num-title-qs-hsc

Financial Maths, STD2 F1 2010 HSC 5 MC

Minjy invests $2000 for 1 year and 5 months. The simple interest is calculated at a rate of 6% per annum.

What is the total value of the investment at the end of this period?

$2170
$2180
$3003
$3700

Show Answers Only

`A`

Show Worked Solution

`text(Interest)`	`=Prn`
	`=2000 xx\ text(6%)\ xx 17/12`
	`=$170`

`:.\ text(Value of Investment)`	`=2000+170`
	`=$2170`

`=> A`

Probability, STD2 S2 2012 HSC 26e

The dot plot shows the number of push-ups that 13 members of a fitness class can do in one minute.

What is the probability that a member selected at random from the class can do more than 38 push-ups in one minute? (1 mark)

--- 1 WORK AREA LINES (style=lined) ---
A new member who can do 32 push-ups in one minute joins the class.

Does the addition of this new member to the class change the probability calculated in part (i)? Justify your answer. (1 mark)

--- 2 WORK AREA LINES (style=lined) ---

Show Answers Only

`7/13`
`text{Yes (See Worked Solutions)}`

Show Worked Solution

i. `P`	`= text(# Members > 38 push-ups)/text(Total members)`
	`= 7/13`

ii. `text(Yes.)`

`Ptext{(+ New member)}`	`= text(Members > 38 push-ups)/text(Total members)`
	`= 7/14≠ 7/13`

MARKER’S COMMENT: The most successful candidates used the fraction `7/14` in their part (ii) answer rather than relying solely on words.

Financial Maths, STD2 F1 2012 HSC 18 MC

Jo qualifies for both Rent Assistance and Youth Allowance and receives a fortnightly payment from the government.

Rent Assistance is $119.40 per fortnight.

The maximum Youth Allowance is $402.70 per fortnight. It is reduced by 50 cents in the dollar for any income earned over $236 per fortnight.

Jo earns $300 per fortnight from a part-time job.

What is the total payment Jo receives each fortnight from the government?

$370.70
$372.10
$458.60
$490.10

Show Answers Only

`D`

Show Worked Solution

`text(Rent assistance)\ = $119.40`

`text(Youth allowance)`	`= 402.70\ text(less 50c per dollar)\ \ (text(income) > $236)`
	`= 402.70-0.5(300-236)`
	`= 402.70-32`
	`= $370.70`

`:.\ text{Total Payment}`	`=119.40 + 370.70`
	`=$490.10`

`=> D`

Probability, STD2 S2 2012 HSC 17 MC

A spinner with different coloured sectors is spun 40 times. The results are recorded in the table.

What is the relative frequency of obtaining the colour orange?

`3/20`
`1/5`
`6`
`8`

Show Answers Only

`A`

Show Worked Solution

♦♦ Mean mark 34%
COMMENT: Note that relative frequency is the frequency of an event divided by the total frequencies (i.e. the probability).

`text(Total frequency)`	`= 40\ text(spins)`
`text(Orange freq.)`	`= 40\-(2 + 4 + 6 + 10 +12)`
	`=6`
`:.\ text(Relative freq.)`	`= 6/40 = 3/20`

`=> A`

Financial Maths, STD2 F4 2012 HSC 16 MC

A machine was bought for $25 000.

Which graph best represents the salvage value of the machine over 10 years using the declining balance method of depreciation?

(A)			(B)

(C)			(D)

Show Answers Only

`A`

Show Worked Solution

`text(By Elimination)`

`B\ \ text(and)\ \ D\ \ text(represent straight line depreciation.)`

`C\ \ text(incorrectly has no salvage value after 10 years)`

`=>A`

Algebra, STD2 A2 2012 HSC 13 MC

Conversion graphs can be used to convert from one currency to another.

Sarah converted 60 Australian dollars into Euros. She then converted all of these Euros
into New Zealand dollars.

How much money, in New Zealand dollars, should Sarah have?

$26
$45
$78
$135

Show Answers Only

`C`

Show Worked Solution

`text(Using the graphs)`

`$60\ text(Australian)`	`=46\ text(Euro)`
`46 \ text(Euro)`	`=$78\ text(New Zealand)`

`=> C`

Probability, STD2 S2 2012 HSC 12 MC

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

What is the probability of a 6 appearing on at least one of the dice?

`1/6`
`11/36`
`25/36`
`5/6`

Show Answers Only

`B`

Show Worked Solution

`P(text(at least 1 six))`

`= 1-P(text(no six)) xx P(text(no six))`

`=1-5/6 xx 5/6`

`=11/36`

`=> B`

♦♦♦ Mean mark 25%
COMMENT: The term “at least” should flag that calculating the probability of `1-P text{(event not happening)}` is likely to be the most efficient way to solve.

Statistics, STD2 S4 2012 HSC 11 MC

Which of the following relationships would most likely show a negative correlation?

The population of a town and the number of hospitals in that town.
The hours spent training for a race and the time taken to complete the race.
The price per litre of petrol and the number of people riding bicycles to work.
The number of pets per household and the number of computers per household.

Show Answers Only

$B$

Show Worked Solution

$\text{Increased hours training should reduce the time}$

$\text{to complete a race.}$

$\Rightarrow B$

♦ Mean mark 43%.

Measurement, STD2 M6 2012 HSC 10 MC

What is the area of this triangle, to the nearest square metre?

`33\ text(m²)`
`37\ text(m²)`
`42\ text(m²)`
`44\ text(m²)`

Show Answers Only

`C`

Show Worked Solution

`text(Let unknown angle)=/_C`

`/_C`	`= 180-(50 + 57)\ \ \ \ \ (180^@ \ text(in)\ Delta)`
	`=73^@`

`:. A`	`= 1/2 ab\ sinC`
	`= 1/2 xx 9.9 xx 8.8 xx sin73^@`
	`= 41.656 \ text(m²)`

`=> C`

Measurement, STD2 M1 2012 HSC 6 MC

What is the volume of this rectangular prism in cubic centimetres?

6 cm³
600 cm³
60 000 cm³
6 000 000 cm³

Show Answers Only

`C`

Show Worked Solution

`text{Convert all measurements to centimetres:}`

`V`	`= l xx b xx h`
	`=30 xx 5 xx 400`
	`=60\ 000\ \ text(cm)^3`

`=> C`

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?

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?

10 m
11 m
13 m
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 ` ?

`-p/q`
`-q/p`
`\ \ \ p/q`
`\ \ \ q/p`

Show Answers Only

`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?

`29 xx cos40^@`
`29 xx cos 50^@`
`cos40^@/29`
`cos50^@/29`

Show Answers Only

`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?

Show Answers Only

`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(cm²)`
`33\ text(cm²)`
`132\ text(cm²)`
`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?

`1/6`
`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

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.

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.

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?

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

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?

$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

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?

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?

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.)`

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\ text(is the least likely.)`

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`