NAPX-MultipleChoice

Number, NAPX-G4-NC07

Dars has 560 grams of ice cream.

He serves it in 8 equal servings.

How much does the ice cream in each serving weigh?

60 g	70 g	80 g	90 g

Show Answers Only

`text(70 g)`

Show Worked Solution

`text(Weight of 1 serving)`	`= 1/8 xx 560`
	`= 70\ text(grams)`

Number, NAPX-G4-NC06, NAPX-G3-NC13

20 school children went to Leyland Brothers World for an excursion.

Entry into Leyland Brothers World was $15 per student and the total cost of the bus was $140.

Which expression shows the total cost of the excursion for everybody?

`(15 + 140) xx 20`	`140 + 15 + 20`	`20 xx 15`	`(20 xx 15) + 140`

Show Answers Only

`(20 xx 15) + 140`

Show Worked Solution

`(20 xx 15) + 140`

Algebra, NAPX-G4-NC05

Which expression equals `b^4`?

`4 xx b`	`(b^3 + b^3)/(b^2)`	`b xx b xx b xx b`	`2b + 2b`

Show Answers Only

`b xx b xx b xx b`

Show Worked Solution

`b^4 = b xx b xx b xx b`

Measurement, NAPX-G4-NC04

A basketball player's height is measured at 1.9 metres.

What is her height in centimetres?

`109`	`190`	`1090`	`1900`

Show Answers Only

`text(190 cm)`

Show Worked Solution

`text(S)text(ince 1 metre = 100 cm)`

`text(1.9 m)`	`= 1.9 xx 100`
	`= 190\ text(cm)`

Measurement, NAPX-G4-NC03

A football game take 135 minutes from start to finish.

If the game started at 6:15 pm, what time will it finish?

`text(7:30 pm)`	`text(7:50 pm)`	`text(8:30 pm)`	`text(8:50 pm)`

Show Answers Only

`text(8:30 pm)`

Show Worked Solution

`text(Finishing time)`

`=\ text(6:15 + 2 hrs 15 mins)`

`=\ text(8:30 pm)`

Algebra, NAPX-G4-NC02

Starsky spent twice as much money as Hutch.

If they spent a total of $120, how much did Hutch spend?

`$20`	`$40`	`$80`	`$240`

Show Answers Only

`$40`

Show Worked Solution

`text(Let)\ \ $x = text(Amount Hutch spent)`

`2x + x`	`= 120`
`3x`	`= 120`
`x`	`= $40`

Geometry, NAPX-G4-NC01

The two 2-dimensional shapes that make up the figure below can be best described as

	a trapezium and a square.
	a rectangle and a cube.
	a parallelogram and a rhombus.
	a square and a rhombus.

Show Answers Only

`text(A square and a rhombus.)`

Show Worked Solution

`text(A square and a rhombus.)`

Measurement, NAPX-G4-CA32

The rectangular prism, shown below, is cut into 3 identical cubes.

What is the ratio of the surface area of the rectangular prism to one of the cubes?

`7 : 3`	`9 : 2`	`3 : 1`	`5 : 2`

Show Answers Only

`7 : 3`

Show Worked Solution

`text(S.A. of rectangular prism)`

`= 2 xx (x xx x) + 4 xx (3x xx x)`

`= 2x^2 + 12x^2`

`= 14 x^2`

`text(S.A. of cube)`

`= 6 xx (x xx x)`

`= 6x^2`

`:.\ text(Ratio of prism to cube)`

`= 14x^2 : 6x^2`

`= 7 : 3`

Algebra, NAPX-G4-CA30

Bellarose collects insects.

`1/4` of her collection are beetles and `1/6` of her collection are bees.

Bellarose has 6 more beetles than bees in her collection.

How many insects are in Bellarose's collection in total?

`24`	`36`	`60`	`72`

Show Answers Only

`72`

Show Worked Solution

`text(Solution 1)`

`text(Let)\ \ x = text(total number of insects)`

`1/4 x – 1/6 x`	`= 6`
`1/12 x`	`= 6`
`x`	`= 72`

`text(Solution 2)`

`text(By trial and error)`

`1/4 xx 72 = 18\ text(beetles)`

`1/6 xx 72 = 12\ text(bees)`

`:. 72\ text(in total.)`

Geometry, NAPX-G4-CA28

`ABCD` is a square. `ED` and `FD` are the same length as the square sides.

If the three triangles drawn in the square are identical, what is the size of `angleDAE`?

`60^@`	`75^@`	`82.5^@`	`88.5^@`	`90^@`

Show Answers Only

`75°`

Show Worked Solution

`text(S) text(ince triangles are identical,)`

`/_ EDA = 90 ÷ 3 = 30°`

`DeltaEDA\ text(is isosceles)`

`:. /_ DAE`	`= 1/2(180 – 30)`
	`= 75°`

Number, NAPX-G4-CA24

Scientists estimate that a meteor travels at 600 000 metres every minute.

Which value is the closest to the number of metres that the meteor would travel in one day?

`1.44 xx 10^6`	`1.44 xx 10^7`	`8.64 xx 10^7`	`8.64 xx 10^8`

Show Answers Only

`8.64 xx 10^8`

Show Worked Solution

`text(Total distance travelled in one day)`

`= 600\ 000 xx 60 xx 24`

`= 864\ 000\ 000`

`= 8.64 xx 10^8`

Geometry, NAPX-G4-CA21

Harpo's house is 3 kilometres due south of Groucho's house.

Curly's house is 3 kilometres due east of Harpo's.

Curly is at his house facing south. He then turns anticlockwise until he is facing in the exact direction of Groucho 's house.

How many degrees does Curly turn though?

`30^@`	`450^@`	`135^@`	`150^@`	`225^@`

Show Answers Only

`135^@`

Show Worked Solution

`text(Degrees Curly turns through)`

`= 180 + 45`

`= 225^@`

Geometry, NAPX-G4-CA19

Which one of the following triangles has an area of 16 cm² ?

(Triangles are not drawn to scale)

Show Answers Only

Show Worked Solution

`text(Area)`	`= 1/2 xx b xx h`
	`= 1/2 xx 8 xx 4`
	`= 16\ text(cm²)`

Number, NAPX-G4-CA18

Marjorie and Deek ran in a 20 km road race.

Marjorie finished in a time of 1 hour and 15 minutes.

Deek took 15% longer than Marjorie.

Approximately how long did Deek take to finish the race?

`86\ text(minutes)`	`90\ text(minutes)`	`130\ text(minutes)`	`132\ text(minutes)`

Show Answers Only

`86\ text(minutes)`

Show Worked Solution

`text(Marjorie’s time = 75 minutes)`

`text(Deek’s time)`	`= 75 + 15text(%) xx 75`
	`= 86.25\ text(minutes)`

Geometry, NAPX-G4-CA17, NAPX-G3-CA20

TJ walks his horse from the barn to the horse track.

The distance is 8 cm on the map.

What is the actual distance from the barn to the racetrack?

`3200\ text(m)`	`500\ text(m)`	`320\ text(m)`	`50\ text(m)`

Show Answers Only

`3200\ text(m)`

Show Worked Solution

`text(Distance)`	`= 8 xx 40\ 000`
	`= 320\ 000\ text(cm)`
	`= 3200\ text(metres)`

Measurement, NAPX-G4-CA16, NAPX-G3-CA19

The level of water in a dam is measured by the indicator below.

What is the height of the water in the dam?

`1.5\ text(metres)`	`1.6\ text(metres)`	`1.8\ text(metres)`	`2.2\ text(metres)`	`2.4\ text(metres)`

Show Answers Only

`1.6\ text(metres)`

Show Worked Solution

`text(Each increment)`	`= 1 ÷ 5`
	`= 0.2\ text(metres)`

`:.\ text(Height)`	`= 2 – (2 xx 0.2)`
	`= 1.6\ text(metres)`

Algebra, NAPX-G4-CA15

Grover earns $48 for delivering 8 pizzas.

Which expression shows how much he will earn for delivering `x` pizzas?

`(48 xx 8) xx x`	`(48 ÷ 8) ÷ x`	`(48 xx 8) ÷ x`	`(48 ÷ 8) xx x`

Show Answers Only

`(48 ÷ 8) xx x`

Show Worked Solution

`text(Earning from 1 pizza delivered)`

`= 48 ÷ 8`

`:. text(Earnings from)\ x\ text(pizzas)`

`= (48 ÷ 8) xx x`

Number, NAPX-G4-CA14

Daxx participates in a walkathon at the local cross country track.

His grandfather donates $30.

His neighbor donates $15 per kilometer that Daxx walks.

How many kilometres does Daxx need to walk to raise $150?

`5`	`6`	`8`	`10`	`12`

Show Answers Only

`8\ text(kilometers)`

Show Worked Solution

`text(Strategy 1)`

`text(1 km = 30 + 15 = $45)`

`text(2 km = 45 + 15 = $60)`

`vdots`

`text(8 km = 135 + 15 = $150)`

`text(Strategy 2)`

`text(Let)\ \ n =\ text(number of kilometers walked.)`

`text(Total money raised = 30 + 15) xx n`

`30 + 15n`	`= 150`
`15n`	`= 120`
`n`	`= 8`

Number, NAPX-G4-CA13

Kylie has 5-cent, 20-cent and 50-cent coins in her pocket.

In total she has $2.35.

What is the smallest number of coins she could have?

`5`	`6`	`7`	`8`	`9`

Show Answers Only

`8\ text(coins)`

Show Worked Solution

`text(Least number of coins to get $2.35 is:)`

`4 xx 50text(c)`

`1 xx 20text(c)`

`3 xx 5text(c)`

`:. 8\ text(coins is the least)`

Geometry, NAPX-G4-CA12, NAPX-G3-CA11

A ramp rises 1 metre for every 12 metres of its base length.

If the ramp rises 0.8 metres, what is its base length?

`8.2\ text(metres)`	`9.6\ text(metres)`	`12.8\ text(metres)`	`15\ text(metres)`

Show Answers Only

`9.6\ text(metres)`

Show Worked Solution

`text(Base length)`	`= 12 xx 0.8`
	`= 9.6\ text(metres)`

Statistics and Probability, NAPX-G4-CA11

Dennis is a fast bowler. In a cricket game, the chance of him getting a wicket on a given ball is unlikely.

Which probability best describes Dennis' chance of getting a wicket from one particular ball?

`16/17`	`1/2`	`1/17`	`1`

Show Answers Only

`1/17`

Show Worked Solution

`text(Unlikely means the probability is)`

`text(close to zero.)`

`:. 1/17`

Geometry, NAPX-G4-CA10

Rufus is shading squares in a grid.

Rufus needs to shade some extra squares so that the dotted line is a line of symmetry.

What is the smallest number of squares he has to shade?

`2`	`3`	`4`	`5`	`6`

Show Answers Only

`3\ text(squares)`

Show Worked Solution

`text{3 squares need to be shaded (see below).}`

Number, NAPX-G4-CA09

The colour pink can be made by mixing 5 litres of white paint with 3 litres of red paint.

If 80 litres of white paint are used in this mixture, how much red paint is needed?

`text(10 litres)`	`text(16 litres)`	`text(48 litres)`	`text(128 litres)`

Show Answers Only

`text(48 litres)`

Show Worked Solution

`text(Let)\ \ x =\ text(litres of red paint needed)`

`5/3`	`= 80/x`
`5x`	`= 3 xx 80`
`:. x`	`= 240/5`
	`= 48\ text(litres)`

Geometry, NAPX-G4-CA08

Serena draws a sketch of her background.

What is the size of angle `x°`?

`65^@`	`72^@`	`152^@`	`162^@`

Show Answers Only

`72^@`

Show Worked Solution

`text(Interior angles of a quadrilateral)`

`text(add up to)\ 360^@.`

`:. /_ x`	`= 360 – 89 – 115 – 84`
	`= 72^@`

Number, NAPX-G4-CA07

Two arrows point to numbers on a number line.

Which one of these numbers lies between the two arrows?

	`45`
	`130`
	`225`
	`250`

Show Answers Only

`130`

Show Worked Solution

`text(First arrow ≈ 125)`

`text(Second arrow ≈ 220)`

`:. 130\ text(lies between the arrows.)`

Number, NAPX-G4-CA06

Which number shows 9 thousands, 2 tens and 4 tenths?

`920.04`	`9020.4`	`9200.04`	`9200.4`

Show Answers Only

`9020.4`

Show Worked Solution

`9020.4`

Geometry, NAPX-G4-CA05v1

In which of these are the two shaded triangles the same size and shape?

Show Answers Only

Show Worked Solution

Geometry, NAPX-G4-CA04

Maya walks along the path from `A` to `B.`

How far does she walk in kilometres?

`0.12`	`1.2`	`12`	`120`

Show Answers Only

`1.2\ text(km)`

Show Worked Solution

`text(Distance)`	`= 12 xx 100\ text(m)`
	`= 1.2\ text (km)`

Statistics and Probability, NAPX-G4-CA03

10 of the tallest mountains in the United States are listed in the table below:

How much taller than Colorado's tallest mountain is Alaska's tallest mountain?

`1792\ text(metres)`	`1838\ text(metres)`	`1840\ text(metres)`	`4650\ text(metres)`

Show Answers Only

`1792\ text(metres)`

Show Worked Solution

`text(Extra Height)`	`= 6190 – 4398`
	`= 1792\ text(metres)`

Statistics and Probability, NAPX-G4-CA02

Clover flips an unbiased coin 100 times.

Which result is most likely?

`97\ text(tails)`	`52\ text(tails)`	`46\ text(tails)`	`24\ text(tails)`

Show Answers Only

`52\ text(tails)`

Show Worked Solution

`text(S)text(ince a tail has a 50% chance,)`

`text(Expected tails)`	`= 50text(%) xx 100`
	`= 50`

`:. 52\ text(tails is closest to 50 and)`

`text(the most likely.)`

Number, NAPX-G4-CA01, NAPX-G3-CA01

In Australia, 271 522 children were registered to play soccer in 2017.

Of these children, 217 223 were boys.

How many girls were registered to play soccer in 2017?

`54\ 299`	`63\ 301`	`72\ 319`	`488\ 745`

Show Answers Only

`54\ 299`

Show Worked Solution

`text(Girls)`	`= 271\ 522 – 217\ 223`
	`= 54\ 299`

Measurement, NAPX-H4-NC30

Lily's backyard is in the shape of a rectangle and has an area of 30 m².

Kim's backyard is also rectangular but with side lengths that are triple those of Lily's backyard.

What is the area of Kim's backyard.

`10\ text(m²)`	`90\ text(m²)`	`120\ text(m²)`	`270\ text(m²)`

Show Answers Only

`270\ text(m²)`

Show Worked Solution

`text(Let the dimensions of Lily’s backyard be:)\ \ x, y`

`text(Area) = xy = 30\ text(m²)`

`text(Kim’s backyard is:)\ \ 3x xx 3y`

`text(Area)`	`= 3x xx 3y`
	`= 9xy`
	`= 9 xx 30\ text(m²)`
	`= 270\ text(m²)`

Algebra, NAPX-H4-NC28

Jen drew the line `y = 5 - x` on a grid.

She then drew `y = x - 1` on the same grid.

What are the coordinates of the intersection point of these two lines?

`(−2,3)`	`(2,3)`	`(3,−2)`	`(3,2)`

Show Answers Only

`(3,2)`

Show Worked Solution

`text(Strategy 1)`

`text(Draw the graphs and estimate intersection.)`

`text(Strategy 2)`

`text(Intersection occurs when)`

`x – 1`	`= 5 – x`
`2x`	`= 6`
`x`	`= 3`
`y`	`= 2`

Geometry, NAPX-H4-NC27

A regular hexagon has a perimeter of 30 cm

Ima cuts it into 6 equilateral triangles.

What it the perimeter of one of the triangles?

`text(5 cm)`	`text(10 cm)`	`text(12 cm)`	`text(15 cm)`	`text(18 cm)`

Show Answers Only

`text(15 cm)`

Show Worked Solution

`text(Perimeter)`	`= 5 + 5 + 5`
	`= 15\ text(cm)`

Algebra, NAPX-H4-NC26

`x/4 = 5/7`

What is the value of `x`?

`5/28`	`20/28`	`9/7`	`20/7`

Show Answers Only

`20/7`

Show Worked Solution

`x/4`	`= 5/7`
`x`	`= (5 xx 4)/7`
	`= 20/7`

Number, NAPX-H4-NC25

A backwards running group in Europe have a ratio of men to women of 7:4.

There are 12 more men than women in this group.

How many people are in this group altogether?

`12`	`13`	`18`	`44`

Show Answers Only

`44`

Show Worked Solution

`text(A ratio of 7:4 means if there are 11 members)`

`=> 7\ text(men : 4 women)`

`text(In 22 members ⇒ 14 men : 8 women)`

`text(In 44 members ⇒ 28 men : 16 women)`

`:. 44\ text(Total members in group when there)`

`text(are 12 more men.)`

Algebra, NAPX-H4-NC24

Herb made a number pattern using this rule:

next number = previous number ×

−

and

are whole numbers.

His number pattern is:

`4,3,1,−3,−11`

What is the next number in Herb's pattern?

`−19`	`-21`	`−27`	`−29`

Show Answers Only

`−27`

Show Worked Solution

`text(Using the rule and first 3 terms:)`

`text(Let)\ x =`

`text(and)\ y =`

`3`	`= 4x – y`	`…\ (1)`
`1`	`= 3x – y`	`…\ (2)`

`text(Subtract)\ \ (1) – (2),`

`x = 2`

`text(Substitute)\ x = 2\ text{into (1)}`

`y = 5`

`:.\ text(Next term)`	`= −11 xx 2 – 5`
	`= −27`

Geometry, NAPX-H4-NC22

Hugh is using a computer graphics program to draw the following shapes.

Three of his commands and the resulting shapes are drawn below:

`text(shape)\ (1,4,180)`	`text(shape)\ (2,4,90)`	`text(shape)\ (1,6,45)`

Which shape would be drawn by the command: `text(shape)\ (2,6,135)`?

Show Answers Only

Show Worked Solution

`text(Short axis = 4)`

`text(Long axis = 6)`

`text{Tilt: long axis at 45° to the vertical (clockwise)}`

Number, NAPX-H4-NC21

Simplify: `(3^3 xx 2^2 xx 4^4)/(4 xx 3^2 xx 4^3 xx 2)`

`6`	`1`	`1/4`	`1/3`

Show Answers Only

`6`

Show Worked Solution

`(3^3 xx 2^2 xx 4^4)/(4 xx 3^2 xx 4^3 xx 2)`	`= (2^2 xx 3^3 xx 4^4)/(2 xx 3^2 xx 4^4)`
	`= 2 xx 3`
	`= 6`

Statistics and Probability, NAPX-H4-NC20, NAPX-H3-NC26

A standard six-sided die is rolled once.

What is the probability that the number on the top face is a factor of 6?

`5/6`	`2/3`	`1/3`	`1/6`

Show Answers Only

`2/3`

Show Worked Solution

`text(Factors of 6 are: 6, 1, 3, 2)`

`:.\ text{P(rolling a factor of 6)}`

`= 4/6`

`= 2/3`

Geometry, NAPX-H4-NC18

Bo draws and labels 3 points, on a Cartesian plane.

He wants to add another point so that all 4 points can be joined to make a parallelogram.

Which of these is a possible coordinate for the 4th point?

`(2,6)`	`(5,2)`	`(5,1)`	`(−2,2)`

Show Answers Only

`(−2,2)`

Show Worked Solution

`text(Possibilities are:)`

`(−2,2)\ text(and)\ (6,2)`

`:. (−2,2)\ text(is the only possible option.)`

Number, NAPX-H4-NC17

Which of these is the closest to 1?

`0.98`	`0.908`	`1.02`	`1.002`

Show Answers Only

`1.002`

Show Worked Solution

`text(Differences from 1:)`

`0.02`	`= 1 – 0.98`
`0.092`	`= 1 – 0.908`
`0.02`	`= 1.02 – 1`
`0.002`	`= 1.002 – 1`

`:. 1.002\ text(is the closest to 1.)`

Number, NAPX-H4-NC16, NAPX-H3-NC22

Enya made a mobile phone call that lasted 41 minutes.

Her mobile phone provider charges her 31 cents per minute for calls.

Enya estimated that the total cost of the phone call was about $12.

Enya's estimate was

	more than the actual cost.
	equal to the actual cost.
	less than the actual cost.

Show Answers Only

`text(more than the actual cost.)`

Show Worked Solution

`text(An estimate of the cost could be just over:)`

`text(40 minutes × 30 cents = $12)`

`:.\ text($12 estimate is less than the actual cost.)`

Number, NAPX-H4-NC15, NAPX-H3-NC21

Alota and Bea are sisters and are setting up their study desks.

They want their desks positioned the same distance from the centre of the room.

What is the distance `x` from the edge of each desk to the middle of the room?

`1.00\ text(m)`	`1.25\ text(m)`	`1.50\ text(m)`	`2.00\ text(m)`	`5.25\ text(m)`

Show Answers Only

`1.00\ text(m)`

Show Worked Solution

`text(Half the room = 4.75 m)`

`:. x`	`= 4.75 – (2.25 + 1.5)`
	`= 4.75 – 3.75`
	`= 1.00\ text(m)`

Number, NAPX-H4-NC14

Ben and Megs were playing a game where they both started with zero points.

Ben's final score was 550 points and Meg's final score was − 70.

How many more points did Ben have than Megs?

`−620`	`−480`	`480`	`620`

Show Answers Only

`620`

Show Worked Solution

`text(Difference)`	`= 550 – (−70)`
	`= 550 + 70`
	`= 620`

Algebra, NAPX-H4-NC13

Which expression is equal to `9x - 3 + 3x + 1`?

`6x`	`12x - 2`	`12x - 4`	`6x - 4`

Show Answers Only

`12x – 2`

Show Worked Solution

`9x – 3 + 3x + 1`

`= 12x – 2`

Geometry, NAPX-H4-NC12

`ABCD` is a trapezium.

Which of these must be a property of `ABCD`?

	Line `AB` is parallel to line `CD`.
	Diagonals `AC` and `BD` bisect each other.
	Line `AD` is perpendicular to line `CD`.
	Line `BC` is parallel to line `AD`.

Show Answers Only

`text(Line)\ BC\ text(is parallel to line)\ AD.`

Show Worked Solution

`text(A trapezium must have a pair of parallel sides.)`

`text(Line)\ BC\ text(is parallel to line)\ AD.`

Algebra, NAPX-H4-NC11

Elvis walks from his home to the beach through a park.

Which of the following situations best fits the distance/time graph above, where distance is Elvis' distance from home?

	Elvis ran to the park, sat down on a bench, and then ran home.
	Elvis walked to the park, sat down on a bench, then ran to the beach.
	Elvis ran to the beach, sat down, then ran home.
	Elvis walked to the park, sat down on a bench, then walked to the beach.

Show Answers Only

`text(Elvis walked, rested then walked.)`

Show Worked Solution

`text(The horizontal section of the graph indicates Elvis’ distance)`

`text{from home is not changing and he is resting.}`

`text(The slope before and after the rest break is the same, so Elvis’)`

`text(speed of travel was the same before and after the rest.)`

`:.\ text(Elvis walked, rested then walked.)`

Measurement, NAPX-H4-NC10

The volume of the liquid in the measuring cylinder below is closest to:

`text(800 millilitres)`	`text(850 millilitres)`	`text(7.5 litres)`	`text(0.9 litres)`

Show Answers Only

`text(0.9 litres)`

Show Worked Solution

`text(Each long dash = 250 mL)`

`=>\ text(Each short dash = 50 mL)`

`:.\ text(Liquid in the cylinder)`

`= 750 + (3 xx 50)`

`= 750 + 150`

`= 900\ text(mL)`

`= 0.9\ text(L)`

Geometry, NAPX-H4-NC09

Kobe is drawing a rectangular prism on an isometric grid.

Which pair of points could Kobe draw as vertices on the prism?

`A and D`	`B and C`	`A and C`	`B and D`

Show Answers Only

`B and D`

Show Worked Solution

`B and D`

Algebra, NAPX-H4-NC08, NAPX-H3-NC15

`= 8`

`xx`	`= (` `xx 3) + ` `+`

What is the value of

`1`	`2`	`4`	`6`	`8`

Show Answers Only

`4`

Show Worked Solution

`8 xx`	`= 8 xx 3 +` `+`
`6 xx`	`= 24`
`:.\ \ `	`= 4`

Number, NAPX-H4-NC07

`3 xx 2^4 =`

`24`	`48`	`96`	`1296`

Show Answers Only

`48`

Show Worked Solution

`3 xx 2^4`	`= 3 xx 2 xx 2 xx 2 xx 2`
	`= 3 xx 16`
	`= 48`

Geometry, NAPX-H4-NC06, NAPX-H3-NC11

Wally drew the net of a rectangular prism.

One of the prism's faces is drawn incorrectly.

Which face did Wally draw incorrectly?

`A`	`B`	`C`	`D`

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`A`

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`text(Side)\ A\ text(is drawn incorrectly. It should be)`

`text(the same size as side)\ B.`

Statistics and Probability, NAPX-H4-NC05

The world high jump record between 1960 and 1995 is graphed below.

By about how many centimeters did the world record increase between 1995 and 1965?

`35`	`40`	`44`	`50`

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`35\ text(cm)`

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`text(Estimating from the graph:)`

`text(Increase)`	`~~ 2.35 – 2.00`
	`~~ 0.35\ text(m)`
	`~~ 35\ text(cm)`

Geometry, NAPX-H4-NC04, NAPX-H3-NC10

Some tiles are missing from this pattern of tiles.

When complete the pattern has two lines of symmetry.

Which of these could be the missing part of the pattern?

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Show Worked Solution

Statistics and Probability, NAPX-H4-NC03, NAPX-H3-NC09

Two identical spinners are spun at the same time and the two numbers they land on are added up.

Which total is most likely?

`4`	`7`	`10`	`12`

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`7`

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`text(Seven can be achieved in 6 different ways.)`

`text(All other totals have less possible combinations.)`

`:. 7\ text(is the most likely.)`

Number, NAPX-H4-NC02

Lily has $12 to buy batteries for her torch.

Each battery costs $2.40 and Lily buys 4 batteries.

Which expression shows how much money she has left?

	`4 xx ($12 - $2.40)`
	`$12 - $2.40 + $2.40 + $2.40 + $2.40`
	`$12 - $2.40`
	`$12 - (4 xx $2.40)`

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`$12 – (4 xx $2.40)`

Show Worked Solution

`text(Money left) = $12 – (4 xx $2.40)`

Algebra, NAPX-H4-NC01

The table below shows a pattern.

What is the top number when the bottom number is 36?

`6`	`7`	`8`	`9`

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`6`

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`text(The pattern is:)`

`text(Top number)\xx 6 =\ text(Bottom number)`

`:.\ text(When the bottom number is 36,)`

`text(top number = 6.)`

Algebra, NAPX-H4-CA29

Which of these equations represents the line in the graph?

`y = 5 + 4x`	`y = 5 - 1.25x`	`y = 5 - 4x`	`y = 5 + 1.25x`

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`y = 5 – 4x`

Show Worked Solution

`y\ text(intercept = 5)`

`text(Gradient)`	`= text(rise)/text(run)`
	`= −5/1.25`
	`= −4`

`:. text(Equation is)\ y = 5 – 4x`

Number, NAPX-H4-CA27

A loaf of bread is on sale with a 15% discount.

In the last hour of trading, the bread is reduced a further 20% on the already discounted price.

What is the overall percentage discount on the bread?

`text(1.5%)`	`text(7.25%)`	`text(27.5%)`	`text(32%)`	`text(35%)`

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`text(32%)`

Show Worked Solution

`text(Strategy 1)`

`text{Assume the bread costs $1.00 (say)}`

`text(C)text(ost after 15% discount = $0.85)`

`text(C)text(ost after further 20% discount)`

`= 0.85 – (20text(%) xx 0.85)`

`= 0.85 – 0.17`

`= $0.68`

`:.\ text(Overall discount)`	`= (1 – 0.68) xx 100`
	`= 32text(%)`

`text{Strategy 2 (advanced)}`

`text(Overall discount)`	`= 1 – (0.85 xx 0.80)`
	`= 1 – 0.68`
	`= 0.32`
	`= 32text(%)`