Algebra worksheet — GCSE Higher

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

2.Work out the gradient of the straight line that passes through the points (−1, 5) and (3, −7).

3.The first five terms of a quadratic sequence are 4, 7, 12, 19, 28. Work out an expression, in terms of n, for the nth term.

4.The solution set of an inequality is described as: x is less than −3, or x is greater than or equal to 1. Write this solution set using set notation.

5.A gym charges a reduced price for the first month of membership and a standard price for every month after that. The total cost is £5 for 1 month, £12 for 2 months, £19 for 3 months and £26 for 4 months. Work out an expression, in terms of n, for the total cost, in pounds, of n months of membership.

6.A student is proving that (n + 1)² − n² is always an odd number. Which of these correctly completes the first line of algebra?

7.A region R satisfies y ≤ x + 1, x + y ≤ 5 and y ≥ 0. Which of these correctly describes R in words?

8.The graph of y = x³ − 5x is reflected in the y-axis. Work out the equation of the image.

9.A rule turns each input x into an output y. The inputs are x = 0, 1, 2, 3 and the outputs are y = 4, 7, 10, 13. Work out the output when x = 5.

10.Expand and simplify (x − 3)²

11.Which of these equations represents the graph of y = 2ˣ translated by 3 units in the positive y-direction?

12.Matchsticks are laid out as a row of squares, with each new square sharing a side with the square before it. The first square uses 4 matchsticks and every extra square uses 3 more. Work out how many matchsticks a row of 4 squares uses.

13.Solve the simultaneous equations 3x + y = 14 and x + y = 6. Work out the value of x.

14.For the equation 2x + 3 = 11, and the inequality 2x + 3 > 11, which statement correctly compares their solutions?

15.The point A(−6, 8) lies on the circle x² + y² = 100, whose centre is the origin O. The tangent to the circle at A crosses the y-axis at the point B. Work out the length of OB.