Measurement, STD2 M7 SM-Bank 7
The scale on a given map is
If the actual distance between two points is 3.4 kilometres, how far apart on the map would be the two points be, in centimetres? (2 marks)
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Measurement, STD2 M2 SM-Bank 2
Bert is in Moscow, which is three hours behind of Coordinated Universal Time (UTC).
Karen is in Sydney, which is eleven hours ahead of UTC.
- Bert is going to ring Karen at 9 pm on Tuesday, Moscow time. What day and time will it be in Sydney when he rings? (1 mark)
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- Karen is going to fly from Sydney to Moscow. Her flight will leave on Wednesday at 8 am, Sydney time, and will take 15 hours. What day and time will it be in Moscow when she arrives? (2 marks)
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Measurement, STD2 M7 SM-Bank 6
In a raffle, the total prize money is shared among the first two tickets drawn in the ratio 6 : 4.
The prize for the second ticket drawn is $360.
What is the total prize money? (2 marks)
Measurement, STD2 M7 SM-Bank 4
Blood pressure is measured using two numbers: systolic pressure and diastolic pressure. If the measurement shows 120 systolic and 80 diastolic, it is written as 120/80.
The bars on the graph show the normal range of blood pressure for people of various ages.
- What is the normal range of blood pressure for a 53-year-old? (2 marks)
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- Ralph, aged 53, had a blood pressure reading of 173 over 120. A doctor prescribed Ralph a medication to reduce his blood pressure to be within the normal range. To check that the medication was being effective, the doctor measured Ralph's blood pressure for 10 weeks and recorded the following results.
With reference to the data provided, comment on the effectiveness of the medication during the 10-week period in returning Ralph’s blood pressure to the normal range. (3 marks)
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Measurement, STD2 M1 SM-Bank 26 MC
During a flood, 12.5 hectares of land was covered by water to a depth of 30 cm.
How many kilolitres of water covered the land?
(1 hectare = 10 000 m² and 1 m³ = 1000 L)
- 3.75 kL
- 37.5 kL
- 37 500 kL
- 37 500 000 kL
Measurement, STD2 M6 SM-Bank 2 MC
Which of the following expresses S25°E as a true bearing?
Algebra, SPEC2 2018 VCAA 2 MC
Consider the function
The domain of
A.
B.
C.
D.
E.
Algebra, STD2 A4 EQ-Bank 8
Two friends, Sequoia and Raven, sold organic chapsticks at the the local market.
Sequoia sold her chapsticks for $4 and Raven sold hers for $3 each. In the first hour, their total combined sales were $20.
If Sequoia sold
In the first hour, the friends sold a total of 6 chapsticks between them.
Find the number of chapsticks each of the friends sold during this time by forming a second equation and solving the simultaneous equations graphically. (5 marks)
Algebra, STD2 A4 SM-Bank 7
Algebra, STD2 A4 SM-Bank 6
A student was asked to solve the following simultaneous equations.
After graphing the equations, the student found the point of intersection to be
Is the student correct? Support your answer with calculations. (2 marks)
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Probability, STD2 S2 SM-Bank 1
A game consists of two tokens being drawn at random from a barrel containing 20 tokens. There are 17 red tokens and 3 black tokens. The player keeps the two tokens drawn.
Financial Maths, STD2 F4 SM-Bank 1
An investment fund purchases 4500 shares of Bank ABC for a total cost of $274 500 (ignore any transaction costs).
The investment fund is paid a divided of $3.66 per share in the first year.
- What was the purchase price of 1 share? (1 mark)
- Calculate the divided yield. (1 mark)
Functions, 2ADV F2 SM-Bank 1
- Draw the graph
. (1 mark)
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- Explain how the above graph can be transformed to produce the graph
and sketch the graph, clearly identifying all intercepts. (3 marks)
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Calculus, 2ADV C1 SM-Bank 3
The displacement
- Calculate the velocity when
. (1 mark)
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- When is the particle stationary? (2 marks)
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Calculus, 2ADV C1 SM-Bank 2
- Find the equations of the tangents to the curve
at the points where the curve cuts the -axis. (2 marks)
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- Where do the tangents intersect? (2 marks)
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Trigonometry, 2ADV T2 SM-Bank 33
Given
find the exact value of
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Trigonometry, 2ADV T2 SM-Bank 32
Express
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Trigonometry, 2ADV T2 SM-Bank 31
Given
-
(2 marks)
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-
(1 mark)
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Functions, 2ADV F1 EQ-Bank 27
The stopping distance of a car on a certain road, once the brakes are applied, is directly proportional to the square of the speed of the car when the brakes are first applied.
A car travelling at 70 km/h takes 58.8 metres to stop.
How far does it take to stop if it is travelling at 105 km/h? (3 marks)
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Functions, 2ADV F1 EQ-Bank 26
Fuifui finds that for Giant moray eels, the mass of an eel is directly proportional to the cube of its length.
An eel of this species has a length of 25 cm and a mass of 4350 grams.
What is the expected length of a Giant moray eel with a mass of 6.2 kg? Give your answer to one decimal place. (3 marks)
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Functions, 2ADV F1 SM-Bank 25
Damon owns a swim school and purchased a new pool pump for $3250.
He writes down the value of the pool pump by 8% of the original price each year.
- Construct a function to represent the value of the pool pump after
years. (1 mark)
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- Draw the graph of the function and state its domain and range. (2 marks)
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Functions, 2ADV F1 SM-Bank 23
Find the values of
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Functions, 2ADV F1 EQ-Bank 22
Worker A picks a bucket of blueberries in
- Write an algebraic expression for the fraction of a bucket of blueberries that could be picked in one hour if A and B worked together. (2 marks)
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- What does the reciprocal of this fraction represent? (1 mark)
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Functions, 2ADV F1 EQ-Bank 21
Simplify
Calculus, 2ADV C1 SM-Bank 11
A particle is moving along the
Find the acceleration of the particle when
Express your answer as an exact value in its simplest form. (3 marks)
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Trigonometry, EXT1 T2 EQ-Bank 7
Find the exact value of
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Trigonometry, EXT1 T2 EQ-Bank 5
If
determine the exact value of
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Trigonometry, EXT1 T2 SM-Bank 2
Find the exact value of
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Functions, EXT1 F1 SM-Bank 3
A circle has centre
- Describe, with inequalities, the region that consists of the interior of the circle and more than 2 units above the
-axis. (2 marks)
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- Sketch the region. (1 mark)
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Combinatorics, EXT1 A1 EQ-Bank 3
Find the coefficient of
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Combinatorics, EXT1 A1 SM-Bank 1
Evaluate the value of
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Trigonometry, 2ADV T1 EQ-Bank 2
Determine all possible dimensions for triangle
Give all dimensions correct to one decimal place. (3 marks)
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Calculus, EXT1 C3 SM-Bank 1
The region enclosed by the semicircle
The two pieces are rotated about the
Show that
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Calculus, SPEC2 2017 VCAA 7 MC
With a suitable substitution
Complex Numbers, SPEC2 2017 VCAA 4 MC
The solutions to
Functions, EXT1 F1 2010 HSC 3b*
Let
- The graph has two points of inflection.
Find the
coordinates of these points. (3 marks)
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- Explain why the domain of
must be restricted if is to have an inverse function. (1 mark)
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- Find a formula for
if the domain of is restricted to . (2 marks)
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- State the domain of
. (1 mark)
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- Sketch the curve
. (1 mark)
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Functions, EXT1 F1 2004 HSC 5b*
The diagram below shows a sketch of the graph of
- On the same set of axes, sketch the graph of the inverse function,
. (1 mark) - State the domain of
. (1 mark)
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- Find an expression for
in terms of . (2 marks)
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- The graphs of
and meet at exactly one point .
Let
be theα -coordinate of . Explain why is a root of the equationα . (1 mark)
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Functions, 2ADV F1 SM-Bank 15 MC
If the equation
A.
B.
C.
D.
Functions, 2ADV F1 SM-Bank 13 MC
Which one of the following functions satisfies the functional equation
A.
B.
C.
D.
Functions, 2ADV F1 SM-Bank 12 MC
If
A.
B.
C.
D.
Functions, 2ADV F1 SM-Bank 8 MC
Let
Which one of the following is not true?
A.
B.
C.
D.
Functions, 2ADV F1 SM-Bank 7
Let
- Find
, where . (1 mark)
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- State the domain and range of
. (2 marks)
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- Show that
. (2 marks)--- 4 WORK AREA LINES (style=lined) ---
Functions, 2ADV F1 SM-Bank 3
Let
- State the range of
. (1 mark)
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- Let
, where and . - Find the largest possible value of
such that the range of is a subset of the domain of . (2 marks)
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Calculus, 2ADV C4 2007* HSC 10a
An object is moving on the
- The object is initially at the origin. During which time(s) is the displacement of the object decreasing? (1 mark)
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- If the object travels 7 units in the first 4 seconds, estimate the time at which the object returns to the origin. Justify your answer. (2 marks)
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- Sketch the displacement,
, as a function of time. (2 marks)
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Statistics, NAPX-K2-04 SA
Probability, 2ADV S1 2017 MET1 8
For events
- Find
in terms of . (1 mark)
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- Find
in terms of . (2 marks)
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- Given that
, state the largest possible interval for . (2 marks)
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Probability, 2ADV S1 2014 MET1 9
Sally aims to walk her dog, Mack, most mornings. If the weather is pleasant, the probability that she will walk Mack is
Assume that pleasant weather on any morning is independent of pleasant weather on any other morning.
- In a particular week, the weather was pleasant on Monday morning and unpleasant on Tuesday morning.
Find the probability that Sally walked Mack on at least one of these two mornings. (2 marks)
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- In the month of April, the probability of pleasant weather in the morning was
.- Find the probability that on a particular morning in April, Sally walked Mack. (2 marks)
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- Using your answer from part b.i., or otherwise, find the probability that on a particular morning in April, the weather was pleasant, given that Sally walked Mack that morning. (2 marks)
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- Find the probability that on a particular morning in April, Sally walked Mack. (2 marks)
Probability, 2ADV S1 2011 MET1 8
Two events,
If
(2 marks)
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and are mutually exclusive. (1 mark)
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Probability, 2ADV S1 2007 MET1 11
There is a daily flight from Paradise Island to Melbourne. The probability of the flight departing on time, given that there is fine weather on the island, is 0.8, and the probability of the flight departing on time, given that the weather on the island is not fine, is 0.6.
In March the probability of a day being fine is 0.4.
Find the probability that on a particular day in March
- the flight from Paradise Island departs on time (2 marks)
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- the weather is fine on Paradise Island, given that the flight departs on time. (2 marks)
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Probability, 2ADV S1 2015 MET1 8
For events
- Calculate
. (1 mark)
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- Calculate
, where denotes the complement of . (1 mark)
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- If events
and are independent, calculate . (1 mark)
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Probability, 2ADV S1 2009 MET1 5
Four identical balls are numbered 1, 2, 3 and 4 and put into a box. A ball is randomly drawn from the box, and not returned to the box. A second ball is then randomly drawn from the box.
- What is the probability that the first ball drawn is numbered 4 and the second ball drawn is numbered 1? (1 mark)
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- What is the probability that the sum of the numbers on the two balls is 5? (1 mark)
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- Given that the sum of the numbers on the two balls is 5, what is the probability that the second ball drawn is numbered 1? (2 marks)
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Probability, 2ADV S1 2013 MET2 10 MC
For events
If
Probability, 2ADV S1 2012 MET2 13 MC
Probability, 2ADV S1 2013 MET1 7
The probability distribution of a discrete random variable,
- Show that
. (3 marks)
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- Let
.
- Calculate
. Answer in exact form. (2 marks)
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- Find
. (1 mark)
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- Calculate
Probability, 2ADV S1 2012 MET1 4
On any given day, the number
- Find the mean of
. (2 marks)
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- What is the probability that Daniel receives only one telephone call on each of three consecutive days? (1 mark)
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- Daniel receives telephone calls on both Monday and Tuesday.
What is the probability that Daniel receives a total of four calls over these two days? (3 marks)
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Probability, 2ADV S1 2010 MET1 8
The discrete random variable
Find the value of
Probability, 2ADV S1 2009 MET1 7
The random variable
Find
-
(2 marks)
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-
the variance of (3 marks)--- 8 WORK AREA LINES (style=lined) ---
Probability, 2ADV S1 2008 MET1 7
Jane drives to work each morning and passes through three intersections with traffic lights. The number
- What is the mode of
? (1 mark)
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- Jane drives to work on two consecutive days. What is the probability that the number of traffic lights that are red is the same on both days? (2 marks)
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Probability, 2ADV S1 2009 MET2 10 MC
The discrete random variable
The median of
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