Algebra worksheet — GCSE Higher

1.One solution of the equation x² − (k + 1)x + k = 0 is x = 3. Work out the value of k.

2.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.

3.Work out the value of 3a − 2b when a = 5 and b = 4

4.A car is decelerating. The tangent to its velocity-time graph at t = 12 seconds passes through the points (8, 22) and (16, 6), where velocity is in m/s and time is in seconds. Work out the gradient of this tangent, in m/s².

5.Describe the single transformation that maps the graph of y = f(x) onto the graph of y = f(−x).

6.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?

7.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.

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

9.Solve the inequality 2(x − 1) ≤ 8.

10.A curve has equation y = x³ − 4x. Work out the coordinates of the point where the curve crosses the y-axis.

11.A number, n, is doubled and then 7 is subtracted. The result is 15. Form an equation and solve it to find n.

12.Points A(−1, 2) and B(5, 8) are the endpoints of a line segment. Work out the equation of the perpendicular bisector of AB.

13.Factorise fully 56x − 24

14.A circle has centre (0, 0) and equation x² + y² = 25. Work out the x-coordinates of the two points where the circle crosses the line y = 3.

15.Four sequences are shown below. Sequence P: 4, 8, 16, 32, ... Sequence Q: 4, 8, 12, 16, ... Sequence R: 4, 7, 12, 19, ... Sequence S: 4, 9, 16, 25, ... Work out which of the sequences P, Q, R and S is geometric.