On a tourist map, two landmarks are measured to be 12.2 centimetres apart.
On the map, 1 centimetre represents 5 kilometres.
What is the actual distance between the landmarks?
|
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2.44 km |
|
|
24.4 km |
|
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6.1 km |
|
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61.0 km |
Geometry, NAPX-p168012v01
Two stores are 8.2 cm apart on a map.
On the map, 1 cm represents 2 km.
What is the actual distance between the stores?
|
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4.1 km |
|
|
1.64 km |
|
|
16.4 km |
|
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41.0 km |
Algebra, NAPX-p168008v02
If `z= 7`, what is the value of `5z`?
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35 |
|
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55 |
|
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57 |
|
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75 |
Algebra, NAPX-p168008v01
If `y= 4`, what is the value of `3y`?
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7 |
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10 |
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12 |
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34 |
Algebra, NAPX-p168006v02
Izzie and Miranda saved $66 altogether.
Miranda saved half as much money as Izzie.
How much money did Izzie saved?
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$11 |
|
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$22 |
|
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$30 |
|
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$44 |
Algebra, NAPX-p168006v01
Adam and Kenneth bought a bike together that cost $150.
Adam paid twice as much money as Kenneth.
How much money did Kenneth paid?
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$50 |
|
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$75 |
|
|
$100 |
|
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$120 |
Number, NAPX-p169007v02 SA
Eisha won a jar of candy with 366 pieces of candy in it at her school fete.
She gave a hand full each to five of her friends.
Eisha then counted the remaining candy and found she had 232 pieces left.
How many pieces of candy did Eisha give to her friends?
Number, NAPX-p169007v01 SA
Jason bought 325 eggs from the market.
When he was driving home, he had an accident and some of the eggs broke.
He counted that there were 241 eggs without any cracks.
How many eggs broke?
Measurement, NAPX-p169002v02
Anne was driving from her house to the supermarket to buy some groceries.
She drove a total distance of 2 kilometres and 54 metres.
Which of these shows the distance, in metres, that Anne drove to get to the supermarket?
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2.054 m |
|
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254 m |
|
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2054 m |
|
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2540 m |
Measurement, NAPX-p169002v01
John walked from his office to his home.
He walked a total of 1 kilometre and 62 metres.
Which of these shows the distance John walked in metres.
|
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106.2 m |
|
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162 m |
|
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1062 m |
|
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1620 m |
Probability, NAPX-p168996v02
A standard deck of 52 cards is made up four suits - Hearts, Diamonds, Clubs and Spades - that have 13 cards each.
Lara has a standard deck of cards and draws a King without looking and returns it to the deck.
She repeats this three times and draws a King each time.
If she randomly draws a card for the 4th time, which of the following is true?
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She is certain to draw a King. |
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She is more likely to draw a King than a Spade. |
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She is less likely to draw a King than a Queen. |
|
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She is more likely to draw a Heart than a King. |
Probability, NAPX-p168996v01
Aaron rolls a fair dice four times.
Each time he rolls the dice he gets a three.
Aaron rolls the dice for the fifth time.
Which of the following is true?
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|
He is less likely to roll a two than a three. |
|
|
He is more likely to roll a three than a one. |
|
|
He has an equal chance of rolling a three as a six. |
|
|
He is certain to roll a three. |
Number, NAPX-p111573v02
| `320 ÷` |
|
`= 40` |
Which of the following numbers make the number sentence above correct?
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8 |
|
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16 |
|
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20 |
|
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80 |
Number, NAPX-p111573v01
| `7 xx` |
|
`= 161` |
What number will make the number sentence correct?
|
|
13 |
|
|
23 |
|
|
154 |
|
|
1127 |
Number, NAPX-p115150v02
Sheryl has 90 cupcakes to sell to her customers.
She packed the cupcakes in boxes that fit 4 cupcakes inside.
How many full boxes of cupcakes can she sell?
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21 |
|
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23 |
|
|
22 |
|
|
20 |
Number, NAPX-p115150v01
Darren bought 141 eggs from the market.
He decided to put the eggs in cartons of 12.
How many full cartons of eggs does he have?
|
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9 |
|
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10 |
|
|
11 |
|
|
12 |
Measurement, NAPX-p167325v02
Leo painted the patterns shown below.
All the triangles that make up the shape have the same area.
Which of the following has the largest area painted grey?
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 |
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 |
Show Answers Only
Statistics, NAPX-p167389v02
The graph below shows the number of people in a supermarket at 15-minute intervals during a 4 hour period.
What time were the least amount of people in the supermarket?
|
|
11:15 AM |
|
|
12:00 PM |
|
|
12:30 PM |
|
|
1:45 PM |
Statistics, NAPX-p167389v01
The graph below shows the number of vehicles in a parking station at 30 minute intervals over a 6 hour period.
What time were the highest number of vehicles in the parking station?
|
|
5:30 PM |
|
|
4:30 PM |
|
|
3:30 PM |
|
|
5:00 PM |
Number, NAPX-p167381v02
The image below shows a game of noughts and crosses in progress.
What fraction of the available boxes are not filled in?
|
|
`frac{5}{9}` |
|
|
`frac{3}{8}` |
|
|
`frac{1}{2}` |
|
|
`frac{4}{9}` |
Number, NAPX-p167381v01
The image below is the plan of a farming plot.
Squares containing plants represent land that is growing crops.
Which fraction shows the amount of land that is used for growing crops?
|
|
`frac{4}{5}` |
|
|
`frac{5}{8}` |
|
|
`frac{1}{2}` |
|
|
`frac{3}{8}` |
Geometry, NAPX-p100504v02
Kendrick was driving on Sterling Road in the direction of the arrow on the map below.
Which direction is Kendrick heading?
|
|
North-East |
|
|
North-West |
|
|
South-East |
|
|
South-West |
Show Worked Solution
`text{Kendrick was heading in the North-East direction.}`
Geometry, NAPX-p100504v01
Alexa was walking on Ruby Street in the direction of the arrow shown below.
In what direction is Alexa heading?
|
|
North-East |
|
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North-West |
|
|
South-East |
|
|
South-West |
Show Worked Solution
`text{Alexa was heading in the South-East direction.}`
Measurement, NAPX-p167365v02
Which shape has an area of exactly 12 square units?
|
|
A |
|
|
B |
|
|
C |
|
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D |
Measurement, NAPX-p167365v01
What shape has an area greater than 11 square units?
|
|
A |
|
|
B |
|
|
C |
|
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D |
Measurement, NAPX-p124624v04
Barnsy owned a carp that was one quarter of a metre long.
How long was Barnsy's carp in millimetres?
|
|
4000 |
|
|
2000 |
|
|
400 |
|
|
250 |
|
|
50 |
Measurement, NAPX-p124624v03
Calvin bought half a kilogram of prawns from the fish market.
How many grams of prawns did Calvin buy?
|
|
5 |
|
|
25 |
|
|
50 |
|
|
500 |
|
|
750 |
Number, NAPX-p146458v08
What is the highest number that can be made using two of these cards?
Write the number in the box below.
Number, NAPX-p146458v07 SA
What is the smallest number that can be made using two of these cards?
Write the number in the box.
Measurement, NAPX-p116865v04
Scott expects his wine to be delivered on the 28th March.
He is told by the distributor that its delivery will be delayed by 5 days.
What day of the week will the wine now be delivered?
| Monday | Tuesday | Wednesday | Saturday |
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|
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Measurement, NAPX-p116865v03
Marty expects his gold mining drench to be delivered on the 28th of June.
Delays at customs mean it will be delivered 6 days later.
Which day of the week should the drench now be delivered?
| Saturday | Sunday | Monday | Tuesday |
|
|
|
|
|
Measurement, NAPX-p116876v04
Flanno builds the shape below using identical small blocks.
What is the smallest number of blocks Flanno needs to build a cube?
| 10 | 11 | 12 | 13 |
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|
|
|
Measurement, NAPX-p116876v03
Ella builds the shape below using identical small blocks.
What is the smallest number of blocks Ella needs to build a cube?
| 8 | 9 | 10 | 11 |
|
|
|
|
|
Algebra, MET1 2015 VCAA 7b
Solve `3e^t = 5 + 8e^(−t)` for `t`. (3 marks)
Mechanics, SPEC2 2020 VCAA 5
Two objects, each of mass `m` kilograms, are connected by a light inextensible strings that passes over a smooth pulley, as shown below. The object on the platform is initially at point A and, when it is released, it moves towards point C. The distance from point A to point C is 10 m. The platform has a rough surface and, when it moves along the platform, the object experiences a horizontal force opposing the motion of magnitude `F_1` newtons in the section AB and a horizontal force opposing the motion of magnitude `F_2` newtons when it moves in the section BC.
- On the diagram above, mark all forces that act on each object once the object on the platform has been released and the system is in motion. (2 marks)
The force `F_1` is given by `F_1 = kmg, \ k ∈ R^+`.
- i. Show that an expression for the acceleration, in `text(ms)^(−2)`, of the object on the platform, in terms of `k`, as it moves from point A to point B is given by `(g(1 - k))/2`. (2 marks)
- ii. The system will only be in motion for certain values of `k`.
- Find these values of `k`. (1 mark)
Point B is midway between points A and C.
- Find, in terms of `k`, the time taken, is seconds, for the object on the platform to reach point B. (2 marks)
- Express, in terms of `k`, the speed `v_B`, in `text(ms)^(−1)`, of the object on the platform when it reaches point B. (2 marks)
- When the object on the platform is at point B, the string breaks. The velocity of the object at point B is `v_B = 2.5\ text(ms)^(−1)`. The force that opposes motion from point B to point C is `F_2 = 0.075 mg + 0.4 mv^2`, where `v` is the velocity of the object when it is a distance of `x` metres from point B. The object on the platform comes to rest before point C.
- Find the object's distance from point C when it comes to rest. Give your answer in metres, correct to two decimal places. (4 marks)
Show Answers Only
-
- i. `text(See Worked Solutions)`
- ii. `k ∈ (0, 1), k ∈ R^+`
- `2sqrt(5/(g(1 – k)))`
- `v_text(B) = sqrt(5g(1 – k))`
- `3.15\ text(m)`
Show Worked Solution
| a. | |
b. i. `text(Horizontally:)`
`ma = T – F_1 = T – kmg\ …\ (1)`
`text(Vertically:)`
`ma = mg – T\ …\ (2)`
`text(Add)\ \ (1) + (2) :`
`2ma = mg – kmg`
| `:. a` | `= (g – kg)/2` |
| `= (g(1 – k))/2` |
♦ Mean mark (b)(ii) 45%.
b. ii. `text(System in motion when)\ a > 0`
`(g(1 – k))/2 > 0`
`:. k ∈ (0, 1), \ k ∈ R^+`
c. `text(AB) = 5\ (text(given)), u = 0\ (text(given))`
`text(Find)\ t\ text(when)\ s = 5:`
`s = ut + 1/2at^2`
`5 = 0 + 1/2 · (g(1 – k))/2 · t^2`
| `t^2` | `= 20/(g(1 – k))` |
| `t` | `= sqrt(20/(g(1 – k)))` |
| `= 2sqrt(5/(g(1 – k)))` |
d. `text(At B,)\ s = 5`
| `v_text(B)^2` | `= u^2 + 2as` |
| `= 0 + 2 · (g(1 – k))/2 · 5` | |
| `= 5g(1 – k)` |
`:. v_text(B) = sqrt(5g(1 – k))`
e. `text(Acceleration is against the direction of motion.)`
♦♦ Mean mark (e) 35%.
| `a` | `= −F/m` |
| `= −0.075g – 0.4v^2` | |
| `= −0.4(0.1875g + v^2)` |
| `d/(dx)(1/2 v^2)` | `= −0.4(0.1875g + v^2)` |
| `d/(dx)(v^2)` | `= −0.8(0.1875g + v^2)` |
| `(dx)/(d(v^2))` | `= −1.25(1/(0.1875g + v^2))` |
| `:. x` | `= −1.25 int_(2.5^2)^0 1/(0.1875 + v^2)\ dv^2` |
| `= 1.85\ text(m)` |
| `:.\ text(Distance from C)` | `= 5 – 1.85` |
| `= 3.15\ text(m)` |
Complex Numbers, EXT2 N2 2020 SPEC2 2
Two complex numbers, `u` and `v`, are defined as `u = −2 - i` and `v = −4 - 3i`.
- Express the relation `|z - u| = |z - v|` in the cartesian form `y = mx + c`, where `m, c ∈ R`. (3 marks)
--- 5 WORK AREA LINES (style=lined) ---
- Plot the points that represent `u` and `v` and the relation `|z - u| = |z - v|` on the Argand diagram below. (2 marks)
- State a geometrical interpretation of the graph of `|z - u| = |z - v|` in relation to the points that represent `u` and `v`. (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
- i. Sketch the ray given by `text(Arg)(z - u) = pi/4` on the Argand diagram in part b. (1 mark)
--- 10 WORK AREA LINES (style=lined) ---
- ii. In Cartesian form, write down the function that describes the ray `text(Arg)(z - u) = pi/4`. (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
Show Answers Only
- `y = −x – 5`
-
- `|z – u| = |z – v|\ text(is the perpendicular bisector of the line joining)\ u and v.`
- i.
- ii. `f: (−2, ∞) ->, f(x) = x + 1`
Show Worked Solution
a. `text(Let)\ \ z = x + iy`
`z – u = x + 2 + iy + i`
`z – v = x + 4 + iy + 3i`
`|z – u| = |z – v|`
| `(x + 2)^2 + (y + 1)^2` | `= (x + 4)^2 + (y + 3)^2` |
| `x^2 + 4x + 4 + y^2 + 2y + 1` | `= x^2 + 8x + 16 + y^2 + 6y + 9` |
| `-4y` | `= 4x + 20` |
| `y` | `= −x – 5` |
| b. |
|
c. `|z – u| = |z – v|\ text(is the graph of the perpendicular bisector of the)`
`text(line joining)\ u and v.`
| d.i. |
|
d.ii. `text(Arg)(z – u) = pi/4 =>\ text(gradient) = 1, ytext(-intercept at)\ (0, 1)`
`:. f: (−2, ∞) -> RR, \ f(x) = x + 1`
Complex Numbers, SPEC2 2020 VCAA 2
Two complex numbers, `u` and `v`, are defined as `u = −2 - i` and `v = −4 - 3i`.
- Express the relation `|z - u| = |z - v|` in the cartesian form `y = mx + c`, where `m, c ∈ R`. (3 marks)
- Plot the points that represent `u` and `v` and the relation `|z - u| = |z - v|` on the Argand diagram below. (2 marks)
- State a geometrical interpretation of the graph of `|z - u| = |z - v|` in relation to the points that represent `u` and `v`. (1 mark)
- i. Sketch the ray given by `text(Arg)(z - u) = pi/4` on the Argand diagram in part b. (1 mark)
- ii. Write down the function that describes the ray `text(Arg)(z - u) = pi/4`, giving the rule in cartesian form. (1 mark)
- The points representing `u` and `v` and `−5i` lie on the circle given by `|z - z_c| = r`, where `z_c` is the centre of the circle and `r` is the radius.
- Find `z_c` in the form `a + ib`, where `a, b ∈ R`, and find the radius `r`. (3 marks)
Show Answers Only
- `y = −x – 5`
-
- `|z – u| = |z – v|\ text(is the perpendicular bisector of the line joining)\ u and v.`
- i.
- ii. `f: (−2, ∞) ->, f(x) = x + 1`
- `z_c = −5/3 – 10/3 i and r = (5sqrt2)/3`
Show Worked Solution
a. `text(Let)\ \ z = x + iy`
`z – u = x + 2 + iy + i`
`z – v = x + 4 + iy + 3i`
`|z – u| = |z – v|`
| `(x + 2)^2 + (y + 1)^2` | `= (x + 4)^2 + (y + 3)^2` |
| `x^2 + 4x + 4 + y^2 + 2y + 1` | `= x^2 + 8x + 16 + y^2 + 6y + 9` |
| `-4y` | `= 4x + 20` |
| `y` | `= −x – 5` |
| b. |
|
c. `|z – u| = |z – v|\ text(is the graph of the perpendicular bisector of the)`
`text(line joining)\ u and v.`
| d.i. |
|
♦♦ Mean mark (d)(ii) 25%.
d.ii. `text(Arg)(z – u) = pi/4 =>\ text(gradient) = 1, ytext(-intercept at)\ (0, 1)`
`:. f: (−2, ∞) -> RR, \ f(x) = x + 1`
e. `|z_c – u| = |z_c – v| = |z_c – (−5i)|`
♦ Mean mark (e) 40%.
| `z_c – u` | `= (a + 2) + (b + 1)i` |
| `z_c – v` | `= (a + 4) + (b + 3)i` |
| `z_c +5i` | `= a + (b + 5)i` |
`a^2 + (b + 5)^2 = (a + 2)^2 + (b + 1)^2\ …\ (1)`
`a^2 + (b + 5)^2 = (a + 4)^2 + (b + 3)^2\ …\ (2)`
`a = −5/3, b = −10/3\ \ text{(by CAS)}`
`:.z_c = −5/3 – 10/3 i`
| `:.r` | `= |z_c – (−5i)|` |
| `= sqrt((−5/3)^2 + (−10/3 + 5)^2)` | |
| `= (5sqrt2)/3` |
Vectors, SPEC2 2020 VCAA 1
A particle moves in the `x\ – y` plane such that its position in terms of `x` and `y` metres at `t` seconds is given by the parametric equations
`x = 2sin(2t)`
`y = 3cos(t)`
where `t >= 0`
- Find the distance, in metres, of the particle from the origin when `t = pi/6`. (2 marks)
- i. Express `(dy)/(dx)` in terms of `t` and, hence, find the equation of the tangent to the path of the particle at `t = pi` seconds. (3 marks)
- ii. Find the velocity, `underset ~ v`, in `text(ms)^(−1)`, of the particle when `t = pi`. (2 marks)
- iii. Find the magnitude of the acceleration, in `text(ms)^(−2)`, when `t = pi`. (2 marks)
- Find the time, in seconds, when the particle first passes through the origin. (1 mark)
- Express the distance, `d` metres, travelled by the particle from `t = 0` to `t = pi/6` as a definite integral and find this distance correct to three decimal places. (2 marks)
Number, NAPX-p116764v04
Pringle has 55 twenty-cent coins in his money pouch.
How much money does Pringle have?
|
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$9.50 |
|
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$11.00 |
|
|
$20.50 |
|
|
$55.00 |
Number, NAPX-p116764v03
Sheena has 26 twenty-cent coins in her piggy bank.
How much money does Sheena have?
|
|
$26.20 |
|
|
$5.20 |
|
|
$5.00 |
|
|
$4.40 |
Measurement, NAPX-p116903v03
Wilde compared the weight of four different solid figures by using a balancing scale.
Which of the four objects is the heaviest?
 |
 |
 |
 |
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Show Answers Only
Show Worked Solution
`text{By inspection:}`
`text(Triangle → heavier than the hexagon.)`
`text(Triangle → same weight as the oval.)`
`text(Star → heavier than the oval.)`
`:.\ text(Star is the heaviest.)`
Measurement, NAPX-p116903v02
Banjo compared the weight of four different solid figures by using a balancing scale.
Which of the four objects is the lightest?
 |
 |
 |
 |
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|
Show Answers Only
Show Worked Solution
`text{By inspection:}`
`text(Sphere → lighter than the cube.)`
`text(Sphere → same weight as the cylinder.)`
`text(Cylinder → heavier than the pentagonal prism.)`
`:.\ text(Pentagonal prism is the lightest.)`
Measurement, NAPX-p116893v03
Mince decided to paint some triangles red in the four figures below.
All triangles are the same size.
Which of these figures has the smallest area that is painted red.
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Show Answers Only
Measurement, NAPX-p116893v02
Jane painted some hexagons in the four figures pictured below.
All hexagons are the same size.
Which of these figures has the largest area that is painted green.
 |
 |
 |
 |
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Show Answers Only
Number, NAPX-p116838v04
In a bakery Michelle bought one slice of cake, one donut and a croissant.
She gave the cashier $10.00.
How much change should Michelle receive?
| $5.10 | $5.60 | $5.80 | $6.00 |
|
|
|
|
|
Number, NAPX-p116838v03
Alexander went shopping and bought the following items.
He gave the cashier $50.
How much change should Alexander receive?
| $17.00 | $18.20 | $31.80 | $33.00 |
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Measurement, NAPX p124557v03
Timothy started with 53 millilitres of oil in a beaker.
He saw that there was some unused oil in a test tube and returned it to the beaker.
How much of the chemical solution was poured int0 the test tube?
|
|
13 millilitres |
|
|
23 millilitres |
|
|
27 millilitres |
|
|
37 millilitres |
Measurement, NAPX p124557v02
A chemist started with 685 millilitres of a solution.
He then poured some of the solution into a test tube.
How much of the chemical solution was poured into the test tube?
|
|
90 millilitres |
|
|
135 millilitres |
|
|
145 millilitres |
|
|
185 millilitres |
Statistics, NAPX-p116802v04
In a neighborhood 10 villagers were asked if how many pets they own.
The results were: 3, 2, 1, 1, 1, 4, 2, 4, 5, 2
Select the dot plot that displays the data recorded
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 |
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 |
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 |
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 |
Show Answers Only
Show Worked Solution
`text{A dot represents the number of persons that owns N pets}`
`text{From the data above:}`
`text{Owns one pet = 3}`
`text{Owns two pets = 3}`
`text{Owns three pets = 1}`
`text{Owns four pets = 2}`
`text{Owns five pets = 1}`
`therefore \ text{the correct dot plot is:}`
Statistics, NAPX-p116802v03
10 people were asked how often they went to the doctor in the last 12 months.
Their responses were: 2, 3, 3, 4, 1, 2, 5, 1, 1, 2
Choose the dot plot which correctly displays the data.
|
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 |
|
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|
 |
Show Answers Only
Show Worked Solution
`text{From the data above:}`
`text{1 visit = 3 people}`
`text{2 visits = 3 people}`
`text{3 visits = 2 people}`
`text{4 visits = 1 person}`
`text{5 visits = 1 person}`
Geometry, NAPX-p116732v03
A bridge is drawn below.
The angle `y°` is marked from the foot of the bridge to the diagonal support.
The value of angle `y°` is
|
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Less than 90° |
|
|
More than 180° |
|
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Equal to 90° |
|
|
More than 90° but less than 180° |
Show Worked Solution
`text{The angle from the foot to the diagonal support is less than} \ 90^@`
Geometry, NAPX-p116732v02
A door was opened and not closed.
The angle `x°`, measured from the opening to the door is
|
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Exactly 90° |
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More than 90° |
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Less than 90° |
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More than 180° |
Show Worked Solution
`text{The door is opened more than} \ 90^@`
Statistics, NAPX-p110558v02
A charity event was held for three weeks. On the first week $5000 was raised, on the second week $3500 was raised and on the last week $2000 was raised.
In the tables below, O = $500
Which table correctly shows the amount of donations raised in the 3 weeks?
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Statistics, NAPX-p110558v01
In a certain school, the number of Year 7 students is 120, Year 8 students is 80, and Year 9 students is 100.
In the tables below, V = 20 students
Which table correctly shows the number of students per year level?
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Geometry, NAPX-p116721v03
Sarah drew a straight line on a shape.
The line divided the shape into two rectangles.
Which of these could have been Sarah’s shape?
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Show Worked Solution
`text{Drawing any horizontal straight line on this shape divides it}`
`text{into two rectangles.}`
Geometry, NAPX-p116721v02
Troy drew a straight line through a shape.
The line divided the shape into two equal triangles.
Which of these could not have been Troy’s shape?
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Show Worked Solution
`text{Drawing a diagonal line will produce two quadrilaterals.}`
Algebra, NAPX-p116672v03
Rudy uses the number sentence 24 – 6 = 18
Which of the following problems can he solve with this number sentence?
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Rudy shared 24 slices of cake equally between 6 of his friends. How many slices does each of his friends get? |
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Rudy has 24 slices of cake and gave 6 slices to his friends. How many slices does Rudy have left? |
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Rudy took 6 slices of cake and shared them between 24 of his friends. How many slices does each friend receive? |
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Rudy has 24 slices of cake and gave 18 of them to his friends. How many slices does Rudy have left? |
Algebra, NAPX-p116672v02
Shawn uses the number sentence 20 × 6 = 120
Which of the following problems can he solve with this number sentence?
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Shawn buys 20 toys and gave 6 of them to his nephew. How many toys does Shaun's nephew have now? |
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Shawn buys 20 toys and received another 6 toys from friends. How many toys does Shaun have now? |
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Shawn buys 20 toys and divides them up between his 6 nephews. How many toys does each nephew get? |
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Shawn has 20 nephews and gives 6 toys to each one. Altogether, how many toys does Shaun give to his nephews? |
Measurement, NAPX-p167325v01
Sam painted grids in the larger square areas pictured below.
All of the grids are the same size.
Which of the following squares has the largest area painted?
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Mechanics, EXT2 M1 2017 SPEC2 17 MC
The acceleration, `a\ text(ms)^(-2)`, of a particle moving in a straight line is given by `a = v^2 + 1`, where `v` is the velocity of the particle at any time `t`. The initial velocity of the particle when at origin O is `2\ text(ms)^(-1)`.
The displacement of the particle from O when its velocity is `3\ text(ms)^(-1)` is
- `log_e(2)`
- `1/2 log_e(10/3)`
- `1/2 log_e(2)`
- `1/2 log_e(5/2)`
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