Algebra worksheet — GCSE Foundation

1.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.

2.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.

3.A sequence has the position-to-term rule 5n − 2, where n is the position number. Which of these is a term in the sequence?

4.There are 30 students in a Year 10 maths class. There are 2 more boys than girls. Work out the number of boys and the number of girls.

5.The perimeter of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. A rectangular garden has a perimeter of 46 m and a length of 14 m. Rearrange the formula to make w the subject, then work out the width of the garden.

6.A number machine multiplies its input by 3 and then adds 7. The output is 1. Work out the input.

7.A car's speed-time graph shows the following: its speed increases steadily from 0 m/s to 20 m/s over the first 10 seconds, then stays constant at 20 m/s for the next 15 seconds. Work out the total distance travelled in the first 25 seconds.

8.Solve 3x − 1 = 8

9.Which of these numbers is a cube number?

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

11.The first five cube numbers are 1, 8, 27, 64, 125. Write down the next cube number in the sequence.

12.Which expression means 'triple c, then add double d'?

13.Which of these equations gives a graph shaped like a U, symmetrical about a vertical line?

14.Solve x² − 2x − 24 = 0.

15.Work out the equation of the straight line through the points (−3, 4) and (1, −8).