Algebra worksheet — GCSE Foundation

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

2.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.

3.Solve the inequality 5 − x ≤ 2.

4.The point C is 6 units to the right of the origin and 0 units up. Write down the coordinates of C.

5.A plant is 4 cm tall in week 1. Each week after that, its height increases by 5 cm. Work out the first week in which the plant is taller than 30 cm.

6.Work out the value of 3x² − 4x when x = −2.

7.Solve 3x − 1 = 8

8.Expand and simplify 4(2x − 1) − 3(x + 2) − 5x

9.The diagram shows a straight line passing through the origin, drawn on a numbered grid. Which of these points lies on the line?

10.The formula for the energy stored in a stretched spring is E = (1/2)kx², where E is in joules, k is the spring constant in N/m and x is the extension in m. A spring with a spring constant of 40 N/m is stretched so that its extension is 0.3 m. Work out the energy stored in the spring.

11.A quadratic curve has a minimum turning point at (3, −4). Which of these statements about the curve must be true?

12.A box contains 6 chocolates. Write down an expression for the total number of chocolates in c boxes.

13.Which expression means the same as 3 × a × b?

14.On Monday, a runner covers 15 km in 2.5 hours. On Tuesday, she covers 12 km in 1.5 hours. Using the formula speed = distance ÷ time, work out on which day she ran faster, and by how much.

15.Write down the coefficient of xy in the expression 4x²y − 7xy + 2.