GCSE Algebraic vocabulary Practice Questions

Free GCSE Algebraic vocabulary practice questions with full step-by-step worked solutions. Covers expression, equals sign, equation, terms. Practise exam-style problems and check your method.

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

Worked solution

  1. Look for an equals sign

    3x+53x + 5

    Scan the statement: there is no = sign anywhere.

  2. Recall the definition

    3x+5→terms 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 5x−2=85x - 2 = 8 an expression or an equation?
Show worked solution

Worked solution

  1. Look for an equals sign

    5x−2=85x - 2 = 8

    There is an = sign.

  2. Recall the definition

    true only when x=2\text{true only when } x = 2

    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 5x−2=85x - 2 = 8 is an equation.

Answer
Equation
Question 3
2 marksintermediate
Is x2=9x^2 = 9 an equation or an identity? Explain your choice.
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Worked solution

  1. Recall equation versus identity

    = vs ≡= \text{ vs } \equiv

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

  2. Ask whether it is true for all x

    x2=9x^2 = 9

    Check whether every value of x works.

  3. Test some values

    x=3:  9=9,x=2:  4≠9x=3:\; 9=9, \quad x=2:\; 4 \neq 9

    True for x=3x = 3 but not for x=2x = 2.

  4. Find the solutions

    x=3 or x=−3x = 3 \text{ or } x = -3

    Only these two values make it true.

  5. Decide equation or identity

    true for some x only\text{true for some } x \text{ only}

    Since it is not true for all x, it is not an identity.

  6. State the answer

    equation\text{equation}

    So x2=9x^2 = 9 is an equation.

Answer
Equation
Question 4
4 markshard
For the expression x2+9x+20x^2 + 9x + 20: (a) how many terms, (b) the coefficient of x2x^2, (c) the coefficient of xx, (d) the constant term, and (e) verify that x2+9x+20=(x+4)(x+5)x^2 + 9x + 20 = (x + 4)(x + 5) is an identity by expanding.
Show worked solution

Worked solution

  1. Identify the terms

    x2,  9x,  20x^2,\; 9x,\; 20

    Split at each + sign.

  2. Count the terms

    33

    There are 3 terms.

  3. Find the x squared term

    x2=1x2x^2 = 1x^2

    A lone x2x^2 means 1 times x2x^2.

  4. Coefficient of x squared

    x2→1x^2 \rightarrow 1

    The coefficient of x2x^2 is 1.

  5. Coefficient of x

    9x→99x \rightarrow 9

    The number multiplying x is 9.

  6. Find the constant term

    2020

    The term with no letter is 20.

  7. Expand the brackets

    (x+4)(x+5)=x2+5x+4x+20(x + 4)(x + 5) = x^2 + 5x + 4x + 20

    Multiply every term in the first bracket by each in the second.

  8. Collect like terms

    x2+9x+20x^2 + 9x + 20

    5x + 4x combine to 9x.

  9. Compare both sides

    x2+9x+20=x2+9x+20x^2 + 9x + 20 = x^2 + 9x + 20

    The two sides match for all x, so it is an identity.

  10. State all the answers

    3,  1,  9,  20,  identity3,\; 1,\; 9,\; 20,\; \text{identity}

    3 terms; coefficients 1 and 9; constant 20; the factorisation is an identity.

Answer
3terms;coefficientofx2is1;coefficientofxis9;constant20;thefactorisationisanidentity3 terms; coefficient of x^2 is 1; coefficient of x is 9; constant 20; the factorisation is an identity
Question 5
6 markschallenging
A taxi charges a fixed fee plus a rate per mile. The total cost is C=3+2mC = 3 + 2m, where mm is the number of miles. (a) Classify C=3+2mC = 3 + 2m. (b) Name the subject. (c) List the variables. (d) State the constant (fixed fee). (e) State the coefficient of mm and explain what it represents. (f) Classify 3+2m3 + 2m on its own.
Show worked solution

Worked solution

  1. Look at the whole statement

    C=3+2mC = 3 + 2m

    It has an equals sign and two letters.

  2. Check for a formula

    C←mC \leftarrow m

    It gives a rule for cost from miles, so it is a formula.

  3. Classify the whole statement

    formula\text{formula}

    So C=3+2mC = 3 + 2m is a formula.

  4. Identify the subject

    C=…C = \ldots

    The subject is the letter on its own: C.

  5. List the letters

    C,\; m

    The letters used are C and m.

  6. State the variables

    C,\; m

    The variables are C and m.

  7. Find the constant term

    33

    The fixed fee is the constant term 3.

  8. Interpret the constant

    fixed fee=3\text{fixed fee} = 3

    The 3 is a fixed charge that does not depend on distance.

  9. Find the term in m

    2m2m

    The term containing m is 2m.

  10. Read off the coefficient of m

    2m→22m \rightarrow 2

    The coefficient of m is 2.

  11. Interpret the coefficient

    2=cost per mile2 = \text{cost per mile}

    The 2 is the cost per mile travelled.

  12. Look at 3 + 2m alone

    3+2m  (no =)3 + 2m \;(\text{no } =)

    On its own there is no equals sign.

  13. Classify 3 + 2m alone

    expression\text{expression}

    So 3 + 2m by itself is an expression.

  14. Bring the parts together

    formula;  C;  C,m;  3;  2;  expression\text{formula};\; C;\; C,m;\; 3;\; 2;\; \text{expression}

    Collect all answers.

  15. State all the answers

    formula;  C;  C,m;  3;  2;  expression\text{formula};\; C;\; C,m;\; 3;\; 2;\; \text{expression}

    It is a formula; subject C; variables C and m; constant 3; coefficient of m is 2 (cost per mile); and 3 + 2m alone is an expression.

Answer
formula; subject C; variables C and m; constant 3; coefficient of m is 2 (cost per mile); 3 + 2m alone is an expression

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