The size of the angle
A.
B.
C.
D.
E.
Show Worked Solution
GEOMETRY, FUR1 2015 VCAA 7 MC
A 50 cent coin has 12 sides of equal length.
Two 50 cent coins are balanced next to each other on a table so that they meet along one edge, as shown below.
The angle,
A.
B.
C.
D.
E.
Show Worked Solution
GEOMETRY, FUR1 2015 VCAA 6 MC
A cylindrical block of wood has a diameter of 12 cm and a height of 8 cm.
A hemisphere is removed from the top of the cylinder, 1 cm from the edge, as shown below.
The volume of the block of wood, in cubic centimetres, after the hemisphere has been removed is closest to
A.
B.
C.
D.
E.
GEOMETRY, FUR1 2015 VCAA 5 MC
A company logo is in the shape of a regular hexagon with side length 2 cm, as shown below.
The hexagon is divided into six equilateral triangles. Every second triangle is shaded.
The shaded area of the logo, in square centimetres, is closest to
A.
B.
C.
D.
E.
GEOMETRY, FUR1 2015 VCAA 4 MC
Town A is due west of town B.
Town C is due south of town B.
The bearing of town A from town C is
A. between
B. between
C. exactly
D. between
E. between
Show Worked Solution
GEOMETRY, FUR1 2015 VCAA 2 MC
A one-on-one basketball court is a composite shape made up of a rectangle and a semicircle, as shown below.
A boundary line is painted around the perimeter of the shape.
The total length of the boundary line, in metres, is closest to
A.
B.
C.
D.
E.
CORE*, FUR1 2015 VCAA 7 MC
The following graph shows the depreciating value of a van.
The graph could represent the van being depreciated using
- flat rate depreciation with an initial value of $35 000 and a depreciation rate of $25 per year.
- flat rate depreciation with an initial value of $35 000 and a depreciation rate of 25 cents per year.
- reducing balance depreciation with an initial value of $35 000 and a depreciation rate of 2.5% per annum.
- unit cost depreciation with an initial value of $35 000 and a depreciation rate of 25 cents per kilometre travelled.
- unit cost depreciation with an initial value of $35 000 and a depreciation rate of $25 per kilometre travelled.
CORE*, FUR1 2015 VCAA 5 MC
The purchase price of a car is $20 000.
A deposit of $5000 is paid.
The balance will be repaid with 60 monthly repayments of $400.
The total amount of interest charged is
A. $1000
B. $4000
C. $9000
D. $19 000
E. $24 000
CORE*, FUR1 2015 VCAA 4 MC
Mary invests $1200 for two years.
Interest is calculated at the rate of 3.35% per annum, compounding monthly.
The amount of interest she earns in two years is closest to
A.
B.
C.
D.
E.
CORE*, FUR1 2015 VCAA 2 MC
An investment property was purchased for $600 000.
Over a 10-year period, its value increased to $850 000.
The increase in value, as a percentage of the purchase price, is closest to
A.
B.
C.
D.
E.
CORE*, FUR1 2015 VCAA 6 MC
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
Calculus, SPEC2 2014 VCAA 13 MC
Using the substitution
A.
B.
C.
D.
E.
Calculus, SPEC2 2014 VCAA 12 MC
If
CORE*, FUR1 2008 VCAA 8 MC
A loan of $300 000 is taken out to finance a new business venture.
The loan is to be repaid fully over twenty years with quarterly payments of $6727.80.
Interest is calculated quarterly on the reducing balance.
The annual interest rate for this loan is closest to
A. 4.1%
B. 6.5%
C. 7.3%
D. 19.5%
E. 26.7%
CORE*, FUR1 2009 VCAA 7 MC
A loan of $17 500 is to be paid back over four years at an interest rate of 6.25% per annum on a reducing monthly balance.
The monthly repayment, correct to the nearest cent, will be
A. $364.58
B. $413.00
C. $802.08
D. $1156.77
E. $5079.29
CORE*, FUR1 2010 VCAA 7 MC
A loan of $300 000 is to be repaid over a period of 20 years. Interest is charged at the rate of 7.25% per annum compounding quarterly.
The quarterly repayment to the nearest cent is
A. $2371.13
B. $5511.46
C. $7113.39
D. $7132.42
E. $7156.45
CORE*, FUR1 2010 VCAA 5 MC
A file server costs $30 000.
The file server depreciates by 20% of its value each year.
After three years its value is
A.
B.
C.
D.
E.
CORE*, FUR1 2012 VCAA 5 MC
A second-hand car is purchased for $9000.
A deposit of $2500 is paid.
Interest is calculated at the rate of 14.95% per annum on the reducing monthly balance.
The balance and interest will be repaid over two years with equal monthly payments.
The monthly payment is closest to
A. $315
B. $415
C. $436
D. $575
E. $587
CORE, FUR1 2010 VCAA 13 MC
A garden supplies outlet sells water tanks. The monthly seasonal indices for the revenue from the sale of water tanks are given below.
The seasonal index for September is missing.
The revenue from the sale of water tanks in September 2009 was $104 500.
The deseasonalised revenue for September 2009 is closest to
A.
B.
C.
D.
E.
CORE, FUR1 2010 VCAA 10 MC
For a set of bivariate data that involves the variables
The equation of the least squares regression line is closest to
A.
B.
C.
D.
E.
PATTERNS, FUR1 2015 VCAA 4 MC
The amount added to a new savings account each month follows a geometric sequence.
In the first month, $64 was added to the account.
In the second month, $80 was added to the account.
In the third month, $100 was added to the account.
Assuming this sequence continues, the total amount that will have been added to this savings account after five months is closest to
A.
B.
C.
D.
E.
CORE*, FUR1 2015 VCAA 3 MC
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
| A. |
|
| B. |
|
| C. |
|
| D. |
|
| E. |
CORE, FUR1 2015 VCAA 12 MC
The time series plot below charts the number of calls per year to a computer help centre over a 10-year period.
Using five-median smoothing, the smoothed number of calls in year 6 was closest to
A.
B.
C.
D.
E.
CORE, FUR1 2015 VCAA 10 MC
For a set of bivariate data that involves the variables
Given the information above, the least squares regression line predicting
A.
B.
C.
D.
E.
CORE, FUR1 2015 VCAA 9 MC
CORE, FUR1 2015 VCAA 6-7 MC
The following information relates to Parts 1 and 2.
In New Zealand, rivers flow into either the Pacific Ocean (the Pacific rivers) or the Tasman Sea (the Tasman rivers).
The boxplots below can be used to compare the distribution of the lengths of the Pacific rivers and the Tasman rivers.
Part 1
The five-number summary for the lengths of the Tasman rivers is closest to
Part 2
Which one of the following statements is not true?
- The lengths of two of the Tasman rivers are outliers.
- The median length of the Pacific rivers is greater than the length of more than 75% of the Tasman rivers.
- The Pacific rivers are more variable in length than the Tasman rivers.
- More than half of the Pacific rivers are less than 100 km in length.
- More than half of the Tasman rivers are greater than 60 km in length.
CORE, FUR1 2015 VCAA 4-5 MC
The foot lengths of a sample of 2400 women were approximately normally distributed with a mean of 23.8 cm and a standard deviation of 1.2 cm.
Part 1
The expected number of these women with foot lengths less than 21.4 cm is closest to
A.
B.
C.
D.
E.
Part 2
The standardised foot length of one of these women is
Her actual foot length, in centimetres, is closest to
A.
B.
C.
D.
E.
CORE, FUR1 2015 VCAA 3 MC
The dot plot below displays the difference between female and male life expectancy, in years, for a sample of 20 countries.
The mean (
| A. |
|
| B. |
|
| C. |
|
| D. |
|
| E. |
CORE, FUR1 2015 VCAA 1 MC
The stem plot below displays the average number of decayed teeth in 12-year-old children from
Based on this stem plot, the distribution of the average number of decayed teeth for these countries is best described as
- negatively skewed with a median of 15 decayed teeth and a range of 45
- positively skewed with a median of 15 decayed teeth and a range of 45
- approximately symmetric with a median of 1.5 decayed teeth and a range of 4.5
- negatively skewed with a median of 1.5 decayed teeth and a range of 4.5
- positively skewed with a median of 1.5 decayed teeth and a range of 4.5
CORE*, FUR1 2006 VCAA 7 MC
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
| A. |
|
| B. |
|
| C. |
|
| D. |
|
| E. |
CORE*, FUR1 2006 VCAA 5 MC
A difference equation is defined by
The sequence
A.
B.
C.
D.
E.
CORE, FUR1 2006 VCAA 11-13 MC
The following information relates to Parts 1, 2 and 3.
The table shows the seasonal indices for the monthly unemployment numbers for workers in a regional town.
Part 1
The seasonal index for October is missing from the table.
The value of the missing seasonal index for October is
A.
B.
C.
D.
E.
Part 2
The actual number of unemployed in the regional town in September is 330.
The deseasonalised number of unemployed in September is closest to
A.
B.
C.
D.
E.
Part 3
A trend line that can be used to forecast the deseasonalised number of unemployed workers in the regional town for the first nine months of the year is given by
deseasonalised number of unemployed = 373.3 – 3.38 × month number
where month 1 is January, month 2 is February, and so on.
The actual number of unemployed for June is predicted to be closest to
A.
B.
C.
D.
E.
CORE, FUR1 2006 VCAA 10 MC
The table below displays the total monthly rainfall (in mm) in a reservoir catchment area over a one-year period.
Using three mean moving average smoothing, the smoothed value for the total rainfall in April is closest to
A.
B.
C.
D.
E.
CORE, FUR1 2006 VCAA 8 MC
The waist measurement (cm) and weight (kg) of 12 men are displayed in the table below.
Using this data, the equation of the least squares regression line that enables weight to be predicted from waist measurement is
When this equation is used to predict the weight of the man with a waist measurement of 80 cm, the residual value is closest to
A.
B.
C.
D.
E.
CORE, FUR1 2006 VCAA 7 MC
For a set of bivariate data, involving the variables
The equation of the least squares regression line
A.
B.
C.
D.
E.
CORE, FUR1 2006 VCAA 5-6 MC
The distribution of test marks obtained by a large group of students is displayed in the percentage frequency histogram below.
Part 1
The pass mark on the test was 30 marks.
The percentage of students who passed the test is
A.
B.
C.
D.
E.
Part 2
The median mark lies between
A.
B.
C.
D.
E.
CORE, FUR1 2006 VCAA 4 MC
The head circumference (in cm) of a population of infant boys is normally distributed with a mean of 49.5 cm and a standard deviation of 1.5 cm.
Four hundred of these boys are selected at random and each boy’s head circumference is measured.
The number of these boys with a head circumference of less than 48.0 cm is closest to
A.
B.
C.
D.
E.
CORE, FUR1 2006 VCAA 1-3 MC
The back-to-back ordered stemplot below shows the distribution of maximum temperatures (in °Celsius) of two towns, Beachside and Flattown, over 21 days in January.
Part 1
The variables
temperature (°Celsius), and
town (Beachside or Flattown), are
A. both categorical variables.
B. both numerical variables.
C. categorical and numerical variables respectively.
D. numerical and categorical variables respectively.
E. neither categorical nor numerical variables.
Part 2
For Beachside, the range of maximum temperatures is
A.
B.
C.
D.
E.
Part 3
The distribution of maximum temperatures for Flattown is best described as
A. negatively skewed.
B. positively skewed.
C. positively skewed with outliers.
D. approximately symmetric.
E. approximately symmetric with outliers.
CORE*, FUR1 2007 VCAA 8 MC
The first four terms of a sequence are
A difference equation that generates this sequence is
| A. |
||
| B. |
||
| C. |
||
| D. |
||
| E. |
PATTERNS, FUR1 2007 VCAA 7 MC
CORE*, FUR1 2007 VCAA 4-5 MC
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.
CORE, FUR1 2007 VCAA 11-13 MC
The following information relates to Parts 1, 2 and 3.
The time series plot below shows the revenue from sales (in dollars) each month made by a Queensland souvenir shop over a three-year period.
Part 1
This time series plot indicates that, over the three-year period, revenue from sales each month showed
A. no overall trend.
B. no correlation.
C. positive skew.
D. an increasing trend only.
E. an increasing trend with seasonal variation.
Part 2
A three median trend line is fitted to this data.
Its slope (in dollars per month) is closest to
A.
B.
C.
D.
E.
Part 3
The revenue from sales (in dollars) each month for the first year of the three-year period is shown below.
If this information is used to determine the seasonal index for each month, the seasonal index for September will be closest to
A.
B.
C.
D.
E.
CORE, FUR1 2007 VCAA 7-8 MC
The lengths and diameters (in mm) of a sample of jellyfish selected were recorded and displayed in the scatterplot below. The least squares regression line for this data is shown.
The equation of the least squares regression line is
length = 3.5 + 0.87 × diameter
The correlation coefficient is
Part 1
Written as a percentage, the coefficient of determination is closest to
Part 2
From the equation of the least squares regression line, it can be concluded that for these jellyfish, on average
- there is a 3.5 mm increase in diameter for each 1 mm increase in length.
- there is a 3.5 mm increase in length for each 1 mm increase in diameter.
- there is a 0.87 mm increase in diameter for each 1 mm increase in length.
- there is a 0.87 mm increase in length for each 1 mm increase in diameter.
- there is a 4.37 mm increase in diameter for each 1 mm increase in length.
CORE, FUR1 2007 VCAA 5-6 MC
Samples of jellyfish were selected from two different locations, A and B. The diameter (in mm) of each jellyfish was recorded and the resulting data is summarised in the boxplots shown below.
Part 1
The percentage of jellyfish taken from location A with a diameter greater than 14 mm is closest to
Part 2
From the boxplots, it can be concluded that the diameters of the jellyfish taken from location A are generally
- similar to the diameters of the jellyfish taken from location B.
- less than the diameters of the jellyfish taken from location B and less variable.
- less than the diameters of the jellyfish taken from location B and more variable.
- greater than the diameters of the jellyfish taken from location B and less variable.
- greater than the diameters of the jellyfish taken from location B and more variable.
CORE, FUR1 2007 VCAA 4 MC
The length of 3-month-old baby boys is approximately normally distributed with a mean of 61.1 cm and a standard deviation of 1.6 cm.
The percentage of 3-month-old baby boys with length greater than 59.5 cm is closest to
A.
B.
C.
D.
E.
Show Worked Solution
CORE, FUR1 2007 VCAA 3 MC
A student obtains a mark of 56 on a test for which the mean mark is 67 and the standard deviation is 10.2.
The student’s standardised mark (standard
A.
B.
C.
D.
E.
PATTERNS, FUR1 2008 VCAA 6 MC
Kai commenced a 12-day program of daily exercise. The time, in minutes, that he spent exercising on each of the first four days of the program is shown in the table below.
If this pattern continues, the total time (in minutes) that Kai will have spent exercising after 12 days is
A.
B.
C.
D.
E.
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
--- 10 WORK AREA LINES (style=lined) ---
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
Consider the graph of
If the total area of the shaded rectangles is 44, then the value of
A.
B.
C.
D.
E.
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.
Show Worked Solution
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
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