Algebra worksheet — GCSE Foundation

1.A line segment has one endpoint at (−6, 2) and its midpoint at (−1, 5). Work out the coordinates of the other endpoint.

2.A taxi company charges a £2.50 booking fee plus £1.80 per mile. A journey costs £15.10 in total. Work out the number of miles travelled.

3.Write down the first four terms of the sequence with nth term 6n − 5.

4.Which of these is a factor of 15x + 20?

5.Simplify k + k + k + k + k.

6.A sequence has the position-to-term rule n² + 2, where n is the position number. Work out the 6th term.

7.A person's body mass index is given by the formula B = m ÷ h², where m is the mass in kg and h is the height in metres. Work out B, to 1 decimal place, when m = 68 and h = 1.6.

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

9.A pattern is made from tiles. Pattern 1 has 7 tiles, pattern 2 has 11 tiles, pattern 3 has 15 tiles, and pattern 4 has 19 tiles, with each new pattern having 4 more tiles than the one before it. Work out an expression, in terms of n, for the number of tiles in pattern n.

10.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.

11.The formula connecting speed, distance and time is v = s ÷ t. Work out v, in km/h, when s = 180 and t = 4.

12.Work out the equation of the straight line through the points (−3, 4) and (1, −8).

13.A rule turns each input x into an output y. The inputs are x = −1, 0, 1, 2 and the matching outputs are y = 5, 3, 1, −1. Work out the rule.

14.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.

15.Mia buys 3 identical notebooks and a pen costing £1.50. She pays a total of £9.90. Form an equation using n for the cost of one notebook, and solve it to find n.