[discia] GCSE Maths › Algebra › Expressions, Equations and Identities

Expressions, Equations and Identities

discia.org 10 questions · 23 marks
Name Date
  1. Either paper 3 marks

    Here is an expression.

    \(8t^2 - 4t + 2\)

    (a)

    State how many terms the expression has.

    (b)

    State the coefficient of \(t^2\).

    (c)

    State the constant term.

    Show answer
    (a) \(3\)
    (b) \(8\)
    (c) \(2\)
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  2. Either paper 1 mark
    Here are four statements.

    A  \(3x - 9\)

    B  \(3x - 9 = 27\)

    C  \(y = 3x - 9\)

    D  \(5(x + 5) \equiv 5x + 25\)

    Write down the letter of the statement that is a formula.
    Show answer
    C
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  3. Either paper 3 marks

    Tomas charges for repairing a bike using the formula

    \(C = 9n + 17\)

    where \(C\) is the total charge in pounds and \(n\) is the number of parts. The call-out fee is included in the formula.

    (a)

    Work out the total charge when \(n = 7\).

    (b)

    Explain why \(C = 9n + 17\) is a formula and not an equation.

    Show answer
    (a) \(\text{£}80\)
    (b) It is a rule for working the charge out from the number of parts, and it holds for any number of parts. An equation such as \(9n + 17 = 80\) is true only when \(n = 7\).
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  4. Either paper 3 marks
    Match each box on the left to the box on the right with the same value. One has been done for you.
    LeftRight
    A  \(x · x · x\)P  \(x^2\)
    B  \(3x - x\)Q  \(x^3\)
    C  \(x · x\)R  \(x^4\)
    D  \(5x - 2x\)S  \(2x\)
     T  \(3x\)
    Box A on the left has been linked to box Q on the right. Link the other three boxes on the left. Give your answer as pairs of letters, for example A to P.
    Show answer
    B to S; C to P; D to T
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  5. Either paper 1 mark
    One of these four statements is an identity.

    A  \(6x + 8 \equiv 50\)

    B  \(4x \equiv 8\)

    C  \(3x - 4x \equiv x\)

    D  \(3x - 4x \equiv -x\)

    Circle the identity.
    Show answer
    \(3x - 4x \equiv -x\)
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  6. Either paper 1 mark
    Here is a statement about \(x\). \(6(x - 2) = 8x - 15\) Tick one box.

    ☐  It is true for all values of \(x\)

    ☐  It is true for some values of \(x\)

    ☐  It is true for no values of \(x\)

    Show answer
    It is true for some values of \(x\)
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  7. Either paper 2 marks

    \(8(x + c) \equiv 8x - 32\)

    Find the value of \(c\).

    Show answer
    \(-4\)
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  8. Either paper 2 marks

    Show that

    \(6(x + 2) + 2 \equiv 6x + 14\)

    Show answer
    Expanding gives \(6x + 12 + 2 = 6x + 14\), which is the right-hand side.
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  9. Either paper 3 marks

    \(m\) and \(n\) are numbers.

    \(m - n = 16\)

    (a)

    Find the value of \(2(m - n)\)

    (b)

    Find the value of \(n - m\)

    (c)

    Find the value of \(3m - 3n\)

    Show answer
    (a) \(32\)
    (b) \(-16\)
    (c) \(48\)
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  10. Either paper 4 marks

    Work out the values of \(a\) and \(b\) in the identity

    \(3(9x + 3) + 4(9x + b) \equiv ax - 3\)

    Give your answer as \(a = \ldots\), \(b = \ldots\)

    Show answer
    \(a = 63\), \(b = -3\)
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discia.org Expressions, Equations and Identities · sheet 1
Answers Expressions, Equations and Identities · sheet 1
  1. (a) \(3\)
    (b) \(8\)
    (c) \(2\)
  2. C
  3. (a) \(\text{£}80\)
    (b) It is a rule for working the charge out from the number of parts, and it holds for any number of parts. An equation such as \(9n + 17 = 80\) is true only when \(n = 7\).
  4. B to S; C to P; D to T
  5. \(3x - 4x \equiv -x\)
  6. It is true for some values of \(x\)
  7. \(-4\)
  8. Expanding gives \(6x + 12 + 2 = 6x + 14\), which is the right-hand side.
  9. (a) \(32\)
    (b) \(-16\)
    (c) \(48\)
  10. \(a = 63\), \(b = -3\)
discia.org Expressions, Equations and Identities · sheet 1