Algebra worksheet — GCSE Foundation

1.Which of these is an identity?

2.Simplify 2a + 3b − a + 2b − b

3.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.

4.Harry will spend at most £150 on a party. The cake costs £60 and each helium balloon costs £3. Solve an inequality to find all the possible numbers of balloons, x, that he can buy.

5.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.

6.A number machine adds 1 to its input. Isla says that an input of 5 gives an output of 6. Which statement is correct?

7.A straight line has equation y = 2x − 7. Write down the coordinates of the point where the line crosses the y-axis.

8.A rectangle is x cm wide and twice as long as it is wide, so its area A cm² is given by A = 2x². Work out A when x = 3.

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.The triangular numbers begin 1, 3, 6, 10, 15, ... Work out the next term in the sequence.

11.Make x the subject of the formula y = x/2 − 5.

12.A straight line passes through the points (−1, 2) and (3, 14). Work out the equation of the line.

13.A sequence has the position-to-term rule n² − 3, where n is the position number. Work out the difference between the 6th term and the 5th term.

14.The simultaneous equations x = 2 and x + y = 9 are given. Work out the value of y.

15.A sequence starts at 2. Each term after that is found using the rule "double the previous term, then add 1". Work out the 4th term of the sequence.