Algebraic vocabulary Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Algebraic vocabulary questions. See exactly how to solve problems on expression, equals sign, equation, terms.

expressionequals signequationtermscounting termscoefficient
GCSE Foundation70 questionsStep-by-step solutions
Question 1
1 markeasy
Is 3x+53x + 5 an expression or an equation?

Worked solution

  1. Look for an equals sign

    3x+53x + 5

    Scan the statement: there is no = sign anywhere.

  2. Recall the definition

    3x+5terms only3x + 5 \rightarrow \text{terms only}

    An expression is just a collection of terms with no equals sign.

  3. State the answer

    expression\text{expression}

    So 3x + 5 is an expression.

Answer
Expression
Question 2
1 markeasy
Is 4x=124x = 12 an expression or an equation?

Worked solution

  1. Look for an equals sign

    4x=124x = 12

    There is an = sign in the statement.

  2. Recall the definition

    4x=12 true when x=34x = 12 \text{ true when } x = 3

    An equation has an equals sign and is true only for particular value(s) of the letter.

  3. State the answer

    equation\text{equation}

    So 4x=124x = 12 is an equation.

Answer
Equation
Question 3
1 markeasy
How many terms are in the expression 2x+3y52x + 3y - 5?

Worked solution

  1. Terms are separated by + or - signs

    2x+3y52x + 3y - 5

    Split the expression at each + or - sign.

  2. List the terms

    2x,  3y,  52x,\; 3y,\; -5

    The parts are 2x, 3y and -5.

  3. Count them

    33

    There are 3 terms.

Answer
33
Question 4
1 markeasy
Write down the coefficient of xx in 7x+27x + 2.

Worked solution

  1. Find the term in x

    7x7x

    The term containing x is 7x.

  2. The coefficient is the number multiplying x

    7×x7 \times x

    The number in front of x is 7.

  3. State the answer

    77

    The coefficient of x is 7.

Answer
77
Question 5
1 markeasy
Is A=πr2A = \pi r^2 an expression or a formula?

Worked solution

  1. Look at the features

    A=πr2A = \pi r^2

    It has an = sign and links two different letters, A and r.

  2. Recall the definition

    rule linking A and r\text{rule linking } A \text{ and } r

    A formula has an equals sign and links two or more different letters (variables).

  3. State the answer

    formula\text{formula}

    This is the formula for the area of a circle.

Answer
Formula

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