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Simplifying Algebra

discia.org 10 questions · 23 marks
Name Date
  1. Either paper 2 marks

    Simplify \(8s + 8t + 4 - 6s - 3 +t\)

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    \(2s + 9t + 1\)
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  2. Either paper 2 marks
    (a)

    Simplify \(3a \times 6b\)

    (b)

    Simplify \(2a \times 6a\)

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    (a) \(18ab\)
    (b) \(12a^2\)
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  3. Either paper 3 marks

    Simplify fully.

    (a)

    \(c \times c \times c\)

    (b)

    \(p + p\)

    (c)

    \(b + b + b + b + 3 \times a \times a\)

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    (a) \(c^{3}\)
    (b) \(2p\)
    (c) \(4b + 3a^{2}\)
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  4. Either paper 1 mark

    Circle the expression that is equal to \(8m + 3 - 2m\)

    \(9m\) \qquad \(11 - 2m\) \qquad \(10m + 3\) \qquad \(6m + 3\)

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    \(6m + 3\)
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  5. Either paper 2 marks

    Simplify \(9n^2 + 3n -n^2 - 6n\)

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    \(8n^2 - 3n\)
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  6. Either paper 2 marks

    Simplify \(\frac{ 12k^{ 6 } }{ 2k^{ 3 } }\)

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    \(6k^{ 3 }\)
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  7. Either paper 4 marks

    Here is an expression.

    \(8s + 3t - 5s + 2t\)

    (a)

    Simplify the expression.

    (b)

    Work out the value of the expression when \(s = 2\) and \(t = -7\).

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    (a) \(3s + 5t\)
    (b) \(-29\)
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  8. Either paper 2 marks

    When \(4p + 3q + kp + 7q\) is simplified, the result is \(3p + 10q\).

    Work out the value of \(k\).

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    \(-1\)
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  9. Either paper 4 marks
    Match each expression on the left with the simplified expression on the right. One of the simplified expressions is not needed.
    ExpressionSimplified expression
    \(9(n + 4) - 36 - 2n\)A \(25n^2\)
    \(12n + 4 - 4 - n\)B \(13n\)
    \(3n + 16n - 6n\)C \(25n\)
    \(5n \times 5n\)D \(7n\)
    E \(11n\)
    Write the letter of the matching simplified expression for each expression.
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    Expression \(3n + 16n - 6n\) matches B; \(5n \times 5n\) matches A; \(9(n + 4) - 36 - 2n\) matches D; \(12n + 4 - 4 - n\) matches E. Option C is not needed.
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  10. Either paper 1 mark

    Zainab is asked to simplify \(8 \times 8n + 5n\)

    Here is her working.

    \(8 \times 8n + 5n = 88n + 5n = 93n\)

    Explain what is wrong with her working.

    Show answer
    The two numbers have been written side by side instead of being multiplied together. \(8 \times 8n = 64n\), not \(88n\).
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discia.org Simplifying Algebra · sheet 1
Answers Simplifying Algebra · sheet 1
  1. \(2s + 9t + 1\)
  2. (a) \(18ab\)
    (b) \(12a^2\)
  3. (a) \(c^{3}\)
    (b) \(2p\)
    (c) \(4b + 3a^{2}\)
  4. \(6m + 3\)
  5. \(8n^2 - 3n\)
  6. \(6k^{ 3 }\)
  7. (a) \(3s + 5t\)
    (b) \(-29\)
  8. \(-1\)
  9. Expression \(3n + 16n - 6n\) matches B; \(5n \times 5n\) matches A; \(9(n + 4) - 36 - 2n\) matches D; \(12n + 4 - 4 - n\) matches E. Option C is not needed.
  10. The two numbers have been written side by side instead of being multiplied together. \(8 \times 8n = 64n\), not \(88n\).
discia.org Simplifying Algebra · sheet 1