num-title-qs-hsc

Measurement, STD2 M6 2012 HSC 4 MC

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

`29 xx cos40^@`
`29 xx cos 50^@`
`cos40^@/29`
`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.

What is the median of these scores?

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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)`?

`r=(800-S)/800`
`r=(S-800)/800`
`r=800-S`
`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?

`25\ text(cm)^2`
`33\ text(cm)^2`
`132\ text(cm)^2`
`143\ text(cm)^2`

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(cm)^2\ text{(nearest cm}^2 text{)}`

`=> 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?

`1/6`
`1/12`
`5/12`
`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`?

`yxx10/15`
`yxx10/23`
`yxx15/10`
`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?

38 cm²
52 cm²
61 cm²
70 cm²

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`B`

Show Worked Solution

`text(Shaded area)`	`=text(Area of segment)-text(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.

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

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?

Both the mean and median would have changed.
Neither the mean nor the median would have changed.
The mean would have changed and the median would have stayed the same.
The mean would have stayed the same and the median would have changed.

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`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?

4.17%
4.55%
8.33%
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.

What is the volume of the solid?

513 cm³
999 cm³
1242 cm³
1539 cm³

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`B`

Show Worked Solution

`text(Volume )`	`=text{Vol (cube)} +text{Vol (pyramid)}`
	`=s^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?

$4375.00
$4412.50
$4600.00
$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?

$1046.88
$1047.09
$1296.88
$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?

All Year 7 students
All physics students in Year 11 and 12
20 students chosen at random from each year group
120 students chosen at random from the school roll

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`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?

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`B`

Show Worked Solution

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

`text{After 72 rolls, expected number of times (of any specific number)}`

`=1/6 xx 72=12`

`=>\ 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?

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`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.)`

`=> D`

Algebra, 2UG 2013 HSC 5 MC

Which of the following is `(12T^2)/(3Txx2W)` in its simplest form?

`(2T)/W`
`2TW`
`(8T)/W`
`8TW`

Show Answers Only

`A`

Show Worked Solution

`(12T^2)/(3Txx2W)=(12T^2)/(6TW)=(2T)/W`

`=>\ A`

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?

$583.20
$620.40
$669.60
$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?

Tossing a fair coin and obtaining a head
Rolling a standard six-sided die and obtaining a 3
Randomly selecting the letter 'G' from the 26 letters of the alphabet
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`

L&E, 2ADV E1 2011 HSC 1c

Solve `2^(2x+1)=32`. (2 marks)

Show Answer Only

`x=2`

Show Worked Solutions

MARKER’S COMMENT: Many students correctly solved this by taking the logarithms of both sides.

`2^(2x+1)`	`=32`
`2^(2x+1)`	`=2^5`
`2x+1`	`=5`
`:. x`	`=2`

L&E, 2ADV E1 2013 HSC 9 MC

What is the solution of `5^x=4`?

`x=(log_2 4)/5`
`x=4/(log_2 5)`
`x=(log_2 4)/(log_2 5)`
`x=log_2(4/5)`

Show Answer Only

`C`

Show Worked Solutions

`5^x`	`=4`
`log_2 5^x`	`=log_2 4`
`x log_2 5`	`=log_2 4`
`:.x`	`=(log_2 4)/(log_2 5)`

`=>C`