What is
Conics, EXT2 2016 HSC 7 MC
The hyperbola with equation
What is the value of
Show Worked Solution
♦♦ Mean mark 35%.
Algebra, 2UG 2016 HSC 18 MC
The value of
It is known that
What is the value of
Algebra, 2UG 2016 HSC 4 MC
A company manufactures phones. The company’s income equation and cost equation are drawn on the same graph.
Which region of the graph is the profit zone?
(A)
(B)
(C)
(D)
L&E, 2UA 2016 HSC 10 MC
Which expression is equivalent to
(A)
(B)
(C)
(D)
Probability, 2UA 2016 HSC 2 MC
In a raffle,
What is the probability that someone buying
(A)
(B)
(C)
(D)
NETWORKS, FUR1 2010 VCAA 3 MC
A graph that can be drawn from the adjacency matrix above is
NETWORKS, FUR1 2006 VCAA 1 MC
The number of vertices with an odd degree in the network above is
A.
B.
C.
D.
E.
NETWORKS, FUR1 2009 VCAA 5-6 MC
The network shows the activities that are needed to complete a particular project.
Part 1
The total number of activities that need to be completed before activity
A.
B.
C.
D.
E.
Part 2
The duration of every activity is initially 5 hours. For an extra cost, the completion times of both activity
If this is done, the completion time for the project will be
A. decreased by 2 hours.
B. decreased by 3 hours.
C. decreased by 4 hours.
D. decreased by 6 hours.
E. unchanged.
NETWORKS, FUR1 2011 VCAA 1 MC
In the network shown, the number of vertices of even degree is
A.
B.
C.
D.
E.
NETWORKS, FUR1 2012 VCAA 6 MC
In the digraph above, all vertices are reachable from every other vertex.
All vertices would still be reachable from every other vertex if we remove the edge in the direction from
A.
B.
C.
D.
E.
MATRICES, FUR1 2009 VCAA 3 MC
The number of people attending the morning, afternoon and evening sessions at a cinema is given in the table
below. The admission charges (in dollars) for each session are also shown in the table.
A column matrix that can be used to list the number of people attending each of the three sessions is
A.
B.
C.
D.
E.
MATRICES, FUR1 2010 VCAA 5 MC
A system of three simultaneous linear equations is written in matrix form as follows.
One of the three linear equations is
A.
B.
C.
D.
E.
MATRICES, FUR1 2012 VCAA 8 MC
There are 30 children in a Year 6 class. Each week every child participates in one of three activities: cycling (C), orienteering (O) or swimming (S).
The activities that the children select each week change according to the transition matrix below.
From the transition matrix it can be concluded that
A. in the first week of the program, ten children do cycling, ten children do orienteering and ten children do swimming.
B. at least 50% of the children do not change their activities from the first week to the second week.
C. in the long term, all of the children will choose the same activity.
D. orienteering is the most popular activity in the first week.
E. 50% of the children will do swimming each week.
MATRICES, FUR1 2012 VCAA 1 MC
MATRICES, FUR1 2014 VCAA 6 MC
The order of matrix
The element in row
The matrix
MATRICES, FUR1 2015 VCAA 9 MC
A fast-food stand at the football sells pies (
Each week, 300 customers regularly buy either a pie or chips, but not both, from this stand.
For the first five weeks, the customers’ choice of pie or chips is expected to change weekly according to the transition matrix
After the first five weeks, due to expected cold weather, the customers’ choice of pie or chips is expected to change weekly according to the transition matrix
In week 1, 150 customers bought a pie and 150 customers bought chips.
Let
The number of customers expected to buy a pie or chips in week 8 can be found by evaluating
A.
B.
C.
D.
E.
MATRICES, FUR1 2006 VCAA 9 MC
A large population of birds lives on a remote island. Every night each bird settles at either location A or location B.
It was found on the first night that the number of birds at each location was the same.
On each subsequent night, a percentage of birds changed the location at which they settled.
This movement of birds is described by the transition matrix
Assume this pattern of movement continues.
In the long term, the number of birds that settle at location A will
A. not change.
B. gradually decrease to zero.
C. eventually settle at around 20% of the island’s bird population.
D. eventually settle at around 80% of the island’s bird population.
E. gradually increase.
MATRICES, FUR1 2006 VCAA 8 MC
Australians go on holidays either within Australia or overseas.
Market research shows that
- 95% of those who had their last holiday in Australia said that their next holiday would be in Australia
- 20% of those who had their last holiday overseas said that their next holiday would also be overseas.
A transition matrix that could be used to describe this situation is
| A. | |
B. | |
| C. | |
D. | |
| E. | |
MATRICES, FUR1 2007 VCAA 8 MC
Kerry sat for a multiple-choice test consisting of six questions.
Each question had four alternative answers,
He selected
He then determined the answers to the remaining questions by following the transition matrix
The answers that he gave to the six test questions, starting with
MATRICES, FUR1 2007 VCAA 7 MC
Each year, a family always goes on its holiday to one of three places; Portland (
They never go to the same place two years in a row. For example, if they went to Portland one year, they would not go to Portland the next year; they would go to Quambatook or Rochester instead.
A transition matrix that can be used to model this situation is
MATRICES, FUR1 2007 VCAA 5 MC
An international mathematics competition is conducted in three sections – Junior, Intermediate and Senior.
There are money prizes for gold, silver and bronze levels of achievement in each of these sections.
Table 1 shows the number of students who were awarded prizes in each section.
Table 2 shows the value, in dollars, of each prize.
A matrix product that gives the total value of all the Silver prizes that were awarded is
MATRICES, FUR1 2007 VCAA 3 MC
If
| A. |
B. |
| C. |
D. |
| E. |
MATRICES, FUR1 2007 VCAA 2 MC
The number of tourists visiting three towns, Oldtown, Newtown and Twixtown, was recorded for three years.
The data is summarised in the table below.
The
| A. |
B. |
| C. |
D. |
| E. |
MATRICES, FUR1 2011 VCAA 7 MC
Each night, a large group of mountain goats sleep at one of two locations,
On the first night, equal numbers of goats are observed to be sleeping at each location.
From night to night, goats change their sleeping locations according to a transition matrix
It is expected that, in the long term, more goats will sleep at location
Assuming the total number of goats remains constant, a transition matrix
MATRICES, FUR1 2011 VCAA 2 MC
If
A.
B.
C.
D.
E.
MATRICES, FUR1 2011 VCAA 1 MC
The matrix below shows the airfares (in dollars) that are charged by Zeniff Airlines to fly between Adelaide (
The cost to fly from Melbourne to Sydney with Zeniff Airlines is
A.
B.
C.
D.
E.
MATRICES, FUR1 2014 VCAA 9 MC
Which one of the following statements is not true?
A.
B.
C.
D.
E.
MATRICES, FUR1 2014 VCAA 5 MC
Students from Year 7 and Year 8 in a school sold trees to raise funds for a school trip.
The number of large, medium and small trees that were sold by each year group is shown in the table below.
The large trees were sold for $32 each, the medium trees were sold for $26 each and the small trees were sold for $18 each.
A matrix product that can be used to calculate the amount, in dollars, raised by each year group by selling trees is
MATRICES, FUR1 2014 VCAA 1 MC
Probability, 2UG SM-Bank 01 MC
A circle has 5 equally spaced points on its circumference, as shown.
How many different triangles using 3 of these points as vertices can be drawn? (3 marks)
A.
B.
C.
D.
MATRICES, FUR1 2015 VCAA 5 MC
Wendy buys one type of flower each day.
She chooses from tulips (
The type of flower she buys on one day depends on the type of flower she bought the previous day, according to a transition matrix.
Today, Wendy bought tulips.
The transition matrix that, starting tomorrow, ensures Wendy buys flowers in alphabetical order (
MATRICES, FUR1 2015 VCAA 4 MC
The numbers of adult and child tickets purchased for five performances of a stage show are shown in the table below.
Which one of the following matrix calculations can be used to determine both the total number of adult tickets and the total number of child tickets purchased for all five performances?
A.
B.
C.
D.
E.
MATRICES, FUR1 2015 VCAA 2 MC
Four matrices are shown below.
Which one of the following matrix products is not defined?
MATRICES, FUR1 2015 VCAA 1 MC
Matrix
The element in row
The element
A. art books owned by Trevor.
B. art books owned by Ursula.
C. art books owned by Veronica.
D. cooking books owned by Ursula.
E. cooking books owned by Trevor.
Graphs, MET2 2015 VCAA 22 MC
The graphs of the functions with rules
Which one of the following best represents the graph of the function with rule
Algebra, MET2 2015 VCAA 18 MC
**Won't be asked in METHODS from 2016 onwards due to absolute value signs.
For which one of the following functions is the equation
A.
B.
C.
D.
E.
MATRICES, FUR1 2014 VCAA 3 MC
Regular customers at a hairdressing salon can choose to have their hair cut by Shirley, Jen or Narj.
The salon has 600 regular customers who get their hair cut each month.
In June, 200 customers chose Shirley (S) to cut their hair, 200 chose Jen (J) to cut their hair and 200 chose Narj (N) to cut their hair.
The regular customers’ choice of hairdresser is expected to change from month to month as shown in the transition matrix,
In the long term, the number of regular customers who are expected to choose Shirley is closest to
A.
B.
C.
D.
E.
MATRICES, FUR1 2014 VCAA 4 MC
Two hundred and fifty people buy bread each day from a corner store. They have a choice of two brands of bread: Megaslice (M) and Superloaf (S).
The customers’ choice of brand changes daily according to the transition diagram below.
On a given day, 100 of these people bought Megaslice bread while the remaining 150 people bought Superloaf bread.
The number of people who are expected to buy each brand of bread the next day is found by evaluating the matrix product
Probability, 2UG 2015 HSC 18 MC
A Student Representative Council (SRC) consists of five members. Three of the members are being selected to attend a conference.
In how many ways can the three members be selected?
(A)
(B)
(C)
(D)
Measurement, 2UG 2015 HSC 14 MC
Stockholm is located at
What is the time difference between Stockholm and Darwin? (Ignore time zones and daylight saving.)
(A)
(B)
(C)
(D)
Algebra, 2UG 2015 HSC 5 MC
Which of the following graphs best represents the equation
Trig Calculus, 2UA 2015 HSC 6 MC
What is the value of the derivative of
(A)
(B)
(C)
(D)
Functions, 2ADV F1 2015 HSC 1 MC
What is
Measurement, 2UG MM6 SM-Bank 02 MC
This is a sketch of a sector of a circle.
Find the value of
(A)
(B)
(C)
(D)
Measurement, 2UG MM6 SM-Bank 01 MC
Mapupu and Minoha are two towns on the equator.
The longitude of Mapupu is
How far apart are these two towns if the radius of Earth is approximately
(A)
(B)
(C)
(D)