Algebra worksheet — GCSE Foundation

1.The graph of y = x² − 2x − 8 takes these values: when x = −2, y = 0; when x = −1, y = −5; when x = 0, y = −8; when x = 3, y = −5; when x = 4, y = 0. Use these values to write down the two solutions of x² − 2x − 8 = 0.

2.Which of these is an inequality?

3.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.

4.Write down the number of terms in the expression 4x² − 7x + 3.

5.Work out the coordinates of the midpoint of the line segment joining (−3, 5) and (7, 9).

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

7.A straight line has equation y = 5x. Work out the value of y when x = 3.

8.A geometric sequence starts at 3, and each term after that is found by multiplying the term before it by 2. Write down the first four terms.

9.The first four terms of a sequence are 4, 6, 8, 10. Work out an expression, in terms of n, for the nth term.

10.A taxi charges a £3 fixed fee plus £2 for each mile travelled. Write an expression, in pounds, for the total cost of a journey of n miles.

11.Solve the simultaneous equations 5x − 2y = 16 and 3x + 2y = 16. Work out the value of x.

12.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.

13.Solve (2x + 1)/3 = 5

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

15.The graph of y = 24/x is drawn for x > 0. Work out the value of y when x = 6.