Algebra worksheet — GCSE Foundation

1.A recipe gives the cooking time, in minutes, for a chicken as T = 40m + 20, where m is the mass in kg. A chicken has a mass of 1.8 kg. Work out the cooking time in hours and minutes.

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

3.A rectangular field has length (3a + 2) metres and width (a − 1) metres. Write a simplified expression for the perimeter of the field.

4.A taxi fare, in pounds, for a journey of m miles is given by the formula F = 3 + 2.5m. A journey costs £15.50. Work out the distance travelled, m, by first rearranging the formula to make m the subject, then substituting F = 15.50.

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.Write down the expression that means the same as m² × m × 3.

7.Write down the y-intercept of the line with equation y = 3x + 8.

8.Expand and simplify (x − 3)²

9.The formula for converting a temperature in Fahrenheit, F, to Celsius, C, is C = 5(F − 32) ÷ 9. Work out C, to 1 decimal place, when F = 98.6.

10.A quadratic graph y = ax² + bx + c has its turning point on the y-axis. Which statement about its roots must be true?

11.Make x the subject of the formula y = 2x − 9.

12.Noah says that y = 3 is the solution of the equation y + 10 = 12. Noah is wrong. Work out the correct value of y.

13.The formula y = x² + 1 gives y in terms of x. Work out the value of y when x = −2.

14.In which quadrant does the point (−3, 0.5) lie?

15.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.