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Algebra, STD2 A1 2005 HSC 14 MC

Using the formula  `d = 5t^3 - 2`, Marcia tried to find the value of  `t`  when `d = 137`.

Here is her solution. She has made one mistake.
 

2UG-2005-14MC

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` `= 5t^3 – 2`  
 `137` `= 5t^3 – 2 \ \ \ ` ` …text( Line A)`
 `139` `= 5t^3` `…text( Line B)`

 

`:.\ text(Line)\ B\ text(doesn’t follow on correctly.)`

`=>  B`

Algebra, STD2 A1 2013 HSC 29a

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

`(W+4)/3-(2W-1)/5` `=1` `text(... Line 1)`
`5W+ 20-6W-3` `=15` `text(... Line 2)`
`17-W` `=15` `text(... Line 3)`
`W` `=2` `text(... Line 4)`

 
Copy the equation in Line 1 and continue your solution to solve this equation for `W`.

Show all lines of working.   (2 marks)

Show Answers Only
`(W+4)/3-(2W-1)/5` `=1` `text(… Line 1)`
`5W+ 20-6W+ 3` `=15` `text(… Line 2)`
`23-W` `=15` `text(… Line 3)`
`W` `=8` `text(… Line 4)`
Show Worked Solution
♦♦ Mean mark 27%
STRATEGY: The RHS of the equation increases from 1 to 15 (from Line 1 to Line 2), indicating both sides must have been multiplied by 15.
`(W+4)/3-(2W-1)/5` `=1` `text(… Line 1)`
`5W+ 20-6W+3` `=15` `text(… Line 2)`
`23-W` `=15` `text(… Line 2)`
`W` `=8` `text(… Line 4)`

Algebra, STD2 A1 2010 HSC 24a

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

\begin{array}{rl}
4(y+2)-3(y+1)= -3\ & \ \ \ \text{Line 1} \\
4y+8-3y+3= -3\ &\ \ \ \text{Line 2} \\
y+11 =-3\ &\ \ \ \text{Line 3} \\
y =-14& \ \ \ \text{Line 3}
\end{array}

Copy the equation in Line 1.

  1. Rewrite Line 2 correcting his mistake.   (1 mark)

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

Show Answers Only
  1.  `4y+8+3y-3=-3`
  2. `y+5=-3`

     

    `y=-8`

Show Worked Solution
i.    `4(y+2)-3(y+1)` `=-3\ \ \ \ \ \ \ text(Line)\ 1`
  `4y+8-3y-3` `=-3\ \ \ \ \ \  text(Line)\ 2`

 

ii.    `y+5` `=-3\ \ \ \ \ \ \ text(Line)\ 3`
  `y` `=-8\ \ \ \ \ \ \ text(Line)\ 4`