Algebra worksheet — GCSE Higher

1.A straight line passes through the points (2, 7) and (5, 16). Work out the value of y when x = 0.

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

3.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.

4.The nth term of a sequence is n² + 3. Work out the first term of the sequence that is greater than 50.

5.Work out the value of 3x² − 4x when x = −2.

6.The graph of y = sin x is reflected in the x-axis to give the graph of y = g(x). Work out the value of g(90), where x is measured in degrees.

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

8.A cinema sells adult tickets for £10 and child tickets for £6. A family group buys 9 tickets in total, spending £74. Work out how many adult tickets were bought.

9.Which of these values of x is a solution of x² + 2x − 15 = 0?

10.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?

11.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.

12.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

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

14.Solve 3(2x − 1) = 27

15.The nth term of a sequence is 4n − 3. Work out the 7th term of the sequence.