Algebra worksheet — GCSE Higher

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

2.A circle has equation x² + y² = 49. Work out the coordinates of the point(s) on the circle where the tangent is horizontal.

3.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.

4.Two numbers have a sum of 50. The larger number is twice the smaller number. Work out the smaller number.

5.Priya has a budget of £50 for a school trip. The coach costs £14 and each student ticket costs £4. Using the inequality 14 + 4s ≤ 50, work out the greatest number of student tickets, s, she can buy.

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

7.A car's velocity–time graph is a straight line from (0 s, 4 m/s) rising to (6 s, V m/s), followed by a straight line falling from (6 s, V m/s) to (9 s, 0 m/s). The gradient of the second line is −8 m/s². Work out the total distance travelled between t = 0 and t = 9 seconds.

8.A geometric sequence has first term 3 and common ratio √2. Work out the 6th term of the sequence, giving your answer in the form a√2.

9.Solve 5x² − 15x = 0.

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

11.The graph of y = cos x is transformed onto the graph of y = cos(x − 90°). State the direction of the translation and which standard graph the image is.

12.The 2nd term of a geometric sequence is 6 and the 4th term is 24. Given that all the terms of the sequence are positive, work out the common ratio.

13.f(x) = x + 2 and g(x) = x². Work out the value of x for which fg(x) = gf(x).

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

15.The graph of y = f(x) has a minimum turning point at (3, 2). Write down the coordinates of the minimum turning point of the graph of y = f(x) + 5.