[discia] GCSE Maths › Algebra › Substitution

Substitution

discia.org 10 questions · 27 marks
Name Date
  1. Either paper 3 marks

    \(y = 7x + 6\)

    (a)

    Work out the value of \(y\) when \(x = 12\).

    (b)

    Work out the value of \(y\) when \(x = -9\).

    Show answer
    (a) \(90\)
    (b) \(-57\)
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  2. Either paper 1 mark

    Circle the expression that has the smallest value when \(x = 3\).

    \(10 - x\)      \(\frac{ 11 }{ x }\)      \(x + 3\)      \(x + 4\)

    Show answer
    the second expression: \(10 - 3 = 7\), \(\frac{ 11 }{ 3 } = 3\frac{2}{3}\), \(3 + 3 = 6\), \(3 + 4 = 7\), so the smallest value is \(3\frac{2}{3}\)
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  3. Either paper 2 marks

    Work out the value of \(6p - 2q\) when \(p = 6\) and \(q = -2\).

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    \(40\)
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  4. Either paper 4 marks

    A taxi firm works out the cost of a journey using the formula

    \(C = 3m + 5\)

    where \(C\) is the cost in pounds and \(m\) is the number of miles travelled.

    (a)

    Ben travels 5 miles. Work out the cost of his journey.

    (b)

    Calculate how much more a journey of 11 miles costs than a journey of 5 miles.

    Show answer
    (a) \(\text{£}20\)
    (b) \(\text{£}18\)
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  5. Either paper 1 mark

    Circle the point that does not lie on the curve \(y = x^{2} + x - 1\)

    \((-2, 1)\) \((-9, 71)\) \((-5, 29)\) \((-3, 5)\)

    Show answer
    \((-5, 29)\)
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  6. Either paper 3 marks

    Find the value of \(5x^2 + 2x + 2\) when \(x = -4\).

    Show answer
    \(74\)
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  7. Either paper 3 marks

    \(y = \frac{ 3x + 30 }{ 6 }\)

    Work out the value of \(y\) when \(x = -4\).

    Show answer
    \(3\)
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  8. Either paper 3 marks

    A formula connecting four quantities is

    \(v = u + at\)

    \(v = 50\), \(u = 8\) and \(t = 6\).

    Work out the value of \(a\).

    Show answer
    \(7\)
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  9. Either paper 3 marks

    Here is a formula.

    \(t = 2n^2 - 3n\)

    (a)

    Find \(t\) when \(n = 5\).

    (b)

    Explain why \(t\) is always positive when \(n\) is negative.

    Show answer
    (a) \(35\)
    (b) When \(n\) is negative, \(n^2\) is positive (a negative times a negative), and multiplying by the positive coefficient keeps it positive. Also \(3n\) is negative, so \(-3n\) is positive. Both terms are positive, so their sum \(t\) is positive.
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  10. Either paper 4 marks

    This formula converts a temperature in degrees Celsius (°C) to degrees Fahrenheit (°F).

    \(F = 1.8C + 32\)

    \(F\) is the number of degrees Fahrenheit and \(C\) is the number of degrees Celsius.

    (a)

    Show that 5°C is the same temperature as 41°F.

    (b)

    The temperature is -2°C.

    Nick says, "Because the temperature is negative in Celsius, it must be negative in Fahrenheit."

    Is Nick correct? You must show your working.

    Show answer
    (a) Substituting \(C = 5\) gives \(F = 1.8 \times 5 + 32 = 9 + 32 = 41\)
    (b) No. \(F = 1.8 \times (-2) + 32 = -3.6 + 32 = 28.4\), which is positive.
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discia.org Substitution · sheet 1
Answers Substitution · sheet 1
  1. (a) \(90\)
    (b) \(-57\)
  2. the second expression: \(10 - 3 = 7\), \(\frac{ 11 }{ 3 } = 3\frac{2}{3}\), \(3 + 3 = 6\), \(3 + 4 = 7\), so the smallest value is \(3\frac{2}{3}\)
  3. \(40\)
  4. (a) \(\text{£}20\)
    (b) \(\text{£}18\)
  5. \((-5, 29)\)
  6. \(74\)
  7. \(3\)
  8. \(7\)
  9. (a) \(35\)
    (b) When \(n\) is negative, \(n^2\) is positive (a negative times a negative), and multiplying by the positive coefficient keeps it positive. Also \(3n\) is negative, so \(-3n\) is positive. Both terms are positive, so their sum \(t\) is positive.
  10. (a) Substituting \(C = 5\) gives \(F = 1.8 \times 5 + 32 = 9 + 32 = 41\)
    (b) No. \(F = 1.8 \times (-2) + 32 = -3.6 + 32 = 28.4\), which is positive.
discia.org Substitution · sheet 1