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Algebra, NAP-A4-CA27

The plan of a square area of land is drawn below.

A mining licence is granted over part of the land.

All measurements are given in kilometres.
 

The area of land the mining licence covers is

`x^2-20` `x^2 + 20` `2x^2-9` `2x^2-20`
 
 
 
 
Show Answers Only

`x^2-20`

Show Worked Solution

`text{Area of original land}\ = x xx x = x^2\ text{km}^2`

`text{Size of non-mining area}\ = 20\ text{km}^2`

`:.\ text(Area of mining)\ = x^2-20\ text{km}^2`

Number, NAP-B4-NC31

Which number has the largest value?

`1/3` `sqrt (0.16)` `0.38` `(0.6)^2`
 
 
 
 
Show Answers Only

`sqrt (0.16)`

Show Worked Solution

`text(Express each as a decimal:)`

`1/3` `= 0.333…`
`sqrt(0.16)` `= 0.4`
`0.38` `= 0.38`
`(0.6)^2` `= 0.36`

 

`:. sqrt(0.16)\ text(is the largest value.)`

Algebra, NAP-B4-NC30 SA

`2 (4x - 2) + 1 +`
?
 `= 9x - 3`

What term makes this equation true for all values of `x`?
Show Answers Only
?
 `= x`
Show Worked Solution
`2(4x – 2) + 1 +`
?
 `= 9x – 3`
`8x – 4 + 1 +`
?
 `= 9x – 3`
`8x – 3 +`
?
 `= 9x – 3`
 
?
 `= x`

Probability, NAP-B4-NC28 SA

A coin is tossed 3 times. There are 8 possible outcomes.

What is the probability of getting 2 heads and 1 tail in any order?
Show Answers Only

`3/8`

Show Worked Solution

`text(Strategy 1)`

`text{The table (array) below lists the possible outcomes:}`
 

  1st toss H H H H T T T T
  2nd toss H H T T H H T T
  3rd toss H T H T H T H T
       ✓  ✓    ✓      

`text(From table,)`

`Ptext{(2H, 1T)} = 3/8`
 

`text(Strategy 2)`

`text(This problem can also be efficiently solved using a)`

`text(probability tree.)`

Number, NAP-B4-CA31 SA

Write 1001 as the product of its prime factors.

 
Show Answers Only

`7 xx 11 xx 13 = 1001`

Show Worked Solution

`text(By trial and error, divide 1001 by prime numbers)`

`text(until the result is a whole number.)`

`1001 ÷ 7` `= 143`
`143 ÷ 11` `= 13`

 

`:. 7 xx 11 xx 13 = 1001`

Number, NAP-B4-CA29 SA

In a class of 28 students, the ratio of boys to girls is  3 : 4.

Two boys and one girl leave the class. No student joins the class.

What is the new ratio of boys to girls?

 
Show Answers Only

`2 : 3`

Show Worked Solution
`text(Original ratio)\ \ \ 3` `: 4`
`12\ text(boys)` `: 16\ text(girls)`

 

`text(After students leave, new ratio is:)`

`10` `: 15`
`2` `: 3`

Statistics, NAP-B4-CA28 SA

A kindergarten class has 15 students. The average (mean) weight of a child in the class is 24 kilograms.

5 new children join the class and the average class weight increases to 26 kilograms.

What was the average weight of the 5 new children?

    kilograms
Show Answers Only

`32`

Show Worked Solution

`text(Total weight of original class)`

`= 15 xx 24`

`= 360\ text(kilograms)`

 

`text(Extra weight from 5 new children)`

`= (26 xx 20) – 360`

`= 520 – 360`

`= 160\ text(kg)`

 

`:.\ text(Average weight of new children)`

`= 160/5`

`= 32\ text(kilograms)`

Number, NAP-J3-NC08 SA

Bert and Ernie are standing in a line, waiting to go into their classroom.

There are:

  • 9 people between Bert and Ernie.
  • 14 people in front of Bert including Ernie.
  • 20 people behind Ernie including Bert.

In total, how many people are in the line?
Show Answers Only

`25`

Show Worked Solution

`text(The line-up will be:)`

`text(10 people → Bert → 9 people → Ernie → 4 people)`

`:.\ text(Total people in line)`

`= 10 + 1 + 9 + 1 + 4`

`= 25`

Probability, NAP-J3-CA40 SA

A random sample of people were asked what their favourite winter sport was.

The table below recorded the results.
 

   

Using the data from the survey, predict how many people would choose rugby league if 2000 people were surveyed.
Show Answers Only

`1250`

Show Worked Solution

`text(Total people surveyed)`

`= 49 + 19 + 135 + 13`

`= 216`

`:.\ text(Predicted number to choose rugby league)`

`= 135/216 xx 2000`

`= 1250`

Measurement, NAP-J3-CA39 SA

Two identical solid cubes are placed at the bottom of a fish tank.
 

 

 
The fish tank is then completely filled, as shown below.

What is the volume of the water that surrounds the cubes?

Give your answer in cubic centimetres.

  cm3
Show Answers Only

`185\ 250\ text(cm)^3`

Show Worked Solution
`text(Volume of tank)` `= 80 xx 60 xx 40`
  `= 192\ 000\ text(cm)^3`
`text(Volume of cubes)` `= 2 xx 15 xx 15 xx 15`
  `= 6750\ text(cm)^3`

 

`:.\ text(Volume of water)` `= 192\ 000 – 6750`
  `= 185\ 250\ text(cm)^3`

Statistics, NAP-J3-CA37

The Stars and the Thunder are playing cricket in a 20 over competition.

The stem-and-leaf plots show the number of runs each side has scored in their last 15 games.
 

   

Select all the true statements about the data.

 
 The Stars had the lowest run score.
 
 The Stars had the highest run score.
 
 The Stars scored over 135 runs more times than the Thunder.
 
 The median score for The Stars is higher than the median score for The Thunder.
 
 The range of scores for The Stars is smaller than the range of scores for The Thunder.
Show Answers Only

`text{The Stars had the highest run score.}`

`text{The range of scores for The Stars is smaller than the}`

`text{range of scores for The Thunder.}`

Show Worked Solution

`text(Correct statements are:)`

`text{The Stars had the highest run score (149 vs 148).}`

`text{The range of scores for The Stars is smaller than the}`

`text{range of scores for The Thunder (39 vs 40).}`

Measurement, NAP-J3-CA36

A poster has an area of 5250 square centimetres.

What is the area of the poster in square millimetres?

 
 5.25 square millimetres
 
 52.50 square millimetres
 
 52 500 square millimetres
 
 525 000 square millimetres
Show Answers Only

`text(525 000 square millimetres)`

Show Worked Solution

`text(Solution 1:)`

`text(One example of the dimensions of a 5250 cm²)`

`text(rectangle can be:  525 cm × 10 cm)`

`text(Converting to millimetres:)`

`5250\ text(mm) xx 100\ text(mm) = 525\ 000\ text(square millimetres)`

 

`text(Solution 2:)`

`text(Scale factor of converting cm to mm = 10)`

`text(Scale factor of converting cm² to mm²)\ = 10 xx 10 = 100`

`:. 5250\ text(cm²) xx 100 = 525\ 000\ text(mm²)`

Measurement, NAP-J3-CA32

A block is in the shape of a prism.

Its surface is covered in triangles and squares.
 

 
How many triangles and how many squares cover the entire surface of the block?

 
   triangles
 
   squares
Show Answers Only

`text(Triangles = 12)`

`text(Squares = 18)`

Show Worked Solution
`text(Triangles)` `=\ text(6 at either end)`
  `= 12`
`text(Squares)` `=\ text(3 in each row per side)`
  `=3 xx 6`
  `= 18`

Number, NAP-J3-CA30 SA

Don buys a cricket ball, originally marked $30, that is discounted by 25%.

He also has a loyalty card that gives him another 20% off the sale price.

What is the final cost of the ball?

$  
Show Answers Only

`$18`

Show Worked Solution

`text(Solution 1)`

`text(Sale price)` `= 30 – (25text(%) xx 30)`
  `=30 – 7.50`
  `= $22.50`

 

`:.\ text(Final cost)` `= 22.50 – (20text(%) xx 22.50)`
  `= $18`

 

`text{Solution 2 (advanced)}`

`text(Final cost)` `= 30 xx 0.75 xx 0.8 `
  `= $18`

Number, NAP-J4-NC07 SA

A wildlife sanctuary has 240 Tasmanian devils.

Of the 240 devils, `3/8` of them weigh more than 6 kilograms.

Of the devils that weigh more than 6 kilograms, `1/3` weigh more than 7 kilograms.

How many devils in the sanctuary weigh more than 7 kilograms.
Show Answers Only

`30`

Show Worked Solution

`text(Number of devils) > 6\ text(kilograms)`

`= 3/8 xx 240`

`= 90`

 

`text(Number of devils) > 7\ text(kilograms)`

`= 1/3 xx 90`

`= 30`

Algebra, NAP-J4-CA40 SA

Michelle creates a snack food which is a mixture of 4 different types of nuts.

She makes 300 grams of the mixture and weighs each ingredient as follows:

  • 40% of the mixture is almonds.
  • The rest of the mixture is made up of walnuts, pecans and macadamia nuts.
  • The mass of walnuts is the same as the mass of pecans.
  • The mass of walnuts is twice the mass of macadamias.

How many grams of pecans are in the 300 grams of nut mixture.

 grams
Show Answers Only

`72\ text(grams)`

Show Worked Solution
`text(Weight of almonds)` `= 40text(%) xx 300`
  `= 120\ text(grams)`

 

`text(Weight of remaining nut mixture)`

`= 300 – 120`

`= 180\ text(g)`

 

`text(Let)\ \ x = text(weight of pecans)`

`x + x + 1/2x` `= 180`
`:. x` `= 180/2.5`
  `= 72\ text(grams)`

Measurement, NAP-J4-CA39 SA

A rectangular prism is made by using 6 identical triangular prisms.
 

  
What is the volume of one rectangular prism, in cubic centimetres?

 cubic centimetres
Show Answers Only

`37 200 text(cm³)`

Show Worked Solution

`text(Volume of rectangular prism)`

`= 62 xx 50 xx 72`

`= 223\ 200\ text(cm³)`

 

`:.\ text(Volume of 1 triangular prism)`

`= 223\ 200 ÷ 6`

`= 37\ 200\ text(cm³)`

Statistics, NAP-J4-CA38

The Stars and the Thunder are playing cricket in a 20 over competition.

The stem-and-leaf plots show the number of runs each side has scored in their last 15 games.
 

   
 

Select all the true statements about the data.

 
 The Stars had the lowest run score.
 
 The Stars had the highest run score.
 
 The Stars scored over 135 runs more times than the Thunder.
 
 The median score for The Stars is higher than the median score for The Thunder.
 
 The range of scores for The Stars is smaller than the range of scores for The Thunder.
Show Answers Only

`text{The Stars had the highest run score.}`

`text{The range of scores for The Stars is smaller than the}`

`text{range of scores for The Thunder.}`

Show Worked Solution

`text(Correct statements are:)`

`text{The Stars had the highest run score (149 vs 148).}`

`text{The range of scores for The Stars is smaller than the}`

`text{range of scores for The Thunder (39 vs 40).}`

Algebra, NAP-J4-CA36 SA

In this inequality `n` is a whole number.

`8/n < 5/8`

What is the smallest possible value for `n` to make this inequality true?
Show Answers Only

`13`

Show Worked Solution
`8/n` `< 5/8`
`5n` `> 64`
`n` `> 64/5`
  `> 12.8`

 

`:. text(Smallest)\ \ n = 13.`

Number, NAP-J4-CA35 SA

The original price of a refrigerator is $3200.

Saroo buys the refrigerator at a sale for 20% off the original price.

He has a discount voucher that gives him a further $64 off the sale price.

What percentage of the original price does Saroo pay for the refrigerator?

 %
Show Answers Only

`text(78%)`

Show Worked Solution
`text(Sale price)` `= 80text(%) xx $3200`
  `= $2560`

 

`text(Purchase price)` `= 2560 – 64`
  `= $2496`

 

`text(Percentage of original price)`

`= 2496/3200 xx 100`

`= 78text(%)`

Probability, NAP-J4-CA34 SA

Phil throws darts at a board split into 4 sections and records which section they hit.
 

 
Based on Phil's data, what is the probability that a dart he throws will land in section 2 or 3?

Express your answer as a percentage rounded to the nearest tenth.

 %
Show Answers Only

`text(89.4%)`

Show Worked Solution
`text(Number of throws)` `= 13 + 78 + 48 + 2`
  `= 141`

 

`:.\ text(Probability)` `= (78 + 48)/141`
  `= 126/141`
  `= 0.8936`
  `= 89.4text(%)`

Measurement, NAP-J4-CA28

A poster has an area of 5250 square centimetres.

What is the area of the poster in square millimetres?

 
 5.25 square millimetres
 
 52.50 square millimetres
 
 52 500 square millimetres
 
 525 000 square millimetres
Show Answers Only

`text(525 000 square millimetres)`

Show Worked Solution

`text(Solution 1:)`

`text(One example of the dimensions of a 5250 cm²)`

`text(rectangle is:  525 cm × 10 cm)`

`text(Converting to millimetres:)`

`5250\ text(mm) xx 100\ text(mm) = 525\ 000\ text(square millimetres)`

 

`text(Solution 2:)`

`text(Scale factor of converting cm to mm = 10)`

`text(Scale factor of converting cm² to mm²)\ = 10 xx 10 = 100`

`:. 5250\ text(cm²) xx 100 = 525\ 000\ text(mm²)`

Algebra, NAP-C4-CA32 SA

The surface area of a brick is given by the rule:

total surface area = 2 × [(width × height) + (width × length) + (height × length)]

The brick shown has a total surface area of 982 square centimetres.
 

 

What is the width of the brick?

   centimetres
Show Answers Only

`10.5\ text(cm)`

Show Worked Solution

`text(Let)\ \ w = text(width of the brick)`

`text(Surface Area)` `= 2 xx [8w + 22w + (8 xx 22)]`
`982` `= 2(30w + 176)`
  `= 60w + 352`
`60w` `= 630`
`:. w` `= 10.5\ text(cm)`

Geometry, NAP-C4-CA31 SA

Euclid created the shape below using similar triangles.
 


 

What is the value of `x`?  
Show Answers Only

`87^@`

Show Worked Solution

`text(S) text(ince there are 180° in a triangle,)`

`text(Centre angle)` `=180-(90+51)`
  `=39^@`

`text(The angles at the centre in each triangle will be)`

`text(the same because all traingles are similar.)`

`:. x^@` `= 360 – (7 xx 39)`
  `= 360 – 273`
  `= 87^@`

Measurement, NAP-C4-CA30 SA

Bozo the clown rides a unicycle.

If Bozo's tyre does one full turn, he moves forward by 135 cm.

What is the diameter of his unicycle tyre to the nearest centimetre?

   cm
Show Answers Only

`43\ text(cm)`

Show Worked Solution

`text(The circumference of the tyre = 135 cm)`

`text(135)` `= pi xx text(diameter)`
 `:.\ text(diameter)` `= 135/pi`
  `= 42.97…`
  `= 43\ text{cm  (nearest cm)}`

Statistics, NAP-C4-CA29

The points scored by a basketball team in their first 11 games of the season is recorded.

  `62, \ 71, \ 72, \ 76, \ 63, \ 66, \ 60, \ 77, \ 72, \ 72, \ 71`

In the 12th game, they scored 58.

Which of these values would increase?

`text(mean)` `text(mode)` `text(median)` `text(range)`
 
 
 
 
Show Answers Only

`text(range)`

Show Worked Solution

`text(Consider each option:)`

`text(Mean – decreases)`

`text(Mode – unchanged as 72)`

`text(Median – unchanged at 71)`

`text{Range – increases (highest – lowest)}`

Probability, NAP-C4-CA26

Wally asked all Year 9 students at his school what their favourite sport was.

He recorded the results in a table.
 

 
Which sport did 4 out of every 10 Year 9 students choose as their favourite?

`text(Water polo)` `text(Tennis)` `text(Cricket)` `text(Surfing)`
 
 
 
 
Show Answers Only

`text(Cricket)`

Show Worked Solution
`text(Total students)` `= 15 + 45 + 60 + 30`
  `= 150`

 
`text(Number of students needed)`

`= 4/10 xx 150`

`= 60`
 

`:. 4\ text(out of 10 chose cricket.)`

Measurement, NAP-C4-CA27 SA

Tom decided to cover a rectangular floor with tiles.

The tiles are twice as wide as they are long.

The floor is  `5 1/2`  tiles wide and  `11 1/2`  tiles long.
 

 
Using this pattern, what is the total number of tiles Tom will use to cover the floor?
Show Answers Only

`226.5\ text(tiles)` 

Show Worked Solution

`text(Strategy 1:)`

`text(Tiles in bottom row =)\ 11 1/2`

`text(Tiles in top rows)` `=5 xx 23`
  `=115`

 

`:.\ text(Total tiles) = 115 + 11.5 = 126.5`

 

`text(Strategy 2:)` 

`text(Let)\ \ x= text(length of 1 tile)`

`=>\ text(Area of 1 tile)\ = 1 xx 1/2 = 1/2\ text(u²)`

`text{Area of the floor}` `= 5 1/2 xx 11 1/2`
  `=63.25\ text(u²)`

 

`:.\ text(Total tiles )` `=63.25/0.5` 
  `=126.5\ text(tiles)`

Number and Algebra, NAP-B2-40 SA

Peter sets up a fruit stall outside his house and sells oranges, pears and plums.

The table below shows the price of each fruit.
 

 
Peter sold 12 pieces of fruit and was paid $28.

Peter received $8 for all the pears he sold.

How many plums did Peter sell?
Show Answers Only

`6\ text(plums)`

Show Worked Solution
`text(Pears sold)` `=$8 -: 2`
  `=4`

 
`=>\ text(The other 8 pieces were sold for $20)`
 

`text(Testing some guesses for the other 8 pieces:)`

`text(If 5 plums and 3 oranges,)`

`text(C)text(ost) = (5 xx3) + (3 xx 1) = $18\ \ text{(too low)}`

`text(If 6 plums and 2 oranges,)`

`text(C)text(ost) = (6 xx3) + (2 xx 1) = $20\ \ text{(correct)}`

 

`=>\ text(Peter sold a total of 6 plums.)`

Statistics, NAP-B2-39 SA

32 students are shown 5 colours and they choose their favourite.

The fractions in the graph below show how the students voted.

How many more students voted for green than blue?
Show Answers Only

`4`

Show Worked Solution
`text(Votes for green)` `=1/4 xx 32`
  `=8`
   
`text(Votes for blue)` `=1/8 xx 32`
  `=4`

 

`:.\ text(4 more students voted for green than blue.)`

Number and Algebra, NAP-B2-38 SA

Meredith made 133 cookies for two parties.

She made 13 more cookies for the party on Thursday than she did for the party on Friday.

How many cookies did she take to the party on Thursday?
Show Answers Only

`73`

Show Worked Solution

`text(Strategy one:)`

`text(Test some educated guesses,)`

`text(If 60 made for Thursday,)`

`=>\ text{Total = 60 + 47 = 107  (too low)}`

`text(If 70 made for Thursday,)`

`=>\ text{Total = 70 + 57 = 127  (close to 133)}`

`text(If 73 made for Thursday,)`

`=>\ text{Total = 73 + 60 = 133  (correct)}`

 

`text{Strategy two (using algebra):}`

`text(Let)\ n =\ text(cookies made on Thursday)`

`=> n+n-13` `=133`
`2n` `=146`
`n` `=73`

Number and Algebra, NAP-C2-40

Roger mixes different fruit juices to make a ‘Special Juice Blend’ that he sells in his cafe.
 

 
He only uses full bottles and uses at least one bottle of each juice.

How many full bottles of each juice does he use to make exactly 2.5 L of the ‘Special Juice Blend’?
 

Show Answers Only

Show Worked Solution

`text(There must be at least 1 bottle of each.)`

`=>\ text(Volume)` `= 1000 + 600 + 300 + 200`
  `= 2100\ text(mL)`

 

`text(Volume needed to reach 2.5L)`

`= 2500 – 2100`

`= 400\ text(mL)`

 

`=>  400\ text(mL can only be added by using)`

 `text{2 (full) bottles of apple juice.}`

Number and Algebra, NAP-C2-38 SA

In an orchard there are 4 lemon trees for every 9 orange trees.

There are 81 orange trees.

How many lemon trees are in the orchard?
Show Answers Only

`text(36 lemon trees)`

Show Worked Solution

`text(Check some numbers of orange trees:)`

`text(9 orange trees)\ ->\ text(4 lemon)`

`text(18 orange trees) -> 2 xx 4 = 8\ text(lemon)`

`text(27 orange trees) -> 3 xx 4 = 12\ text(lemon)`

`vdots`

`text(81 orange trees) -> 9 xx 4 = 36\ text(lemon)`

`:.\ text(There are 36 lemon trees.)`

Measurement, NAP-F2-39 SA

Srinath needs 1.4 kg of sugar for a cookie recipe.

He places some sugar on the scale as shown.
 

 
How many more grams of sugar does Srinath need?

  grams
Show Answers Only

`800\ text(grams)`

Show Worked Solution

`text(5 intervals on the scale = 1 kg)`

`=>\ text(1 interval = 200 grams)`

`=>\ text(There are 600 grams on the scale)`

`:.\ text(Sugar needed)` `=1.4\ text(kg) – 600\ text(g)`
  `=1400\ text(g) – 600\ text(g)`
  `=800\ text(grams)`

Statistics, NAP-F2-NC40 SA

Tom collected data on the number of big game animals in an African wildlife park.

This graph shows how many big game animals lived in the park.

 

 

There were 16 more elephants than rhinos in the wildlife park.

How many big game animals were in the park in total?
Show Answers Only

`80`

Show Worked Solution

`text(Let)\ \ n = text(total big games animal in the park)`

`text(Elephants − Rhinos)` `= 16`
`7/20 n – 3/20 n` `= 16`
`4/20 n` `= 16`
`n` `= (16 xx 20)/4`
  `= 80`

Geometry, NAP-D4-CA32

Triangle `PRS`, below, is an isosceles triangle, and `QR = ST`
 

 

 
What are the sizes of the angles marked `x` and `y`?

`x =` 
 
  `­°` `y =` 
 
  `­°`
Show Answers Only

`x = 74°\ \ \ y = 106°`

Show Worked Solution

`text(S) text(ince)\ \ Delta PRS\ \ text(is isosceles,)`

`2x + 32` `= 180`
`2x` `= 148`
`:. x` `= 74°`

 
`text(S) text(ince)\ QR = ST`

 `=> Delta PQT\ text(is isosceles)`
 

`text(Let)\ \ /_ PTQ = z°`

`2z + 32` `= 180`
`2z` `= 148`
`z` `= 74°`

 

`:. y` `= 180 – 74\ \ \ text{(180° in a straight line)}`
  `= 106°`

Measurement, NAP-D4-CA31 SA

A rectangle has an area of 1 square metre.

It has a length of 1222 millimetres.

What is its width to the nearest millimetre?

   millimetres
Show Answers Only

`818\ text{mm  (nearest mm)}`

Show Worked Solution

`1222\ text(mm) = 1.222\ text(m)`

`text(S) text(ince the area is 1m)^2,`

`1.222 xx text(Width)` `= 1`
`text(Width)` `= 1/1.222`
  `= 0.8183…`

 

`:.\ text(Width) = 818\ text{mm  (nearest mm)}`

Number, NAP-D4-CA30 SA

Michelle makes 7.0 litres of a healthy shake to sell at her cafe.

The table below shows the mixture of ingredients that go into the shake.
 

   

 
How many litres of milk does Michelle need?

   litres
Show Answers Only

`2.0\ text(litres)`

Show Worked Solution
`text(Litres of milk)` `= text(parts milk)/text(total parts) xx 7.0`
  `= 4/14 xx 7.0`
  `= 2.0\ text(litres)`

Number and Algebra, NAP-D2-40 SA

In the Japanese calendar, 2013 is the Year of the Snake.

The Year of the Snake occurs every 12 years.

What year was the second Year of the Snake after 1970?
Show Answers Only

`1989`

Show Worked Solution

`text(Going backwards, the Years of the Snake are:)`

`2013, 2001, 1989, 1977, 1965`

`:.\ text(S)text(econd Year of the Snake after 1970)`

`text(was 1989.)`

Statistics, NAP-D2-39 SA

48 girls were asked if they played netball or soccer and the results were recorded in the table below.

How many girls play both netball and soccer?
Show Answers Only

`11`

Show Worked Solution

`text(S)text(ince 16 play neither, 32 must)`

`text(play at least one.)`
 

`text(S)text(ince)\ \ 22 + 21 = 43,`

`:.\ text(11 girls must be playing both)`

`text(netball and soccer.)`

Number and Algebra, NAP-I2-39 SA

A box of golf balls normally cost $19.50.

During a sale, the golf shop took 10% off the regular price of the balls.

What is the new sale price of the golf balls?

$  
Show Answers Only

`$17.55` 

Show Worked Solution
`text(10% discount)` `= 19.50/10`
  `= $1.95`
`:.\ text(Sale price)` `= $19.50 – $1.95`
  `= $17.55`

Measurement, NAP-D4-CA27 SA

Poppy draws a quadrilateral with a perimeter of 50 centimetres.

What is the maximum possible area of Poppy's quadrilateral?

   square centimetres
Show Answers Only

`156.25\ text(cm²)`

Show Worked Solution

`text(The maximum area will occur when the)`

`text(quadrilateral is a square.)`

`=>\ text(Length of side) = 50/4 = 12.5\ text(cm)`

 

`:.\ text(Maximum area)` `= 12.5 xx 12.5`
  `= 156.25\ text(cm²)`

Geometry, NAP-B3-NC32 SA

This clock shows 8 o'clock.
 

 

 
What is the size of the larger angle between the minute and hour hands?

  °
Show Answers Only

`240^@`

Show Worked Solution

`text(Angle between any two adjacent numbers)`

`=360/12`

`=30^@`

`:.\ text(Large angle between the minute and hour hand)`

`=8 xx 30`

`=240^@`

Probability, NAP-B3-NC31 SA

Jon spins each pointer 50 times.

 

Each time he added the numbers that the pointers landed on.

His results are shown below.

\begin{array} {|c|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex}\textbf{Sum of numbers}\rule[-1ex]{0pt}{0pt} & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & \textbf{Total}\\
\hline
\rule{0pt}{2.5ex}\textbf{Number of spins}\rule[-1ex]{0pt}{0pt} & 1 & 2 & 3 & 6 & 8 & 9 & 7 & 5 & 4 & 4 & 1 & \textbf{50} \\
\hline
\end{array}

What percentage of the spins resulted in a sum of 9?

  %
Show Answers Only

`text(10%)`

Show Worked Solution
`text(Percentage)` `= text(number of 9’s)/text(number of spins) xx 100`
  `=5/50 xx 100`
  `=10 text(%)`

Number, NAP-B3-NC30

Which set of fractions is ordered smallest to largest?

 
 `1/6, 5/24, 1/4, 5/8, 1/2`
 
 `1/4, 7/24, 1/3, 5/12, 1/2`
 
 `1/6, 7/24, 5/12, 3/8, 2/3`
 
 `1/4, 1/3, 7/24, 3/12, 1/2`
Show Answers Only

`1/4, 7/24, 1/3, 5/12, 1/2`

Show Worked Solution

`text(Converting option 2 to a common denominator:)`

`1/4, 7/24, 1/3, 5/12, 1/2\ \ text(becomes:)`

`6/24, 7/24, 8/24, 10/24, 12/24`

 

`=>\ text(Smallest to largest.)`

Measurement, NAP-B3-NC29

A small shipping container is the shape of a rectangular prism.

The volume of the small shipping container is 6 cubic metres.

A large shipping container has dimensions that are double the dimensions of the small shipping container.

What is the volume of the large shipping container?

 
 `text(12 cubic metres)`
 
 `text(24 cubic metres)`
 
 `text(48 cubic metres)`
 
 `text(96 cubic metres)`
Show Answers Only

`text(48 cubic metres)`

Show Worked Solution

`text(The dimensions of the small container could be:)`

STRATEGY: Doubling dimensions that satisfy a volume of 6 m³ (although we don’t know the exact dimensions) can be used in this type of question.

`2 xx 3 xx 1 = 6\ text(m³)`

`text(If these dimensions are all doubled:)`

`text(Volume)` `=4 xx 6 xx 2`
  ` = 48\ text(m³)`

Geometry, NAP-B3-CA32

John draws a polygon.

It has a certain number of 110° angles and the same number of 130° angles.

It has no other angles.

The polygon is

`text(a hexagon)` `text(a heptagon)` `text(an octagon)` `text(a decagon)`
 
 
 
 
Show Answers Only

`text(a hexagon)`

Show Worked Solution

`text(The angle sum of the polygon must be a)`

`text(multiple of 240°.)`

`text(Also, the angle sum of any polygon with)\ \ n`

`text(sides)\ = (n-2) xx 180°`

`=>\ text(240° is not possible.)`

`=>\ text(480° is not possible.)`

`=>\ text(720° is possible,)`

`(n-2) xx 180` `=720`
`n-2` `=720/180`
  `=4`
`:. n` `=6`

 

`:.\ text{The polygon is a hexagon (6 sides).}`

Number, NAP-B3-CA31 SA

Jordan has 4 times as many blue pencils as black pencils.

Altogether he has 90 pencils.

How many blue pencils does he have?
Show Answers Only

`72\ text(blue pencils)`

Show Worked Solution

`text(Let)\ \ x = text(be the number of black pencils)`

`x + 4x` `= 90`
`5x` `= 90`
`:. x` `= 90/5`
  `= 18`

 

`:.\ text(The number of blue pencils)`

`=90 – 18`

`= 72`

Geometry, NAP-D3-CA32 SA

Blair was walking in bush trails. He started walking due north and then made three direction changes:

    1. 25° right turn
    2. 70° left turn
    3. a final right turn until he was walking in a due east direction.

How many degrees did Blair turn on his final right turn?

   degrees
Show Answers Only

`135°`

Show Worked Solution

`text(Blair’s final right turn)` `= 45 + 90`
  `= 135°`

Algebra, NAP-D3-CA30 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`

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(number 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)`

Measurement, NAP-D3-CA29 SA

Poppy draws a quadrilateral with a perimeter of 50 centimetres.

What is the maximum possible area of Poppy's quadrilateral?

   square centimetres
Show Answers Only

`156.25\ text(cm²)`

Show Worked Solution

`text(The maximum area will occur when the)`

`text(quadrilateral is a square.)`

`=>\ text(Length of side) = 50/4 = 12.5\ text(cm)`

 

`:.\ text(Maximum area)` `= 12.5 xx 12.5`
  `= 156.25\ text(cm²)`

Number, NAP-D4-NC31 SA

A greyhound runs a 1500 metre race.

The time it takes for each 500 metres is recorded in the table below.
 

 
What was the average speed of the greyhound over the full 1500 metre race, in metres per second?

  metres per second
Show Answers Only

`25\ \ text(metres per second)`

Show Worked Solution

`text(Total seconds to complete the race)`

`=23 + 19 +18`

`=60`

`:.\ text(Average speed)` `=1500/60`
  `=150/6`
  `=25\ \ text(metres per second)`