Algebra worksheet — GCSE Higher

1.The point (9, 12) lies on the circle x² + y² = 225, which has centre (0, 0). The tangent to the circle at (9, 12) crosses the x-axis at the point P. Work out the x-coordinate of P.

2.By completing the square, find the turning point of the curve y = 2x² − 8x + 3.

3.A company's profit is £500 in its first year. Each year after that, the profit is £300 more than the year before. Work out the profit in the company's 6th year.

4.a = 2 and b = 5. Work out the value of a²b.

5.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?

6.The solution set of a quadratic inequality is {x : x ≤ −3} ∪ {x : x ≥ 5}. Which of these inequalities has this solution set?

7.Which expression is equivalent to 3(2x − 5) + 4x?

8.A rectangular sheep pen has perimeter P, length l and width w, connected by the formula P = 2l + 2w. A farmer has 60 m of fencing for the perimeter and sets the width at 8 m. Work out the length of the pen.

9.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.

10.A mobile phone plan charges a fixed monthly fee plus an amount for each gigabyte of data used. The total cost £C for using g gigabytes in a month is given by C = 15 + 2g. What does the number 2 represent in this formula?

11.Solve 6x − 5 = 3x + 13.

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

13.Solve the simultaneous equations 3x + 2y = 16 and x + y = 7. Work out the value of y.

14.A table of values is being drawn for the graph of y = x³. Work out the value of y when x = −2.

15.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.