Algebra worksheet — GCSE Foundation

1.The first four terms of a sequence are 4, 9, 14, 19. Work out an expression, in terms of n, for the nth term.

2.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.

3.The graph of y = (x − 2)(x + 5) crosses the x-axis at two points. Work out the x-coordinates of these two points.

4.A Fibonacci-type sequence begins 3, 5, 8, 13, ... where each term after the second is the sum of the two terms before it. Work out the 7th term of the sequence.

5.The point A is at (5, −3). In which quadrant does A lie?

6.A straight line has equation y = 4x + 3. A second line is parallel to the first line and passes through the point (0, −5). Work out the equation of the second line.

7.Which expression means 'y squared, multiplied by 3'?

8.The first five terms of a quadratic sequence are 5, 8, 13, 20, 29. Work out the next term in the sequence.

9.A cinema sells adult tickets and child tickets. On one evening, 40 tickets are sold in total. There are 8 more adult tickets sold than child tickets. Work out the number of child tickets sold.

10.Which of these is an inequality?

11.Three vertices of a rectangle are (−4, −1), (2, −1) and (2, 3). The sides of the rectangle are parallel to the axes. Write down the coordinates of the fourth vertex.

12.The solution set of an inequality is x ≥ 7. Write down the value that does NOT satisfy this inequality.

13.Given that (x − 4)(x + 9) = 0, write down the two solutions of x.

14.Simplify p + p + p.

15.A rectangle has area 24x + 18. Ffion factorises the area as 6(4x + 3). Work out the value of the area when x = 2, and decide whether 6 and (4x + 3) are correctly identified as factors of 24x + 18.