Algebra worksheet — GCSE Higher

1.A circle has centre O(0, 0) and equation x² + y² = 169. The point Q has coordinates (10, 11). Work out which of these gives the correct position of Q together with correct working.

2.The first five terms of a quadratic sequence are −1, 4, 13, 26, 43. Work out an expression, in terms of n, for the nth term.

3.On a distance-time graph, a horizontal line segment shows a period when the graph's gradient is 0. What does this tell you about the journey during that time?

4.Solve the inequality 2(3x − 1) ≥ 4x + 8.

5.The curve y = −x² + 6x − 5 has a maximum point. Use completing the square to find its coordinates.

6.A theatre has rows of seats arranged so that row 1 has 12 seats, row 2 has 17 seats, row 3 has 22 seats and row 4 has 27 seats, with each row having 5 more seats than the row before. Work out an expression, in terms of n, for the number of seats in row n.

7.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.

8.The trapezium rule is used to estimate the area under a curve between x = 2 and x = 6. The curve is concave up (it curves upwards, like the inside of a bowl) throughout this interval. Which statement about the estimate is correct?

9.The graph of y = f(x) passes through the point (0, 4). Work out the y-coordinate of the point where the graph of y = −f(x) + 5 crosses the y-axis.

10.By completing the square, find the turning point of the curve y = x² − 4x + 9.

11.The first five terms of a quadratic sequence are 2, 5, 10, 17, 26. Work out the next term in the sequence.

12.Work out the value of (x − 4)/2 + 3 when x = 10

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

14.A straight line has gradient 3 and passes through the point (1, 4). Work out the equation of the line.

15.A cyclist's speed rises from rest to a maximum — quickly at first, then more and more slowly — so her speed-time graph is a curve that is concave down (its gradient decreases as time goes on). A trapezium estimate is made for the distance travelled during this phase, using two points on the curve. Is the trapezium estimate an overestimate or an underestimate of the true distance, and why?