Algebra worksheet — GCSE Foundation

1.The braking distance of a car, in metres, is estimated using the formula d = 0.4v² + 6, where v is the speed in mph. A car travelling at 35 mph brakes. Work out the estimated braking distance.

2.Which expression is equivalent to 3(x + 4) − 2(x − 1)?

3.Kai writes the expression 8 − 3x + 5x² and says it has three terms. Ryan says it only has two terms because a number on its own is not a term. Work out the correct number of terms in the expression.

4.Which expression means 'add 3 to n, then multiply the result by 4'?

5.Which of these values of x is a solution of x² + 2x − 15 = 0?

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

7.A number machine multiplies its input by 3. The output is 15. Work out the input.

8.A company's profit was £2000 in its first year. Each following year, the profit increases by £800. Work out the first year in which the profit is more than £7000.

9.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.

10.Isla says that the lines y = 2x + 1 and y = −2x + 3 are parallel. Write down the statement that gives the correct answer for the correct reason.

11.The formula for converting a temperature from degrees Celsius, C, to degrees Fahrenheit, F, is F = 1.8C + 32. Work out F when C = 20, and identify what kind of mathematical statement F = 1.8C + 32 is.

12.Which of these points lies in the first quadrant?

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

14.The diagram shows the graph of the cost, in pounds, of a taxi journey plotted against the distance travelled, in miles, for journeys of up to 4 miles. The same fixed charge and the same cost per mile apply to longer journeys. Work out the cost of a 6-mile journey.

15.Solve the simultaneous equations 3x + 2y = 16 and x + y = 7. Work out the value of y.