the sequence that is greater than 1000.

15.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.