Algebra worksheet — GCSE Foundation

1.Solve the simultaneous equations 3x + y = 14 and x + y = 6. Work out the value of x.

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

3.A cinema sells adult tickets for £10 and child tickets for £6. A family group buys 9 tickets in total, spending £74. Work out how many adult tickets were bought.

4.Work out the value of 4p² − 3 when p = 2.5

5.To solve 6x − 4 = 2x + 20, Yusuf's first step is to subtract 2x from both sides. Work out what equation this gives.

6.A photo printing service has two adverts for its price. Advert A: cost in pounds = 3(2n + 4) for n photos. Advert B: cost in pounds = 6n + 12. A customer says the two adverts always charge the same amount. Is the customer correct?

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

8.The solution to an inequality is n ≤ 5. Write down the largest integer value of n that satisfies this inequality.

9.Solve 2x² − 32 = 0.

10.Which of these is a formula?

11.Work out the value of 3n − 2 when n = 1

12.Factorise fully 5x + 5y − 5

13.A sequence begins at 60, and each term after that is found by subtracting 7 from the term before it. Work out the 5th term of the sequence.

14.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.

15.A rectangle has length k cm and width 5 cm less than its length. Write down an expression for the width of the rectangle, in cm.