Algebra worksheet — GCSE Foundation

1.Make x the subject of the formula y = 4x − 3.

2.A coach company charges a booking fee plus a price for each passenger. A booking for 1 passenger costs £9, for 2 passengers costs £15, for 3 passengers costs £21, and for 4 passengers costs £27. Work out an expression, in terms of n, for the cost in pounds of a booking for n passengers.

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.Solve 3x + 14 = 8x − 6

5.The expression 6n + 15 is written as 3(2n + 5). Which statement is correct?

6.A square has vertices at (−2, 3), (−2, −3) and (4, −3). Write down the coordinates of the fourth vertex.

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

8.Oliver buys b pens. Each pen costs £2. Write down an expression for the total cost, in pounds.

9.Simplify 5a/6 − a/3

10.A number machine adds 6 to its input. Work out the output when the input is −4.

11.ABCD is a parallelogram. A has coordinates (−3, 1), B has coordinates (2, 1) and C has coordinates (4, 4). Work out the coordinates of D.

12.A colony of bacteria doubles in number every hour. At 9am there are 5 bacteria in the colony. Work out how many bacteria there will be at 12 noon.

13.The solution set of an inequality is x ≥ 7. Write down the value that does NOT satisfy this inequality.

14.The formula connecting distance (d), speed (s) and time (t) is d = st. Make s the subject of the formula.

15.A sequence begins at 7. Each term after the first is found by adding 6 to the term before it. Work out the 6th term of the sequence.