The length of a netball court is measured to be 30.50 metres, correct to the nearest centimetre.
What is the lower limit for the length of the netball court?
- 30.45 m
- 30.49 m
- 30.495 m
- 30.499 m
Aussie Maths & Science Teachers: Save your time with SmarterEd
The length of a netball court is measured to be 30.50 metres, correct to the nearest centimetre.
What is the lower limit for the length of the netball court?
A pentagon is created using matches.
By adding more matches, a row of two pentagons is formed.
Continuing to add matches, a row of three pentagons can be formed.
Continuing this pattern, what is the maximum number of complete pentagons that can be formed if 100 matches in total are available?
A.
B.
C.
D.
The faces on a twenty-sided die are labelled $0.05, $0.10, $0.15, … , $1.00.
The die is rolled once.
What is the probability that the amount showing on the upper face is more than 50 cents but less than 80 cents?
A.
B.
C.
D.
Bryan is estimating the amount of water he needs to fill up his swimming pool.
Which of these units of measurement would be the most helpful?
cubic metres | kilograms | millilitres | centimetres | litres |
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Cameron grew 146 lettuces in his vegetable garden.
A goat got into his garden and ate some lettuces, so there was only 112 lettuces left.
How many lettuces did the goat eat?
Ms Richards asked her class a question and recorded the results in the table below.
Which question could Ms Richards have asked?
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What type of farm animals do you own? |
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How many farm animals do you have? |
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What month was your farm animal born? |
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How old are your farm animals? |
Patrick gets $7.35 in pocket money each week.
He does extra jobs one week and earns $4.75 more.
How much money did Patrick receive in total in the week?
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Emily has 85 cents in 5-cent pieces.
How many 5-cent pieces does she have?
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Bryan is estimating the amount of water he needs to fill up his swimming pool.
Which of these units of measurement would be the most helpful?
cubic metres | kilograms | millilitres | centimetres | litres |
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Solve
Solve the equation
The expression
is equal to
Kim lives in Perth (32°S, 115°E). He wants to watch an ice hockey game being played in Toronto (44°N, 80°W) starting at 10.00 pm on Wednesday.
What is the time in Perth when the game starts?
A. 9.00 am on Wednesday
B. 7.40 pm on Wednesday
C. 9.00 pm on Wednesday
D. 12.20 am on Thursday
E. 11.00 am on Thursday
Osaka is at 34°N, 135°E, and Denver is at 40°N, 105°W.
What time and day is it in Osaka then? (1 mark)
What was the time and day in Denver when John received the text? (1 mark)
a. | |
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b.
c.
Pontianak has a longitude of 109°E, and Jarvis Island has a longitude of 160°W.
Both places lie on the Equator
a. | ||
b. | |
The function
The rule for the function is
The simultaneous linear equations
have a unique solution only for
Let
For all
The transformation
maps the curve with equation
The simultaneous linear equations
where
If
A.
B.
C.
D.
E.
The function
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a.
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b. | ![]() |
c. |
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The rule for
Show that the inverse function is given by
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The function
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The rule for function
The graph has two points of inflection.
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Solve the equation
Solve the equation
Let
Part of the graph of
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a.
b.
A company produces motors for refrigerators. There are two assembly lines, Line A and Line B. 5% of the motors assembled on Line A are faulty and 8% of the motors assembled on Line B are faulty. In one hour, 40 motors are produced from Line A and 50 motors are produced from Line B. At the end of an hour, one motor is selected at random from all the motors that have been produced during that hour.
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Let
Calculate the average rate of change of
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Let
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ii. State the domain and range of
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a.i. | ||
a.ii.
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a.iv.
b.i.
b.ii.
Let
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b. | ||
The Bouncy Ball Company (BBC) makes tennis balls whose diameters are normally distributed with mean 67 mm and standard deviation 1 mm. The tennis balls are packed and sold in cylindrical tins that each hold four balls. A tennis ball fits into such a tin if the diameter of the ball is less than 68.5 mm.
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BBC management would like each ball produced to have diameter between 65.6 and 68.4 mm.
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BBC management wants engineers to change the manufacturing process so that 99% of all balls produced have diameter between 65.6 and 68.4 mm. The mean is to stay at 67 mm but the standard deviation is to be changed.
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a.
b.
c.i.
c.ii.
d.
A train is travelling at a constant speed of
The train will travel along a section of track
Section
Section
Section
From
All measurements are in kilometres.
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The driver sees a large rock on the track at a point
From its initial speed of
where
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a.i.
a.ii.
a.iii.
a.i.
ii.
b.i.
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ii.
iii.
c.
d.
e.
The tangent at the point (1, 5) on the graph of the curve
The tangent at the point (3, 8) on the curve
A.
B.
C.
D.
E.
The simultaneous linear equations
where
Deep in the South American jungle, Tasmania Jones has been working to help the Quetzacotl tribe to get drinking water from the very salty water of the Parabolic River. The river follows the curve with equation
Tasmania has his camp site at
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The desalination plant is actually built at
If the desalination plant stops working, Tasmania needs to get to the plant in the minimum time.
Tasmania runs in a straight line from his camp to a point
Tasmania runs from his camp to the river at 2 km per hour. The time that he takes to swim to the desalination plant is proportional to the difference between the
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The value of
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a.
b.i.
b.ii. | ||
c.
d.i.
d.ii.
e.
f.
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a.i.
a.ii.
b.i.
b.ii.
c.i.
c.ii.
d.i. | ||
d.ii.
In a chocolate factory the material for making each chocolate is sent to one of two machines, machine A or machine B.
The time,
The time,
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All of the chocolates produced by machine A and machine B are stored in a large bin. There is an equal number of chocolates from each machine in the bin.
It is found that if a chocolate, produced by either machine, takes longer than 3 seconds to produce then it can easily be identified by its darker colour.
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a.i.
a.ii.
b.
c.
d.
Two ships, the Elsa and the Violet, have collided. Fuel immediately starts leaking from the Elsa into the sea.
The captain of the Elsa estimates that at the time of the collision his ship has 6075 litres of fuel on board and he also forecasts that it will leak into the sea at a rate of
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*Parts (b) - (d) are no longer in the syllabus.
a.
*Parts (b) – (d) are no longer in the syllabus.
Damon runs a swim school.
The value of his pool pump is depreciated over time using flat rate depreciation.
Damon purchased the pool pump for $28 000 and its value in dollars after
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The reducing balance depreciation method can also be used by Damon.
Using this method, the value of the pump is depreciated by 15% each year.
A recursion relation that models its value in dollars after
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a. | ||
b.
c.
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The point
Find the exact values of
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Let
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Find the values of
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Let
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A school has a class set of 22 new laptops kept in a recharging trolley. Provided each laptop is correctly plugged into the trolley after use, its battery recharges.
On a particular day, a class of 22 students uses the laptops. All laptop batteries are fully charged at the start of the lesson. Each student uses and returns exactly one laptop. The probability that a student does not correctly plug their laptop into the trolley at the end of the lesson is 10%. The correctness of any student’s plugging-in is independent of any other student’s correctness.
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The time for which a laptop will work without recharging (the battery life) is normally distributed, with a mean of three hours and 10 minutes and standard deviation of six minutes. Suppose that the laptops remain out of the recharging trolley for three hours.
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A supplier of laptops decides to take a sample of 100 new laptops from a number of different schools. For samples of size 100 from the population of laptops with a mean battery life of three hours and 10 minutes and standard deviation of six minutes,
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It is known that when laptops have been used regularly in a school for six months, their battery life is still normally distributed but the mean battery life drops to three hours. It is also known that only 12% of such laptops work for more than three hours and 10 minutes.
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The laptop supplier collects a sample of 100 laptops that have been used for six months from a number of different schools and tests their battery life. The laptop supplier wishes to estimate the proportion of such laptops with a battery life of less than three hours.
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The laptop supplier finds that, in a particular sample of 100 laptops, six of them have a battery life of less than three hours.
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Consider the function
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The diagram below shows part of the graph of
The tangent cuts the
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i. Find the coordinates of
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Let
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Find the value of
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a.
b.
c.
d.
e.
f.
A soccer player is practising her goal kicking. She has a probability of
The probability that the number of goals she scores is less than 7 is closest to
A.
B.
C.
D.
E.
The simultaneous linear equations
The function
Which one of the following is a possible rule for the function?
Given that