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CORE, FUR1 2016 VCAA 6-7 MC

Part 1

The histogram below shows the distribution of the number of billionaires per million people for 53 countries.
 

Using this histogram, the percentage of these 53 countries with less than two billionaires per million people is closest to

  1. `text(49%)`
  2. `text(53%)`
  3. `text(89%)`
  4. `text(92%)`
  5. `text(98%)`

 

Part 2

The histogram below shows the distribution of the number of billionaires per million people for the same 53 countries as in Part 1, but this time plotted on a `log_10` scale.
 

Based on this histogram, the number of countries with one or more billionaires per million people is

  1.   `text(1)`
  2.   `text(3)`
  3.   `text(8)`
  4.   `text(9)`
  5. `text(10)`
Show Answers Only

`text(Part 1:)\ D`

`text(Part 1:)\ E`

Show Worked Solution

`text(Part 1)`

`text(Percentage with less than 2)`

`= text(countries with less than 2)/text(total countries)`

`= 49/((49 + 2 + 1 + 1))`

`= 49/53`

`~~ 92.4text(%)`

`=> D`

 

`text(Part 2)`

`text(Let)\ \ x=\ text(number of billionaires per million,)`

`text(Number of countries where)\ \ x >= 1,`

♦ Mean mark 45%.
MARKER’S COMMENT: On a `log_10` scale, 1 is plotted as 0 because `log_10\ 1 = 0`, or `10^0=1`

`=> log_10 x >= 0`

`:.\ text(Number of countries)`

`= 9 + 1`

`= 10`

`=> E`

CORE, FUR1 2016 VCAA 4-5 MC

The weights of male players in a basketball competition are approximately normally distributed with a mean of 78.6 kg and a standard deviation of 9.3 kg.

Part 1

There are 456 male players in the competition.

The expected number of male players in the competition with weights above 60 kg is closest to

  1.     `3`
  2.   `11`
  3.   `23`
  4. `433`
  5. `445`

 

Part 2

Brett and Sanjeeva both play in the basketball competition.

When the weights of all players in the competition are considered, Brett has a standardised weight of  `z` = – 0.96 and Sanjeeva has a standardised weight of  `z` = – 0.26

Which one of the following statements is not true?

  1. Brett and Sanjeeva are both below the mean weight for players in the basketball competition.
  2. Sanjeeva weighs more than Brett.
  3. If Sanjeeva increases his weight by 2 kg, he would be above the mean weight for players in the basketball competition.
  4. Brett weighs more than 68 kg.
  5. More than 50% of the players in the basketball competition weigh more than Sanjeeva 
Show Answers Only

`text(Part 1:)\ E`

`text(Part 2:)\ C`

Show Worked Solution

`text(Part 1)`

`text(Find)\ ztext(-score of 60 kg)`

`ztext(-score)` `= (x – barx)/s`
  `= (60 – 78.6)/9.3`
  `= −2`

 

 

`text(Players with weight above 60 kg)`

`= 97.5text(%) xx 456`

`= 445`

`=> E`

 

`text(Part 2)`

`text(Calculate the weight of each player:)`

`text(Brett)`

`−0.96` `= (x – 78.6)/9.3`
`x` `= (9.3 xx −0.96) + 78.6`
  `~~ 69.7\ text(kg)`

 
`text(Sanjeev)`

`−0.26` `= (x – 78.6)/9.3`
`x` `= (9.3 xx −0.26) + 78.6`
  `~~ 76.2\ text(kg)`

 
`text(Consider)\ C,`

`76.182 + 2 = 78.182 < 78.6`

`:. C\ text(is not true.)`

`=> C`

Number and Algebra, NAP-C1-20

Hillary is running a cooking class.

She has 31 students in the class and needs to give them 1 egg each for a recipe.

Eggs are sold in cartons of 12.

What is the least number of egg cartons that Hillary needs to buy? 

`1` `2` `3` `4`
 
 
 
 
Show Answers Only

`text(3 cartons)`

Show Worked Solution

`text(The number of cartons needed)`

`= 31 ÷ 12`

`= 2\ \ text(remainder  7)`

`:.\ text(Hillary needs to buy 3 egg cartons.)`

Number and Algebra, NAP-C1-10

Sandy has the exact coins below in her pocket.

She buys fruit for lunch that costs $1.75.

How much money does Sandy have left?

`$0.08` `$1.00` `$1.10` `$1.20`
 
 
 
 
Show Answers Only

`$1.20`

Show Worked Solution

`$1 xx 1 = $1`

`50¢ xx 3 = $1.50`

`20¢ xx 1 = 20¢`

`10¢ xx 2 = 20¢`

`5¢ xx 1 = 5¢`

 

`text(Total worth of coins)`

`= $1 + $1.50 + 20¢ + 20¢ + 5¢`

`= $2.95`

`:.\ text(Money left)` `= $2.95 – $1.75`
  `= $1.20`

Statistics, NAP-D1-21

Benson asked his friends what their favourite ice cream flavour was.

He recorded their answers in the table below but left off same labels.

Benson remembered that

  • strawberry was the least liked flavour
  • chocolate was the most liked flavour
  • vanilla was more liked than caramel

How many of Benson's friends liked caramel the most?

 
Show Answers Only

`8`

Show Worked Solution

`text(Using the graph and the information given,)`

`=>\ text(7 preferred strawberry,)`

`=>\ text(13 preferred chocolate.)`

`:.\ text(11 preferred vanilla and 8 liked caramel the most.)`

Number and Algebra, NAP-D1-15

Tori wrote this correct number sentence.

`19 + 31 = 50`

Which of these number sentences is also correct?

 
 `50 - 19 = 31`
 
 `50 + 31 = 19`
 
 `19 - 50 = 31`
 
 `31 + 50 = 19`
Show Answers Only

`50 – 19 = 31`

Show Worked Solution

`19+31=50`

`text(Deduct 19 from both sides,)`

`19+31-19` `=50-19`
`31` `=50-19`
`50 – 19` `=31`

Measurement, NAP-E1-20

Alison buys paper clips that come in three sizes, small, medium and large.

The picture shows the lengths of the small and large clips.

What could the length of the medium paper clip be?

`text(1 centimetre)` `text(5 centimetres)` `text(7 centimetres)` `text(11 centimetres)`
 
 
 
 
Show Answers Only

`text(5 centimetres)`

Show Worked Solution

`text(Small paper clip) = 6-1.5 = 4.5\ text(cm)`

`text(Large paper clip) = 16-9=7\ text(cm)`

 

`text(Among the choices given, only 5 cm is between)`

`text(4.5 cm and 7 cm.)`

 

`:.\ text(The medium paper clip could be 5 cm.)`

Number and Algebra, NAP-E1-15

Grace used sticks to create a pattern.

 

She used 4 sticks in her first shape, 7 sticks in her second shape and 10 sticks in her third shape.

How many sticks are needed for the next shape in Grace's pattern?

`9` `10` `11` `13`
 
 
 
 
Show Answers Only

`13`

Show Worked Solution

`text(Each shape adds an extra 3 sticks.)`

`=>\ text(Sticks in the next shape)`

`=10+3`

`=13`

Number and Algebra, NAP-G1-15 SA

Jonah's soccer team got oranges at half time.

The quarters of oranges were put in a container.
 

 

 
How many whole oranges were cut into quarters and put in the container?
Show Answers Only

`4`

Show Worked Solution

`text(There are 16 orange quarters in the container.)`

`=>\ text(Each orange is cut into 4 quarters.)`

`:.\ 4\ text(full oranges are needed.)`

Number and Algebra, NAP-F1-19

Syd is 15 years old. Barney is 23 years old.

Callum is older than Syd but younger than Barney.

Which of these could be Callum's age?

`8` `21` `26` `38`
 
 
 
 
Show Answers Only

`21`

Show Worked Solution

`text(Syd’s age) < text(Callum’s age) < text(Barney’s age)`

`15 < text(Callum) < 23`

`:.\ text(Callum’s age could be 21)`

Probability, NAP-F1-18

The weather report says there is 80% chance of rain tomorrow.

Which of these describes the chance of it raining tomorrow?

`text(impossible)` `text(unlikely)` `text(likely)` `text(certain)`
 
 
 
 
Show Answers Only

`text(likely)`

Show Worked Solution

`text(Anything over 50% chance is more likely than)`

`text(not of happening. Anything that is certain of)`

`text(happening must be 100% chance.)`

`:.\ text(80% chance is “likely”.)`

Number and Algebra, NAP-F1-14

Five people collected a total of 70 aluminium cans to recycle.

Three of the people collected 20 cans each.

The other two, Randy and Thor, collected the rest of the cans equally.

How many cans did Thor collect?

`5` `10` `35` `50`
 
 
 
 
Show Answers Only

`5`

Show Worked Solution

`text(3 people collected 20 cans each.)`

`=> 60\ text(cans were collected, 10 left.)`

`:.\ text(Cans collected by Thor)`

`= 10 ÷ 2`

`= 5`

Number and Algebra, NAP-G1-18

The table shows the heights of 5 children.

Who is 5 centimetres shorter than the tallest child?

`text(Greg)` `text(Marcia)` `text(Peter)` `text(Jan)` `text(Cindy)`
 
 
 
 
 
Show Answers Only

`text(Jan)`

Show Worked Solution

`text{The tallest is Greg (157 cm).}`

`=>\ text(5cm shorter is 152 cm.)`

`:.\ text(Jan is 5 cm shorter than the tallest child.)`

Measurement, NAP-G1-14

Derek used pencils to measure his desk.
 

 
What is the total length of all four sides?

 
 `text(9 pencils)`
 
 `text(11 pencils)`
 
 `text(13 pencils)`
 
 `text(15 pencils)`
 
 `text(18 pencils)`
Show Answers Only

`text(18 pencils)`

Show Worked Solution

`text(Length of all 4 sides)`

`=6+3+6+3`

`=18\ text(pencils)`

Number and Algebra, NAP-G1-13

Wayne needs to buy 14 pairs of socks for the players in his soccer team.

The socks are sold in packets of 3.

How many packets does Wayne need to buy?

`4` `5` `17` `42`
 
 
 
 
Show Answers Only

`5`

Show Worked Solution

`text(Socks in 4 packets)`

`= 4 xx 3 = 12`

`text(Socks in 5 packets)`

`= 5 xx 3 = 15`
 

`:. 5\ text(packets are needed.)`

Measurement, NAP-H1-17

Stella's birthday is on the 30th of March.

Blanche's birthday is four days after Stella's.
 

 
Which day of the week is Blanche's birthday in 2014?

`text(Saturday)` `text(Sunday)` `text(Monday)` `text(Tuesday)`
 
 
 
 
Show Answers Only

`text(Monday)`

Show Worked Solution

`text(30th March ⇒ Thursday)`

`text(One day after ⇒ Friday)`

`text(Two days after ⇒ Saturday)`

`vdots`

`text(Four days after ⇒ Monday)`

Number and Algebra, NAP-H1-15

Bryan had $24 at the start of his holiday.

He spent $4 each day.

How many days did it take for Bryan to spend all his money?

`4` `6` `8` `20` `28`
 
 
 
 
 
Show Answers Only

`6`

Show Worked Solution
`text(Number of days)` `=24 -: 4`
  `=6\ text(days)`

Statistics, NAP-H1-13

Four people go fishing.

They put an `X` on the chart for each fish they catch.

 

Andrea caught more fish than Mandy but less than Andrew.

How many fish did Andrea catch?

`2` `3` `4` `5`
 
 
 
 
Show Answers Only

`3`

Show Worked Solution

`text(Andrea caught more than Mandy.)`

`=>\ text(more than 2)`

`text(Andrea caught less than Andrew.)`

`=>\ text(less than 4)`

`:.\ text(Andrea caught 3 fish.)`

Number and Algebra, NAP-I1-16

A teacher gives 4 of her students 8 pieces of cardboard each.

Which of the following can be used to find how many pieces of cardboard the teacher gave her students?

 
 `4 + 8`
 
 `4 + 4 + 4 + 4`
 
 `8 + 8 + 8 + 8`
 
 `8 + 8 + 8 + 8 + 8 + 8 + 8 + 8`
Show Answers Only

`8 + 8 + 8 + 8`

Show Worked Solution

`text(Total pieces of cardboard)`

`= 4 xx 8`

`= 8 + 8 + 8 + 8`

Number and Algebra, NAP-I1-13 SA

The scales below are evenly balanced.

What is the weight of the small cube?

  grams
Show Answers Only

`text(13 grams)`

Show Worked Solution

`text(S)text(ince the scales are evenly balanced,)`

`36` `= 23 + text(weight of small cube)`

 

`:.\ text(Weight of small cube)` `= 36 – 23`
  `= 13\ text(grams)`

Measurement, NAP-B2-05

Jenny has an appointment on the third Wednesday of March.
 

 
 

What date is her appointment on?

`2^text(nd)\ text(March)` `9^text(th)\ text(March)` `16^text(th)\ text(March)` `23^text(rd)\ text(March)` 
 
 
 
 
Show Answers Only

`16^text(th)\ text(March)`

Show Worked Solution

`16^text(th)\ text(March)`

Number and Algebra, NAP-C2-5

Sandy has the exact coins below in her pocket.
 

 
She buys fruit for lunch that costs $1.75.

How much money does Sandy have left?

`$0.80` `$1.00` `$1.10` `$1.20`
 
 
 
 
Show Answers Only

`$1.20`

Show Worked Solution

`$1 xx 1 = $1`

`50¢ xx 3 = $1.50`

`20¢ xx 1 = 20¢`

`10¢ xx 2 = 20¢`

`5¢ xx 1 = 5¢`

 

`text(Total worth of coins)`

`= $1 + $1.50 + 20¢ + 20¢ + 5¢`

`= $2.95`

`:.\ text(Money left)` `=$2.95 – $1.75`
  `=$1.20`

Geometry, NAP-F2-09

Gary is drawing 3 triangles on grid paper without crossing the sides of any other triangles.

He has 2 more points to join.

One of these is F5.
 

 
What is the other point?

`text(A5)` `text(C5)` `text(E2)` `text(F2)`
 
 
 
 
Show Answers Only

`text(E2)`

Show Worked Solution

`text(E2)`

Probability, NAP-F2-07

The weather report says there is 80% chance of rain tomorrow.

Which of these describes the chance of it raining tomorrow?

`text(impossible)` `text(unlikely)` `text(likely)` `text(certain)`
 
 
 
 
Show Answers Only

`text(likely)`

Show Worked Solution

`text(Anything over 50% chance is more likely than)`

`text(not of happening. Anything that is certain of)`

`text(happening must be 100% chance.)`

`:.\ text(80% chance is “likely”.)`

Geometry, NAP-F2-05

Amos makes a model with 7 white cubes and 2 grey cubes.
 

 

Amos turns his model around.
 

 
Which two numbers shows the positions of the grey cubes?

 
   and  
 
Show Answers Only

`text(3 and 9)`

Show Worked Solution

`text(3 and 9)`

Number and Algebra, NAP-F2-04

Five surfers owned a total of 58 surfboards between them.

Two of the surfers owned 20 surfboards each.

The other three, Lane, Gordon and Shelly, owned the same number of surfboards.

How many surfboards does Gordon own?

`6` `8` `12` `38`
 
 
 
 
Show Answers Only

`6`

Show Worked Solution

`text(2 surfers own 20 boards each)\ = 40\ text(boards)`

`:.\ text(Surfboards owned by Gordon)`

`= (58-40) ÷ 3`

`=18 -: 3`

`= 6`