Algebra worksheet — GCSE Foundation

1.Simplify p + p + p.

2.A rule turns each input into an output. An input of 0 gives an output of −1, an input of 1 gives an output of 1, and an input of 2 gives an output of 3. Work out the rule, writing the input as x and the output as y.

3.A number machine multiplies its input by 3. The output is 15. Work out the input.

4.x = 5. Work out the value of 3x² − 4.

5.Solve 5x² − 15x = 0.

6.The simple interest, £I, earned on a savings account is given by the formula I = PRT/100, where P is the amount invested in pounds, R is the interest rate per year and T is the time in years. Rearrange the formula to make P the subject.

7.Given that (x − 4)(x + 9) = 0, write down the two solutions of x.

8.Which expression is equivalent to 2(x + 6)?

9.A geometric sequence has first term 5, and each term after that is 3 times the term before it. Work out the first term of the sequence that is greater than 1000.

10.A gym charges a reduced price for the first month of membership and a standard price for every month after that. The total cost is £5 for 1 month, £12 for 2 months, £19 for 3 months and £26 for 4 months. Work out an expression, in terms of n, for the total cost, in pounds, of n months of membership.

11.The point C is 6 units to the right of the origin and 0 units up. Write down the coordinates of C.

12.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.

13.Write down the expression that means 5 more than half of n.

14.A number machine multiplies its input by 5. Work out the output when the input is −1.

15.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.