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Measurement, STD2 M1 2009 HSC 23c

The diagram shows the shape and dimensions of a terrace which is to be tiled.
 

  1. Find the area of the terrace.   (2 marks)

  2. Tiles are sold in boxes. Each box holds one square metre of tiles and costs $55. When buying the tiles, 10% more tiles are needed, due to cutting and wastage.

     

    Find the total cost of the boxes of tiles required for the terrace.   (2 marks)

Show Answers Only

i.    `13.77\ text(m²)`

ii.   `$880`

Show Worked Solution
i.
`text(Area)` `=\ text(Area of big square – Area of 2 cut-out squares`
  `= (2.7 + 1.8) xx (2.7 + 1.8)\-2 xx (1.8 xx 1.8)`
  `= 20.25\-6.48`
  `= 13.77\ text(m²)`

 

ii. `text(Tiles required)` `= (13.77 +10 text{%}) xx 13.77`
    `= 15.147\ text(m²)`

 

 `=>\ text(16 boxes are needed)`

`:.\ text(Total cost of boxes)` `=16 xx $55`
  `= $880`

Financial Maths, STD2 F1 2009 HSC 10 MC

Billy worked for 35 hours at the normal hourly rate of pay and for five hours at double time. He earned $561.60 in total for this work.

What was the normal hourly rate of pay?

  1. $7.02
  2. $12.48
  3. $14.04
  4. $16.05
Show Answers Only

`B`

Show Worked Solution

`text(Let hourly rate) = $X\ text(per hour)`

`35X + 5(2X)` `= 561.60`
`45X` `=561.60`
`X` `= 561.60/45` 
  `= $12.48`

 
`=>  B`

Measurement, STD2 M6 2009 HSC 4 MC

Which is the correct expression for the value of `x` in this triangle? 
 

 

  1. `8/cos30°` 
  2. `8/sin30°` 
  3. `8 xx cos30°`  
  4. `8 xx sin30°` 
Show Answers Only

`A`

Show Worked Solution
`cos30^@`  `= 8/x`
`:.x` `= 8/cos30^@` 

 
`=>  A`

Probability, STD2 S2 2012 HSC 27e

A box contains 33 scarves made from two different fabrics. There are 14 scarves made from silk (S) and 19 made from wool (W).
Two girls each select, at random, a scarf to wear from the box.

  1. Complete the probability tree diagram below.   (2 marks) 
      
       

  2. Calculate the probability that the two scarves selected are made from silk.    (1 mark)

  3. Calculate the probability that the two scarves selected are made from different fabrics.   (2 marks)

Show Answers Only
  1.  
       
     
  2. `P\ text{(2 silk)}= 91/528`
  3. `P\ text{(different fabrics)}= 133/264`
Show Worked Solution

i. 

♦ Mean mark (i) 43%.
ii.  `P\ text{(2 silk)}` `= P(S_1) xx P(S_2)`
  `= 14/33 xx 13/32`
  `= 91/528`

 

iii.  `P\ text{(different)}` `= P (S_1,W_2) + P(W_1,S_2)`
  `= (14/33 xx 19/32) + (19/33 xx 14/32)`
  `= 532/1056`
  `= 133/264`
♦ Mean mark (iii) 41%.
MARKER’S COMMENT: In better responses, students multiplied along the branches and then added these two results together

Measurement, STD2 M6 2012 HSC 27d

A disability ramp is to be constructed to replace steps, as shown in the diagram.

The angle of inclination for the ramp is to be 5°.   
  

Calculate the extra distance, `d`, that the ramp will extend beyond the bottom step.

Give your answer to the nearest centimetre.   (3 marks)

Show Answers Only

 `386\  text(cm)`

Show Worked Solution

`text(Let the horizontal part of the ramp) = x\ text(cm)`

♦♦ Mean mark 35%
MARKER’S COMMENT:  The better responses used a diagram of a simplified version of the ramp as per the Worked Solution.
`tan5^@` `= 39/x`
`x` `= 39/tan5^@`
  `= 445.772…`
   
`text(S)text(ince)\  \ x` `= 60 + d`
`d` `=445.772-60`
  `=385.772\  text(cm)`
  `=386\ text(cm)\ \ text{(nearest cm)}`

Measurement, STD2 M7 2012 HSC 27c

A map has a scale of  1 : 500 000.

  1. Two mountain peaks are 2 cm apart on the map.

     

    What is the actual distance between the two mountain peaks, in kilometres?  (1 mark)

  2. Two cities are 75 km apart. How far apart are the two cities on the map, in centimetres?   (1 mark)

Show Answers Only
  1. `text(10 km)`
  2. `text(15 cm)`
Show Worked Solution
♦ Mean mark 37%
MARKER’S COMMENT: Better responses realised that 1 unit on the map represented 1 unit x 500,000 in real life.
i.  `text{Actual distance (2 cm)}` `= 2 xx 500\ 000`
  `= 1\ 000\ 000\ text(cm)`
  `= 10\ 000\ text(m)`
  `=10\ text(km)`

 

`:.\ text(The 2 mountain peaks are 10 km apart.)`

 

♦ Mean mark 44%

ii.   `text(Cities are 75 km apart.)`

`text{From part (i), we know 2 cm = 10 km}`

`=>\ text(1 cm = 5 km)`

`=>\ text(On the map,  75 km)= 75/5=15\ text(cm)` 

`:.\ text(Distance on the map is 15 cm.)`

Statistics, STD2 S1 2011 HSC 7 MC

A set of data is displayed in this box-and-whisker plot.
 

Which of the following best describes this set of data?

  1. Symmetrical
  2. Positively skewed
  3. Negatively skewed
  4. Normally distributed
Show Answers Only

`B`

Show Worked Solution

`text{Since the median (155) is closer to the lower quartile (150) and range}`

`text{low (140) than the upper quartile (190) and range high (200), it is}`

`text{positively skewed.}`

`=>B`

♦ Mean mark 47%.

Algebra, STD2 A4 2011 HSC 6 MC

 

Which of the following graphs best represents the equation `y = a^x`, where `a` is a positive number greater than 1?
  

Show Answers Only

`D`

Show Worked Solution
 
♦ Mean mark 48%

`text(At) \ x=0,\ y=1`

`text(As)\ x uarr, \ \ y ↑\ text(exponentially)`

`=>D`

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?

  1. $2170
  2. $2180
  3. $3003
  4. $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`

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?

  1. $370.70
  2. $372.10
  3. $458.60
  4. $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`

Measurement, STD2 M1 2012 HSC 6 MC

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

  1. 6 cm³
  2. 600 cm³
  3. 60 000 cm³
  4. 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`

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`  
Show Answers Only

`A`

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

 
`=>  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`

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`

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`

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`