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Number and Algebra Raph14-55, NAP-Z1-19

Kathleen uses the number sentence  `10 xx 6 = 60`  to solve a problem.

Which problem could she solve with this number sentence?

 

  Kathleen has 10 sandwiches and gives 6 to her friends.
  How many sandwiches are left?

  
 

  Kathleen has 10 friends and buys 6 sandwiches for each of them.
  How many sandwiches did she buy?

  
 

  Kathleen has 6 friends and shared 10 sandwiches with them.
  How many sandwiches did each friend eat?

  
 

  Kathleen has 10 sandwiches and gets 6 more sandwiches.
  How many sandwiches does she have now?

  
Show Answers Only

`text(Kathleen has 10 friends and buys 6 sandwiches for each of them.)`

`text(How many sandwiches did she buy?)`

Show Worked Solution

Kathleen has 10 friends and buys 6 sandwiches for each of them.

How many sandwiches did she buy?

Probability Raph14-50, NAP-Z1-17

Dianne spins the arrow on this spinner once.

What is the chance of the arrow landing on a ?

 
   Certain  
 
   Unlikely  
 
   Likely  
 
   Impossible  
Show Answers Only

`text(Unlikely)`

Show Worked Solution

Since there is only one shell and many lightning bolts, the chance

of landing on a shell is “unlikely”.

Probability Raph14-49, NAP-Z1-17

Shawn spins the arrow on this spinner once.

What is the chance of the arrow landing on a ?

 
  Certain  
 
  Unlikely  
 
  Likely    
 
  Impossible  
Show Answers Only

`text(Likely)`

Show Worked Solution

Since there are more stars than clubs, the chance of

landing on a star is “likely”.

Number and Algebra Raph14-47, NAP-Z1-16

Jeremy earns $12 each day for 7 days.

Which of the following can be used to find how much money Jeremy earn altogether?

 
   7 + 7 + 7 + 7 + 7 + 7 + 7  
 
   7 + 12  
 
   12 + 12 + 12 + 12 + 12 + 12 + 12    
 
   12 + 7 + 12 + 7 + 12 + 7 + 12  
Show Answers Only

`12 + 12 + 12 + 12 + 12 + 12 + 12`

Show Worked Solution
`text(Total earned)` `= 12 xx 7`  
  `= 12 + 12 + 12 + 12 + 12 + 12 + 12`  

Number and Algebra Raph14-46, NAP-Z1-16

An uncle gave his 6 nephews $10 each.

Which of the following can be used to find the total amount of money given by the uncle to his nephews?

 
  10 + 6  
 
  6 + 6 + 6 + 6 + 6 + 6   
 
  10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10 + 10   
 
  10 + 10 + 10 + 10 + 10 + 10  
Show Answers Only

`10 + 10 + 10 + 10 + 10 + 10`

Show Worked Solution
`text(Total)` `=6 xx 10`  
  `= 10 + 10 + 10 + 10 + 10 + 10`  

Statistics Raph14-44, NAP-Z1-15

Sharon and Troy purchased plants for their gardens from the local nursery.

The number of each plant is recorded in the table below.

  Acacia Melaleuca Wildflower
Sharon 2 2 1
Troy 3 0 3

They drew a picture graph showing the total number of plants they purchased.

Which picture graph did they draw?

 
 
 
 
Show Answers Only

Show Worked Solution

`text(Total number of Acacia)` = 2 + 3 = 5

`text(Total number of Melaleuca)` = 2

`text(Total number of Wildflower)` = 1 + 3 = 4
 

Statistics Raph14-43, NAP-Z1-15

The table shows the total number of vegetables that Karla and Mario gathered.

  Potatoes Cabbage Tomatoes
Karla 4 2 3
Mario 0 1 2

They draw a picture graph showing the correct number of vegetables gathered altogether.

Which picture graph did they draw?

 
 
 
 
Show Answers Only

Show Worked Solution

`text(Total number of potatoes)` = 4

`text(Total number of tomatoes)` = 3 + 2 = 5

`text(Total number of cabbages)` = 2 + 1 = 3

Number Raph14-29, NAP-Z1-10

Lester has a book which has more than 317 pages but less than 371 pages.

Which of these could be the number of pages in Lester’s book?

  311 376 391 325
 
 
 
 
Show Answers Only

`325`

Show Worked Solution

Check each option:

311 is less than 317 (Incorrect)

376 is more than 371 (Incorrect)

391 is more than 371 (Incorrect)

325 is more than 317 and less than 371 (Correct)

Number Raph14-28, NAP-Z1-10

Luke has a book which has more than 515 pages but less than 551 pages.

Which of these could be the number of pages in Luke’s book? 

  561 519 579 511
 
 
 
 
Show Answers Only

`519`

Show Worked Solution

Consider each option:

561 is more than 551 (Incorrect)

519 is more than 515 and less than 551 (Correct)

579 is more than 551 (Incorrect)

511 is less than 515 (Incorrect)

Number Raph15-10, NAP-Z1-06

Mark is counting down by threes.

28, 25, 22, ?

Which number comes next?

  19 16 20 18
 
 
 
 
Show Answers Only

`19`

Show Worked Solution

`text(Each number is three less the previous number:)`

`text(Next number)` `= 22 – 3`  
  `=19`  

Measurement Raph14-5, NAP-Z1-01

Anne and George each had a pencil.

They measured their pencils against the same pile of stones.
 


 

Which of the following statements is true?

 
  George's pencil is longer than Anne's.  
 
  Anne's pencil is longer than George's.  
 
  Anne's pencil is the same length as George's.  
Show Answers Only

`text(George’s pencil is longer than Anne’s.)`

Show Worked Solution

`text(George’s pencil is longer than Anne’s.)`

Number, NAPX-p107114v02 SA

A charity calculates its total donations every month.

Over a six month period, the amounts they calculate are as follows:

$1520, $1270, $1600, $1310, $1430, $1288

What is the mean monthly donation the charity received over this 6 month period?

Show Answers Only

`$1403`

Show Worked Solution
`text(Mean)` `= (1520 + 1270 + 1600 + 1310 + 1430)/6`
  `= 8418/6`
  `= $1403`

Algebra, NAPX-p106742v02

A Cartesian plane is shown below.
 


 

Which statement is true?

 
   `R` is located where  `x < 0`  and  `y > 0`
 
   `N` is located where  `x < 0`  and  `y < 0`
 
   `M` is located where  `x > 0`  and  `y < 0`
 
   `Q` is located where  `x < 0`  and  `y < 0`

Show Answers Only

`N\ text(is located where)\ \ x < 0\ \ text(and)\ \ y < 0`

Show Worked Solution

`text(Points left of the)\ y text(-axis): \ x<0`

`text(Points below the)\ x text(-axis): \ y<0`

`:. N\ text(is located where)\ \ x < 0\ \ text(and)\ \ y < 0\ \ text(is correct.)`

Algebra, NAPX-p106742v01

A Cartesian plane is shown below..
 


 

Which statement is true?

 
   `S` is located where  `x < 0`  and  `y < 0`
 
   `T` is located where  `x < 0`  and  `y > 0`
 
   `Z` is located where  `x > 0`  and  `y < 0`
 
   `Y` is located where  `x = 0`  and  `y > 0`

Show Answers Only

`Z\ text(is located where)\ \ x > 0\ \ text(and)\ \ y < 0`

Show Worked Solution

`text(Points right of the)\ y text(-axis): \ x>0`

`text(Points below the)\ x text(-axis): \ y<0`

` :. Z\ text(is located where)\ \ x > 0\ \ text(and)\ \ y < 0\ \ text(is correct.)`

Measurement, NAPX-p111988v02

Mario sketches an irregular plot of land, pictured below.
 


 

What is the perimeter of this polygon in metres?

 
   167 m
 
   192 m
 
   244 m
 
   248 m
 
   261 m
Show Answers Only

`248\ text{m}`

Show Worked Solution

`text{Adding sides clockwise from bottom left:}`

`text{Perimeter of the shape}` `= 50 + 15 + 30 + 17 + 14 + 13 + 34 + 45`
  `= 248 \ text{metres}`

Algebra, NAPX-p115106v02

A broadband provider offers 3 types of broadband plans: Standard, High Speed and Fibre To The Door.

The Standard plan costs $50.40 less than the High Speed plan.

The Standard plan costs $72.60 less than the Fibre To The Door plan.

Which of these equations correctly states the cost of the High Speed plan?

 
  Cost of High Speed plan = Cost of Fibre To The Door plan – $72.60
 
  Cost of High Speed plan = Cost of Fibre To The Door plan – $50.40
 
  Cost of High Speed plan = Cost of Fibre To The Door plan – $32.80
 
  Cost of High Speed plan = Cost of Fibre To The Door plan – $22.20
Show Answers Only

`text{C}text{ost of High Speed plan = Cost of Fibre To The Door plan − $22.20}`

Show Worked Solution

`text{Fibre To The Door plan cost over High Speed plan}`

`= 72.60 – 50.40`

`= $22.20`
 

`:.\ text{C}text{ost of High Speed plan = Cost of Fibre To The Door plan − $22.20}`

Algebra, NAPX-p115106v01

A food delivery company provides 3 levels of service: Regular, Moderate and Premium.

Regular service costs $15.50 less than Moderate service.

Regular service costs $45.80 less than Premium service.

Which of these equations correctly represents the cost of Moderate service?

 
   Cost of Moderate Service = Cost of Premium service – $15.50
 
   Cost of Moderate Service = Cost of Premium service – $30.30
 
   Cost of Moderate Service = Cost of Premium service – $20.70
 
   Cost of Moderate Service = Cost of Premium service – $45.80
Show Answers Only

`text{C}text{ost of Moderate Service = Premium service – $30.30}`

Show Worked Solution

`text{Extra cost of Premium service over Moderate service}`

`= 45.80 – 15.50`

`= $30.30`
 

`:.\ text{C}text{ost of Moderate Service = Premium service – $30.30}`

Algebra, NAPX-p170065v02

Ashley makes $152 for every 19 beauty kits she sells online.

Which expression shows how much Ashley would earn if she sells `k` beauty kits?

 
   `(19 × 152) ÷ k`
 
   `(152 ÷ 19) × k`
 
   `(19 ÷ 152) × k`
 
   `(152 + 19) ÷ k`
Show Answers Only

`(152 ÷ 19) xx k`

Show Worked Solution

`152\ → 19\ text(kits)`

`152 -: 19 → \ text(1 kit)`

`:. (152 ÷ 19) xx k\ → \ k\ text(kits)`

Algebra, NAPX-p170065v01

A salesman earns $84 for every 7 litres of paint he sells.

Which expression shows how much would he would earn for selling `x` litres?

 
   `(84 × 7) ÷ x`
 
   `(84 ÷ 7) ÷ x`
 
   `(84 ÷ 7) × x`
 
   `(84 - 7) × x`
Show Answers Only

`(84 ÷ 7) xx x`

Show Worked Solution

`84\ → 7\ text(litres)`

`84 -: 7 → \ text(1 litre)`

`:. (84 ÷ 7) xx x\ → \ x\ text(litres)`

Geometry, NAPX-p170037v02

In the diagram below, line XYZ is a straight line.
 

What is the measurement of angle XYS?

 
     31°
 
     36°
 
     47°
 
     103°
Show Answers Only

`31^@`

Show Worked Solution

`text{Sum of angles in triangle} = 180^@`

`angle ZYT` `= 180 – 102 – 42`
  `= 36^@`

 

`angle XYZ\ text{(straight line)} = 180^@`

`angle XYS` `= 180 – 113 – 36`
  `= 31^@`

 

`therefore angle XYS = 31^@`

Geometry, NAPX-p170037v01

From the diagram shown below, Line ABC is a straight line.
 

   
 

What is the size of angle DBC?

 
     63°
 
     93°
 
   117°
 
   297°
Show Answers Only

`117^@`

Show Worked Solution

`text{Sum of angles in triangle} = 180^@`

`angle DBA` `= 180 – 53 – 64`
  `= 63^@`

 
`angle ABC\ text{(straight line)} = 180^@`

`angle DBC` `= 180 – 63`
  `= 117^@`

 

Statistics, NAPX-p108432v02

The graph below represents data gathered from 9 professional workers.
 

   
 

What kind of data could be represented in the graph shown above?

  Vertical Axis Horizontal Axis
 
  Age Salary
 
  Kind of Job Salary
 
  Name of Company Age
 
  Favourite food Years of Experience
Show Answers Only

`text{Vertical Axis: Age}`

`text{Horizontal Axis: Salary}`

Show Worked Solution

`text(Age and Salary.)`

`text(Each data category needs to have a number of)`

`text(possibilities and the chosen pair need a general)`

`text(relationship where one moves higher at the same )`

`text(time as the other. Age and slary is the most likely.)`

`text{The graph represents varying numerical values. }`

Statistics, NAPX-p108432v01

Cyrene collected some data from 10 of her friends.

The graph represents the data gathered by Cyrene but no labels are used
 

     
 

What kind of data could Cyrene be showing in her graph?

  Vertical Axis Horizontal Axis
 
  Age Name
 
  Gender Weight
 
  Height Favourite food
 
  Height Weight

 

Show Answers Only

`text{Vertical Axis: Height}`

`text{Horizontal Axis: Weight}`

Show Worked Solution

`text(Height and Weight.)`

`text(Each data category needs to have a number of)`

`text(possibilities and the chosen pair need a general)`

`text(relationship where one moves higher at the same )`

`text(time as the other.)`

`text(Height and weight is the most likely.)`

Geometry, NAPX-p110293v02

A quadrilateral FGHI is moved to a new position labelled LMJK.

Which of these processes resulted in the new position of the quadrilateral?

 
   Rotate quadrilateral FGHI 180° counter-clockwise about the origin.
 
   Reflect quadrilateral in the `y`-axis and then translate 8 units downward.
 
   Rotate quadrilateral FGHI 90° clockwise about the origin.
 
   Reflect quadrilateral FGHI in the `x`-axis and then translate 9 units to the left.
Show Answers Only

`text{Reflect triangle ABC in the}\ y text{-axis and then translate 5 units downward}`

Show Worked Solution

`text{Reflection in the}\ x text{-axis}`

`FGHI \ rightarrow \ F′G′H′I′`

`text{Translate the triangle 9 units to the left}`

`F′G′H′I′\ rightarrow \ KJML`

Geometry, NAPX-p110293v01

The triangle ABC is moved to the new position labelled XYZ.

Which of these processes resulted in the new position of the triangle?

 
   Rotate triangle ABC 180° counter-clockwise about the origin.
 
   Reflect triangle ABC in the `y`-axis and then translate 5 units downward
 
   Reflect triangle ABC in the `x`-axis and then translate 9 units to the right
 
   Rotate triangle ABC 270° clockwise about the origin.
Show Answers Only

`text{Reflect triangle ABC in the}\ y text{-axis and then translate 5 units downward.}`

Show Worked Solution

`text{Reflection in the}\ y text{-axis:}`

`A B C \ rightarrow \ A′ B′ C′`

`text{Translate the triangle 5 units downward:}`

`A′ B′ C′ \ rightarrow \ X Y Z`

Algebra, NAPX-p109130v02

On a given day, the RSPCA had 87 lost dogs and cats in its care.

If there was 11 more dogs than cats, how many dogs were there?

 
   38
 
   49
 
   53
 
   76
Show Answers Only

`49`

Show Worked Solution

`text(Strategy 1)`

`text{There are 11 more dogs than cats.}`

`text{Let} \ D \ = \ text{number of dogs}`

`D+ (D – 11)` `= 87`
`2D` `= 98`
`:. D` `= 49`

 

`text(Strategy 2)`

`text{Check each option:}`

`38 + (38 – 11) = 65 \ text{(Incorrect)}`

`49+ (49-11) = 87 \ text{(Correct)}`

`53 + (53 – 11) = 95 \ text{(Incorrect)}`

`76 + (76 – 11) = 141 \ text{(Incorrect)}`

Algebra, NAPX-p109130v01

A college marching band is made up of 102 people.

There are 24 more men than women.

How many women are there?

 
   30
 
   39
 
   65
 
   78
Show Answers Only

`39`

Show Worked Solution

`text(Strategy 1)`

`text{There are 24 more men than women.}`

`text{Let}\ \ W \ = \ text{number of women}`

`W + (W + 24)` `= 102`
`2W` `= 78`
`:. W` `= 39`

 

`text(Strategy 2)`

`text{Check each option:}`

`30 + (30 + 24) = 84 \ text{(Incorrect)}`

`39 + (39 + 24) = 102 \ text{(Correct)}`

`65 + (65 + 24) = 154 \ text{(Incorrect)}`

`78 + (78 + 24) = 180 \ text{(Incorrect)}`

Number, NAPX-p169769v01

Select a number line which correctly represents the following values: 0.09, 0.755, and 0.85.

 
  
   
 
  
   
 
  
   
 
  

Show Answers Only

Show Worked Solution

`text{The line graph shows the smallest number from left to right.}`

Number, NAPX-p169640v02

Ana wants to make some dumplings.

A batch of dumplings requires 4 eggs and 200 grams of flour.

If Ana uses 64 eggs to make a larger batch of dumplings, how much flour will she need?

 
   3.2 kg
 
   4.0 kg
 
   6.2 kg
 
   8.0 kg
Show Answers Only

`3.2 \ text{kg}`

Show Worked Solution

`text(Flour : Eggs)\ = 200:4 = 50:1`

`text{Let} \ \ x =\ text{amount of flour needed}`

`frac{x}{64}` `= frac{50}{1}`
`x` `= 50 xx 64`
  `=3200\ text(g)`
  `=3.2\ text(kg)`

Number, NAPX-p169640v01

A chemist makes 70 millilitres of a compound by mixing 20 millilitres of Chemical A and 50 millilitres of Chemical B.

If 250 millilitres of Chemical B is used to make a larger batch of the compound, how much Chemical A is needed?

 
   200 mL
 
   180 mL
 
   120 mL
 
   100 mL
Show Answers Only

`100 \ text{mL}`

Show Worked Solution

`text(Chemical A : Chemical B)\ = 20:50 = 2:5`

`text{Let} \ \ x =\ text{amount of Chemical A needed}`

`frac{x}{250}` `= frac{2}{5}`
`x` `= frac{2 xx 250}{5}`
  `=100\ text(mL)`

Measurement, NAPX-p169867v02

Emily walks for 17 minutes to get from her house to Diamond Station.

She then travels by train to Ruby Station.

Emily then walks 21 minutes to the supermarket where she works.
  

   

If Emily's shift starts at 6:30, what is the latest time she can leave home to arrive on time?

 
 4:53
 
 5:08
 
 5:23
 
 5:38

Show Answers Only

`5:38`

Show Worked Solution

`text(Working backwards from arriving at the supermarket at 6:30)`

`text(6:30 less 21 minutes walking = 6:09)`

`text(1st train to arrive before 6:09 leaves Diamond Station at 5:55)`

`text(5:55 less than 17 minutes walking = 5:38)`

`:.\ text(Emily must leave her house by 5:38.)`

Measurement, NAPX-p169867v01

It takes Terry 32 minutes to walk from his home to Train Station A.

He then travels by train to Station C.

Terry then walks to an amusement park which takes him 18 minutes.
 

What is the latest time that Terry can leave his home to arrive at the amusement park by 5:00?

 
 2:28
 
 2:48
 
 3:08
 
 3:28

Show Answers Only

`3:08`

Show Worked Solution

`text(Working backwards from arriving at the amusement park at 5:00)`

`text(5:00 less 18 minutes walking = 4:42)`

`text(1st train to arrive before 4:42 leaves Station A at 3:40)`

`text(3:40 less than 32 minutes walking = 3:08)`

`:.\ text(Terry must leave his house by 3:08.)`

Algebra, NAPX-p109760v01

The corners of a certain parallelogram are shown below.
  
 

Which point in the graph represents the fourth point?

 
 `(1, – 4)`
 
 `(3, – 4)`
 
 `(– 4, 1)`
 
 `(4, – 3)`

Show Answers Only

`(1, – 4)`

Show Worked Solution

   

`text{Consider the top left point on the graph (– 1, – 1),}`

`text(The point below is 3 grid lines down and three left.)`

`text{Consider the top right point on the graph (4, – 1),}`

`text{The point (1, – 4) is 3 grid lines down and three left.}`

Algebra, NAPX-p169742v01

Three corners of a rectangle are shown below.
 


 

Which point represents the fourth corner of the rectangle?

 
 (3, –1)
 
 (3, –2)
 
 (–2, 3)
 
 (-1, 3)

Show Answers Only

`(3, -2)`

Show Worked Solution

`text(Consider the top left point on the graph (-1, 1),)`

`text(The point below is 3 grid lines down.)`

`text{Consider the top right point on the graph (3, 1),}`

`text{The point (3, -2) is 3 grid lines down.}`

Number, NAPX-p169733v02

Hilary wants to buy second hand furniture for her new flat.

She went to a charity store that sold furniture with the pricing listed in the table below.
 

   

She decided to buy one of each furniture item listed.

Which of these gives the correct range of the total cost of the furniture that she bought?

 
 $475 – $500
 
 $500 – $525
 
 $525 – $550
 
 $550 – $575

Show Answers Only

`$550 – $575`

Show Worked Solution

`text(Estimate the price of each furniture:)`

`$69.20 ≈ $70`

`$298.75 ≈ $300`

`$79.50 ≈ $80`

`$112.30 ≈ $110`
 

`text(Total cost of furniture)` `= 70 + 300 + 80 + 110`
  `= $560`

 
`:.\ text(The range of the total cost is around $550 – $575.)`

Number, NAPX-p169733v01

Nicolas wants to build his own desktop gaming setup.

The shop’s prices for different gaming components are as follows:
 

   

Nicolas bought all 4 components from the shop.

Which of these gives the correct range of the total cost of his purchase?

 
 $450 – $475
 
 $475 – $500
 
 $500 – $525
 
 $525 – $550

Show Answers Only

`$475 – $500`

Show Worked Solution

`text(Estimate the prices of the components)`

`$54.30 ≈ $ 55`

`$23.50 ≈ $25`

`$248.60 ≈ $250`

`$158.25 ≈ $160`
 

`text(Total estimated price)` `= 55 + 25 + 250 + 160`
  `= $490`

 
`:.\ text(The range of the total cost is around $475 – $500)`

Number, NAPX-p169590v02

Some beverages are for sale in a convenience store.

The table below shows the different prices of beverages being sold.
 


 

Which of the following beverages is the most expensive per litre?

 
 Water
 
 Soft drinks
 
 Milkshake
 
 Tea

Show Answers Only

`text(Milkshake)`

Show Worked Solution

`text(Conversion: 1000 millilitres = 1 litre)`

`text(Check each option:)`

`text(Water: $1 per 1 litre)`

`text(Soft drinks: $0.65 per 500 millilitres = 2 x 0.65 = $1.30 per litre)`

`text(Milkshake: $0.45 per 250 millilitres = 4 x 0.45 = $1.80 per litre)`

`text(Tea: $0.30 per 200 millilitres = 5 x 0.30 = $1.50 per litre)`

`:.\ text(Milkshake is the most expensive per litre.)`

Measurement, NAPX-p169727v02

Brock decided to cut out a small rectangle from a piece of rectangular paper.
 


 

The rectangle cut out has a length of 60 mm and a height of 40 mm.

Which of the following expressions gives the area of Brock’s paper that was left after cutting out the smaller rectangle?

 
 `(120 xx 200) - (60 xx 160)`
 
 `60 xx 160`
 
 `(120 xx 200) + (40 xx 60)`
 
 `(120 xx 200) - (60 xx 40)`

Show Answers Only

`(120 xx 200) – (60 xx 40)`

Show Worked Solution
`text(Area)` `= text(Area of large rectangle) – text(Area of small rectangle)`
  `= (120 xx 200) – (60 xx 40)`

Measurement, NAPX-p169727v01

Trisha cuts out a triangular shape from a rectangular piece of cardboard.
 


 

The triangle has a height of 2 cm and base of 8 cm.

Which of the following expression gives the area of Trisha’s cardboard after cutting out the triangle?

 
 `(32 xx 60) - (8 xx 2)`
 
 `(52 xx 30)`
 
 `(32 xx 60) - (1/2 xx 8 xx 2)`
 
 `(60 xx 32) - (1/2 + 8 + 2)`

Show Answers Only

`(32 xx 60) – (1/2 xx 8 xx 2)`

Show Worked Solution
`text(Area)` `= text(Area of rectangle) – text(Area of triangle)`
  `= (32 xx 60) – (1/2 xx 8 xx 2)`

Number, NAPX-p169590v01

The table below shows the prices of different kinds of fruit sold at a supermarket.

   

Which type of fruit is the most expensive per kilogram?

 
 Banana
 
 Apple
 
 Orange
 
 Melon

Show Answers Only

`text(Orange)`

Show Worked Solution

`text(Conversion: 1000 grams = 1 kilogram)`

`text(Check each option:)`

`text(Banana: $2.50 for 500 g = 2 x 2.50 = $5 per kilogram)`

`text(Apple: $1.3 for 250 g = 4 x 1.30 = $5.20 per kilogram)`

`text(Orange: $1.15 for 200 g = 5 x 1.15 = $5.75 per kilogram)`

`text(Melon: $5.25 for 1 kilogram = $5.25 per kilogram)`

`:\.text(Oranges are the most expensive per kilogram.)`

Measurement, NAPX-p169635v01

Two circles have radii of different lengths.
 

   
 

The larger circle’s radius is 3.5 times the radius of the smaller circle.

Which of the following is the circumference of the larger circle?

 
   `56pi\ text(cm)`
 
   `42pi\ text(cm)`
 
   `40pi\ text(cm)`
 
   `36pi\ text(cm)`
Show Answers Only

`42 pi \ text{cm}`

Show Worked Solution
`text{Large radius}` `= 6 xx 3.5`
  `= 21 \ text{cm}`

 

`text{C}_text(large)` `= 2 xx R xx pi`
  `= 2 xx 21 xx pi`
  `= 42 pi \ text{cm}`

Measurement, NAPX-p169631v01

Derrick has a backyard in the shape of a rectangle.
 

   
 

The longer side is  `1 1/3`  times longer than the shorter side.

What is the perimeter of Derick’s backyard?

 
    82 m
 
    98 m
 
   115.5 m
 
   133.5 m
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`98 \ text{m}`

Show Worked Solution
`text{Longer side}` `= 21 xx 1 1/3`
  `= 28 \ text{m}`

 

`:.\ text{Perimeter}` `= (2 xx 21) + (2 xx 28)`
  `= 42 + 56`
  `= 98 \ text{m}`

Number, NAPX-p169627v02

A box of fruit contains 12 apples, 16 oranges, and 13 pears.

About what percentage of the fruit in the box are apples?

 
   29%
 
   32%
 
   37%
 
   41%
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`29text(%)`

Show Worked Solution
`text(Percentage of apples)` `= text(number of apples)/text(total pieces of fruit)`  
  `=12/(12+16+13)`  
  `=0.292`  
  `=29text(%)`  

Number, NAPX-p169627v01

In a classroom there are 24 boys and 36 girls.

About what percentage of the students in the classroom are girls?

 
   48%
 
   57%
 
   60%
 
   64%
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`60text(%)`

Show Worked Solution
`text(Percentage of girls)` `= text(number of girls)/text(total students)`  
  `=36/(24+36)`  
  `=0.6`  
  `=60text(%)`