Discia GCSE Maths › Algebra › Expressions, Equations and Identities

Expressions, Equations and Identities worksheet

10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.

10 questions 22 marks Sheet 1
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  1. 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.

  2. 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.
  3. 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.

  4. 2 marks

    \(8(x + c) \equiv 8x - 56\)

    Find the value of \(c\).

  5. 2 marks

    Show that

    \(6(x - 1) + 7 \equiv 6x + 1\)

  6. 3 marks

    Here is an expression.

    \(9y^2 - 4y + 2\)

    (a)

    Write down how many terms the expression has.

    (b)

    Write down the coefficient of \(y^2\).

    (c)

    Write down the constant term.

  7. 1 mark Here are four statements.

    A  \(3x - 1\)

    B  \(3x - 1 = 13\)

    C  \(y = 3x - 1\)

    D  \(6(x - 6) \equiv 6x - 36\)

    Write down the letter of the statement that is an identity.
  8. 3 marks

    Aisha charges for cleaning windows using the formula

    \(C = 9n + 44\)

    where \(C\) is the total charge in pounds and \(n\) is the number of windows. The travel charge is included in the formula.

    (a)

    Calculate the total charge when \(n = 14\).

    (b)

    Explain why \(C = 9n + 44\) is a formula and not an equation.

  9. 2 marks

    \(6(x + c) \equiv 6x - 48\)

    Find the value of \(c\).

  10. 2 marks

    Show that

    \(8(x + 4) - 1 \equiv 8x + 31\)

Answers

  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. \(-7\)
  5. Expanding gives \(6x - 6 + 7 = 6x + 1\), which is the right-hand side.
  6. (a) \(3\)
    (b) \(9\)
    (c) \(2\)
  7. D
  8. (a) \(\text{£}170\)
    (b) It is a rule for working the charge out from the number of windows, and it holds for any number of windows. An equation such as \(9n + 44 = 170\) is true only when \(n = 14\).
  9. \(-8\)
  10. Expanding gives \(8x + 32 - 1 = 8x + 31\), which is the right-hand side.

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