Algebraic notation worksheet — GCSE Higher

1.Tom buys 2 notebooks and 6 pencils on Monday, priced at p pence each for a notebook and q pence each for a pencil. On Tuesday he buys 3 more notebooks and 1 more pencil. Write a simplified expression, in pence, for the total amount Tom has spent on notebooks and pencils.

2.p = 4. Work out the value of 2p³.

3.A rope of length L metres is cut into 6 equal pieces, and 4 metres is then removed from one piece. Write an expression, in metres, for the length of that piece after the cut.

4.Write down the expression that means 5 more than half of n.

5.n = 3. Work out the value of (2n)².

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

7.Which expression means 'y squared, multiplied by 3'?

8.Which expression means 'triple c, then add double d'?

9.A box holds n pencils. A shop has 6 full boxes and 4 loose pencils. All of these pencils are shared equally between 2 classes. Write down the expression for the number of pencils each class receives.

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

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

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

13.Write down the expression that means the same as 'subtract 5 from n, then divide the result by 2'.

14.A ribbon of length L metres is cut into 5 equal pieces, and then 3 metres is removed from one piece. Write down an expression, in metres, for the length of that piece after 3 metres is removed.

15.a = 2 and b = 5. Work out the value of a²b.