Algebra worksheet — GCSE Foundation

1.Yusuf has £40 saved and adds £6 each week. His sister Aisha has £10 saved and adds £11 each week. After how many weeks will they have saved the same amount?

2.Here are the first four terms of an arithmetic sequence: 5, 9, 13, 17. Work out the 5th term.

3.A zip-line runs from a platform 25 m high to a landing point 5 m high, over a horizontal distance of 40 m. Work out the gradient of the zip-line.

4.The mean of four numbers is 12.5. Three of the numbers are 8, 15 and 19. Form an equation using n for the fourth number, and solve it to find n.

5.Work out the value of 5y + 9 when y = 0

6.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.

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

8.The formula for the perimeter of a rectangle is P = 2(l + w). One rectangle has l = 9 cm and w = 4 cm. A second rectangle has l = 6 cm and w = 5 cm. Work out how many cm greater the perimeter of the first rectangle is than the perimeter of the second.

9.Solve x² = 81.

10.Work out the values of x and y that satisfy both x + y = 10 and x − y = 4.

11.A company's profit is £500 in its first year. Each year after that, the profit is £300 more than the year before. Work out the profit in the company's 6th year.

12.A vertical line passes through the point (4, 7). Write down the equation of this line.

13.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.

14.Solve the inequality 2(x − 1) ≤ 8.

15.The point F has x-coordinate −1 and lies 6 units above the x-axis. Write down the coordinates of F.