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Financial, STD2 EQ-Bank 02

  1. Kylie is a financial broker who earns a salary of \(\$93\,600\) per annum.
  2. She has 35% of her salary deducted for tax.
  3. Show that her net weekly pay is $1170.   (1 marks)
  5. Ben, Kylie's partner, works as a carpenter.
  6. He works 36 hours per week at a normal rate of $40 per hour and averages 6 hours overtime at time-and-a-half.
  7. Show that his average weekly pay before tax is $1800.  (2 marks)
  9. Kylie and Ben drew up the weekly budget below.
  10. They need to save $400 per week for an overseas holiday and also want to continue to save for a home.
  11. Ben has 25% of his gross wage deducted for taxation.

    1.   
  12. Comment on the budget as it appears in the table, indicating where they may have made an error, and suggest some practical ways to make the budget work for them.   (3 marks)
Show Answers Only
a.     \(\text{Kylie’s net salary}\) \(=\dfrac{$93\,600\times 0.65}{52}\)
    \(=$1170\)

 

b.     \(\text{Ben’s gross pay}\) \(=$40\times (36+1.5\times 6)\)
    \(=$1800\)
c.     \(\text{Ben’s net pay}\) \(=1800\times 0.75\)
    \(=$1350\)
  \(\text{Total net income}\) \(=1170+1350=$2520\)
  \(\text{Total expenses}\) \(=1000+360+210+250+250+400+500\)
    \(=$2720\)

\(\text{They have mistakenly used Ben’s gross salary in their}\)

\(\text{calculations which will leave them short of their savings}\)

\(\text{target of }$500\ \text{per week by } $200. \)

\(\text{Option 1.  Reduce savings by }$200\ \text{per week.}\)

\(\text{Option 2.  Reduce entertainment by by }$100 \)

\(\text{per week and reduce savings by }$100\ \text{per week.}\)

Show Worked Solution
a.     \(\text{Kylie’s net salary}\) \(=\dfrac{93\,600\times 0.65}{52}\)
    \(=$1170\)

 

b.     \(\text{Ben’s gross pay}\) \(=40\times (36+1.5\times 6)\)
    \(=$1800\)

 

c.     \(\text{Ben’s net pay}\) \(=1800\times 0.75\)
    \(=$1350\)
  \(\text{Total net income}\) \(=1170+1350=$2520\)
  \(\text{Total expenses}\) \(=1000+360+210+250+250+400+500\)
    \(=$2720\)

\(\text{They have mistakenly used Ben’s gross salary in their}\)

\(\text{calculations which will leave them short of their savings}\)

\(\text{target of }$500\ \text{per week by } $200. \)

\(\text{Option 1.  Reduce savings by }$200\ \text{per week.}\)

\(\text{Option 2.  Reduce entertainment by by }$100 \)

\(\text{per week and reduce savings by }$100\ \text{per week.}\)

Functions, 2ADV EQ-Bank 01

A set of ordered pairs \((x, y)\) on the coordinate plane are represented by set \(A\) below:

\(A=\{(1,3),(4,6),(5,6),(0,1),(1,7)\}\)

Explain if Set \(A\) a function or a relation?   (2 marks)

Show Answers Only

\(\text {If set \(A\) is a function, there can only be one \(y\)-value}\)

\(\text{for any given } x \text{-value.}\)

\(\text{This is not the case} \ \Rightarrow\ (1,3),(1,7)\)

\(\therefore\ \text{Set} \ A \ \text {is a relation.}\)

Show Worked Solution

\(\text {If set \(A\) is a function, there can only be one \(y\)-value}\)

\(\text{for any given } x \text{-value.}\)

\(\text{This is not the case} \ \Rightarrow\ (1,3),(1,7)\)

\(\therefore\ \text{Set} \ A \ \text {is a relation.}\)

Functions, 2ADV EQ-Bank 5

  1. Identify where the graph  \(f(x)=\dfrac{x^2-1}{x-1}\)  is not continuous.   (1 mark)

  2. Sketch the graph of \(f(x)\).   (2 marks)

Show Answers Only

a.    \(f(x)=\dfrac{x^2-1}{x-1}=\dfrac{(x+1)(x-1)}{(x-1)}=x+1\)

\(\text{Since denominator} \neq 0\)

\(f(x) \ \ \text{is not continuous when} \ \ x=1.\)
 

b.
       

Show Worked Solution

a.    \(f(x)=\dfrac{x^2-1}{x-1}=\dfrac{(x+1)(x-1)}{(x-1)}=x+1\)

\(\text{Since denominator} \neq 0\)

\(f(x) \ \ \text{is not continuous when} \ \ x=1.\)
 

b.
       

Functions, 2ADV EQ-Bank 4

Consider the function  \(y=f(x)\)  where

\(f(x)= \begin{cases}x^2+6, & \text { for } x \leqslant 0 \\ 6, & \text { for } 0<x \leqslant 3 \\ 2^x, & \text { for } x>3\end{cases}\)

  1. Sketch  \(y=f(x)\)   (3 marks)

  2. For what value of \(x\) is  \(y=f(x)\)  NOT continuous?   (1 mark)

Show Answers Only

a.
   

b.    \(f(x)\ \ \text {is NOT continuous at}\ \  x=3.\)

Show Worked Solution

a.
   

b.    \(f(x)\ \ \text {is NOT continuous at}\ \  x=3.\)

Measurement, STD2 EQ-Bank 06

The distance between planets is measured in Astronomical Units (AU).

\(1\ \text{AU}\ \approx 1.496\times 10^8\) kilometres.

Given Venus is approximately 0.7 AU from Earth, calculate this distance in kilometres giving your answer in scientific notation, correct to 3 significant figures.  (2 marks)

Show Answers Only

\(1.03\times 10^8\ \text{(3 sig. fig.)}\)

Show Worked Solution
\(\text{Distance}\) \(=0.7\times \left(1.496\times 10^8\right)\)
  \(=102\,830\,000\)
  \(=1.0283\times 10^8\)
  \(=1.03\times 10^8\ \text{(3 sig. fig.)}\)

Statistics, STD2 EQ-Bank 03 MC

For the data below, which is the correct five figure summary?

\(12,\ \ 16, \ \ 4,\ \ 6, \ \ 4, \ \ 5, \ \  22, \ \ 20, \ \ 12, \ 8\ \)

  1. \(4,\ \ 5, \ \ 8,\ \ 16, \ \ 21\)
  2. \(4,\ \ 5, \ \ 8,\ \ 16, \ \ 22\)
  3. \(4,\ \ 5, \ \ 10,\ \ 16, \ \ 21\)
  4. \(4,\ \ 5, \ \ 10,\ \ 16, \ \ 22\)
Show Answers Only

\(D\)

Show Worked Solution

\(\text{Ordered data set}\ \rightarrow\ \ 4,\ \ 4, \ \ 5,\ \ 6, \ \ 8, \ \ 12, \ \  12, \ \ 16, \ \ 20, \ 22\ \)

\(\text{Five number Summary}\)

\begin{array} {|l|c|}
\hline
\rule{0pt}{2.5ex} \text{Minimum} \rule[-1ex]{0pt}{0pt} &  4\\
\hline
\rule{0pt}{2.5ex} \ Q_1 \rule[-1ex]{0pt}{0pt} & 5 \\
\hline
\rule{0pt}{2.5ex} \text{Median} \rule[-1ex]{0pt}{0pt} &  \dfrac{8+12}{2}=10\\
\hline
\rule{0pt}{2.5ex} \ Q_3 \rule[-1ex]{0pt}{0pt} & 16 \\
\hline
\rule{0pt}{2.5ex} \text{Maximum} \rule[-1ex]{0pt}{0pt} &  22\\
\hline
\end{array}

\(\Rightarrow D\)

Statistics, STD2 EQ-Bank 02 MC

The results of a test are displayed in the box-and-whisker plot below.
 

Which of the following statements is false?

  1. The median is 155
  2. The range is 60
  3. The interquartile range is 50
  4. 25% of the scores are below 150
Show Answers Only

\(C\)

Show Worked Solution

\(\text{Five number Summary}\)

\begin{array} {|l|c|}
\hline
\rule{0pt}{2.5ex} \text{Minimum} \rule[-1ex]{0pt}{0pt} &  140\\
\hline
\rule{0pt}{2.5ex} \ Q_1 \rule[-1ex]{0pt}{0pt} & 150 \\
\hline
\rule{0pt}{2.5ex} \text{Median} \rule[-1ex]{0pt}{0pt} &  155\\
\hline
\rule{0pt}{2.5ex} \ Q_3 \rule[-1ex]{0pt}{0pt} & 190 \\
\hline
\rule{0pt}{2.5ex} \text{Maximum} \rule[-1ex]{0pt}{0pt} &  200\\
\hline
\end{array}

\(\text{Median}\ =\ 155\ \checkmark\)

\(\text{Range}\ =\ 200-140=60\ \checkmark\)

\(\text{IQR}\ =\ 190-150=40\ \text{not}\ 50\ \)X

\(\text{Q1}\ =\ 150\ \therefore\ 25\%\ \text{of scores lie below 150}\ \checkmark\)

\(\Rightarrow C\)

Financial Maths, STD2 EQ-Bank 01 MC

Jacinta buys several items at the supermarket. The docket for her purchases is shown below.

What is the amount of GST included in the total? 

  1. $1.15
  2. $1.27
  3. $1.55
  4. $1.71
Show Answers Only

\(A\)

Show Worked Solution

\(\text{Total price of taxable items}\ +\ 10\%\ \text{ GST}\ =1.29+7.23+4.13=$12.65\)

\(\therefore\ 110\%\ \text{of original price}\) \(=$12.65\)
\(\therefore\ \text{GST}\) \(=$12.65\times\dfrac{100}{110}\)
  \(=$1.15\)

\(\Rightarrow A\)

Measurement, STD2 EQ-Bank 04 MC

Kathmandu is  30\(^{\circ}\) west of Perth. Using longitudinal distance, what is the time in Kathmandu when it is noon in Perth?

  1. 10:00 am
  2. 11:30 am
  3. 12:30 pm
  4. 2:00 pm
Show Answers Only

\(A\)

Show Worked Solution

\(15^{\circ}\ =\text{1 hour time difference}\)

\(\text{Longitudinal distance}\) \(=30^{\circ}\)
\(\therefore\ \text{Time Difference}\) \(=\dfrac{30}{15}\)
  \(=2\ \text{hours}\)

  
\(\text{Time in Perth}\ =\ 12\ \text{pm}\)

\(\therefore\ \text{Time in Kathmandu}\) \( =\ 12\ \text{pm}\ -\ 2\ \text{hours}\)
  \(=\ 10:00\ \text{am}\)

\(\Rightarrow A\)

Measurement, STD2 EQ-Bank 03

The table shows the approximate coordinates of two cities.

\begin{array} {|l|c|c|}
\hline
\rule{0pt}{2.5ex} \textit{City} \rule[-1ex]{0pt}{0pt} & \textit{Latitude} \rule[-1ex]{0pt}{0pt} & \textit{Longitude}\\
\hline
\rule{0pt}{2.5ex} \text{Buenos Aires} \rule[-1ex]{0pt}{0pt} & 35^{\circ}\ \text{S} \rule[-1ex]{0pt}{0pt} & 60^{\circ}\ \text{W}  \\
\hline
\rule{0pt}{2.5ex} \text{Adelaide} \rule[-1ex]{0pt}{0pt} & 35^{\circ}\ \text{S}  \rule[-1ex]{0pt}{0pt} & 140^{\circ}\ \text{E}  \\
\hline
\end{array}

  1. What is the time difference between Adelaide and Buenos Aires?   (2 marks)
  3. Roy lives in Adelaide and his cousin Juan lives in Buenos Aires. Roy wants to telephone Juan at 7 pm on Friday night, Buenos Aires time.
  4. At what time, and on what day, should Roy make the call?   (2 marks)
Show Answers Only

a.    \(13\ \text{hours}\ 20\ \text{minutes}\)

b.    \(8:20\ \text{am on Saturday}\)

Show Worked Solution

a.    \(15^{\circ}\ =\text{1 hour time difference}\)

\(\text{Angular distance}\) \(=60+140=200^{\circ}\)
\(\therefore\ \text{Time Difference}\) \(=\dfrac{200}{15}\)
  \(=13.\dot{3}\)
  \(=13\ \text{hours}\ 20\ \text{minutes}\)

  
b.    \(\text{Time in Buenos Aires}\ =\ 7\ \text{pm Friday night}\)

\(\therefore\ \text{Time in Adelaide}\) \( =\ 7\ \text{pm}\ +\ 13\ \text{hours}\ 20\ \text{minutes}\)
  \(=\ 8:20\ \text{am on Saturday}\)
   

Statistics, STD2 EQ-Bank 01

A Physics class of  12 students is going on a 4 day excursion by bus.

The students are asked to each pack one bag for the trip. The bags are weighed, and the weights (in kg) are listed in order as follows:

\(8,\ \ 9, \ \ 10,\ \ 10, \ \ 15, \ \  18, \ \  22, \ \ 25, \ \ 29, \ \ 35, \ \ 38, \ \ 41 \)

  1. Use the above data to produce a five number summary for the weights of the bags.   (2 marks)
  3. Using your five number summary from part (a), calculate the interquartile range of the weights.   (2 marks)
Show Answers Only

a.    \(\text{Five number Summary}\)

\begin{array} {|l|c|}
\hline
\rule{0pt}{2.5ex} \text{Minimum} \rule[-1ex]{0pt}{0pt} &  8\\
\hline
\rule{0pt}{2.5ex} \ Q_1 \rule[-1ex]{0pt}{0pt} & 10 \\
\hline
\rule{0pt}{2.5ex} \text{Median} \rule[-1ex]{0pt}{0pt} &  20\\
\hline
\rule{0pt}{2.5ex} \ Q_3 \rule[-1ex]{0pt}{0pt} & 32 \\
\hline
\rule{0pt}{2.5ex} \text{Maximum} \rule[-1ex]{0pt}{0pt} &  41\\
\hline
\end{array}

b.     \(22\)

Show Worked Solution

a.    \(\text{Five number Summary}\)

\begin{array} {|l|c|}
\hline
\rule{0pt}{2.5ex} \text{Minimum} \rule[-1ex]{0pt}{0pt} &  8\\
\hline
\rule{0pt}{2.5ex} \ Q_1 \rule[-1ex]{0pt}{0pt} & 10 \\
\hline
\rule{0pt}{2.5ex} \text{Median} \rule[-1ex]{0pt}{0pt} &  20\\
\hline
\rule{0pt}{2.5ex} \ Q_3 \rule[-1ex]{0pt}{0pt} & 32 \\
\hline
\rule{0pt}{2.5ex} \text{Maximum} \rule[-1ex]{0pt}{0pt} &  41\\
\hline
\end{array}

b.     \(\text{IQR}\) \(=Q_3-Q_1\)
    \(=32-10=22\)

Algebra, STD2 EQ-Bank 05

Jordan visits Italy on his holidays. He pays €180 (180 euros) for a pair of Italian leather boots.

How much is €180 in Australian dollars if AUD1 is worth €0.58?   (2 marks)

Show Answers Only

\($310.34\)

Show Worked Solution

\(0.58\ \)€ \(\ =\ \text{AUD 1}\)

\(\rightarrow\ 1\ \)€\(\ =\)\(\ \text{AUD }\)\(\dfrac{1}{0.58}\)

\(\rightarrow\ 180\ \)€\(=180\times\dfrac{1}{0.58}=310.344…\)

\(\therefore\ \text{Jordan’s boots cost }$310.34\ \text{in Australian dollars.}\)

Algebra, STD2 EQ-Bank 04 MC

The graph shows the tax payable against taxable incomes up to $60 000 in a proposed tax system.

How much of each dollar earned over \($30\,000\) is payable in tax?

  1.  10 cents
  2. 12 cents
  3. 20 cents
  4. 23 cents
Show Answers Only

\(C\)

Show Worked Solution

\(\text{The gradient of line represents the tax payable per dollar.}\)

\(\text{Tax payable per dollar}:\)

\(= \dfrac{\text{rise}}{\text{run}}\)

\(= \dfrac{7000-1000}{60\ 000-30\ 000}\)

\(=\dfrac{1}{5}=0.20\)

\(\therefore\ \text{20 cents per dollar is payable in tax after }$30\, 000.\)

\(\Rightarrow C\)

Measurement, STD2 EQ-Bank 02 MC

Arrange the numbers \(5.6\times 10^{-2}\), \(4.8\times 10^{-1}\), \(7.2\times 10^{-2}\) from smallest to largest.

  1. \(5.6\times 10^{-2}\),  \(7.2\times 10^{-2}\),  \(4.8\times 10^{-1}\)
  2. \(4.8\times 10^{-1}\),  \(5.6\times 10^{-2}\),  \(7.2\times 10^{-2}\)
  3. \(7.2\times 10^{-2}\),  \(5.6\times 10^{-2}\),  \(4.8\times 10^{-1}\)
  4. \(4.8\times 10^{-1}\),  \(7.2\times 10^{-2}\),  \(5.6\times 10^{-2}\)
Show Answers Only

\(A\)

Show Worked Solution

\(5.6\times 10^{-2}=0.052\)

\(4.8\times 10^{-1}=0.48\)

\(7.2\times 10^{-2}=0.072\)

\(\therefore\ \text{Correct order is: }\ 5.6\times 10^{-2}\),  \(7.2\times 10^{-2}\),  \(4.8\times 10^{-1}\)

\(\Rightarrow A\)

Measurement, STD2 EQ-Bank 01 MC

The sheets of paper Jenny uses in her photocopier are 21 cm by 30 cm. The paper is 80 gsm, which means that one square metre of this paper has a mass of 80 grams. Jenny has a pile of this paper weighing 25.2 kg.

How many sheets of paper are in the pile?

  1. 500
  2. 2000
  3. 2500
  4. 5000
Show Answers Only

\(D\)

Show Worked Solution

\(1\ \text{square metre} = 100\ \text{cm}\times 100\ \text{cm}=10\,000\ \text{cm}^2\)

\(\text{Area of paper sheet}\ = \ 21\times 30=630\ \text{cm}^2\)

\(\text{Number of 80 gsm sheets in 25.2 kg}\ =\dfrac{25.2\times 1000}{80}=315\)

\(\therefore\ \text{Sheets in pile}\) \(=315\times\dfrac{10\,000}{630}\)
  \(=5000\)

  

Algebra, STD2 EQ-Bank 01

Jerico is the manager of a weekend market in which there are 220 stalls for rent. From past experience, Jerico knows that if he charges \(d\) dollars to rent a stall. then the number of stalls, \(s\), that will be rented is given by:

\(s=220-4d\)

  1. How many stalls will be rented if Jerico charges $7.50 per stall .  (1 mark)

  2. Complete the following table for the function  \(s=220-4d\).   (1 mark)

\begin{array} {|c|c|c|}
\hline
\rule{0pt}{2.5ex} \quad d\quad \rule[-1ex]{0pt}{0pt} & \rule{0pt}{2.5ex} \quad 10\quad\rule[-1ex]{0pt}{0pt} & \rule{0pt}{2.5ex} \quad 30\quad & \rule{0pt}{2.5ex} \quad 50\quad \\
\hline
\rule{0pt}{2.5ex} \quad s\quad \rule[-1ex]{0pt}{0pt} & \ & \ & \\
\hline
\end{array}

  1. Using an appropriate vertical scale and labelled axes, graph the function  \(s=220-4d\) on the grid below.  (2 marks)
  1. Does it make sense to use the formula \(s=220-4d\)  to calculate the number of stalls rented if Jerico charges $60 per stall? Explain your answer.   (2 marks)

Show Answers Only
  

a.    \(190\ \text{stalls will be rented}\)

b.

\begin{array} {|c|c|c|}
\hline
\rule{0pt}{2.5ex} \quad d\quad \rule[-1ex]{0pt}{0pt} & \rule{0pt}{2.5ex} \quad 10\quad\rule[-1ex]{0pt}{0pt} & \rule{0pt}{2.5ex} \quad 30\quad & \rule{0pt}{2.5ex} \quad 50\quad \\
\hline
\rule{0pt}{2.5ex} \quad s\quad \rule[-1ex]{0pt}{0pt} & 180 \ & 100 \ & 20  \\
\hline
\end{array}

c.

d.    \(\text{When}\ d=60, s=220-4\times 60=-20\)

\(\therefore\ \text{It does not make sense to charge }$60\ \text{ per stall}\)

\(\text{as you cannot have a negative number of stalls.}\)

 

Show Worked Solution
a.     \(s\) \(=220-4d\)
    \(=220-4\times 7.50\)
    \(=190\)

  
\(190\ \text{stalls will be rented}\)

b.

\begin{array} {|c|c|c|}
\hline
\rule{0pt}{2.5ex} \quad d\quad \rule[-1ex]{0pt}{0pt} & \rule{0pt}{2.5ex} \quad 10\quad\rule[-1ex]{0pt}{0pt} & \rule{0pt}{2.5ex} \quad 30\quad & \rule{0pt}{2.5ex} \quad 50\quad \\
\hline
\rule{0pt}{2.5ex} \quad s\quad \rule[-1ex]{0pt}{0pt} & 180 \ & 100 \ & 20  \\
\hline
\end{array}

c.

d.    \(\text{When}\ d=60, s=220-4\times 60=-20\)

\(\therefore\ \text{It does not make sense to charge }$60\ \text{ per stall}\)

\(\text{as you cannot have a negative number of stalls.}\)

Functions, 2ADV EQ-Bank 03

Find \(a\) and \(b\) such that \(a\) and \(b\) are real and   \(\dfrac{2\sqrt{3}+2}{\sqrt{6}-\sqrt{2}} = a\,\sqrt{2} + b\,\sqrt{6}\).   (2 marks)

Show Answers Only

\(a=2\ \ \text{and}\ \ b=1 \)

Show Worked Solution

\(\dfrac{2\sqrt{3}+2}{\sqrt{6}-\sqrt{2}} \times \dfrac{\sqrt{6}+\sqrt{2}}{\sqrt{6}+\sqrt{2}} \)

\(=\dfrac{(2\sqrt{3}+2)(\sqrt{6}+\sqrt{2})}{6-2}\)

\(=\dfrac{2\sqrt{18}+2\sqrt{6}+2\sqrt{6}+2\sqrt{2}}{4}\)

\(=\dfrac{6\sqrt{2}+4\sqrt{6}+2\sqrt{2}}{4}\)

\(=\dfrac{8\sqrt{2}+4\sqrt{6}}{4}\)

\(=2\sqrt{2}+\sqrt{6}\)
 

\(\therefore a=2\ \ \text{and}\ \ b=1 \)

Functions, 2ADV EQ-Bank 02

Rationalise the denominator in \(\dfrac{\sqrt{3}-\sqrt{2}}{\sqrt{5}+\sqrt{2}}\), and express in the simplest form.   (2 marks)

Show Answers Only

\(\dfrac{\sqrt{15}-\sqrt{6}-\sqrt{10}+2}{3} \)

Show Worked Solution

\(\dfrac{\sqrt{3}-\sqrt{2}}{\sqrt{5}+\sqrt{2}} \times \dfrac{\sqrt{5}-\sqrt{2}}{\sqrt{5}-\sqrt{2}}\)

\(=\dfrac{(\sqrt{3}-\sqrt{2})(\sqrt{5}-\sqrt{2})}{5-2}\)

\(=\dfrac{\sqrt{15}-\sqrt{6}-\sqrt{10}+2}{3}\)

Functions, 2ADV EQ-Bank 01

Find \(x\) and \(y\) such that \(x\) and \(y\) are real and   \(\dfrac{\sqrt{2}+1}{\sqrt{6}-\sqrt{3}} = x\,\sqrt{3} + y\,\sqrt{6}\).   (2 marks)

Show Answers Only

\(x=1\ \ \text{and}\ \ y=\dfrac{2}{3} \)

Show Worked Solution

\(\dfrac{\sqrt{2}+1}{\sqrt{6}-\sqrt{3}} \times \dfrac{\sqrt{6}+\sqrt{3}}{\sqrt{6}+\sqrt{3}} \)

\(=\dfrac{(\sqrt{2}+1)(\sqrt{6}+\sqrt{3})}{6-3}\)

\(=\dfrac{\sqrt{12}+2\sqrt{6}+\sqrt{3}}{3}\)

\(=\dfrac{3\sqrt{3}+2\sqrt{6}}{3}\)

\(= \sqrt{3}+\dfrac{2}{3} \sqrt{6}\)
 

\(\therefore x=1\ \ \text{and}\ \ y=\dfrac{2}{3} \)

Functions, 2ADV F1 EQ-Bank 24 MC

Given that  \(f(x)=\left\{\begin{array}{ll}3-(x-2)^2, & \text { for } x \leqslant 2 \\ m x+5, & \text { for } x>2\end{array}\right.\)

What is the value of \(m\) for which \(f(x)\) is continuous at  \(x=2\) ?

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

\(C\)

Show Worked Solution

\(\text {If continuous at}\ x=2:\)

  \(3-(x-2)^2\) \(=mx+5\)
  \(3-(2-2)^2\) \(=2m+5\)
   \(2m\) \(=-2\)
  \(m\) \(=-1\)

 
\(\Rightarrow C\)

Functions, 2ADV F1 2012 HSC 2 MC

Which of the following is equal to  `1/(2sqrt5-sqrt3)`? 

  1. `(2sqrt5\-sqrt3)/7`  
  2. `(2sqrt5 + sqrt3)/7`
  3. `(2sqrt5\-sqrt3)/17` 
  4. `(2sqrt5 + sqrt3)/17` 
Show Answers Only

`D`

Show Worked Solution

`1/(2sqrt5\-sqrt3) xx (2sqrt5 + sqrt3)/(2sqrt5 + sqrt3)`

`= (2sqrt5 + sqrt3)/( (2sqrt5\-sqrt3)(2sqrt5 + sqrt3) )`

`= (2sqrt5 + sqrt3)/{(2sqrt5)^2-(sqrt3)^2)`

`= (2sqrt5 + sqrt3)/17`

 
`=>  D`