Algebra worksheet — GCSE Foundation

1.Simplify p + p + p.

2.Solve the simultaneous equations x + y = 15 and x − y = 3. Work out the value of x.

3.Simplify x + x + 4

4.Which of these is a factor of 15x + 20?

5.Which of these is a formula?

6.Solve 4x − (2x − 6) = 18

7.Write down the gradient of the line with equation y = −x + 3.

8.Priya has a budget of £50 for a school trip. The coach costs £14 and each student ticket costs £4. Using the inequality 14 + 4s ≤ 50, work out the greatest number of student tickets, s, she can buy.

9.Solve the inequality 2(x − 1) ≤ 8.

10.A rectangle has length (2x + 5) cm and width (x − 2) cm. Work out an expression, in terms of x, for the perimeter of the rectangle. Give your answer in its simplest form.

11.The graph of y = x² − 5x + 6 crosses the x-axis at two points. By factorising, work out the x-coordinates of these two points.

12.Write down 0.2x with its coefficient written as a fraction in its simplest form.

13.A rectangular garden has length (x + 7) m and width (x − 7) m. Work out an expression for the area of the garden, giving your answer in its simplest form.

14.A hall is set out in rows of chairs for an assembly. Row 1 has 50 chairs, row 2 has 45 chairs, row 3 has 40 chairs, and row 4 has 35 chairs, with each row after the first having 5 fewer chairs than the one before. Work out an expression, in terms of n, for the number of chairs in row n.

15.A pizza shop charges a fixed delivery fee of £3, plus £9 for each pizza ordered. Write down the function for the total cost y, in pounds, of ordering x pizzas.