Evaluate
Financial Maths, 2ADV M1 2020 HSC 12
Calculate the sum of the arithmetic series
--- 6 WORK AREA LINES (style=lined) ---
Trigonometry, 2ADV T3 2020 HSC 6 MC
Which interval gives the range of the function
Algebra, STD2 A1 2020 HSC 3 MC
The distance between Bricktown and Koala Creek is 75 km. A person travels from Bricktown to Koala Creek at an average speed of 50 km/h.
How long does it take the person to complete the journey?
- 40 minutes
- 1 hour 25 minutes
- 1 hour 30 minutes
- 1 hour 50 minutes
Functions, 2ADV F2 2020 HSC 2 MC
Mechanics, EXT2 M1 EQ-Bank 4
A torpedo with a mass of 80 kilograms has a propeller system that delivers a force of
- Explain why
whereis a positive constant. (1 mark)
--- 4 WORK AREA LINES (style=lined) ---
- If the torpedo increases its velocity from
to , show that the distance it travels in this time, , is given by
(3 marks)
--- 6 WORK AREA LINES (style=lined) ---
Mechanics, EXT2 M1 EQ-Bank 1
A canon ball of mass 9 kilograms is dropped from the top of a castle at a height of
The canon ball experiences a resistance force due to air resistance equivalent to
- Show the equation of motion is given by
(1 mark)
--- 4 WORK AREA LINES (style=lined) ---
- Show, by integrating using partial fractions, that
(5 marks)
--- 12 WORK AREA LINES (style=lined) ---
- If the canon hits the ground after 4 seconds, calculate the height of the castle, to the nearest metre. (3 marks)
--- 8 WORK AREA LINES (style=lined) ---
Complex Numbers, EXT2 N1 SM-Bank 4
- Express
in the form , given (2 marks)
--- 7 WORK AREA LINES (style=lined) ---
- Hence, using the quadratic formula, solve
(1 mark)
--- 3 WORK AREA LINES (style=lined) ---
Complex Numbers, EXT2 N1 EQ-Bank 3
Find the values of
--- 6 WORK AREA LINES (style=lined) ---
Complex Numbers, EXT2 N1 EQ-Bank 2
Find the values of
Algebra, STD2 A2 SM-Bank 11 MC
Algebra, STD2 A1 SM-Bank 15
Fabio drove 300 km in
His average speed for the first 210 km was 70 km per hour.
How long did he take to travel the last 90 km? (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
Calculus, EXT1 C3 EQ-Bank 1
- Sketch the region bounded by the curve
and the lines and . (1 mark)
--- 8 WORK AREA LINES (style=lined) ---
- Calculate the area of this region. (3 marks)
--- 6 WORK AREA LINES (style=lined) ---
Functions, 2ADV F2 EQ-Bank 2 MC
Which diagram best shows the graph
A. | B. | ||
C. | D. |
Functions, 2ADV F2 EQ-Bank 16
- Describe each transformation and state the equation of the graph after each transformation. (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
- Sketch the graph. (1 mark)
--- 6 WORK AREA LINES (style=lined) ---
Calculus, EXT1 C1 EQ-Bank 1
A particle is moving along the
Find the acceleration of the particle when
--- 6 WORK AREA LINES (style=lined) ---
Statistics, 2ADV S3 EQ-Bank 2
Let
The random variable
The diagram shows the graph of
- Complete the table of values for the given function, correct to four decimal places. (1 mark)
- Use the trapezoidal rule and 5 function values in the table in part i. to estimate
(2 marks)
--- 5 WORK AREA LINES (style=lined) ---
- The weights of Rhodesian ridgebacks are normally distributed with a mean of 48 kilograms and a standard deviation of 6 kilograms.
Using the result from part ii., calculate the probability of a randomly selected Rhodesian ridgeback weighing less than 36 kilograms. (2 marks)
--- 5 WORK AREA LINES (style=lined) ---
Trigonometry, 2ADV T3 EQ-Bank 5
The function
Describe in words how the amplitude and period have changed in this transformation. (2 marks)
Statistics, 2ADV S2 EQ-Bank 3
The table below lists the average life span (in years) and average sleeping time (in hours/day) of 9 animal species.
- Using sleeping time as the independent variable, calculate the least squares regression line. (1 mark)
--- 1 WORK AREA LINES (style=lined) ---
- A wallaby species sleeps for 4.5 hours, on average, each day.
Use your equation from part i to predict its expected life span, to the nearest year. (1 mark)
--- 1 WORK AREA LINES (style=lined) ---
Statistics, 2ADV S2 EQ-Bank 2
The table below lists the average body weight (in kilograms) and average brain weight (in grams) of nine animal species.
A least squares regression line is fitted to the data using body weight as the independent variable.
- Calculate the equation of the least squares regression line. (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
- If dingos have an average body weight of 22.3 kilograms, calculate the predicted average brain weight of a dingo using your answer to part i. (1 mark)
--- 1 WORK AREA LINES (style=lined) ---
Statistics, 2ADV S2 EQ-Bank 1
The arm spans (in cm) and heights (in cm) for a group of 13 boys have been measured. The results are displayed in the table below.
The aim is to find a linear equation that allows arm span to be predicted from height.
- What will be the independent variable in the equation? (1 mark)
--- 1 WORK AREA LINES (style=lined) ---
- Assuming a linear association, determine the equation of the least squares regression line that enables arm span to be predicted from height. Write this equation in terms of the variables arm span and height. Give the coefficients correct to two decimal places. (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
- Using the equation that you have determined in part b., interpret the slope of the least squares regression line in terms of the variables height and arm span. (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
Calculus, 2ADV C1 EQ-Bank 2
When differentiating
Complete the solution. (2 marks)
Calculus, 2ADV C2 EQ-Bank 2
Differentiate with respect to
NETWORKS, FUR2-NHT 2019 VCAA 3
The zoo’s management requests quotes for parts of the new building works.
Four businesses each submit quotes for four different tasks.
Each business will be offered only one task.
The quoted cost, in $100 000, of providing the work is shown in Table 1 below.
The zoo’s management wants to complete the new building works at minimum cost.
The Hungarian algorithm is used to determine the allocation of tasks to businesses.
The first step of the Hungarian algorithm involves row reduction; that is, subtracting the smallest element in each row of Table 1 from each of the elements in that row.
The result of the first step is shown in Table 2 below.
The second step of the Hungarian algorithm involves column reduction; that is, subtracting the smallest element in each column of Table 2 from each of the elements in that column.
The results of the second step of the Hungarian algorithm are shown in Table 3 below. The values of Task 1 are given as
- Write down the values of
and . (1 mark)
--- 1 WORK AREA LINES (style=lined) ---
- The next step of the Hungarian algorithm involves covering all the zero elements with horizontal or vertical lines. The minimum number of lines required to cover the zeros is three.
Draw these three lines on Table 3 above. (1 mark)
--- 0 WORK AREA LINES (style=lined) ---
- An allocation for minimum cost is not yet possible.
When all steps of the Hungarian algorithm are complete, a bipartite graph can show the allocation for minimum cost.
Complete the bipartite graph below to show this allocation for minimum cost. (1 mark)
--- 4 WORK AREA LINES (style=lined) ---
- Business 4 has changed its quote for the construction of the pathways. The new cost is $1 000 000. The overall minimum cost of the building works is now reduced by reallocating the tasks.
How much is this reduction? (1 mark)
--- 6 WORK AREA LINES (style=lined) ---
GEOMETRY, FUR1-NHT 2019 VCAA 2 MC
Which one of the following locations is closest to the Greenwich meridian?
- 32° S, 40° E
- 32° S, 80° E
- 32° S, 60° W
- 32° S, 120° E
- 32° S, 160° W
GEOMETRY, FUR1-NHT 2019 VCAA 1 MC
Networks, STD2 N3 2019 FUR2-N 2
The construction of the new reptile exhibit is a project involving nine activities,
The directed network below shows these activities and their completion times in weeks.
- Which activities have more than one immediate predecessor? (1 mark)
--- 1 WORK AREA LINES (style=lined) ---
- Write down the critical path for this project. (1 mark)
--- 1 WORK AREA LINES (style=lined) ---
- What is the latest start time, in weeks, for activity
? (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
NETWORKS, FUR2-NHT 2019 VCAA 1
A zoo has an entrance, a cafe and nine animal exhibits: bears
The edges on the graph below represent the paths between the entrance, the cafe and the animal exhibits. The numbers on each edge represent the length, in metres, along that path. Visitors to the zoo can use only these paths to travel around the zoo.
- What is the shortest distance, in metres, between the entrance and the seal exhibit
? (1 mark)
--- 1 WORK AREA LINES (style=lined) ---
- Freddy is a visitor to the zoo. He wishes to visit the cafe and each animal exhibit just once, starting and ending at the entrance.
- i. What is the mathematical term used to describe this route? (1 mark)
--- 1 WORK AREA LINES (style=lined) ---
- ii. Draw one possible route that Freddy may take on the graph below. (1 mark)
--- 0 WORK AREA LINES (style=lined) ---
A reptile exhibit
A new path of length 20 m will be built between the reptile exhibit
A second new path, of length 35 m, will be built between the reptile exhibit
- Complete the graph below with the new reptile exhibit and the two new paths added. Label the new vertex
and write the distances on the new edges. (1 mark)
--- 0 WORK AREA LINES (style=lined) ---
- The new paths reduce the minimum distance that visitors have to walk between the giraffe exhibit
and the cafe. By how many metres will these new paths reduce the minimum distance between the giraffe exhibit
and the cafe? (1 mark)
--- 5 WORK AREA LINES (style=lined) ---
MATRICES, FUR2-NHT 2019 VCAA 1
A total of six residents from two towns will be competing at the International Games.
Matrix
- How many of these athletes are residents of Haldaw? (1 mark)
--- 1 WORK AREA LINES (style=lined) ---
Each of the six athletes will compete in one event: table tennis, running or basketball.
Matrices
Table tennis | Running | |
|
|
- Matrix
contains the number of male and female athletes from each town who will compete in basketball.
Complete matrix
below. (1 mark)
--- 0 WORK AREA LINES (style=lined) ---
Matrix
-
- For which event will the total cost of uniforms for the athletes be $1030? (1 mark)
--- 1 WORK AREA LINES (style=lined) ---
- Write a matrix calculation, that includes matrix
, to show that the total cost of uniforms for the event named in part c.i. is contained in the matrix answer of [1030]. (1 mark)
--- 3 WORK AREA LINES (style=lined) ---
- For which event will the total cost of uniforms for the athletes be $1030? (1 mark)
- Matrix
and matrix are two new matrices where and:
- matrix
is a matrix - element
total cost of uniforms for all female athletes from Gillen - element
total cost of uniforms for all female athletes from Haldaw - element
total cost of uniforms for all male athletes from Gillen - element
total cost of uniforms for all male athletes from Haldaw
- Complete matrix
with the missing values. (1 mark)
--- 0 WORK AREA LINES (style=lined) ---
Functions, EXT1 F1 2019 MET1-N 5
Let
- State the range of
. (1 mark)
--- 3 WORK AREA LINES (style=lined) ---
- Find the rule for
. (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
Functions, 2ADV F1 2019 MET1-N 2
Let
- Find
. (2 marks)
--- 6 WORK AREA LINES (style=lined) ---
- Express
in the form , where , and are non-zero integers. (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
Calculus, 2ADV C2 SM-Bank 8
Let
Find
Calculus, 2ADV C2 SM-Bank 7
Let
Find
Functions, MET1-NHT 2018 VCAA 5
Let
- State the range of
. (1 mark)
--- 4 WORK AREA LINES (style=lined) ---
- Find the rule for
. (2 marks)
--- 6 WORK AREA LINES (style=lined) ---
Functions, MET1-NHT 2018 VCAA 2
Let
- Find
. (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
Calculus, MET1-NHT 2018 VCAA 1a
Let
Find
--- 4 WORK AREA LINES (style=lined) ---
Vectors, EXT1 V1 EQ-Bank 7
The vectors
Find the values of
--- 6 WORK AREA LINES (style=lined) ---
Vectors, EXT1 V1 EQ-Bank 4
Let the vectors
- Calculate
(1 mark)--- 3 WORK AREA LINES (style=lined) ---
- Verify
(1 mark)
--- 3 WORK AREA LINES (style=lined) ---
CORE, FUR2-NHT 2019 VCAA 6
Marlon plays guitar in a band.
He paid $3264 for a new guitar.
The value of Marlon's guitar will be depreciated by a fixed amount for each concert that he plays.
After 25 concerts, the value of the guitar will have decreased by $200.
- What will be the value of Marlon's guitar after 25 concerts? (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
- Write a calculation that shows that the value of Marlon's guitar will depreciate by $8 per concert. (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
- The value of Marlon's guitar after
concerts, , can be determined using a rule.
Complete the rule below by writing the appropriate numbers in the boxes provided. (1 mark)
--- 1 WORK AREA LINES (style=lined) ---
– ×
- The value of the guitar continues to be depreciated by $8 per concert.
After how many concerts will the value of Marlon's guitar first fall below $2500? (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
CORE, FUR2-NHT 2019 VCAA 4
The scatterplot below plots the variable life span, in years, against the variable sleep time, in hours, for a sample of 19 types of mammals.
On the assumption that the association between sleep time and life span is linear, a least squares line is fitted to this data with sleep time as the explanatory variable.
The equation of this least squares line is
life span = 42.1 – 1.90 × sleep time
The coefficient of determination is 0.416
- Draw the graph of the least squares line on the scatterplot above. (1 mark)
--- 0 WORK AREA LINES (style=lined) ---
- Describe the linear association between life span and sleep time in terms of strength and direction. (2 marks)
--- 2 WORK AREA LINES (style=lined) ---
- Interpret the slope of the least squares line in terms of life span and sleep time. (2 marks)
--- 2 WORK AREA LINES (style=lined) ---
- Interpret the coefficient of determination in terms of life span and sleep time. (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
- The life of the mammal with a sleep time of 12 hours is 39.2 years.
- Show that, when the least squares line is used to predict the life span of this mammal, the residual is 19.9 years. (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
CORE, FUR2-NHT 2019 VCAA 3
The life span, in years, and gestation period, in days, for 19 types of mammals are displayed in the table below.
- A least squares line that enables life span to be predicted from gestation period is fitted to this data.
- Name the explanatory variable in the equation of this least squares line. (1 mark)
--- 1 WORK AREA LINES (style=lined) ---
- Determine the equation of the least squares line in terms of the variables life span and gestation period.
- Round the numbers representing the intercept and slope to three significant figures. (2 marks)
--- 2 WORK AREA LINES (style=lined) ---
- Write the value of the correlation rounded to three decimal places. (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
CORE, FUR2-NHT 2019 VCAA 1
The table below displays the average sleep time, in hours, for a sample of 19 types of mammals.
- Which of the two variables, type of mammal or average sleep time, is a nominal variable? (1 mark)
--- 1 WORK AREA LINES (style=lined) ---
- Determine the mean and standard deviation of the variable average sleep time for this sample of mammals.
- Round your answer to one decimal place. (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
- The average sleep time for a human is eight hours.
- What percentage of this sample of mammals has an average sleep time that is less than the average sleep time for a human.
- Round your answer to one decimal place. (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
- The sample is increase in size by adding in the average sleep time of the little brown bat.
- Its average sleep time is 19.9 hours.
- By how many many hours will the range for average sleep time increase when the average sleep time for the little brown bat is added to the sample? (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
Statistics, EXT1 S1 EQ-Bank 10
Four cards are placed face down on a table. The cards are made up of a Jack, Queen, King and Ace.
A gambler bets that she will choose the Queen in a random pick of one of the cards.
If this process is repeated 7 times, express the gambler's success as a Bernoulli random variable and calculate
- the mean. (1 mark)
--- 1 WORK AREA LINES (style=lined) ---
- the variance. (1 mark)
--- 1 WORK AREA LINES (style=lined) ---
Statistics, EXT1 S1 EQ-Bank 1 MC
If
GRAPHS, FUR1-NHT 2019 VCAA 2 MC
Two straight lines have the equations
These lines have one point of intersection.
Another line that also passes through this point of intersection has the equation
MATRICES, FUR1-NHT 2019 VCAA 3 MC
In matrix
The order of matrix
Matrix
Matrix
A. | B. | C. | |||
D. | E. |
MATRICES, FUR1-NHT 2019 VCAA 1 MC
The number of individual points scored by Rhianna (
Who scored the highest number of points and in which match?
- Suzy in match
- Tina in match
- Vicki in match
- Ursula in match
- Rhianna in match
NETWORKS, FUR1-NHT 2019 VCAA 2 MC
Vectors, EXT1 V1 EQ-Bank 5 MC
What is the angle between the vectors
A.
B.
C.
D.
Graphs, MET2-NHT 2019 VCAA 1
Parts of the graphs of
The two graphs intersect at three points, (–2, 0), (1, 0) and (
- Find the values of
and . (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
- Find the values of
such that . (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
- State the values of
for which (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
(1 mark)
--- 2 WORK AREA LINES (style=lined) ---
- Show that
for all . (1 mark)
--- 3 WORK AREA LINES (style=lined) ---
- Find the values of
such that has exactly one negative solution. (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
- Find the values of
such that has no solutions. (1 mark)
--- 2 WORK AREA LINES (style=lined) ---
Functions, EXT1 F2 2019 MET2-N 3 MC
If
Trigonometry, 2ADV T3 SM-Bank 8 MC
CORE, FUR1-NHT 2019 VCAA 17 MC
A sequence of numbers is generated by the recurrence relation shown below.
What is the value of
- 2
- 5
- 11
- 41
- 122
CORE, FUR1-NHT 2019 VCAA 5-7 MC
The birth weights of a large population of babies are approximately normally distributed with a mean of 3300 g and a standard deviation of 550 g.
Part 1
A baby selected at random from this population has a standardised weight of
Which one of the following calculations will result in the actual birth weight of this baby?
Part 2
Using the 68–95–99.7% rule, the percentage of babies with a birth weight of less than 1650 g is closest to
- 0.14%
- 0.15%
- 0.17%
- 0.3%
- 2.5%
Part 3
A sample of 600 babies was drawn at random from this population.
Using the 68–95–99.7% rule, the number of these babies with a birth weight between 2200 g and 3850 g is closest to
- 111
- 113
- 185
- 408
- 489
CORE, FUR1-NHT 2019 VCAA 1-2 MC
The histogram and boxplot shown below both display the distribution of the birth weight, in grams, of 200 babies.
Part 1
The shape of the distribution of the babies’ birth weight is best described as
- positively skewed with no outliers.
- negatively skewed with no outliers.
- approximately symmetric with no outliers.
- positively skewed with outliers.
- approximately symmetric with outliers.
Part 2
The number of babies with a birth weight between 3000 g and 3500 g is closest to
- 30
- 32
- 37
- 74
- 80
Algebra, MET2-NHT 2019 VCAA 3 MC
If
- 7
- 4
- 1
- –2
- –1
Graphs, MET2-NHT 2019 VCAA 2 MC
Algebra, MET2-NHT 2019 VCAA 1 MC
The maximal domain of the function with rule
Calculus, 2ADV C3 2019 MET1 4
Given the function
- State the domain and range of
. (1 mark)
--- 1 WORK AREA LINES (style=lined) ---
- i. Find the equation of the tangent to the graph of
at . (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
ii. On the axes below, sketch the graph of the function
, labelling any asymptote with its equation.
Also draw the tangent to the graph of
at . (4 marks)
--- 0 WORK AREA LINES (style=lined) ---
Calculus, 2ADV C2 2019 MET1 1a
Let
Find
--- 4 WORK AREA LINES (style=lined) ---
- « Previous Page
- 1
- …
- 17
- 18
- 19
- 20
- 21
- …
- 45
- Next Page »