Algebra worksheet — GCSE Foundation

1.The first term of an arithmetic sequence is 5, and each term after that increases by 6. Work out the 8th term of the sequence.

2.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.

3.A company charges for hiring chairs for a day. Hiring 1 chair costs £12, hiring 2 chairs costs £19, hiring 3 chairs costs £26, and hiring 4 chairs costs £33. Work out an expression, in terms of n, for the cost in pounds of hiring n chairs for a day.

4.Solve (3x + 2)/5 = (x + 4)/3

5.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.

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

7.Point R has coordinates (3, −5). Point R is reflected in the line y = 2 to point S. Write down the coordinates of S.

9.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.

10.Water is poured into a container at a constant rate. A graph of the depth of the water, in cm, against the time since pouring began, in minutes, is a straight line through the origin, and it passes through the point (3, 12). Use the graph to work out the depth of the water after 7 minutes.

11.A square has sides of length y cm. Write down an expression for the perimeter of the square.

12.A hiker's distance-time graph shows the following: he walks 5 km in the first 1 hour at a steady speed, rests for 1 hour, then walks a further 9 km in the next 2 hours, also at a steady speed. Work out his average speed for the whole journey, in km/h.

13.Simplify 5x + 3y − 2x + y.

14.y = x + 10. Work out the value of y when x = 0.

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