Algebra worksheet — GCSE Foundation

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

2.To rearrange the formula y = 3x − 8 to make x the subject, Priya writes: 'Add 8 to both sides to get y + 8 = 3x, then divide both sides by 3 to get x = y + 8 ÷ 3.' Work out the correct expression for x.

3.The nth term of a sequence is 2n² + 1. Work out the 4th term of the sequence.

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.Two numbers have a sum of 24. Their difference is 6. Work out the two numbers.

6.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.

7.The first five terms of a sequence are 2, 5, 8, 11, 14. Work out an expression, in terms of n, for the nth term.

8.A sequence has the position-to-term rule n² + 1, where n is the position number. Work out how much bigger the 5th term is than the 4th term.

9.Work out the value of 5a + 2 when a = 3

10.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.

11.Write down the coordinates of the point where the line y = 2x + 4 crosses the y-axis.

12.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.

13.Which expression is equivalent to 0.5(4x + 6) − x?

14.A ramp rises 3 m over a horizontal distance of 12 m. Work out the gradient of the ramp.

15.The solution set of x ≥ −1 is drawn on a number line. Which description of that number line is correct?