Algebra worksheet — GCSE Foundation

1.Which expression means the same as a × a × a?

2.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.

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

4.Solve the inequality 5 − x ≤ 2.

5.A charity's fundraising total, T pounds, over d days follows T = (d − 3)(30 − d) for 3 ≤ d ≤ 30, where T = 0 marks the start and end of the campaign. Work out how many days the campaign runs for, from start to end.

6.Solve 4(x − 3) = 2x + 6.

7.A number, w, satisfies the statement "three times w, minus 5, is at least 16". Which of these is the correct inequality for w?

8.Which of these is a formula, rather than an expression, an equation, or an identity?

9.A packet contains s sweets. The sweets are shared equally between f friends. Write an expression for the number of sweets each friend receives.

10.Solve 3x + 14 = 8x − 6

11.A car's speed-time graph shows the following: its speed increases steadily from 0 m/s to 20 m/s over the first 10 seconds, then stays constant at 20 m/s for the next 15 seconds. Work out the total distance travelled in the first 25 seconds.

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

13.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.

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

15.A rectangular photo has length (x + 3) cm and width x cm. Its area is 40 cm². Work out the value of x.