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Probability, NAP-B1-34

Penny gets to take 1 marble from a dish.

Penny wants to choose this type of marble  .
Which dish gives Penny the best chance of choosing a   ?
 
 
 
 
Show Answers Only

Show Worked Solution

`text(Looking at each dish, the chances of choosing)`

`text(the marble she wants is:)`

`text(Dish 1:)\ \ 4/10`

`text(Dish 2:)\ \ 2/6`

`text(Dish 3:)\ \ 3/7`

`text(Dish 4:)\ \ 3/6`

`=>\ text{Best chance is with the dish (above)}`

`text(as the chances are)\ 1/2.`

Number and Algebra, NAP-D1-35 SA

Amanda has $2.10 in coins.

She only has 20¢, 10¢, and 5¢ coins and has an equal amount of each.

How many 5¢ coins does she have?
Show Answers Only

`text(She has six 5¢ coins.)`

Show Worked Solution

`text(Total if she has 1 of each coin,)`

`20 + 10 + 5 = 35¢`

`text(Total if she has 2 of each coin,)`

`2 xx 35¢ = 70¢`

`vdots`

`text(Total if she has 6 of each coin,)`

`6 xx 35¢ = $2.10`

`:.\ text(She has six 5¢ coins.)`

Number and Algebra, NAP-F1-33 SA

Clancy bought some pens using a $20 note.

Each pen cost 35 cents.

Clancy got $16.15 change.

How many pens did Clancy buy?
Show Answers Only

`11`

Show Worked Solution

`text(C) text(ost of pens)`

`= $20 – $16.15`

`= $3.85`

STRATEGY: This division is made easy by first working out that 10 pens cost $3.50.

 
`text(Number of pens bought)`

`= 3.85 ÷ 35\ text(cents)`

`= 11`

Number and Algebra, NAP-I1-35 SA

Alvin and Curtly picked 47 apples from an apple tree.

Curtly picked 11 more apples than Alvin.

How many apples did Curtly pick?
Show Answers Only

`29`

Show Worked Solution

`text(Strategy one:)`

`text(Try possible numbers,)`

`text(24 Curtly − 23 Alvin ⇒ 1 difference)`

`text(25 Curtly − 22 Alvin ⇒ 3 difference)`

`vdots`

`text(29 Curtly − 18 Alvin ⇒ 11 difference)`

`:.\ text(Curtly picked 29 apples.)`

 

`text{Strategy two (use of algebra):}`

`text(Let Alvin pick)\ \ x\ \ text(apples)`

`text(Curtly picks)\ \ x + 11\ \ text(apples)`

`x +x + 11` `=47`
`2x` `=36`
`x` `=18`

 

`:.\ text(Curtly picks  18 + 11 = 29 apples)`

Number and Algebra, NAP-H1-35 SA

Soda cans are sold in three different ways at the supermarket.
 


 

What is the cheapest price that someone can buy 13 cans for?

 
Show Answers Only

`$17.50`

Show Worked Solution

`text(Two six packs and a single can:)`

`text(C)text(ost)` `=(2 xx 8) + 1.50`
  `=$17.50`

 

`text(One ten pack and 3 single cans:)`

`text(C)text(ost)` `=(1 xx 14) + (3 xx 1.50)`
  `=14 + 4.50`
  `=$18.50`

 

`:.\ text(The cheapest price is $17.50).`

Geometry, NAP-C2-39 SA

David drew a scale drawing of his road bike on a grid.
 

What scale is David using for his picture?

One unit on the grid represents

   cm
Show Answers Only

`40\ text(cm)`

Show Worked Solution

`text(Strategy 1:)`

`1.5\ text(units)` `= 60\ text(cm)`
 `:. 1\ text(unit)` `= 60 ÷ 1.5`
  `= 40\ text(cm)`

 

`text(Strategy 2:)`

`4\ text(units)` `=160\ text(cm)`
`:. 1\ text(unit)` `=160 -: 4`
  `=40\ text(cm)`

Measurement, NAP-C2-36 SA

Abdul's wages are paid on the first Wednesday of each month.

His wages were paid on 5 July.

What is the date that he can expect his wages to be paid in August?

  August
Show Answers Only

`text(2 August)`

Show Worked Solution

`text(S)text(ince 5 July was a Wednesday, so is 12, 19, and 26.)`

`text(July has 31 days, therefore 31 July is a Monday.)`

`:.\ text(2 August is a Wednesday.)`

Number and Algebra, NAP-F2-36 SA

Horace bought some pens for school with a $5 note.

Each of the pens cost 35 cents.

Horace received $1.15 change.

How many pens did he buy?
Show Answers Only

`11`

Show Worked Solution

`text(One strategy:)`

`text(Consider some different numbers of pens,)`

`text(10 pens cost $3.50 ⇒ change of $1.50)`

`:. 11\ text(pens cost $3.85 ⇒ change of $1.15)`

Geometry, NAP-G2-40 SA

The pictures show the front, side and top views of an object made of cubes.
 

 
How many cubes are needed to make the object?
Show Answers Only

`10`

Show Worked Solution

`=>\ text{Cubes on the base = 6  (from top view)}`

`=>\ text{Only stacked cubes will be on the line of the}`

`\ text{first left cube (from the front view).}`

`=>\ text(Side view shows that only 4 cubes in total are)`

`\ text(higher than the base level of cubes.)`

 

`:.\ text(Total cubes in the object = 10.)`

Number and Algebra, NAP-G2-39 SA

Oscar and Patrick both competed in the shot put at their school's athletics carnival.

Oscar's best throw was 5.22 metres.

Patrick's best throw was 4.35 metres.

What was the difference, in centimetres, between their best throws?

  centimetres
Show Answers Only

`text(87 cm)`

Show Worked Solution
`text(Difference)` `= 5.22\ text(m) – 4.35\ text(m)`
  `= 522\ text(cm) – 435\ text(cm)`
  `= 87\ text(cm)`

Measurement, NAP-G2-37

Lucy times how long it takes her to get home on the bus each day.

Last year, Lucy's quickest bus ride home from school was 18 minutes and 12 seconds.

She recorded the time like this.

This year, Lucy's quickest bus ride home was 1 minute and 28 seconds faster.

What is the quickest time this year?

Show Answers Only

Show Worked Solution

`text(One strategy:)`

`text(18:12 less 1:28)` `=\ text(17:12 less 0:28)`
  `=\ text(17:00 less 0:16)`
  `=\ text(16:44)`

  

Number and Algebra, NAP-H2-40 SA

Grant was making a scale drawing of a pipeline on grid paper.

The full length of the pipeline is drawn below. Its construction requires 8 identical sections to be made and joined together (not shown on the diagram).
  

 
What is the length of each section of pipeline?

   metres
Show Answers Only

`25`

Show Worked Solution
`text(S)text(ection length)` `= text(total length)/text(number of sections)`
  `= (5 xx 40)/8`
  `=200/8`
  `= 25\ text(metres)`

Measurement, NAP-H2-37

Andrew drew a shape as pictured below.
 

 
What is the perimeter of this shape in centimetres?

`101` `112` `127` `148` `154`
 
 
 
 
 
Show Answers Only

`154\ text(cm)`

Show Worked Solution

`text(Starting at the bottom left corner and)`

`text(moving clockwise:)`

`text(Perimeter)` `= 26 + 30 + 26 + 8 + 21 + 16 + 21 + 6`
  `= 154\ text(cm)`

Number and Algebra, NAP-H2-35 SA

Byron spent $12.80 on pens for the new school year.

Each pen cost 40 cents.

How many pens did he buy?

 
Show Answers Only

`32\ text(pens)`

Show Worked Solution

`text(Strategy 1:)`

`=> 10\ text(pens cost $4.00)`

`=> 30\ text(pens cost $12.00)`

`:. 32\ text(pens cost $12.80)`

 

`text(Strategy 2:)`

`text(Using long division,)`

`$12.80 = 1280¢`
 

`\ \ \ 32`

`40` `\ 1280`

`120\ \ \ `

`qquad 80`

`qquad 80\ \ \ `

Number, NAP-D4-CA29 SA

Chloe sells beach umbrellas from her beach shack for $20 each.

Chloe pays $480 rent per week for her beach shack and each beach umbrella costs her $12.

How many beach umbrellas does Chloe need to sell per week to equal her weekly costs?
Show Answers Only

`60`

Show Worked Solution

`text(Selling price) = $20`

`text(C)text(ost per umbrella) = $12`

 `text(Profit per umbrella)` `= $20 – 12`
  `= $8`

 

`:.\ text(Umbrellas needed to pay for weekly costs)`

`=480 ÷ 8`

`= 60`

Probability, NAP-D2-38 SA

In any standard six-sided dice, the sum of the opposite faces is 7.

Milo rolls 3 dice and the total of the top faces is 5.

What is the sum of the three opposite faces?
Show Answers Only

`16`

Show Worked Solution

`text(Sum of 3 top faces + 3 opposite)`

`= 3 xx 7`

`= 21`

`:.\ text(Sum of 3 opposite faces)`

`= 21 – 5`

`= 16`

Number and Algebra, NAP-D2-37 SA

An AFL squad of 38 players were voting for a captain.

Each player had one vote and had to vote for Harrison, Patrick or Charles.

Harrison got 4 more votes than Patrick.

Harrison got 3 more votes than Charles.

How many votes did Harrison get?
Show Answers Only

`15`

Show Worked Solution

`text(Solution 1:)`

`text(By trial and error)`

`text(Harrison gets the most votes → must be more than 13)`

`text(Consider Harrison gets 15 votes)`

`text(→ Patrick gets 11 and Charles gets 12)`

`text(→ Total votes = 15 + 11 +12 = 38)`

 

`text{Solution 2 (using algebra):}`

`text(Let)\ \ \ H` `=\ text(votes for Harrison)`
`P` `=\ text(votes for Patrick)`
`C` `=\ text(votes for Charles)`

 

`text(Total votes)` `= H + P + C`
`38` `= H + (H – 4) + (H – 3)`
  `= 3H – 7`
`3H` `= 45`
`H` `= 15`

 
`:.\ text(Harrison got 15 votes.)`

Geometry, NAP-D2-36 SA

Nathan stacked 30 blocks into a rectangular prism as shown below.
 

 
The prism has 6 faces.

Nathan removes some blocks and the remaining shape has 14 faces.

What was the smallest number of blocks that he could have removed?
Show Answers Only

`2`

Show Worked Solution

`text(If Nathan removes the middle block in the second)`

`text(column, the number of faces on the new shape)`

`text(increases by 4.)`

`:.\ text(If he removes the middle block of the second and)`

`text(fourth column, the shape has 14 faces.)`

`:.\ text(2 blocks is the smallest number.)`

Measurement, NAP-D2-35 SA

Justin connects three of his restaurant tables together to make one long table.

The view from above the tables is shown below.
 

 
Each table is 70 cm long and 50 cm wide.

What is the perimeter of the long table?

  cm
Show Answers Only

`520\ text(cm)`

Show Worked Solution

`text(Perimeter)` `= 2 xx (210 + 50)`
  `= 2 xx 260`
  `= 520\ text(cm)`

Number and Algebra, NAP-I2-40 SA

There are 48 students in Year 7 at a school.

Every student is either right-handed or left-handed.

There are 7 times more right-handers than left-handers.

How many left handers are there in Year 7?
Show Answers Only

`6\ text(left handers)` 

Show Worked Solution

`text(S) text(ince there are 7 times more right-handers,)`

`=>\ text(1 out of 8 are left-handers.)`
 

`:.\ text(Number of left-handers)`

`= 1/8 xx 48`

`= 6`

Number and Algebra, NAP-I2-36 SA

A group of 8 friends are planning a trip to Reptile World.

Lunch will cost $9 per person.

Entry will cost $16 per person.

Hiring a bus for transport will cost $250 for the whole group.

What is the expected total cost of the trip for the whole group?

$   
Show Answers Only

`$450` 

Show Worked Solution
`text(Lunch cost)` `= 8 xx 9`
  `= $72`
`text(Entry cost)` `= 8 xx 16`
  `= $128`
`text(Bus hire)` ` = $250`

 

`:.\ text(Total cost)` `= 72 +128 + 250`
  `= $450`

Number, NAP-D4-CA26

A company sells its iced tea in four different containers.
 

Which volume container has the cheapest price per mL?

`text(150 mL)` `text(750 mL)` `text(375 mL)` `text(200 mL)`
 
 
 
 
Show Answers Only

`text(375 mL)`

Show Worked Solution

`text(Consider the price per mL of each option)`

`text(150 mL :)\ \ 1.50/150 = 1\ text(cent/mL)`

`text(750 mL :)\ \ 6.10/750 = 0.81\ text(cent/mL)`

`text(375 mL :)\ \ 3.00/375 = 0.8\ text(cent/mL)`

`text(200 mL :)\ \ 1.80/200 = 0.9\ text(cent/mL)`

 

`:.\ text(375 mL is the cheapest price per mL)`

Measurement, NAP-D4-CA25

Guerra slings a fire torch in a circle at the end of a 3 metre rope.
 

 
About how far has the fire torch travelled after completing 15 circles?

`text(30 metres)` `text(45 metres)` `text(140 metres)` `text(280 metres)`
 
 
 
 
Show Answers Only

`text(280 metres)`

Show Worked Solution
`C` `= 2 pi r`
  `= 2 xx pi xx 3` 
  `= 18.85…`

 

`:.\ text(Distance travelled in 15 circles)`

`=15 xx 18.85…`

`= 282.74…`

`~~280\ text(metres)`

Algebra, NAP-D4-CA28 SA

The table shows the height of the grid on new tyres after being driven different distances.
 

 
The tyres will be replaced when the grid is 11 mm high.

How many kilometres do the tyres need to be driven to be worn down to a 11 mm high grid?

   kilometres
Show Answers Only

`6000\ text(km)`

Show Worked Solution

`text(Grid is initially 20 mm.)`

`text(After 500 km) -> 19.25\ text(mm)`

`text(After 1000 km) -> 18.5\ text(mm)`

`=>\ text(grid decreases 0.75 mm each 500 km.)`

 

`text(Let)\ \ n = text(multiple of 500 km tyres are driven)`

`20 – (n xx 0.75)` `= 11`
`n xx 0.75` `= 9`
`:. n` `= 9/0.75`
  `= 12`

 

`:.\ text(Distance tyres will be driven)`

`= 12 xx 500`

`= 6000\ text(km)`

Number, NAP-B3-NC27 SA

The temperature at the summit of a large mountain is − 6°C.

The temperature at the base of the mountain is 32°C warmer than at the summit.

What is the temperature at the base of the mountain?

  °C
Show Answers Only

`26^@text(C)`

Show Worked Solution

`text(Temperature at the base of the mountain)`

`= – 6 + 32`

`=26^@ text(C)`

Statistics, NAP-B3-NC24

The train travel times between major Australian cities are listed in the table below:
   

 
The train travel time from Melbourne to Adelaide is about 4 times the travel time from

 
 `text(Sydney to Melbourne)`
 
 `text(Sydney to Canberra)`
 
 `text(Canberra to Adelaide)`
 
 `text(Canberra to Melbourne)`
Show Answers Only

`text(Sydney to Canberra)`

Show Worked Solution

`text(Melbourne to Adelaide is 733 minutes.)`

`=>\ text(Travel time needed)` `~~1/4 xx 733`
  `~~183.25\ text(minutes)`

 

`:.\ text{Sydney to Canberra (at 176 mins).}`

Number, NAP-B3-NC23

  and    stand for numbers.

  and    are related by a rule.
 

 
What is the rule?

 
  `= 6 xx`  `- 2` 
 
  `= 10 xx `  `- 10`
 
  `= 2 xx`  `xx`   `+ 2`
 
  `= 4 xx`  `+ 2`
Show Answers Only

 `= 2 xx`  `xx`   `+ 2`

Show Worked Solution

`text(Consider option 3:)`

`10` `=2 xx2 xx2 +2 =8+2=10`
`20` `=2 xx 3xx 3 +2=18+2=20`
`34` `=2 xx 4 xx 4 +2=32+2=34`
`52` `=2 xx 5 xx 5 +2 = 50 + 2=52`

 

`:.\ text(The rule is:)`

 `= 2 xx`  `xx`   `+ 2`

Measurement, NAP-B3-CA29

This plan shows 3 fenced paddocks.

Their areas are measured in hectares.
 

 
1 hectare = 2.47 acres.

The total area of the 3 paddocks in acres is closest to

`2.73` `6.75` `16.67` `16.77`
 
 
 
 
Show Answers Only

`16.67\ text(acres)`

Show Worked Solution
`3/4` `= 0.75`
`2 1/4` `= 2.25`
`3 3/4` `= 3.75`

 

`text(Total acres)` `=(0.75 + 2.25 + 3.75) xx 2.47`
  `=6.75 xx 2.47`
  `=16.67\ text(acres)`

Geometry, NAP-B3-CA28

A triangle is divided into 2 parts by a straight line.

The angles are then labelled.

Which statement is true about the sum of angles?

 
 `b + c + d = 180^@`
 
 `c + d + e = 360^@`
 
 `a + b + f + g = 360^@`
 
 `d + e + f + g = 180^@`
Show Answers Only

`a + b + f + g = 360^@`

Show Worked Solution

`text(Consider each option:)`

`text(Option 1:)\ \ b + c + d != 180`

  `=> b+c = 180^@`

`text(Option 2:)\ \ c + d + e != 360^@`

  `=> c + d + e = 180^@\ \ text{(angle sum of triangle)}`

`text(Option 3:)\ \ a + b + f + g = 360^@`

  `=>\ text(Correct since the angle sum of a quadrilateral = 360°)`

`text(Option 4:)\ \ d + e + f + g != 180`

  `=> e + f  = 180^@`

Algebra, NAP-B3-CA27 SA

A vet uses a rule to calculate the volume of medicine needed for a calf (baby cow).

The amount of medicine (mL) a calf needs is:

Volume for calf = (Minor dose × Age of calf) ÷ (Age of calf + 14)

Use this rule to complete the table:
 
Show Answers Only

`3\ text(mL)`

Show Worked Solution
`text{Volume for calf (mL)}` `= (10 xx 6) ÷ (6 + 14)`
  `= 60/20`
  `= 3\ text(mL)`

Algebra, NAP-B3-CA24

This octagon pattern is made with sticks.
 

  
How many sticks are needed to make 10 of these octagons?

`71` `72` `75` `80`
 
 
 
 
Show Answers Only

`71`

Show Worked Solution

`text(1 octagon has 8 sticks.)`

`text(2 octagons have 15 sticks.)`

`text(3 octagons have 22 sticks.)`

`=>\ text(Each extra octagon needs 7 more sticks.)`

 

`:.\ text(10 octagons)` `= 8 + (9 xx 7)`
  `=8 + 63`
  `=71\ text(sticks)`

Number, NAP-B3-CA23

The diameter of an American 10¢ piece is about 1 cm.
 

 
About how much would a 2 km line of 10¢ pieces be worth?

`$2000` `$5000` `$10\ 000` `$20\ 000`
 
 
 
 
Show Answers Only

`$20\ 000`

Show Worked Solution
`2\ text(km)` `=2000\ text(m)`
  `=200\ 000\ text(cm)`

 

`:.\ text(The value of a 2 km line of 10¢ pieces)`

`= 200\ 000 xx 10¢`

`= $20\ 000` 

Measurement, NAP-B3-CA26

Florence used identical cubes to build a rectangular prism.

There were 16 cubes in its base.

She used 80 cubes altogether.

Which of these could be the dimensions of Florence's prism?

`10 xx 1 xx 8` `2 xx 8 xx 5` `4 xx 4 xx 10` `4 xx 8 xx 5`
 
 
 
 
Show Answers Only

`2 xx 8 xx 5`

Show Worked Solution

`2 xx 8 xx 5`

`=>\ text(The above dimensions have a base that is 16)`

`text{cubes (2 × 8) and require a total of 80 cubes}`

`text{(2 × 8 × 5 = 80).}`

Statistics, NAP-B3-CA25

The mean (average) of four numbers is 26.

One more number is added and the mean number becomes 27.

The number added is?

`26` `27` `31` `53`
 
 
 
 
Show Answers Only

`31`

Show Worked Solution

`text(Total of the first 4 numbers,)`

`26 xx 4 = 104`

`text(Total including the 5th number added,)`

`27 xx 5 = 135`

`:.\ text(The number added)` `=135-104`
  `=31`

Number, NAP-D3-CA31 SA

Saul's workshop requires lighting for 30 hours per week, every week of the year.

He uses globes that need replacing after 10 000 hours of use.

After how long, to the nearest year, would Saul need to replace any individual globe?

   years
Show Answers Only

`text{6 years (nearest year)}`

Show Worked Solution

`text(Usage per year of one globe)`

`= 30 xx 52`

`= 1560`
 

`:.\ text(Time until replacement of globe)`

`= (10\ 000)/1560`

`= 6.41…`

`= 6\ text{years (nearest year)}`

Geometry, NAP-D3-CA28 SA

On the map below, York is 60 km from Karkoo.

The town of Cootra is not shown on the map.

Cootra is due east of Barwell and due North of Ungarra.

What is the distance from Ungarra to Cootra?
 

   km
Show Answers Only

`90`

Show Worked Solution

`text(4 grids between Karkoo and York)`

`=> 1\ text(grid interval)` `= 60/4`
  `= 15\ text(km)`

 

`:.\ text(Ungarra to Cootra)` `= 6\ text(grid intervals)`
  `= 6 xx 15`
  `= 90\ text(km)`

Measurement, NAP-D3-CA27 SA

Anthony is tiling one wall of a bathroom.

The wall has 2 identical windows as shown in the diagram below.
 

 
What total area does Anthony need to tile?

   square metres
Show Answers Only

`12.9\ text(m²)`

Show Worked Solution
`text(Area)` `= (5.3 xx 3) – 2 xx (1 xx 1.5)`
  `= 15.9 – 3`
  `= 12.9\ text(m²)`

Statistics, NAP-D3-CA26 SA

A school offers two sports during a summer term.

Students can either play hockey or water polo, but not both.
 

   

 
One-quarter of all the students play water polo.

How many girls play hockey?
Show Answers Only

`85`

Show Worked Solution

`text(Water polo players = 40)`

`=>\ text(Total students)` `= 4 xx 40`
  `= 160`

 

`:.\ text(Girls playing hockey)`

`= 160 – (35 + 40)`

`= 85`

Number, NAP-D3-CA23 SA

A scholarship fund of $1 000 000 is allocated between three scholarships as shown in the table below.
 

 
150 students were given a Hardship Scholarship.

How much did each Hardship Scholarship winner get?

$   
Show Answers Only

`$2000`

Show Worked Solution

`text(Hardship Scholarship Funds)`

`= 30text(%) xx 1\ 000\ 000`

`= $300\ 000`
 

`:.\ text(Amount each winner received)`

`= (300\ 000)/150`

`= $2000`

Measurement, NAP-D4-NC28 SA

An irregular shaped lawn is pictured below, with all measurements in metres.

 

What is the area of the lawn in square metres?

  square metres
Show Answers Only

`65`

Show Worked Solution

`text(Split the lawn into 3 areas)`

`text(Area 1) = 9 xx 3 = 27\ text(m²)`

`text(Area 2) = 5 xx 2 = 10\ text(m²)`

`text(Area 3:)`

`text(Height) = 9-2 = 7\ text(m)`

`text(Width)= 12-(5 + 3)= 4\ text(m)`

`=> text(Area 3) = 7 xx 4 = 28\ text(m²)`

 

`:.\ text(Area of lawn)` `= 27 + 10 + 28`
  `= 65\ text(m²)`

Algebra, NAP-D4-NC27 SA

The season goal-scoring statistics of a netball team showed the following results.

Gemma scored 12 more goals than Kate.

Kate scored 6 more goals than Hannah.

In total, Gemma, Kate and Hannah scored 51 goals in the season.

How many goals did Hannah score?
Show Answers Only

`9`

Show Worked Solution

`G = K + 12\ …\ (1)`

`K = H + 6,\ text(or)`

`H = K – 6\ …\ (2)`

`G + K + H = 51\ …\ (3)`

 

`text{Substitute (1) and (2) into (3)}`

`K + 12 + K + K – 6` `= 51`
`3K + 6` `= 51`
`3K` `= 45`
`K` `= 15`
`:. H` `= 15 – 6`
  `= 9`

Algebra, NAP-D4-NC25 SA

A number of retired people were asked this question:

"How many grandchildren do you have?"
 

  • The lowest answer given was 4.
  • The highest answer given was 16.
  • The total of all the answers given was 40.

What is the largest number of retired people who could have been asked?

  retirees
Show Answers Only

`7`

Show Worked Solution

`text(Largest number will occur when the the most)`

`text(retired people have 4 grandchildren.)`

 

`text(Highest “possible” number of retirees with 4 children)`

`=(40-16)/4`

`=6`

 

`:.\ text(The largest number asked = 7.)`

Number, NAP-D4-NC24

In a class there are 36 students.

The ratio of right handed students to left handed students is  7 : 2.

How many students in the class are left handed?

`2` `4` `8` `9`
 
 
 
 
Show Answers Only

`8`

Show Worked Solution

`text(7:2 means that out of 9 students in the class,)`

`text(2 are left handed.)`

`=>\ text(If 18 in class, 4 are left handed)`

`=>\ text(If 27 in class, 6 are left handed)`

`=>\ text(If 36 in class, 8 are left handed)`

Number, NAP-D4-NC23

Lily buys 23 Gold Class tickets to the movies.

The tickets cost $19 each.

Which of the following equations could Lily use to calculate the total cost?

 
 `(19 xx 20) + 3`
 
 `(19 xx 20) xx 3`
 
 `(10 xx 20) + (9 xx 3)`
 
 `(19 xx 20) + (19 xx 3)`
Show Answers Only

`(19 xx 20) + (19 xx 3)`

Show Worked Solution

`text(Rewriting the equation,)`

`19 xx 23` `=19 xx (20 + 3)`
  `=(19 xx 20) + (19 xx 3)`

Measurement, NAP-C4-NC24

The rhombus below has a side length of 8 cm.
 

 

  
Which equation must be true?

`xy = 80` `10x = 8y` `2xy = 40` `5x = 10y`
 
 
 
 
Show Answers Only

`xy=80`

Show Worked Solution

`text(The area of the rhombus can be calculated)`

`text(in two ways:)`

`text(Area)` `= 8 xx 5 =40, or`
`text(Area)`

`=1/2 xx text(product of diagonals)`
  `= 1/2 xx xy`

 

`:. 1/2 xy` `=40`
`xy` `=80`