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Algebraic Techniques, SM-Bank 044

Evaluate the expression  \(x^2+3x-4\)  when:

  1. \(x=1\)  (2 marks)

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  2. \(x=3\)  (2 marks)

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a.    \(0\)

b.    \(14\)

Show Worked Solution
a.    \(x^2+3x-4\) \(=1^2+3\times 1-4 \)
    \(=1\times 1 +3-4\)
    \(=0\)

 

b.    \(x^2+3x-4\) \(=3^2+3\times 3-4\)
    \(=3\times 3 +3\times 3-4\)
    \(=14\)

Filed Under: Substitution Tagged With: num-title-ct-core, smc-4695-10-Substitution

Algebraic Techniques, SM-Bank 043

Evaluate the expression  \(-2x^2\)  when:

  1. \(x=1\)  (1 mark)

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  2. \(x=-2\)  (2 marks)

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  3. \(x=-\dfrac{1}{2}\)  (2 marks)

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a.    \(-2\)

b.    \(-8\)

c.    \(-\dfrac{1}{2}\)

Show Worked Solution
a.    \(-2x^2\) \(=-2\times 1^2\)
    \(=-2\times 1\times 1\)
    \(=-2\)

 

b.    \(-2x^2\) \(=-2\times (-2)^2\)
    \(=-2\times (-2)\times (-2)\)
    \(=-8\)

 

c.    \(-2x^2\) \(=-2\times \bigg(-\dfrac{1}{2}\bigg)^2\)
    \(=-2\times \bigg(-\dfrac{1}{2}\bigg) \times \bigg(-\dfrac{1}{2}\bigg)\)
    \(=-2\times\dfrac{1}{4}\)
    \(=-\dfrac{1}{2}\)

Filed Under: Substitution Tagged With: num-title-ct-core, smc-4695-10-Substitution

Algebraic Techniques, SM-Bank 042

Evaluate the expression  \(w^2\)  when:

  1. \(w=4\)  (1 mark)

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  2. \(w=-1\)  (2 marks)

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  3. \(w=\dfrac{1}{3}\)  (2 marks)

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a.    \(16\)

b.    \(1\)

c.    \(\dfrac{1}{9}\)

Show Worked Solution
a.    \(w^2\) \(=4^2\)
    \(=4\times 4\)
    \(=16\)

 

b.    \(w^2\) \(=(-1)^2\)
    \(=(-1)\times (-1)\)
    \(=1\)

 

c.    \(w^2\) \(=\bigg(\dfrac{1}{3}\bigg)^2\)
    \(=\dfrac{1}{3}\times \dfrac{1}{3}\)
    \(=\dfrac{1}{9}\)

Filed Under: Substitution Tagged With: num-title-ct-core, smc-4695-10-Substitution

Algebraic Techniques, SM-Bank 041

Evaluate the expression  \(\dfrac{c}{2}-\dfrac{b}{3}+a\)  when  \(a=-4\),  \(b=-3\)  and  \(c=10\).  (2 marks)

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\(2\)

Show Worked Solution
\(\dfrac{c}{2}-\dfrac{b}{3}+a\) \(=\dfrac{10}{2}-\bigg(\dfrac{-3}{3}\bigg)+(-4)\)
  \(=5-(-1)-4\)
  \(=2\)

Filed Under: Substitution Tagged With: num-title-ct-core, smc-4695-10-Substitution

Algebraic Techniques, SM-Bank 040

Evaluate the expression  \(\dfrac{20}{c}+\dfrac{15}{d}\)  when  \(c=-2\)  and  \(d=3\).  (2 marks)

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\(-5\)

Show Worked Solution
\(\dfrac{20}{c}+\dfrac{15}{d}\) \(=\dfrac{20}{-2}+\dfrac{15}{3}\)
  \(=-10+5\)
  \(=-5\)

Filed Under: Substitution Tagged With: num-title-ct-core, smc-4695-10-Substitution

Algebraic Techniques, SM-Bank 039

Evaluate the expression  \(11+a-3b\)  when  \(a=13\)  and  \(b=8\).  (2 marks)

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\(0\)

Show Worked Solution
\(11+a-3b\) \(=11+13-3\times 8\)
  \(=11+13-24\)
  \(=0\)

Filed Under: Substitution Tagged With: num-title-ct-core, smc-4695-10-Substitution

Algebraic Techniques, SM-Bank 038

Evaluate the expression \(-2x+7y\)  when  \(x=1\)  and  \(y=-2\).  (2 marks)

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\(-16\)

Show Worked Solution
\(-2x+7y\) \(=-2\times 1+7\times -2\)
  \(=-2-14\)
  \(=-16\)

Filed Under: Substitution Tagged With: num-title-ct-core, smc-4695-10-Substitution

Algebraic Techniques, SM-Bank 037

Evaluate the expression \(4m-5n\)  when  \(m=2\)  and  \(n=4\).  (2 marks)

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\(-12\)

Show Worked Solution
\(4m-5n\) \(=4\times 2-5\times 4\)
  \(=8-20\)
  \(=-12\)

Filed Under: Substitution Tagged With: num-title-ct-core, smc-4695-10-Substitution

Algebraic Techniques, SM-Bank 036

Evaluate the expression \(3z+11\)  when  \(z=3\).  (1 mark)

Show Answers Only

\(20\)

Show Worked Solution
\(3z+11\) \(=3\times 3+11\)
  \(=9+11\)
  \(=20\)

Filed Under: Substitution Tagged With: num-title-ct-core, smc-4695-10-Substitution

Algebraic Techniques, SM-Bank 035

Evaluate the expression \(-2-5m\)  when  \(m=-1\).  (1 mark)

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\(3\)

Show Worked Solution
\(-2-5m\) \(=-2-5\times (-1)\)
  \(=-2+5\)
  \(=3\)

Filed Under: Substitution Tagged With: num-title-ct-core, smc-4695-10-Substitution

Algebraic Techniques, SM-Bank 034

Evaluate the expression \(10-2y\)  when  \(y=4\).  (1 mark)

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\(2\)

Show Worked Solution
\(10-2y\) \(=10-2\times 4\)
  \(=10-8\)
  \(=2\)

Filed Under: Substitution Tagged With: num-title-ct-core, smc-4695-10-Substitution

Algebraic Techniques, SM-Bank 033 MC

When \(\large x\)\(=5\) and \(\large y\)\(=-2\) the value of the expression \(2x+3y\) is:

  1. \(4\)
  2. \(8\)
  3. \(16\)
  4. \(-7\)
Show Answers Only

\(A\)

Show Worked Solution
\(2x+3y\) \(=2\times 5+3\times -2\)
  \(=10+-6\)
  \(=4\)

\(\Rightarrow A\)

Filed Under: Substitution Tagged With: num-title-ct-core, smc-4695-10-Substitution

Algebraic Techniques, SM-Bank 032 MC

When \(\large a\)\(=2\) and \(\large b\)\(=-1\) the value of the expression \(a+b\) is:

  1. \(-21\)
  2. \(-2\)
  3. \(-1\)
  4. \(1\)
Show Answers Only

\(D\)

Show Worked Solution
\(a+b\) \(=2+-1\)
  \(=1\)

\(\Rightarrow D\)

Filed Under: Substitution Tagged With: num-title-ct-core, smc-4695-10-Substitution

Algebraic Techniques, SM-Bank 031 MC

When \(x=4\) the value of the expression \(3\times x\) is:

  1. \(34\)
  2. \(7\)
  3. \(12\)
  4. \(12x\)
Show Answers Only

\(C\)

Show Worked Solution
\(3\times x\) \(=3\times 4\)
  \(=12\)

\(\Rightarrow C\)

Filed Under: Substitution Tagged With: num-title-ct-core, smc-4695-10-Substitution

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