The point of intersection of two lines is
One of these two lines could be
A.
B.
C.
D.
E.
GRAPHS, FUR1 2006 VCAA 5 MC
Which one of the following statements about the line with equation
A. the line passes through the origin
B. the line has a slope of 12
C. the line has the same slope as the line with the equation
D. the point
E. for this line, as
GRAPHS, FUR1 2006 VCAA 3-4 MC
A gas-powered camping lamp is lit and the gas is left on for six hours. During this time the lamp runs out of gas.
The graph shows how the mass,
Part 1
Assume that the loss in weight of the gas container is due only to the gas being burnt.
From the graph it can be seen that the lamp runs out of gas after
A.
B.
C.
D.
E.
Part 2
Which one of the following rules could be used to describe the graph above?
A.
B.
C.
D.
E.
GRAPHS, FUR1 2008 VCAA 8 MC
A region is defined by the following inequalities
A point that lies within this region is
A.
B.
C.
D.
E.
GRAPHS, FUR1 2008 VCAA 7 MC
The graph above shows the relationship between
The relationship between
A.
B.
C.
D.
E.
GRAPHS, FUR1 2008 VCAA 5 MC
A mixture contains two liquids,
Liquid
Let
Let
Which graph below shows all possible volumes of liquid
Statistics, STD2 S5 SM-Bank 3 MC
The time, in hours, that each student spent sleeping on a school night was recorded for
How many students would you expect to spend more than 8.1 hours sleeping on a school night?
You may assume for normally distributed data that:
-
of scores have -scores between and of scores have -scores between and of scores have -scores between and .
A.
B.
C.
D.
GEOMETRY, FUR1 2008 VCAA 5 MC
For the triangle shown, the value of
A.
B.
C.
D.
E.
Measurement, 2UG 2007 HSC 28c
A piece of plaster has a uniform cross-section, which has been shaded, and has dimensions as shown.
- Use two applications of Simpson’s rule to approximate the area of the cross-section. (3 marks)
- The total surface area of the piece of plaster is
. - Calculate the area of the curved surface as shown on the diagram. (2 marks)
Show Worked Solution
| (i) |  |
(ii)
Probability, 2UG 2007 HSC 28a
Two unbiased dice,
The numbers on the uppermost faces are noted. This table shows all the possible outcomes.
A game is played where the difference between the highest number showing and the lowest number showing on the uppermost faces is calculated.
- What is the probability that the difference between the numbers showing on the uppermost faces of the two dice is one? (1 mark)
- In the game, the following applies.
- What is the financial expectation of the game? (3 marks)
- If Jack pays
to play the game, does he expect a gain or a loss, and how much will it be? (1 mark)
GEOMETRY, FUR1 2007 VCAA 9 MC
The points
The bearing of
The bearing of
Three people perform different calculations to determine the length of
| Graeme | ||
| Shelley | ||
| Tran |
The correct length of
A. Graeme only.
B. Tran only.
C. Graeme and Shelley only.
D. Graeme and Tran only.
E. Graeme, Shelley and Tran.
GEOMETRY, FUR1 2007 VCAA 7 MC
GEOMETRY, FUR1 2008 VCAA 9 MC
Two hikers, Anton and Beth, walk in different directions from the same camp.
Beth walks for 12 km on a bearing of 135° to a picnic ground.
Anton walks for 6 km on a bearing of 045° to a lookout tower.
On what bearing (to the nearest degree) should Anton walk from the lookout tower to meet Beth at the picnic ground?
A.
B.
C.
D.
E.
Show Worked Solution
♦ Mean mark 38%.
| |
|
GEOMETRY, FUR1 2008 VCAA 6 MC
A tent with semicircular ends is in the shape of a prism. The diameter of the ends is 1.5 m. The tent is 2.5 m long.
The total surface area (in m2) of the tent, including the base, is closest to
A.
B.
C.
D.
E.
Algebra, MET1 SM-Bank 28
Consider the simultaneous linear equations below.
where
- What are the values of
where no solutions exist? (3 marks)
--- 10 WORK AREA LINES (style=lined) ---
- What values of
do the simultaneous equations have a unique solution? (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
Algebra, STD2 A2 2007 HSC 27b
A clubhouse uses four long-life light globes for five hours every night of the year. The purchase price of each light globe is $6.00 and they each cost
- Write an equation for the total cost (
) of purchasing and running these four light globes for one year in terms of . (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
- Find the value of
(correct to three decimal places) if the total cost of running these four light globes for one year is $250. (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
- If the use of the light globes increases to ten hours per night every night of the year, does the total cost double? Justify your answer with appropriate calculations. (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
- The manufacturer’s specifications state that the expected life of the light globes is normally distributed with a standard deviation of 170 hours.
What is the mean life, in hours, of these light globes if 97.5% will last up to 5000 hours? (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
Show Worked Solution
i.
ii.
iii.
iv.
Financial Maths, 2ADV M1 SM-Bank 13 MC
The first term of a geometric sequence is
The common ratio of this sequence,
Which one of the following graphs best shows the first
Financial Maths, 2ADV M1 SM-Bank 12
There are 10 checkpoints in a 4500 metre orienteering course. Checkpoint 1 is the start and checkpoint 10 is the finish.
The distance between successive checkpoints increases by 50 metres as each checkpoint is passed.
Calculate the distance, in metres, between checkpoint 2 and checkpoint 3. (3 marks)
--- 6 WORK AREA LINES (style=lined) ---
Financial Maths, 2ADV M1 SM-Bank 9 MC
The graph above shows consecutive terms of a sequence.
The sequence could be
- geometric with common ratio r, where r < 0
- geometric with common ratio r, where 0 < r < 1
- geometric with common ratio r, where r > 1
- arithmetic with common difference d, where d < 0
Algebra, STD2 A4 2007 HSC 27a
A rectangular playing surface is to be constructed so that the length is 6 metres more than the width.
- Give an example of a length and width that would be possible for this playing surface. (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
- Write an equation for the area (
) of the playing surface in terms of its length ( ). (1 mark)
--- 1 WORK AREA LINES (style=lined) ---
A graph comparing the area of the playing surface to its length is shown.
- Why are lengths of 0 metres to 6 metres impossible? (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
- What would be the dimensions of the playing surface if it had an area of 135 m²? (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
Company
constructs playing surfaces. 
- Draw a graph to represent the cost of using Company
to construct all playing surface sizes up to and including 200 m². Use the horizontal axis to represent the area and the vertical axis to represent the cost. (2 marks)
--- 8 WORK AREA LINES (style=lined) ---
- Company
charges a rate of $360 per square metre regardless of size. - Which company would charge less to construct a playing surface with an area of 135 m²
Justify your answer with suitable calculations. (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
Show Answers Only
Show Worked Solution
i.
ii.
iii.
iv.
| v. |  |
vi.
Financial Maths, STD2 F1 2007 HSC 26b
Myles is in his third year as an apprentice film editor.
- Myles purchased film-editing equipment for $5000.
After 3 years it has depreciated to $3635 using the straight-line method.
Calculate the rate of depreciation per year as a percentage. (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
- Myles earns $800 per week. Calculate his taxable income for this year if the only allowable deduction is the amount of depreciation of his film-editing equipment in the third year of use. (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
- Use this tax table to calculate Myles’s tax payable. (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
Measurement, STD2 M6 2007 HSC 26a
The diagram shows information about the locations of towns
- It takes Elina 2 hours and 48 minutes to walk directly from Town
to Town .
Calculate her walking speed correct to the nearest km/h. (1 mark)
--- 1 WORK AREA LINES (style=lined) ---
- Elina decides, instead, to walk to Town
from Town and then to Town .
Find the distance from Town
to Town . Give your answer to the nearest km. (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
- Calculate the bearing of Town
from Town . (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
Show Worked Solution
i.
| ii. |  |
| iii |  |
GEOMETRY, FUR1 2013 VCAA 9 MC
GEOMETRY, FUR1 2013 VCAA 8 MC
There are four telecommunications towers in a city. The towers are called Grey Tower, Black Tower, Silver Tower and White Tower.
Grey Tower is 10 km due west of Black Tower.
Silver Tower is 10 km from Grey Tower on a bearing of 300°.
White Tower is 10 km due north of Silver Tower.
Correct to the nearest degree, the bearing of Black Tower from White Tower is
A.
B.
C.
D.
E.
GEOMETRY, FUR1 2013 VCAA 4 MC
GEOMETRY, FUR1 2008 VCAA 2-3 MC
An orienteering course is triangular in shape and is marked by three points,
Part 1
In this course, the bearing of
The bearing of
A.
B.
C.
D.
E.
Part 2
In this course,
The area (in km²) enclosed by this course is closest to
A.
B.
C.
D.
E.
Show Worked Solution
♦ Mean mark (Part 1) 43%.
MARKER’S COMMENT: The low mean mark for this question flagged a fundamental lack of understanding in this area.
MARKER’S COMMENT: The low mean mark for this question flagged a fundamental lack of understanding in this area.
Statistics, STD2 S5 2007 HSC 25d
The results of two class tests are normally distributed. The means and standard deviations of the tests are displayed in the table.
- Stuart scored 63 in Test 1 and 62 in Test 2. He thinks that he has performed better in Test 1. Do you agree? Justify your answer using appropriate calculations. (2 marks)
--- 5 WORK AREA LINES (style=lined) ---
- If 150 students sat for Test 2, how many students would you expect to have scored less than 64? (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
Show Worked Solution
i.
ii.
Probability, STD2 S2 2007 HSC 25c
In a stack of 10 DVDs, there are 5 rated PG, 3 rated G and 2 rated M.
- A DVD is selected at random. What is the probability that it is rated M? (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
Grant chooses two DVDs at random from the stack. Copy or trace the tree diagram into your writing booklet.
- Complete the tree diagram by writing the correct probability on each branch. (2 marks)
--- 0 WORK AREA LINES (style=lined) ---
- Calculate the probability that Grant chooses two DVDs with the same rating. (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
Show Answers Only
Show Worked Solution
i.
| ii. |  |
iii.
Measurement, STD2 M6 2007 HSC 25b
The angle of depression from
Copy or trace this diagram into your writing booklet and calculate the angle of elevation from
--- 8 WORK AREA LINES (style=lined) ---
Show Worked Solution
Statistics, STD2 S1 2007 HSC 24d
Barry constructed a back-to-back stem-and-leaf plot to compare the ages of his students.
- Write a brief statement that compares the distribution of the ages of males and females from this set of data. (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
- What is the mode of this set of data? (1 mark)
--- 1 WORK AREA LINES (style=lined) ---
- Liam decided to use a grouped frequency distribution table to calculate the mean age of the students at Barry’s Ballroom Dancing Studio.
For the age group 30 - 39 years, what is the value of the product of the class centre and the frequency? (2 marks)
--- 3 WORK AREA LINES (style=lined) ---
- Liam correctly calculated the mean from the grouped frequency distribution table to be 39.5.
Caitlyn correctly used the original data in the back-to-back stem-and-leaf plot and calculated the mean to be 38.2.
What is the reason for the difference in the two answers? (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
Measurement, STD2 M7 2007 HSC 23c
A scientific study uses the ‘capture-recapture’ technique.
In the first stage of the study, 24 crocodiles were caught, tagged and released.
Later, in the second stage of the study, some crocodiles were captured from the same area. Eighteen of these were found to be tagged, which was 40% of the total captured during the second stage.
- How many crocodiles were captured in total during the second stage of the study? (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
- Calculate the estimate for the total population of crocodiles in this area. (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
GEOMETRY, FUR1 2012 VCAA 5 MC
The rectangle shown below is 54 cm high and 20 cm wide.
The rhombuses drawn inside the rectangle are all the same size and shape.
The size of the angle
A.
B.
C.
D.
E.
Show Worked Solution
GEOMETRY, FUR1 2009 VCAA 8 MC
A hose with a circular cross-section is 85 metres long.
The outside diameter of the hose is 29 millimetres. Its walls are 2 millimetres thick.
One litre of water occupies a volume of 1000 cm3.
When the hose is full with water, the volume it holds (in litres) is closest to
A.
B.
C.
D.
E.
CORE*, FUR1 2009 VCAA 8 MC
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
| A. |
|
| B. |
|
| C. |
|
| D. |
|
| E. |
CORE*, FUR1 2009 VCAA 6 MC
The
A difference equation that generates the same sequence is
| A. |
|
| B. |
|
| C. |
|
| D. |
|
| E. |
PATTERNS, FUR1 2009 VCAA 5 MC
On Monday morning, Jim told six friends a secret. On Tuesday morning, those six friends each told the secret to six other friends who did not know it. The secret continued to spread in this way on Wednesday, Thursday and Friday mornings.
The total number of people (not counting Jim) who will know the secret on Friday afternoon is
A.
B.
C.
D.
E.
PATTERNS, FUR1 2011 VCAA 9 MC
A toy train track consists of a number of pieces of track which join together.
The shortest piece of the track is 15 centimetres long and each piece of track after the shortest is 2 centimetres longer than the previous piece.
The total length of the complete track is 7.35 metres.
The length of the longest piece of track, in centimetres, is
A.
B.
C.
D.
E.
PATTERNS, FUR1 2011 VCAA 8 MC
The first three terms of an arithmetic sequence are
The sum of the first
A.
B.
C.
D.
E.
PATTERNS, FUR1 2011 VCAA 6 MC
For which one of the following geometric sequences is an infinite sum not able to be determined?
A.
B.
C.
D.
E.
CORE*, FUR1 2011 VCAA 5 MC
The difference equation
generates a sequence with
The value of
A. 0
B. 1
C. 2
D. 3
E. 4
GEOMETRY, FUR1 2012 VCAA 6 MC
A cylinder of radius
The volume of a cylinder with radius
A.
B.
C.
D.
E.
Statistics, STD2 S1 2007 HSC 21 MC
This set of data is arranged in order from smallest to largest.
The range is six less than twice the value of
Which one of the following is true?
- The median is 12 and the interquartile range is 7.
- The median is 12 and the interquartile range is 12.
- The median is 13 and the interquartile range is 7.
- The median is 13 and the interquartile range is 12.
Algebra, STD2 A1 2007 HSC 19 MC
Which of the following correctly expresses
Statistics, STD2 S1 2007 HSC 17 MC
Ms Wigginson decided to survey a sample of 10% of the students at her school.
The school enrolment is shown in the table.
She surveyed the same number of students in each year group.
How would the numbers of students surveyed in Year 10 and Year 11 have changed if Ms Wigginson had chosen to use a stratified sample based on year groups?
- Increased in both Year 10 and Year 11
- Decreased in both Year 10 and Year 11
- Increased in Year 10 and decreased in Year 11
- Decreased in Year 10 and increased in Year 11
Algebra, STD2 A4 2007 HSC 15 MC
If pressure (
GEOMETRY, FUR1 2014 VCAA 6-7 MC
A cross-country race is run on a triangular course. The points
The distance from
The distance from
The distance from
The bearing of
Part 1
The bearing of
A.
B.
C.
D.
E.
Part 2
The area within the triangular course
A.
B.
C.
D.
E.
CORE*, FUR1 2014 VCAA 9 MC
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.
PATTERNS, FUR1 2014 VCAA 8 MC
The first term of a geometric sequence is
The common ratio of this sequence,
Which one of the following graphs best shows the first 10 terms of this sequence?
CORE, FUR1 2014 VCAA 13 MC
The time series plot below shows the hours of sunshine per day at a particular location for 16 consecutive days.
The three median method is used to fit a trend line to the data.
The slope of this trend line will be closest to
A.
B.
C.
D.
E.
CORE, FUR1 2009 VCAA 13 MC
The time series plot below shows the growth in Internet use (%) in a country from 1989 to 1997 inclusive.
If a three-median line is fitted to the data it would show that, on average, the increase in Internet use per year was closest to
A.
B.
C.
D.
E.
CORE, FUR1 2009 VCAA 11 MC
The table below lists the average body weight (in kg) and average brain weight (in g) of nine animal species.
A least squares regression line is fitted to the data using body weight as the explanatory variable.
The equation of the least squares regression line is
This equation is then used to predict the brain weight (in g) of the baboon.
The residual value (in g) for this prediction will be closest to
A.
B.
C.
D.
E.
CORE, FUR1 2009 VCAA 4-6 MC
The percentage histogram below shows the distribution of the fertility rates (in average births per woman) for 173 countries in 1975.
Part 1
In 1975, the percentage of these 173 countries with fertility rates of 4.5 or greater was closest to
A.
B.
C.
D.
E.
Part 2
In 1975, for these 173 countries, fertility rates were most frequently
A. less than 2.5
B. between 1.5 and 2.5
C. between 2.5 and 4.5
D. between 6.5 and 7.5
E. greater than 7.5
Part 3
Which one of the boxplots below could best be used to represent the same fertility rate data as displayed in the percentage histogram?
CORE, FUR1 2008 VCAA 6-7 MC
The pulse rates of a large group of 18-year-old students are approximately normally distributed with a mean of 75 beats/minute and a standard deviation of 11 beats/minute.
Part 1
The percentage of 18-year-old students with pulse rates less than 75 beats/minute is closest to
A. 32%
B. 50%
C. 68%
D. 84%
E. 97.5%
Part 2
The percentage of 18-year-old students with pulse rates less than 53 beats/minute or greater than 86 beats/minute is closest to
A. 2.5%
B. 5%
C. 16%
D. 18.5%
E. 21%
Show Worked Solution
♦ Mean mark 44%.
MARKERS’ COMMENT: Two applications of the 68-95-99.7% rule are required. A good strategy is to first draw a normal curve and shade the required areas.
MARKERS’ COMMENT: Two applications of the 68-95-99.7% rule are required. A good strategy is to first draw a normal curve and shade the required areas.
| |
|
| |
CORE, FUR1 2008 VCAA 1-4 MC
The box plot below shows the distribution of the time, in seconds, that 79 customers spent moving along a particular aisle in a large supermarket.
Part 1
The longest time, in seconds, spent moving along this aisle is closest to
A.
B.
C.
D.
E.
Part 2
The shape of the distribution is best described as
A. symmetric.
B. negatively skewed.
C. negatively skewed with outliers.
D. positively skewed.
E. positively skewed with outliers.
Part 3
The number of customers who spent more than 90 seconds moving along this aisle is closest to
A.
B.
C.
D.
E.
Part 4
From the box plot, it can be concluded that the median time spent moving along the supermarket aisle is
A. less than the mean time.
B. equal to the mean time.
C. greater than the mean time
D. half of the interquartile range.
E. one quarter of the range.
CORE*, FUR1 2012 VCAA 9 MC
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.
PATTERNS, FUR1 2012 VCAA 8 MC
The graph above shows consecutive terms of a sequence.
The sequence could be
A. geometric with common ratio
B. geometric with common ratio
C. geometric with common ratio
D. arithmetic with common difference
E. arithmetic with common difference
PATTERNS, FUR1 2012 VCAA 7 MC
A dragster is travelling at a speed of 100 km/h.
It increases its speed by
- 50 km/h in the 1st second
- 30 km/h in the 2nd second
- 18 km/h in the 3rd second
and so on in this pattern.
Correct to the nearest whole number, the greatest speed, in km/h, that the dragster will reach is
A.
B.
C.
D.
E.
PATTERNS, FUR1 2012 VCAA 5 MC
On the first day of a fundraising program, three boys had their heads shaved.
On the second day, each of those three boys shaved the heads of three other boys.
On the third day, each of the boys who was shaved on the second day shaved the heads of three other boys.
The head-shaving continued in this pattern for seven days.
The total number of boys who had their heads shaved in this fundraising activity was
A.
B.
C.
D.
E.
GEOMETRY, FUR1 2010 VCAA 9 MC
A conical water filter has a diameter of 60 cm and a depth of 24 cm. It is filled to the top with water.
The water filter sits above an empty cylindrical container which has a diameter of 40 cm.
The water is allowed to flow from the water filter into the cylindrical container.
When the water filter is empty, the depth of water in the cylindrical container will be
A.
B.
C.
D.
E.
GEOMETRY, FUR1 2010 VCAA 8 MC
Dan takes his new aircraft on a test flight.
He starts from his local airport and flies 10 km on a bearing of 045 ° until he reaches his brother’s farm.
From here he flies 18 km on a bearing of 300 ° until he reaches his parents’ farm.
Finally he flies back directly from his parents’ farm to his local airport.
The total distance (in km) that he flies is closest to
A.
B.
C.
D.
E.
- « Previous Page
- 1
- …
- 59
- 60
- 61
- 62
- 63
- …
- 66
- Next Page »