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Measurement, NAP-J2-40

Patrick takes 25 minutes to walk to the beach for board training.

Last week he arrived at training at 4:15 pm, which was 20 minutes late.

At what time would Patrick leave home to arrive at board training on time?

   pm
Show Answers Only

`text(3:30 pm)`

Show Worked Solution

`text(Start of training)`

`text(= 4:15 less 20 minutes)`

`text(= 3:55 pm)`
 

`:.\ text(Time to leave home)`

`text(= 3:55 less 25 minutes)`

`text(= 3:30 pm)`

Number and Algebra, NAP-J2-38

Karen stands on a box and her new height is 1.8 metres.

Karen's actual height is twice that of the box.

What is the height of the box in centimetres?

   centimetres
Show Answers Only

`text(60 cm)`

Show Worked Solution
`text(1.8 metres)` `= 180\ text(centimetres)`
`180 ÷ 3` `= 60\ text(cm)`

 
`:.\ text(The height of the box is 60 cm.)`

Statistics, NAP-K2-35

This graph shows the number of men and women that registered to vote before a council election on different days of the week.
  

On which day is the difference between the number of men and women registering closest to 50?

Monday Tuesday Wednesday Thursday Friday
 
 
 
 
 
Show Answers Only

`text(Tuesday)`

Show Worked Solution

`text(Each interval = 20 people)`

`text(Difference needs to be 2.5 intervals)`

`=>\ text(Tuesday is closest)`

Number and Algebra, NAP-K2-33

Gian is writing a number pattern.
 

`13, 16, 19, 22, text(__,  __, )`
?

 
She continues this pattern until she has written 7 numbers.

Select all of the options that will give the 7th number in Gian's pattern.

 
 ` 22 + 4 + 4 + 4`
 
 `22 xx (3 + 3)`
 
 `22 + 3 + 3 + 3`
 
 `22 + (3 xx 3)`
Show Answers Only

`22 + 3 + 3 + 3`

`22 + (3 xx 3)`

Show Worked Solution

`text(Gian’s 7th number) = 31`

`22 + 3 + 3 + 3 = 31`

`22 + (3 xx 3) = 31`

Probability, NAP-K2-32

Ben needs to choose a shirt, a tie and a jacket to wear.

In his wardrobe, he owns the following clothes.
 

 
Which two of these show a way to calculate the number of different combinations that Ben can wear?

`3 + 2 xx 3` `3 xx 2 xx 3` `2 + 3 + 3` `2 xx 3 xx 3`
 
 
 
 
Show Answers Only

`3 xx 2 xx 3`

`2 xx 3 xx 3`

Show Worked Solution

`text(Possible combinations:)`

`3 xx 2 xx 3`

`2 xx 3 xx 3`

Number and Algebra, NAP-K2-30 SA

Pablo buys art supplies for his art studio.

He rounds each price to the nearest dollar to estimate the total cost of the supplies.
 

 
How much is Pablo's estimate?

$  
Show Answers Only

`$22`

Show Worked Solution

`text(After rounding to the nearest dollar,)`

`text(Pablo’s Estimate)` `= 7 + 2 + 3 + 7 + 3`
  `= $22`

Number, NAP-K4-NC02

Blart has a device that counts his steps each day.

He aims to complete 10 000 steps each day.

The fraction of steps he has completed toward his target one day is  `6700/(10\ 000).`

What percentage of steps does Blart need to complete to reach his target?

`0.33 text(%)` `0.67 text(%)` `33 text(%)` `67 text(%)`
 
 
 
 
Show Answers Only

`33 text(%)`

Show Worked Solution

`text(Steps completed) = 67000-:10\ 000=0.67`

`:.\ text(Percentage of steps to complete)`

`=1-0.67`

`=0.33`

`=33 text(%)`

Number, NAP-K3-NC06

In a racing car season, the top three finishers in each race are awarded points.
 

 
Vangio was awarded a total of 25 points.

What is the greatest number of races in which Vangio could have been in the top three?

5 6 7 8
 
 
 
 
Show Answers Only

`6`

Show Worked Solution

`text(The greatest number occur with)`

`text(the following points results:)`

`8 + 5 + 3 + 3 + 3 + 3 = 25`

`:. 6\ text(events is the highest.)`

Algebra, NAP-K3-CA27

Wendy went to the supermarket to buy milk, soup, pineapple and cereal.

The pineapple cost half as much as the cereal.

The cost of different combinations of her items is shown below.
 

 
What is the cost of the milk?

$1 $1.50 $2 $2.50
 
 
 
 
Show Answers Only

`$2`

Show Worked Solution

`text(S)text(ince pineapple)\ (p) = 1/2\ text(cereal)\ (c)`

`c` `= 2p`
`2p+p` `= 7.50`
`p` `= $2.50`

 

`m + s + p + c` `= 13`
`m + 6 + 5` `= 13`
`m` `= $2`

 
`:.\ text(Milk costs)\ $2`

Algebra, NAP-K3-CA25

Georgia is making a number pattern by drawing squares.
 

 
She draws up a table to record the number of squares in each figure.
 

 
How many squares will be in Figure 6?

`28` `34` `36` `40`
 
 
 
 
Show Answers Only

`40`

Show Worked Solution

`text(Consider the increase in squares between figures:)`

`text(Figure 1 → Figure 2 = 4 squares)`

`text(Figure 2 → Figure 3 = 6 squares)`

`text(Figure 3 → Figure 4 = 8 squares)`

`=> text(Figure)\ 5 = 18 + 10 = 28`
 

`:.\ text(Figure 6)` `= 28 + 12`
  `= 40\ text(squares)`

Probability, NAP-K4-CA29

Pedro has 180 students in his year at school.

He surveys 30 students at random and asks them their favourite subject at school.

This column graph shows the results of the survey.
 

 
Which is the best estimate for the total number of students in Pedro's year whose favourite subject is English?

6 18 24 36 60
 
 
 
 
 
Show Answers Only

`18`

Show Worked Solution

`text(30 students surveyed out of 180)`

`=>\ text(1 in 6 surveyed)`

`:.\ text(Expected number who prefer English)`

`= 3 xx 6`

`= 18`

Number, NAP-K3-CA19

Maria has 500 avocados to pack into boxes.

Each box has room for 3 layers of avocados with 27 avocados in each layer.

Maria packs as many full boxes as possible.

How many avocados are left over?

7 12 14 17
 
 
 
 
Show Answers Only

`14`

Show Worked Solution

`text(One solution:)`

`text(Avocados in 1 box)` `= 3 xx 27`
  `= 81`

 

`text(Full boxes)` `= 500 ÷ 81`
  `= 6.17…`
  `= 6\ text(full boxes)`

 

`:.\ text(Leftover)` `= 500 – (6 xx 81)`
  `= 500 – 486`
  `= 14`

Number, NAP-K4-CA20

Polly, Roger and Milly are splitting up two identical chocolate bars.

Polly takes `1/4` of the first chocolate bar and `3/8` of the second bar.

Roger takes `1/2` of the first chocolate bar and `1/4` of the second bar.

What fraction of each bar did Milly get?

 
 Milly got `1/4` of each chocolate bar.
 
 Milly got `1/8` of the first bar and `1/4` of the second bar.
 
 Milly got `1/4` of the first bar and `3/8` of the second bar.
 
 Milly got `1/8` of the first bar and `3/8` of the second bar.
Show Answers Only

`text(Milly got)\ 1/4\ text(of the first bar and)\ 3/8\ text(of the second bar.)`

Show Worked Solution

`text(1st bar:)\ 1 – (1/4 + 1/2) = 1/4`

`text(2nd bar:)\ 1 – (3/8 + 1/4) = 3/8`
 

`:.\ text(Milly got)\ 1/4\ text(of the first bar and)\ 3/8\ text(of the second bar.)`

Geometry, NAP-K4-CA17

Two boats leave from Fremantle. One sails to the Wharf at Rottnest Island and the other sails to Cervantes.

The direction each boat sailed is shown in the map below.
 

 
What is the value of `x` on the map?

35 45 50 60
 
 
 
 
Show Answers Only

`50`

Show Worked Solution

`text(Alternate angles are equal)`

`:. 60` `= x + 10` 
`x` `= 50^@` 

Geometry, NAP-K4-CA16

Arjay folds this net into a cube.
 

 
He places the cube on the table so that the top face is the letter `A`.

Which face is touching the table?

`text(B)` `text(C)` `text(D)` `text(E)` `text(F)`
 
 
 
 
 
Show Answers Only

`text(D)`

Show Worked Solution

`text(D will be touching the table)`

`text{(opposite side of}\ A text{)}.`

Number, NAP-K4-CA13

Maria has 500 avocados to pack into boxes.

Each box has room for 3 layers of avocados with 27 avocados in each layer.

Maria packs as many full boxes as possible.

How many avocados are left over?

7 12 14 17
 
 
 
 
Show Answers Only

`14`

Show Worked Solution

`text(One solution:)`

`text(Avocados in 1 box)` `= 3 xx 27`
  `= 81`

 

`text(Full boxes)` `= 500 ÷ 81`
  `= 6.17…`
  `= 6\ text(full boxes)`

 

`:.\ text(Leftover)` `= 500 – (6 xx 81)`
  `= 500 – 486`
  `= 14`

Geometry, NAP-K4-CA12

Cameron is camping with 4 friends.

They have individual tents shown on the diagram below.
 

 
Brandon's tent is north-west of Cameron and Dan's tent is to Cameron's north.

What is Cameron's position?

B2 B6 D4 F2 F6
 
 
 
 
 
Show Answers Only

`text(F2)`

Show Worked Solution

`text(Cameron’s tent is located at F2.)`

Number, NAP-K4-CA11

Brendan lives in New York and returns to visit his hometown, Perth, every three years.

His next visit in 2020 will also let him attend the Mining Expo that is held once every two years.

When was the last year that Brendan visited Perth at the same time as the Mining Expo was held?

2014 2015 2016 2017
 
 
 
 
Show Answers Only

`2014`

Show Worked Solution

`text(Brendan visits to Perth:)`

`2020, 2017, 2014, 2011`

`text(Mining Expo held in years:)`

`2020, 2018, 2016, 2014`
 

`:. 2014\ text(was the most recent year.)`

Probability, NAP-K4-CA19

A country school surveyed 120 of its students about the type of animals they have at home.

The results are recorded in the Venn diagram below, although the number of students who only own horses is missing.
 

If one of the students is selected at random, what is the probability that the student does not own a goat?

`40/120` `60/120` `80/120` `100/120`
 
 
 
 
Show Answers Only

`80/120`

Show Worked Solution

`text(Number of students who do not own a goat)`

`= 120 – (9 + 7 + 4 + 20)`

`= 120 – 40`

`= 80`

`:.\ text(Probability) = 80/120`

Measurement, NAP-K4-CA07

Ricky lives in Bellerive. He is travelling by train to the ferry terminal to catch a 13:30 ferry.

Ricky needs to arrive 30 minutes before his ferry departs.
 

 
What is the latest time Ricky can catch a train from Bellerive?

10:58 am 11:58 am 12:58 pm 1:58 pm
 
 
 
 
Show Answers Only

`text(11:58 am)`

Show Worked Solution

`text(Working backwards:)`

`text(Ricky must arrive at the ferry terminal before 12:30)`

`=>\ text(12:17 pm is closest time)`

`:.\ text(11:58 am train is latest)`

Statistics, NAP-A3-NC22 SA

A survey asked a group of high school students how much they spend on broadband each month.

The result were recorded in the table below.
 


 

In total, how many students in Year 9 and Year 10 had a monthly broadband spend of more than $20?
Show Answers Only

`33`

Show Worked Solution

`text(Year 9-10 students who spend more than $20)`

`= 17 + 16`

`= 33\ text(students)`

Measurement, NAP-A3-CA22

This shape is made from eight equilateral triangles and one large parallelogram.
 

 
Each side of all the small triangles is 4 cm long.

What is the perimeter of the shape?

`text(12 cm)` `text(44 cm)` `text(48 cm)` `text(68 cm)`
 
 
 
 
Show Answers Only

`text(48 cm)`

Show Worked Solution

`text{Perimeter from the top left corner (clockwise)}`

`=12+4+4+4+4+8+4+8`

`=48\ text(cm)`

Geometry, NAP-A4-NC17

Ruby made this solid object using 36 cubes.

   

She then painted the complete surface area of the object red.

The object is then broken apart into 36 cubes.

How many cubes have at least one side painted red?

27 32 34 36
 
 
 
 
Show Answers Only

`34`

Show Worked Solution

`text(Consider the cube sliced vertically into 3 equal parts:)`

`text(Cubes with red on at least one side)`

`= 12 + 10 + 12`

`= 34`

Algebra, NAP-A4-CA21

A stack of 4 cups is 16 cm tall.

A stack of 7 cups is 25 cm tall.
 

  
Which rule can be used to work out the height, in centimetres, of a stack of `n` cups?

`7n - 24` `7n - 12` `3n + 4` `3n + 7`
 
 
 
 
Show Answers Only

`3n + 4`

Show Worked Solution

`text(7 cups = 25 cm)`

`text(4 cups = 16 cm)`

`=> 3\ text(extra cups add 9 cm)`

`=> 1\ text(extra cup adds 3 cm)`

 

`:. 3n + 4\ text(is the rule.)`

Geometry, NAP-B4-NC23 SA

`ABCD` is a rectangle.

A line is drawn through the point where the two diagonals intersect.

Two triangles are then shaded.
 

 
What fraction of the rectangle is shaded?
Show Answers Only

`1/4`

Show Worked Solution

`Delta BOF ≡ Delta DOE\ \ text{(AAS)}`

`Delta AOD\ text(is)\ 1/4\ text(of the area rectangle)\ ABCD`

`text{(diagonals of a rectangle cut it into}`

`text{4 triangles of equal area)}`

 

`:.\ text(Fraction is)\ 1/4.`

Measurement, NAP-A4-CA19

How many hours and minutes are between 4:43 am and 4:21 pm on the same day?

 
 11 hours and 22 minutes
 
 11 hours and 38 minutes
 
 12 hours and 22 minutes
 
 12 hours and 38 minutes
Show Answers Only

`text(11 hours and 38 minutes)`

Show Worked Solution

`text(One strategy:)`

`text(4:43 am + 12 hours)` `= 4:43\ text(pm)`
`text(4:43 pm − 22 mins)` `= 4:21\ text(pm)`

 

`:.\ text(Time difference = 11 hours and 38 minutes)`

Measurement, NAP-A4-CA17

Here is a plan of Dave's backyard.
 

 
The total area of the paving stones is 18 m².

What is the total area of the grass in Dave's backyard?

`text(36 m²)` `text(48 m²)` `text(54 m²)` `text(72 m²)`
 
 
 
 
Show Answers Only

`text(54 m²)`

Show Worked Solution

`text(9 paving stones = 18 m²)`

`=> 1\ text(grid square = 2 m²)`

 

`:.\ text(Total grass)` `= 27\ text(grid squares)`
  `= 27 xx 2`
  `= 54\ text(m²)`

Geometry, NAP-A4-CA16

A regular pentagon, a square and an equilateral triangle meet at a point.
 

 
What is the size of the angle `x°`?

`112°` `110°` `108°` `102°`
 
 
 
 
Show Answers Only

`102°`

Show Worked Solution

`text(Sum of internal angles of hexagon)`

`= (n-2) xx 180`

`= 3 xx 180`

`= 540^@`
 

`text(Internal angle in hexagon)`

`= 540/5`

`= 108^@`
 

`:. x` `= 360-(108 + 90 + 60)`
  `= 102^@`

Geometry, NAP-A4-CA13

In the diagram, `ACD` is a straight line.
 

 
What is the size of angle `BCE`?

`45°` `48°` `51°` `87°`
 
 
 
 
Show Answers Only

`87^@`

Show Worked Solution

`angleBCA` `= 180 – (81 + 51)qquad(180^@\ text(in triangle))`
  `= 48^@`

 

`:. angleBCE` `= 180 – (48 + 45)qquad(angleACD\ text(is a straight angle))`
  `= 87^@`

Geometry, NAP-B4-NC21 SA

The area of the rectangle in the diagram below is 15 cm2.
 

What is the area of the trapezium `ABCD`?

  cm2
Show Answers Only

`30\ text(cm)^2`

Show Worked Solution

`text{Opposite sides of rectangles are equal}`

`text(Triangles at bottom are congruent with the)`

`text{triangles the at top (RHS).}`
 

`text(Rearranging the diagram:)`

`:.\ text(Area of trapezium)`

`= 2 xx 15`

`= 30\ text(cm)^2`

Statistics, NAP-B4-NC19

Here is a set of 8 scores.

  `1, \ 7, \ 8, \ 9, \ 9, \ 16, \ 16, \ 28`

What will change if score 28 is removed from the set?

 
 mean and mode
 
 mean and median
 
 mean only
 
 mean and range
Show Answers Only

`text(mean and range)`

Show Worked Solution

`text(Mean will decrease.)`

`text(Mode will remain unchanged.)`
 

`text(Median of 8 scores)`

`= {text(4th)\ +\ text(5th)}/2=(9 + 9)/2=9`

`text(Median of 7 scores)`

`= 4 text(th score)=9`
 

`text(Range of 8 scores) =28 – 1 =27`

`text(Range of 7 scores) = 16 – 1 = 15`
 

`:.\ text(Mean and range will change.)`

Algebra, NAP-B4-NC18

The coordinates of point `A` are `(7, 5)`.
 

 
`AB` is parallel to the `y`-axis.

If  `AB = 3, BC = 4 and AC = 5`, what are the coordinates of point `C`?

`(3, 2)` `(2, 3)` `(1, 5)` `(5, 1)`
 
 
 
 
Show Answers Only

`(3, 2)`

Show Worked Solution

`text(Coordinates of)\ C\ text(are):`

`(7 – 4, 5 – 3) = (3, 2)`

Number, NAP-B4-NC16

Which expression is equal to  `6^3 xx 36^2`?

 
 `6 xx 3 xx 36 xx 2`
 
 `6 xx 6 xx 6 xx 6 xx 6`
 
 `6 xx 6 xx 6 xx 36 xx 6`
 
 `6 xx 6 xx 6 xx 6 xx 6 xx 6 xx 6`
Show Answers Only

`6 xx 6 xx 6 xx 6 xx 6 xx 6 xx 6`

Show Worked Solution
`6^3 xx 36^2` `= (6xx6xx6) xx (6xx6)^2`
  `= (6xx6xx6) xx (6xx6) xx (6 xx6)`
  `=6 xx 6 xx 6 xx 6 xx 6 xx 6 xx 6`

Algebra, NAP-B4-CA21

A large telescope lens has a diameter `D` and depth `d`.

The focal length of the lens, `F`, is given by the rule  `F = (D^2)/(9d)`.

When  `D = 6`  and  `F = 0.4`, the value of `d` is

`0.4` `0.1` `1.7` `10`
 
 
 
 
Show Answers Only

`10`

Show Worked Solution
`0.4` `=6^2/(9 xx d)`
`9d` `=36/0.4`
`:.d` `=90/9`
  `=10`