Algebra worksheet — GCSE Foundation

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

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

3.Work out the gradient of the straight line with equation 3y = 12 − 6x.

4.Make m the subject of the formula w = m − 8.

5.The graph of y = 20/x is drawn for x > 0. As the value of x increases, what happens to the value of y?

6.A candle is 30 cm tall and burns down at a steady rate of 1 cm per hour. Write down the function for the height of the candle y, in centimetres, after x hours.

7.Factorise fully 12x² + 18x.

8.Solve x/4 + 1 = 3

9.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.

10.A number, w, satisfies the statement "three times w, minus 5, is at least 16". Which of these is the correct inequality for w?

11.To rearrange y = 2x − 5 to make x the subject, Sam writes: 'Add 5 to both sides to get y + 5 = 2x, then divide both sides by 2 to get x = (y + 5)/2.' Which statement about Sam's method is correct?

12.A hall is set out in rows of chairs for an assembly. Row 1 has 50 chairs, row 2 has 45 chairs, row 3 has 40 chairs, and row 4 has 35 chairs, with each row after the first having 5 fewer chairs than the one before. Work out an expression, in terms of n, for the number of chairs in row n.

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

14.Factorise fully 56x − 24

15.Solve x² = 49.