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v1 Measurement, STD2 M7 2020 HSC 23

In a tropical punch, the ratio of passionfruit juice to guava juice to lime juice is 12 : 10 : 6 .

  1. How much lime juice is needed if the punch is to contain 2.4 litres of passionfruit juice? (2 marks)

  2. The internal dimensions of a drink container, in the shape of a rectangular prism, are shown.
     

    To completely fill the container with the punch, how many litres of guava juice are required? (3 marks)

Show Answers Only
  1. `1.2 text{L}`
  2. `10  text{L}`
Show Worked Solution
a.    `text(12 parts)` `= 2.4\ text(L)`
  `text(1 part)` `= 2.4/12`
    `= 0.2\ text(L)`

 

`:.\ text(6 parts)` `= 6 xx 0.2`  
  `= 1.2\ text(L)`  
b.     `text{Volume of container}` `= 40 xx 20 xx 35`
    `= 28\ 000 \ text{cm}^3`

`1 \ text{mL} \ to \ 1 \ text{cm}^3`

`⇒ \ 28\ 000 \ text{mL of punch}`

`therefore \ text{Guava juice required}` `= text{Guava parts}/text{Total parts} \ xx \ 28\ 000`
  `= \frac{10}{28} \ xx \ 28\ 000`
  `= 10\ 000 \ text{mL}`
  `= 10 \ text{L}`

v1 Measurement, STD2 M7 2019 HSC 18

Dana, Eden and Flynn are the first three players in the school basketball team. In a recent game, Dana scored 24 points, Eden scored 18 points and Flynn scored 30 points.

  1. What is the ratio of Dana's to Eden's to Flynn's points scored, in simplest form?   (2 marks)

  2. In this game, the ratio of the total number of points scored by Dana, Eden and Flynn to the total number of points scored by the whole team is `9:20`.
  3. How many points were scored by the whole team?   (2 marks)

Show Answers Only
  1. `4:3:5`
  2. `160\ text(points)`
Show Worked Solution
a.     `D:E:F` `= 24:18:30`
    `= 4:3:5`

 

b.     `text(Total points by)\ D,E,F` `= 24 + 18 + 30`
    `= 72`

 

`text(Let)\ P` `=\ text(team points)`
`P/72` `= 20/9`
`:. P` `= (20 xx 72)/9`
  `= 160\ text(points)`

v1 Measurement, STD2 M7 2023 HSC 26

Jo is constructing a concrete border around a rectangular vegetable patch, as shown. The border is 0.6 m wide.
 

  1. Find the area of the border.   (2 marks)
  2. Jo is preparing concrete using a mix of gravel, sand, and cement in the ratio 5 : 3 : 2 by weight.
    Jo needs 2 tonnes of concrete in the correct ratio.
    Calculate how many 20 kg bags of cement Jo needs to buy.   (3 marks)

Show Answers Only
  1. `11.4\ \text{m}^2`
  2. `20\ \text{bags}`
Show Worked Solution

a.    `text{Area of outer rectangle} = 6.5 × 4.2 = 27.3\ \text{m}^2`

`text{Area of garden} = 5.3 × 3.0 = 15.9 \ text{m}^2`

`text{Area of border}` `= 27.3-15.9`  
  `=11.4\ text{m}^2`  

 

b.   `text{Ratio parts:} \ 5 + 3 + 2 = 10` parts

`text{Total concrete} = 2\ \text{tonnes} = 2000\ \text{kg}`

`text{Each part} = 2000 ÷ 10 = 200\ \text{kg}`

`text{Cement} = 2 \ text{parts} = 2 × 200 = 400\ \text{kg}`

`text{Bags of cement} = 400 ÷ 20 = 20`

`⇒ \ text{Jo needs 20 bags of cement.}`

Measurement, STD2 M7 2023 HSC 26

Kim is building a path around a garden at the back of a house, as shown. The path is 0.5 m wide.

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

  2. Kim is mixing some concrete for the path. The concrete mix is made up of crushed rock, sand and cement in the ratio of 4 : 2 : 1 by weight.
  3. Kim needs 2.1 tonnes of concrete in the correct ratio.
  4. Calculate how many 15 kg bags of cement Kim needs to buy.   (3 marks)

Show Answers Only
  1. `6.5\ text{m}^2`
  2. `20\ text{bags}`
Show Worked Solution

a.    `text{Area outer rectangle}\ = 3xx8=24\ text{m}^2`

`text{Area garden}\ = 2.5xx7=17.5\ text{m}^2`

`A_text{path}` `=24-17.5`  
  `=6.5\ text{m}^2`  

 
b.    `text{7 parts = 2.1 tonnes}`

`text{1 part}\ = 2.1/7=0.3\ text{tonnes}\ =300\ text{kgs}`

`text{Rock}:text{Sand}:text{Cement} = 4:2:1 = 1200:600:300`

`=>\ text{300 kgs of cement are required}`

`:.\ text{Bags of cement}` `=300/15`  
  `=20\ text{bags}`  

Measurement, STD2 M7 2020 HSC 23

In a tropical drink, the ratio of pineapple juice to mango juice to orange juice is 15 : 9 : 4 .

  1. How much orange juice is needed if the tropical drink is to contain 3 litres of pineapple juice?  (2 marks)

  2. The internal dimensions of a drink container, in the shape of a rectangular prism, are shown.
     
     
         
     
    To completely fill the container with the tropical drink, how many litres of mango juice are required. (3 marks)

Show Answers Only
  1. `0.8 \ text{L}`
  2. `9\ text{L}`
Show Worked Solution
a.    `text(15 parts)` `= 3\ text(L)`
  `text(1 part)` `=3/15`
    `=0.2\ text(L)`

 

`:.\ text(4 parts)` `=4 xx 0.2`  
  `=0.8\ text(L)`  

 

Mean mark 51%.
b.      `text{Volume of container}` `= 40 xx 20 xx 35`
    `= 28 \ 000 \ text{cm}^3`

 
`1 \ text{mL} \ to \ 1 \ text{cm}^3`

`⇒ \ 28 \ 000 \ text{mL of tropical drink}`

`therefore \ text{Mango juice required}` `=text(Mango parts)/text(Total parts) xx 28\ 000`
  `= frac{9}(28} xx 28 \ 000`
  `= 9000 \ text{mL}`
  `=9\ text(L)`

Measurement, STD2 M7 2019 HSC 18

Andrew, Brandon and Cosmo are the first three batters in the school cricket team. In a recent match, Andrew scored 30 runs, Brandon scored 25 runs and Cosmo scored 40 runs.

  1. What is the ratio of Andrew's to Brandon's to Cosmo's runs scored, in simplest form?  (2 marks)

  2. In this match, the ratio of the total number of runs scored by Andrew, Brandon and Cosmo to the total number of runs scored by the whole team is `19:36`.
  3. How many runs were scored by the whole team?  (2 marks)

Show Answers Only
  1. `6:5:8`
  2. `180\ text(runs)`
Show Worked Solution
a.    `A:B:C` `= 30:25:40`
    `= 6:5:8`

 

b.    `text(Total runs by)\ A,B,C` `= 30 + 25 + 40`
    `= 95`

 

`text(Let)\ R` `=\ text(team runs)`
`R/95` `= 36/19`
`:. R` `= (36 xx 95)/19`
  `= 180\ text(runs)`

Measurement, STD2 M7 SM-Bank 9

A farmer sells 216 sheep at a livestock auction.

Three buyers purchased all the sheep in the ratio  7:3:2

How many sheep did the buyer of the highest number of sheep purchase?  (2 marks)

Show Answers Only

`126\ text(sheep)`

Show Worked Solution

`7:3:2 => 7/12: 3/12:2/12`

`:.\ text(Buyer of the most sheep)`

`= 7/12 xx 216`

`= 126\ text(sheep)`