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v1 Algebra, STD2 A1 2010 HSC 24a

Margie tried to solve this equation and made a mistake in Line 2. 

\begin{array}{rl}
3(m+3)-2(m+4)=-5\ &\ \ \ \text{Line 1} \\
3m+9-2m+8=-5\ &\ \ \ \text{Line 2} \\
m+17=-5\ &\ \ \ \text{Line 3} \\
m=-12& \ \ \ \text{Line 4}
\end{array}

  1. Copy the equation in Line 1. Rewrite Line 2 correcting her mistake.   (1 mark)

  2. Continue your solution showing the correct working for Lines 3 and 4 to solve this equation for \(m\).   (1 mark)

Show Answers Only
i.    \(3(m+3)-2(m+4)\) \(=-5\ \ \ \ \ \ \text{Line}\ 1\)
  \(3m+9-2m-8\) \(=-5\ \ \ \ \ \ \text{Line}\ 2\)
ii.    \(m+1\) \(=-5\)
  \(m\) \(=-6\)
Show Worked Solution
i.    \(3(m+3)-2(m+4)\) \(=-5\ \ \ \ \ \ \text{Line}\ 1\)
  \(3m+9-2m-8\) \(=-5\ \ \ \ \ \ \text{Line}\ 2\)

 

ii.    \(m+1\) \(=-5\ \ \ \ \ \ \text{Line}\ 3\)
  \(m\) \(=-6\ \ \ \ \ \ \text{Line}\ 4\)

v1 Algebra, STD2 A1 2013 HSC 29a

Jeremy tried to solve this equation and made a mistake in Line 2. 

\(\dfrac{M+3}{2}-\dfrac{2M-1}{5}\) \(=1\) \(\text{... Line 1}\)
\(5M+15-4M-2\) \(=10\) \(\text{... Line 2}\)
\(M+13\) \(=10\) \(\text{... Line 3}\)
\(M\) \(=-3\) \(\text{... Line 4}\)

  
Copy the equation in Line 1 and continue your solution to solve this equation for \(M\).

Show all lines of working.   (2 marks)

Show Answers Only
\(\dfrac{M+3}{2}-\dfrac{2M-1}{5}\) \(=1\) `text(… Line 1)`
\(5M+15-4M+2\) \(=10\) `text(… Line 2)`
\(M+17\) \(=10\) `text(… Line 3)`
\(M\) \(=-7\) `text(… Line 4)`
Show Worked Solution
♦♦ Mean mark 27%
STRATEGY: The RHS of the equation increases from 1 to 10 (from Line 1 to Line 2), indicating both sides must have been multiplied by 10.
\(\dfrac{M+3}{2}-\dfrac{2M-1}{5}\) \(=1\) `text(… Line 1)`
\(5M+15-4M+2\) \(=10\) `text(… Line 2)`
\(M+17\) \(=10\) `text(… Line 3)`
\(M\) \(=-7\) `text(… Line 4)`

v1 Algebra, STD2 A1 2005 HSC 14 MC

Using the formula  \(d=6t^3-5\), Marcia tried to find the value of  \(t\)  when \(d=389\).

Here is her solution. She has made one mistake.
 

Which line does NOT follow correctly from the previous line?

  1. \(\text{Line}\ A\)
  2. \(\text{Line}\ B\)
  3. \(\text{Line}\ C\)
  4. \(\text{Line}\ D\)
Show Answers Only

\(B\)

Show Worked Solution
\(d\) \(=6t^3-5\)  
\(389\) \(=6t^3-5\ \ \ \) \(\dots\text{ Line A}\)
\(394\) \(=6t^3\) \(\dots\text{ Line B}\)

  
\(\therefore\ \text{Line}\ B\ \text{does not follow on correctly.}\)

\(\Rightarrow B\)