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Algebra, STD2 A2 2024 HSC 2 MC

Consider the function shown.
 

Which of the following could be the equation of this function?

  1. \(y=2 x+3\)
  2. \(y=2 x-3\)
  3. \(y=-2 x+3\)
  4. \(y=-2 x-3\)
Show Answers Only

\(C\)

Show Worked Solution

\(\text {Gradient is negative (top left } \rightarrow \text { bottom right)}\)

\(y \text{-intercept = 3 (only positive option)}\)

\(\Rightarrow C\)

Algebra, STD2 A2 2022 HSC 2 MC

Which of the following could be the graph of  `y= –2 x+2`?
 

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`A`

Show Worked Solution

`text{By elimination:}`

`y text{-intercept = 2  →  Eliminate}\ B and C`

`text{Gradient is negative  → Eliminate}\ D`

`=>A`


♦ Mean mark 48%.

Algebra, STD1 A2 2021 HSC 5 MC

Which of the following best represents the graph of  `y = -3x + 4`?
 

A. B.
C. D.
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`A`

Show Worked Solution

`y = -3x + 4`

♦♦♦ Mean mark 16%.

`ytext(-intercept) = 4`

`text(Gradient is negative → slopes from)`

`text(upper left to lower right)`

`=> A`

Algebra, STD2 A2 2020 HSC 6 MC

Suppose  `y = -1-2x`.

When the value of  `x`  increases by 5, the value of  `y`  decreases by

  1.  1.
  2.  2.
  3.  5.
  4.  10.
Show Answers Only

`D`

Show Worked Solution

`text(Strategy 1)`

`text(If) \ \ x\  \ text(increases by) \ 5`

`=> y \ \ text(decreases by) \ \ 2x = 2 xx 5 = 10`

 
`text(Strategy 2)`

`text(Test) \ 2 \ text(values:)`

`text(If) \ \ x = 0 , \ y = -1`

`text(If) \ \ x = 5 , \ y = -1-10 = -11`

`:.\ y \ text(decreases by) \ 10.`

`=>D`

Algebra, STD2 A2 SM-Bank 12 MC

 
Which of these equations represents the line in the graph?

  1.  `y = 11 - 2x`
  2.  `y = 11 + 5.5x`
  3.  `y = 11 - 5.5x`
  4.  `y = 11 + 2x`
Show Answers Only

`A`

Show Worked Solution

`text{Graph passes through (0, 11) and (5.5, 0)}`

`text(Gradient)` `=(y_2-y_1)/(x_2-x_1)`  
  `=(11-0)/(0-5.5)`  
  `=-2`  

`:.\ text(Equation is:)\ \ y = 11 – 2x`

`=> A`

Algebra, STD2 A2 SM-Bank 11 MC

What is the equation for the line shown?
 

  1. `y = -3/2 x + 2`
  2. `y = 3/2 x + 2`
  3. `y = -2/3 x + 2`
  4. `y = 2/3 x + 2`
Show Answers Only

`=>B`

Show Worked Solution

`text(Graph cuts)\ y text(-axis at 2)`

`text(Gradient) = text(rise)/text(run) = 3/2`

`:. y = 3/2 x + 2`

`=>B`

Algebra, STD2 A2 SM-Bank 10 MC

Leo drew a straight line through the points (0, 5) and (3, -2) as shown in the diagram below.
 

 
What is the gradient of the line that Leo drew?

  1. `7/3`
  2. `3/7`
  3. `-3/7`
  4. `-7/3`
Show Answers Only

`D`

Show Worked Solution

`text{Line passes through (0, 5) and (3, – 2)}`

`text(Gradient)` `= (y_2-y_1)/(x_2-x_1)`
  `= (5-(-2))/(0-3)`
  `= -7/3`

 
`=>D`

Algebra, STD2 A2 SM-Bank 6 MC

Renee went bike riding on a holiday.

The hiring charges are  listed in the table below:

\begin{array} {|l|c|c|}
\hline \text{Hours hired} \ (h) & 1 & 2 & 3 & 4 & 5 \\
\hline \text{Cost} \ (C) & 18 & 24 & 30 & 36 & 42 \\
\hline \end{array}

Which linear equation shows the relationship between `C` and `h`?

  1. `C = 12 + 6h`
  2. `C = 6 + 12h`
  3. `C=18 + 12h`
  4. `C=12 + 18h`
Show Answers Only

`A`

Show Worked Solution

`text(Consider Option 1:)`

`12 + (6 xx 1) = 12+6=18`

`12 + (6 xx 2) = 12+12=24`

`12 + (6 xx 3) = 12+18=30\ \ \ \ text(etc …)`

`:.\ text(The linear equation is:)\ \ C = 12 + 6h`

`=>A`

Algebra, STD2 A2 SM-Bank 5

The diagram shows the graph of a line.
 

 
What is the equation of this line?    (2 marks)

Show Answers Only

`y = 3/5x + 3`

Show Worked Solution

`ytext(-intercept = 3)`

`text(Gradient)` `= text(rise)/text(run)`
  `= 3/5`

 
`:. text(Equation:)\ \ y = 3/5x + 3`

Algebra, STD2 A2 SM-Bank 5 MC

The equation of the line drawn in the diagram below is:
 

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

`D`

Show Worked Solution

`y text(-intercept) = +5`

`text(Gradient)` `= text(rise)/text(run)`
  `=- 5/3`

 

`:.\ text(Equation is):\ y = -5/3x + 5`

`=> D`

Algebra, STD2 A2 SM-Bank 2 MC

What is the gradient of the line  `2x + 3y + 4 = 0`?

  1.   `-2/3`
  2. `2/3`
  3.   `-3/2`
  4.   `3/2`
Show Answers Only

`A`

Show Worked Solution
`2x + 3y + 4` `= 0`
`3y` `= -2x – 4`
`y` `= -2/3 x – 4/3`
`:.\ text(Gradient)` `= -2/3`

`=>  A`

Algebra, STD2 A2 SM-Bank 1 MC

What is the slope of the line with equation  `5x+2y-8 = 0`?

  1. `-5/2`
  2. `-2/5`
  3.  `2/5`
  4. `5/2`
Show Answers Only

`A`

Show Worked Solution
`5x+2y-8` `= 0`
`2y` `= -5x+8`
`y` `= -5/2 x+4`

 
`:.\ text(Slope)\ = -5/2`

`=>A`

Algebra, STD2 A2 SM-Bank 1

Sketch the graph of  `y - 2x = 3`, showing the intercepts on both axes.   (2 marks)

Show Answers Only

 

Show Worked Solution

`y-2x=3\ \ => \ \ y=2x+3`

 

Algebra, STD2 A2 2016 HSC 14 MC

The graph shows a line which has an equation in the form  `y = mx + c`.
 

Which of the following statements is true?

  1. `m` is positive and `c` is negative
  2. `m` is negative and `c` is positive
  3. `m` and `c` are both positive
  4. `m` and `c` are both negative
Show Answers Only

`=> A`

Show Worked Solution

`m` is the gradient and the line slopes to the right so `m` is positive.

`c` is the `y`-intercept which is negative.

`:.\ m` is positive and `c` is negative.

`=> A`

Algebra, STD2 A2 2015 HSC 13 MC

What is the equation of the line `l`?
 

  1. `y = -2x + 2`
  2. `y = 2x + 2`
  3. `y = -x/2 + 2`
  4. `y = x/2 +2`
Show Answers Only

`A`

Show Worked Solution

`l\ text{passes through (0, 2) and (1, 0)}`

♦ Mean mark 48%.
`text(Gradient)` `= (y_2-y_1)/(x_2-x_1)`
  `= (0-2)/(1-0)`
  `= -2`

 
`y\ text(intercept = 2)`

`:.y = -2x + 2`

`=>A`

Algebra, STD2 A2 2005 HSC 17 MC

The total cost, `$C`, of a school excursion is given by  `C = 2n + 5`, where `n` is the number of students.

If three extra students go on the excursion, by how much does the total cost increase?

  1. `$6`
  2. `$11`
  3. `$15`
  4. `$16`
Show Answers Only

`A`

Show Worked Solution

`C = 2n + 5`

`text(If)\ n\ text(increases to)\ n + 3`

`C` `= 2(n + 3) + 5`
  `= 2n + 6 + 5`
  `= 2n + 11`

 

`:.\ text(Total cost increases by $6)`

`=>  A`

Algebra, STD2 A2 2006 HSC 7 MC

Which equation represents the relationship between `x` and `y` in this table?
 

2UG-2006-7MC
 

  1.  `y = 2x+1`
  2. `y = 2x-2` 
  3. `y = x/2-2` 
  4. `y = x/2+1`
Show Answers Only

`D`

Show Worked Solution

`text{By elimination (using the table)}`

`(0, 1)\ text(must satisfy)`

`:.\ text(NOT)\ B\ text(or)\ C`

`(2, 2)\ text(must satisfy)`

`:.\ text(NOT)\ A`

`=>  D`

Algebra, STD2 A2 2004 HSC 2 MC

Susan drew a graph of the height of a plant.
  

What is the gradient of the line?

  1. `1`
  2. `5`
  3. `7.5`
  4. `10`
Show Answers Only

`B`

Show Worked Solution

`text(2 points on graph)\ \ (0, 10),\ (1, 15)`

`text(Gradient)` `= (y_2-y_1) / (x_2-x_1)`
  `= (15-10) / (1-0)`
  `= 5`

`=> B`

Algebra, STD2 A2 2014 HSC 7 MC

Which of the following is the graph of   `y = 2x-2`? 
  


  

Show Answers Only

`D`

Show Worked Solution
♦ Mean mark 46%

`y = 2x-2`

`text(By elimination)`

`text(It has a)\ y\ text(intercept of)\ -2`

`=> text(Cannot be)\ B\ text(or)\ C`

 

`(-1, 0)text{ from}\ A\ text(doesn’t satisfy equation)`

`text(but)\ (1,0)\ text(from)\ D\ text(does)`

`=>  D`

Algebra, STD2 A2 2009 HSC 14 MC

If   `A = 6x + 10`, and  `x`  is increased by  2, what will be the corresponding increase in `A` ?

  1. `2x` 
  2. `6x` 
  3. `2` 
  4. `12` 
Show Answers Only

`D`

Show Worked Solution
♦ Mean mark 50%.
STRATEGY: Substituting real numbers into the equation can work well in these type of questions. eg. If `x=0,\ A=10` and when `x=2,\ A=22`.

`A = 6x + 10`

`text(If)\ x\ text(increases by 2)`

`A\ text(increases by)\ 6 xx 2 = 12`

`=>  D`

Algebra, STD2 A2 2012 HSC 5 MC

The line  `l`  has intercepts  `p`  and  `q`,  where  `p`  and  `q`  are positive integers. 
  

What is the gradient of line  `l ` ? 

  1. `-p/q`  
  2. `-q/p`  
  3. `\ \ \ p/q`  
  4. `\ \ \ q/p`  
Show Answers Only

`A`

Show Worked Solution
 
♦ Mean mark 45%
`text(Gradient)` `= text(rise)/text(run)`
  `= -p/q`

`=>  A`