Algebra worksheet — GCSE Foundation

1.A lift has a weight limit: it must carry no more than 630 kg. Let w be the total weight, in kg, carried by the lift. Which inequality describes this?

2.Expand 4(2x − 3).

3.The line y = 3x + 6 meets the x-axis at one point. Work out the coordinates of that point.

4.Write down the coordinates of the point that is 4 units to the left of the origin and 7 units up.

5.The formula for converting a temperature from degrees Celsius, C, to degrees Fahrenheit, F, is F = 1.8C + 32. Work out F when C = 20, and identify what kind of mathematical statement F = 1.8C + 32 is.

6.A taxi fare in pounds is given by F = 2.50 + 1.20m, where m is the number of miles travelled. Sam takes a taxi for a journey of 6 miles. Work out the fare.

7.The first five terms of a sequence are 6, 10, 14, 18, 22. Work out an expression, in terms of n, for the nth term.

8.A number machine adds 1 to its input. Isla says that an input of 5 gives an output of 6. Which statement is correct?

9.Which of these is an expression?

10.Which expression is equivalent to 6x − (2x − 5)?

11.Three consecutive integers add up to 72. Using n for the smallest integer, form an equation and solve it to find the smallest of the three integers.

12.Which expression means the same as a × a × a?

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

14.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.

15.The nth term of a sequence is 4n + 2. A term in the sequence has value 30. Work out its position, n, in the sequence.