Aussie Maths & Science Teachers: Save your time with SmarterEd
Paul has to replace 3000 m of fencing on his farm.
Let
The difference equation
can be used to calculate the length of fencing left to replace after
In this equation,
After one week, Paul still has 2540 m of fencing left to replace.
After three weeks, the length of fencing, in metres, left to replace will be closest to
A. 1310
B. 1380
C. 1620
D. 1690
E. 2100
Which one of the following expressions does not define a geometric sequence?
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Miki is competing as a runner in a half-marathon.
After 30 minutes, his progress in the race is modelled by the difference equation
where
Using this difference equation, the total distance, in metres, that Miki is expected to have run 32 minutes after the start of the race is closest to
A. 7650
B. 7725
C. 7800
D. 7900
E. 8050
A town has a population of 200 people when a company opens a large mine.
Due to the opening of the mine, the town’s population is expected to increase by 50% each year.
Let
The expected growth in the town’s population can be modelled by
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The second term of a Fibonacci-related sequence is 36 and the third term is 72.
The first term of this sequence is
Paula started a stamp collection. She decided to buy a number of new stamps every week.
The number of stamps bought in the
The total number of stamps in her collection after five weeks is
A.
B.
C.
D.
E.
The values of the first five terms of a sequence are plotted on the graph shown below.
The first order difference equation that could describe the sequence is
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A difference equation is defined by
The sequence
A.
B.
C.
D.
E.
The following information relates to Parts 1 and 2.
A farmer plans to breed sheep to sell.
In the first year she starts with 50 breeding sheep.
During the first year, the sheep numbers increase by 84%.
At the end of the first year, the farmer sells 40 sheep.
Part 1
How many sheep does she have at the start of the second year?
A. 2
B. 42
C. 52
D. 84
E. 92
Part 2
If
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The first four terms of a sequence are
A difference equation that generates this sequence is
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The following information relates to Parts 1 and 2.
The number of waterfowl living in a wetlands area has decreased by 4% each year since 2003.
At the start of 2003 the number of waterfowl was 680.
Part 1
If this percentage decrease continues at the same rate, the number of waterfowl in the wetlands area at the start of 2008 will be closest to
A. 532
B. 544
C. 554
D. 571
E. 578
Part 2
Let
The rule for a difference equation that can be used to model the number of waterfowl in the wetlands area over time is
A.
B.
C.
D.
E.
The difference equation
generates the sequence
The value of
A. – 1
B. 3
C. 4
D. 15
E. 16
A sequence is generated by a first-order linear difference equation.
The first four terms of this sequence are 1, 3, 7, 15.
The next term in the sequence is
A. 17
B. 19
C. 22
D. 23
E. 31
When placed in a pond, the length of a fish was 14.2 centimetres.
During its first month in the pond, the fish increased in length by 3.6 centimetres.
During its
The maximum length this fish can grow to (in cm) is closest to
A. 14.4
B. 16.9
C. 19.0
D. 28.6
E. 17.2
The sequence
A. fibonacci-related
B. arithmetic with
C. arithmetic with
D. geometric with
E. geometric with
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
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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
A patient takes 15 milligrams of a prescribed drug at the start of each day.
Over the next 24 hours, 85% of the drug in his body is used. The remaining 15% stays in his body.
Let
A difference equation for determining
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The difference equation
If
A. 4
B. 8
C. 22
D. 40
E. 42
The
A difference equation that generates the same sequence is
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Let
At the beginning of 2012, Sienna plans to throw out the oldest 10% of pairs of shoes that she owned in 2011.
During 2012 she plans to buy 15 new pairs of shoes to add to her collection.
Let
A rule that enables
A.
B.
C.
D.
E.
The difference equation
generates a sequence with
The value of
A. 0
B. 1
C. 2
D. 3
E. 4
The graph above shows the first five terms of a sequence.
Let
A difference equation that generates the terms of this sequence is
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Sam takes a tablet containing 200 mg of medicine once every 24 hours.
Every 24 hours, 40% of the medicine leaves her body. The remaining 60% of the medicine stays in her body.
Let
The difference equation that can be used to determine the number of milligrams of the medicine in Sam’s body immediately after she takes each tablet is shown below.
Which one of the following statements is not true?
A. The number of milligrams of the medicine in Sam’s body never exceeds 500.
B. Immediately after taking the third tablet, 392 mg of the medicine is in Sam’s body.
C. The number of milligrams of the medicine that leaves Sam’s body during any 24-hour period will always be less than 200.
D. The number of milligrams of the medicine that leaves Sam’s body during any 24-hour period is constant.
E. If Sam stopped taking the medicine after the fifth tablet, the amount of the medicine in her body would drop to below 200 mg after a further 48 hours.
The first term of a Fibonacci-related sequence is
The second term of the same Fibonacci-related sequence is
The difference in value between the fourth and fifth terms of this sequence is
A.
B.
C.
D.
E.
Consider the following sequence.
Which of the following difference equations could generate this sequence?
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On day 1, Vikki spends 90 minutes on a training program.
On each following day, she spends 10 minutes less on the training program than she did the day before.
Let
A difference equation that can be used to model this situation for
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Each trading day, a share trader buys and sells shares according to the rule
where
From this rule, it can be concluded that each day
The value of
A.
B.
C.
D.
E.
Three years after observations began, 12 300 birds were living in a wetland.
The number of birds living in the wetland changes from year to year according to the difference equation
where
The number of birds living in the wetland one year after observations began was closest to
A.
B.
C.
D.
E.
A poultry farmer aims to increase the weight of a turkey by 10% each month.
The turkey’s weight,
A.
B.
C.
D.
E.
1, 9, 10, 19, 29, . . .
The sixth term of the Fibonacci-related sequence shown above is
A. 30
B. 39
C. 40
D. 48
E. 49
The first six terms of a Fibonacci related sequence are shown below.
4, 7, 11, 18, 29, 47, ...
The next term in the sequence is
A. 58
B. 65
C. 76
D. 94
E. 123
A sequence is generated by the difference equation
The
A.
B.
C.
D.
E.