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Statistics, STD2 S1 2010 HSC 1 MC

The results of a survey are displayed in the dot plot.

What is the range of this data?
 

2010 1 MC 
 

  1.    7
  2.    8
  3.    9
  4.    10
Show Answers Only

`C`

Show Worked Solution
`text(Range)` `=text(High)-text(Low)`
  `=9-0`
  `=9`

`=>  C`

Measurement, STD2 M6 2011 HSC 4 MC

The angle of depression from a kookaburra’s feet to a worm on the ground is 40°. The worm is 15 metres from a point on the ground directly below the kookaburra’s feet. 
 

 How high above the ground are the kookaburra's feet, correct to the nearest metre?

  1. 10 m
  2. 11 m
  3. 13 m
  4. 18 m
Show Answers Only

`C`

Show Worked Solution
`  /_ \ text{Elevation (worm)}` `= 40^@`    `text{(alternate angles)}`
`tan 40^@` `=h/15`
`:. h` `=15xxtan 40^@`
  `=12.58…\ text(m)`

`=>C`

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`  
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`A`

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

`=>  A`

Measurement, STD2 M6 2012 HSC 4 MC

 Which expression could be used to calculate the value of `x` in this triangle? 
 

 

  1. `29 xx cos40^@`  
  2. `29 xx cos 50^@`  
  3. `cos40^@/29`  
  4. `cos50^@/29`  
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`A`

Show Worked Solution
♦ Mean mark 42%
`cos40^@` `= x/29`
`x` `= 29xxcos40^@`

 
`=>  A`

Statistics, STD2 S1 2012 HSC 1 MC

A set of 15 scores is displayed in a stem-and-leaf plot.
 

2012 1 mc 
 

 What is the median of these scores?

  1.    7 
  2.    8
  3.   77
  4.   78
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`D`

Show Worked Solution

`text(15 scores)\ \ =>\ \ text(Median is 8th)`

`:.\ \ text(Median is)\ \ 78`

`=>  D`

Algebra, STD2 A1 2013 HSC 21 MC

Which equation correctly shows  `r`  as the subject of  `S=800(1-r)`?

  1. `r=(800-S)/800`
  2. `r=(S-800)/800`
  3. `r=800-S`
  4. `r=S-800`
Show Answers Only

`A`

Show Worked Solution
♦♦♦ Mean mark 27%
`S` `=800(1-r)`
`1-r` `=S/800`
`r` `=1-S/800`
  `=(800-S)/800`

 
`=>\ A`

Measurement, STD2 M1 2013 HSC 19 MC

A logo is designed using half of an annulus.
  

What is the area of the logo, to the nearest cm²?

  1. `25\ text(cm²)`
  2. `33\ text(cm²)`
  3. `132\ text(cm²)`
  4. `143\ text(cm²)`
Show Answers Only

`B`

Show Worked Solution
`text(Area)` `=1/2xxpi(R^2-r^2)`
  `=1/2xxpi(5^2-2^2)`
  `=21/2pi`
  `=33\ text(cm²)\ \ \ text{(nearest cm²)}` 

 
`=>\ B`

Probability, STD2 S2 2013 HSC 18 MC

Two unbiased dice, each with faces numbered  1, 2, 3, 4, 5, 6,  are rolled.

What is the probability of obtaining a sum of 6?

  1. `1/6`
  2. `1/12`
  3. `5/12`
  4. `5/36`
Show Answers Only

`D`

Show Worked Solution

`text(Total outcomes)=6xx6=36`

`text{Outcomes that sum to 6}=text{(1,5) (5,1) (2,4) (4,2) (3,3)} =5`

`:.\ P\text{(sum of 6)} =5/36`

`=>\ D`

♦♦ Mean mark 35%.

Measurement, STD2 M1 2013 HSC 17 MC

Triangles  `ABC`  and  `DEF`  are similar.
  

Which expression could be used to find the value of  `x`?

  1. `yxx10/15`
  2. `yxx10/23`
  3. `yxx15/10`
  4. `yxx23/15`
Show Answers Only

`C`

Show Worked Solution
♦ Mean mark 38%

`text(We know)\ \ Delta ABC\ text(|||)\ Delta DEF`

`:.\ (AB)/(AC)` `=y/10=(DE)/(DF)=x/15`
`x/15` `=y/10`
`x` `=yxx15/10`

 
`=> C`

Measurement, STD2 M1 2013 HSC 16 MC

The shaded region shows a quadrant with a rectangle removed.
  

What is the area of the shaded region, to the nearest cm2?

  1. 38 cm²
  2. 52 cm²
  3. 61 cm²
  4. 70 cm²
Show Answers Only

`B`

Show Worked Solution
`text(Shaded area)` `=\ text(Area of segment – Area of rectangle)`
  `=1/4 pi r^2-(6xx2)`
  `=1/4 pi xx9^2-12`
  `=51.617…\ text(cm²)`

`=>\ B`

Statistics, STD2 S1 2013 HSC 15 MC

The frequency histogram shows the number of goals scored by a football team in each game in a season.
 

2013 15 mc

 
What is the mean number of goals scored per game by this team?

  1.    4
  2.    4.5
  3.    5
  4.    5.5
Show Answers Only

`C`

Show Worked Solution

`text(Total number of goals scored)`

`=(3xx3)+(4xx7)+(5xx5)+(6xx1)+(7xx0)+(8xx4)`

`=9+28+25+6+0+32`

`=100`

`text(Number of games)=3+7+5+1+4=20`

`:.\ text(Mean goals per game)=100/20=5`

`=>\ C`

Statistics, STD2 S1 2013 HSC 14 MC

The July sales prices for properties in a suburb were:

$552 000,  $595 000,  $607 000,  $607 000,  $682 000, and  $685 000.

On 1 August, another property in the same suburb was sold for over one million dollars.

If the property had been sold in July, what effect would it have had on the mean and median sale prices for July?

  1.    Both the mean and median would have changed.
  2.    Neither the mean nor the median would have changed.
  3.    The mean would have changed and the median would have stayed the same.
  4.    The mean would have stayed the same and the median would have changed.
Show Answers Only

`C`

Show Worked Solution

`text(Mean increases because new house is sold above)`

`text(the existing average.)`

`text(Initial median)= (607\ 000+607\ 000)/2=607\ 000` 

`text(New median)=607\ 000\ \ \  text{(4th value in a list of 7)}`

`=>\ C`

Financial Maths, STD2 F1 2013 HSC 13 MC

Polly borrowed $11 000.  She repaid the loan in full at the end of two years with a lump sum of  $12 000.

What annual simple interest rate was she charged?

  1. 4.17%
  2. 4.55%
  3. 8.33%
  4. 9.09%
Show Answers Only

`B`

Show Worked Solution

`text(Total interest paid)=12\ 000-11\ 000=$1000`

`I` `=Prn`
`1000` `=11\ 000 xx r xx2`
`r` `=1000/(22\ 000)`
  `=4.55 text(%)`

 
`=>\ B`

Measurement, STD2 M1 2013 HSC 12 MC

A square pyramid fits exactly on top of a cube to form a solid.

2013 12 mc

What is the volume of the solid?

  1. 513 cm³
  2. 999 cm³
  3. 1242 cm³
  4. 1539 cm³
Show Answers Only

`B`

Show Worked Solution
`text(Volume )` `=text{Vol (cube)} +text{Vol (pyramid)}`
  `=l^3+1/3Ah`
  `=(9xx9xx9)+(1/3xx9xx9xx10)`
  `=999\ text(cm)^3`

 
`=>\ B`

Financial Maths, STD2 F1 2013 HSC 11 MC

An enterprise agreement has the following annual salary arrangements:
 

George's employer pays 6% more than the enterprise agreement. He is on Step 3 and receives an allowance for Leader 2.

What is George's gross monthly pay?

  1. $4375.00
  2. $4412.50
  3. $4600.00
  4. $4637.50
Show Answers Only

`D`

Show Worked Solution
♦ Mean mark 46%
`text(Gross annual pay)` `=(45\ 000+7500)xx1.06`
  `=$55\ 650`

 

`:.\ text(Gross monthly pay)` `=(55\ 650)/12`
  `=$4637.50`

 
`=>\ D`

Financial Maths, STD2 F1 2013 HSC 9 MC

Lynne invests $1000 for a term of 15 months. Simple interest is paid on the investment at a rate of 3.75% per annum.

How much will Lynne's investment be worth at the end of the term?

  1. $1046.88
  2. $1047.09
  3. $1296.88
  4. $1468.75
Show Answers Only

`A`

Show Worked Solution

`I=Prn=1000xx3.75/100xx15/12=$46.88`

`:.\ text(Investment worth)\ = 1000+46.88=$1046.88`

`=>\ A`

Statistics, STD2 S1 2013 HSC 8 MC

A high school has 100 students in each year group, Year 7 to Year 12. A survey is to be conducted to determine the average number of text messages sent per month by students at the school.

Which of the following would provide the most representative sample for this survey?

  1. All Year 7 students
  2. All physics students in Year 11 and 12
  3. 20 students chosen at random from each year group
  4. 120 students chosen at random from the school roll
Show Answers Only

`C`

Show Worked Solution

`text(The best sample would have an equal amount)`

`text(of people in each year randomly selected.)`

`=>\ C`

Probability, STD2 S2 2013 HSC 7 MC

In an experiment, a standard six-sided die was rolled 72 times. The results are shown in the table.
 

Which number on the die was obtained the expected number of times?

  1.    1
  2.    2
  3.    3
  4.    6
Show Answers Only

`B`

Show Worked Solution

`text(Probability of rolling a specific number)=1/6`

`:.\ text(After 72 rolls, a specific number is expected)`

 `1/6xx72=12\ text(times.)`

`=>\ B`

Statistics, STD2 S1 2013 HSC 6 MC

A survey was conducted where people were asked which of two brands of smartphones they preferred. The results were:

  • 48% preferred Brand X
  • 52% preferred Brand Y

A graph displaying the data is to be included in a magazine article. The editor of the magazine wishes to ensure that the graph is not misleading in any way.

Which graph should the editor choose to include in the article?
 

2013 6 mc1

2013 6 mc2

Show Answers Only

`D`

Show Worked Solution

`D\ text(is the best as it starts at zero on the)\ y text(-axis)`

`text(and has the same column widths.)`

Financial Maths, STD2 F1 2013 HSC 3 MC

Luke's normal rate of pay is  $24.80  per hour. In one week he worked 14 hours at the normal rate, 4 hours at time-and-a-half, and 3 .5 hours at double time. He was also paid a wet weather allowance of  $50  for the week.

What was his pay for the week?

  1. $583.20
  2. $620.40
  3. $669.60
  4. $719.60
Show Answers Only

`D`

Show Worked Solution
 `text(Pay)` `=(14xx24.80)+(4xx1.5xx24.80)+(3.5xx2xx24.80)+50` 
   `=347.20+148.80+173.60+50`
   `=$719.60`

 
`=>D`

Probability, STD2 S2 2013 HSC 1 MC

Which of the following events would be LEAST likely to occur?

  1.    Tossing a fair coin and obtaining a head
  2.    Rolling a standard six-sided die and obtaining a 3
  3.    Randomly selecting the letter 'G' from the 26 letters of the alphabet
  4.    Winning first prize in a raffle of 100 tickets in which you have 4 tickets
Show Answers Only

`C`

Show Worked Solution

`P(A)=1/2,\ \ P(B)=1/6`

`P(C)=1/26,\ \ P(D)=4/100=1/25`

 

`=>C\ text(is the least likely.)`