Algebra worksheet — GCSE Foundation

1.A quadratic graph has roots at x = −3 and x = 5, and it crosses the y-axis at (0, −15). Work out the equation of the curve in the form y = (x − a)(x − b).

2.A pattern is made from tiles. Pattern 1 uses 4 tiles, pattern 2 uses 7 tiles, pattern 3 uses 10 tiles and pattern 4 uses 13 tiles, with each pattern using 3 more tiles than the one before. Work out an expression, in terms of n, for the number of tiles used in pattern n.

3.A gas company charges a standing charge plus a rate per unit used. The total cost, y in pounds, for using x units is given by y = 0.15x + 20. Work out the cost of using 200 units.

4.Solve the inequality 3x + 6 ≤ 0.

5.Work out the value of (x − 4)/2 + 3 when x = 10

6.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.

7.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x

8.Which expression means 'add 3 to n, then multiply the result by 4'?

9.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.

10.Solve x − 4 = −9

11.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.

12.Write down the expression that means the same as m² × m × 3.

13.A number machine adds 5 to its input. Work out the output when the input is 0.

14.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.

15.Factorise x² − 64.