GCSE Mathematics (9-1)

8.1 Algebraic notation and vocabulary — Practise with help

Attempt each question before opening a hint. Reveal the full working to check your method.

Warm-up: remember

Answer from memory before checking.

  1. Work out −8+3-8+3.
  2. Work out 323^2.
Answers and feedback
  1. −5-5. 2. 99. If an answer differs, review the earlier method before continuing.

Practise with help

1. Write 7x7x as repeated addition, then state its coefficient.

Hint

Identify the letter, coefficient and constant in the written expression.

Next step

Write xx three times as a sum, then name the number multiplying xx.

Full working

Seven groups of xx; coefficient 77.

2. Write an expression for five more than nn.

Hint

Identify the letter, coefficient and constant in the written expression.

Next step

Which operation combines nn and 55?

Full working

n+5n+5.

3. Evaluate 3x+23x+2 when x=3x=3.

Hint

Identify the letter, coefficient and constant in the written expression.

Next step

Replace xx with 33, then multiply before adding.

Full working

3(3)+2=113(3)+2=11.

4. State the terms and coefficients in 4a+4b4a+4b.

Hint

Identify the letter, coefficient and constant in the written expression.

Next step

List each part separated by a plus sign and identify the number multiplying each letter.

Full working

Terms 4a4a and 4b4b; each coefficient is 44.

5. If each item costs £5, write and evaluate the total cost C=5nC=5n for n=6n=6.

Hint

Identify the letter, coefficient and constant in the written expression.

Next step

Replace nn with 66 in C=5nC=5n, then attach the currency unit.

Full working

C=5(6)=£30C=5(6)=£30.

6. Evaluate 2m+12m+1 when m=4m=4.

Hint

Identify the letter, coefficient and constant in the written expression.

Next step

Replace mm with 44 and follow the order of operations.

Full working

The expression 2m+12m+1 becomes 2(4)+1=92(4)+1=9.

7. Write an expression for three fewer than tt.

Hint

Identify the letter, coefficient and constant in the written expression.

Next step

Subtract 33 from tt.

Full working

t−3t-3.

8. Is 2m+1=92m+1=9 an expression or equation?

Hint

Identify the letter, coefficient and constant in the written expression.

Next step

An equation contains an equals sign. Does this statement have one?

Full working

It is an equation because it states equality.

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