CORE*, FUR1 2008 VCAA 4 MC
In 2008, there are 800 bats living in a park.
After 2008, the number of bats living in the park is expected to increase by 15% per year.
Let
A difference equation that can be used to determine the number of bats living in the park
A. |
|
B. |
|
C. |
|
D. |
|
E. |
Complex Numbers, SPEC1 2011 VCAA 4
Consider
Find the principal argument of
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CORE*, FUR1 2013 VCAA 8 MC
The initial rate of pay for a job is $10 per hour.
A worker’s skill increases the longer she works on this job. As a result, the hourly rate of pay increases each month.
The hourly rate of pay in the
The maximum hourly rate of pay that the worker can earn in this job is closest to
A. $3.00
B. $12.00
C. $12.50
D. $18.75
E. $75.00
PATTERNS, FUR1 2013 VCAA 7 MC
The following are either three consecutive terms of an arithmetic sequence or three consecutive terms of a geometric sequence.
Which one of these sequences could not include 2 as a term?
A.
B.
C.
D.
E.
Calculus, MET2 2013 VCAA 14 MC
Probability, MET2 2013 VCAA 10 MC
For events
If
Calculus, SPEC1 2015 VCAA 6
The acceleration
Given that
Algebra, MET2 2015 VCAA 20 MC
If
Calculus, MET2 2015 VCAA 19 MC
If
A.
B.
C.
D.
E.
Graphs, MET2 2015 VCAA 17 MC
A graph with rule
The set of all possible values of
A.
B.
C.
D.
E.
Calculus, MET2 2015 VCAA 15 MC
If
A.
B.
C.
D.
E.
Probability, MET2 2015 VCAA 13 MC
The function
The value of
Probability, MET2 2015 VCAA 12 MC
A box contains five red balls and three blue balls. John selects three balls from the box, without replacing them.
The probability that at least one of the balls that John selected is red is
Probability, MET2 2015 VCAA 10 MC
The binomial random variable,
A.
B.
C.
D.
E.
Calculus, MET2 2015 VCAA 8 MC
Graphs, MET2 2015 VCAA 7 MC
The range of the function
Graphs, MET2 2015 VCAA 5 MC
Calculus, MET2 2014 VCAA 19 MC
Algebra, MET2 2014 VCAA 18 MC
The graph of
Graphs, MET2 2014 VCAA 12 MC
The transformation
maps the line with equation
Probability, MET2 2014 VCAA 11 MC
A bag contains five red marbles and four blue marbles. Two marbles are drawn from the bag, without replacement, and the results are recorded.
The probability that the marbles are different colours is
Algebra, MET2 2014 VCAA 10 MC
Which one of the following functions satisfies the functional equation
Calculus, MET2 2014 VCAA 8 MC
If
A.
B.
C.
D.
E.
Algebra, MET2 2014 VCAA 6 MC
The function
Probability, MET2 2014 VCAA 5 MC
The random variable
If
Calculus, MET2 2014 VCAA 4 MC
Let
At
- local minimum.
- local maximum
- gradient of 5
- gradient of – 5
- stationary point of inflection.
Calculus, MET2 2014 VCAA 3 MC
The area of the region enclosed by the graph of
A.
B.
C.
D.
E.
Mechanics, EXT2* M1 2008 HSC 7
A projectile is fired from
The equations of motion of the projectile are
- Show that
AND . (2 marks)
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Let
- Show that
. (2 marks)
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- Show that
. (1 mark)
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Let
- Show that
and . (2 marks)
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Let the gradient of the parabola at
- Show that
. (3 marks)
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- Show that
. (2 marks)
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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
Calculus, EXT1 C1 2008 HSC 4a
A turkey is taken from the refrigerator. Its temperature is 5°C when it is placed in an oven preheated to 190°C.
Its temperature,
- Show that
satisfies both this equation and the initial condition. (2 marks)
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- The turkey is placed into the oven at 9 am. At 10 am the turkey reaches a temperature of 29°C. The turkey will be cooked when it reaches a temperature of 80°C.
At what time (to the nearest minute) will it be cooked? (3 marks)
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Calculus, 2ADV C3 2004 HSC 10b
The diagram shows a triangular piece of land
The owner of the land wants to build a straight fence to divide the land into two pieces of equal area. Let
Let
- Show that
. (1 mark)
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- Use the cosine rule in triangle
to show that
(2 marks)
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- Show that the value of
in the equation in part (ii) is a minimum when
. (4 marks)
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- Show that the minimum length of the fence is
metres, where .
(You may assume that the value of
given in part (iii) is feasible.) (2 marks)
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Calculus, 2ADV C3 2004 HSC 9c
Consider the function
- Show that the graph of
has a stationary point at . (2 marks)
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- By considering the gradient on either side of
, or otherwise, show that the stationary point is a maximum. (1 mark)
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- Use the fact that the maximum value of
occurs at to deduce that for all . (2 marks)
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Calculus, 2ADV C4 2004 HSC 8b
The diagram shows the graph of the parabola
- Write down the equation of the directrix of the parabola
. (1 mark) - Find the equation of the tangent to the parabola at the point
. (2 marks) - Show that
is the point . (1 mark) - Given that the equation of the line
is , find the area bounded by the line and the parabola. (2 marks)
- Hence, or otherwise, find the shaded area bounded by the parabola, the tangent at
and the line . (3 marks)
Trigonometry, 2ADV T2 2004 HSC 8a
- Show that
. (1 mark)
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- Hence solve
for . (2 marks)
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Financial Maths, 2ADV M1 2004 HSC 7c
Betty decides to set up a trust fund for her grandson, Luis. She invests $80 at the beginning of each month. The money is invested at 6% per annum, compounded monthly.
The trust fund matures at the end of the month of her final investment, 25 years after her first investment. This means that Betty makes 300 monthly investments.
- After 25 years, what will be the value of the first $80 invested? (2 marks)
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- By writing a geometric series for the value of all Betty’s investments, calculate the final value of Luis’ trust fund. (3 marks)
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Calculus, EXT1* C1 2004 HSC 7b
At the beginning of 1991 Australia’s population was 17 million. At the beginning of 2004 the population was 20 million.
Assume that the population
- Show that
satisfies . (1 mark)
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- What is the value of
? (1 mark)
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- Find the value of
. (2 marks)
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- Predict the year during which Australia’s population will reach 30 million. (2 marks)
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Financial Maths, 2ADV M1 2004 HSC 7a
Evaluate
Probability, 2ADV S1 2004 HSC 6c
In a game, a turn involves rolling two dice, each with faces marked 0, 1, 2, 3, 4 and 5. The score for each turn is calculated by multiplying the two numbers uppermost on the dice.
- What is the probability of scoring zero on the first turn? (2 marks)
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- What is the probability of scoring
or more on the first turn? (1 mark)
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- What is the probability that the sum of the scores in the first two turns is less than 45? (2 marks)
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Plane Geometry, 2UA 2004 HSC 6b
L&E, 2ADV E1 2004 HSC 6a
Solve the following equation for
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Calculus, 2ADV C3 2004 HSC 5b
A particle moves along a straight line so that its displacement,
- What is the initial displacement of the particle? (1 mark)
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- Sketch the graph of
as a function of for . (2 marks)
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- Hence, or otherwise, find when AND where the particle first comes to rest after
. (2 marks)
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- Find a time when the particle reaches its greatest magnitude of velocity. What is this velocity? (2 marks)
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Financial Maths, 2ADV M1 2004 HSC 5a
Clare is learning to drive. Her first lesson is 30 minutes long. Her second lesson is 35 minutes long. Each subsequent lesson is 5 minutes longer than the lesson before.
- How long will Clare’s twenty-first lesson be? (1 mark)
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- How many hours of lessons will Clare have completed after her twenty-first lesson? (2 marks)
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- During which lesson will Clare have completed a total of 50 hours of driving lessons? (2 marks)
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Calculus, EXT1* C3 2004 HSC 4c
Calculus, MET2 2012 VCAA 1
A solid block in the shape of a rectangular prism has a base of width
The block has a total surface area of 6480 sq cm.
- Show that if the height of the block is
cm, (2 marks)
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- The volume,
cm³, of the block is given by - Given that
and , find the possible values of . (2 marks)
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- Find
, expressing your answer in the form , where and are real numbers. (3 marks)
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- Find the exact values of
and if the block is to have maximum volume. (2 marks)
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Calculus, MET2 2012 VCAA 21 MC
The volume,
A.
B.
C.
D.
E.
Calculus, MET2 2012 VCAA 14 MC
Probability, MET2 2012 VCAA 13 MC
Statistics, MET2 2012 VCAA 11 MC
The weights of bags of flour are normally distributed with mean 252 g and standard deviation 12 g. The manufacturer says that 40% of bags weigh more than
The maximum possible value of
Calculus, MET2 2012 VCAA 10 MC
The average value of the function
The value of
Calculus, MET2 2012 VCAA 9 MC
The normal to the graph of
The value of
A.
B.
C.
D.
E.
CORE*, FUR2 2014 VCAA 1
The adult membership fee for a cricket club is $150.
Junior members are offered a discount of $30 off the adult membership fee.
- Write down the discount for junior members as a percentage of the adult membership fee. (1 mark)
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Adult members of the cricket club pay $15 per match in addition to the membership fee of $150.
- If an adult member played 12 matches, what is the total this member would pay to the cricket club? (1 mark)
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If a member does not pay the membership fee by the due date, the club will charge simple interest at the rate of 5% per month until the fee is paid.
Michael paid the $150 membership fee exactly two months after the due date.
- Calculate, in dollars, the interest that Michael will be charged. (1 mark)
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The cricket club received a statement of the transactions in its savings account for the month of January 2014.
The statement is shown below.
-
- Calculate the amount of the withdrawal on 17 January 2014. (1 mark)
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-
Interest for this account is calculated on the minimum balance for the month and added to the account on the last day of the month.
-
What is the annual rate of interest for this account? Write your answer, correct to one decimal place. (1 mark)
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- Calculate the amount of the withdrawal on 17 January 2014. (1 mark)
Calculus, MET2 2012 VCAA 7 MC
The temperature,
The average temperature inside the building between 2 am and 2 pm is
Graphs, MET2 2012 VCAA 3 MC
The range of the function
A.
B.
C.
D.
E.
Graphs, MET2 2012 VCAA 5 MC
Let the rule for a function
- maximal domain
and range - maximal domain
and range - maximal domain
and range - maximal domain
and range - maximal domain
and range
Algebra, STD2 A1 SM-Bank 9
The volume of a sphere is given by
If the volume of a sphere is
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Algebra, MET2 2013 VCAA 13 MC
If the equation
Probability, MET2 2013 VCAA 9 MC
Harry is a soccer player who practises penalty kicks many times each day.
Each time Harry takes a penalty kick, the probability that he scores a goal is 0.7, independent of any other penalty kick.
One day Harry took 20 penalty kicks.
Given that he scored at least 12 goals, the probability that Harry scored exactly 15 goals is closest to
A.
B.
C.
D.
E.
Calculus, MET2 2013 VCAA 6 MC
For the function
A.
B.
C.
D.
E.
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