Algebra worksheet — GCSE Foundation

1.A student says 4(2x − 3) is equivalent to 8x − 3. Which statement gives the correct verdict and reason?

2.Solve 4x + 3 = 19

3.To rearrange the formula y = 3x − 8 to make x the subject, Priya writes: 'Add 8 to both sides to get y + 8 = 3x, then divide both sides by 3 to get x = y + 8 ÷ 3.' Work out the correct expression for x.

4.Work out the distance of the point (−6, 4) from the x-axis.

5.Solve the inequality x − 10 < −3.

6.A pizza shop charges a fixed delivery fee of £3, plus £9 for each pizza ordered. Write down the function for the total cost y, in pounds, of ordering x pizzas.

7.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.

8.Work out the y-intercept of the graph of y = x² + 3x − 10.

9.The first four terms of a sequence are 6, 13, 20, 27. Work out an expression, in terms of n, for the nth term.

10.The first term of an arithmetic sequence is 5, and each term after that increases by 6. Work out the 8th term of the sequence.

11.A point has coordinates (x, y), where x + y = 0 and x is not 0. In which two quadrants could this point lie?

12.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.

13.The equation 3(2x − 1) = 4x + 9 is rearranged by expanding the brackets. Which of these is the correctly expanded equation?

14.The first four terms of a sequence are 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.

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