Networks, STD2 N2 2012 FUR1 1 MC
GRAPHS, FUR2 2017 VCAA 1
NETWORKS, FUR2 2017 VCAA 1
Bus routes connect six towns.
The towns are Northend (`N`), Opera (`O`), Palmer (`P`), Quigley (`Q`), Rosebush (`R`) and Seatown (`S`).
The graph below gives the cost, in dollars, of bus travel along these routes.
Bai lives in Northend (`N`) and he will travel by bus to take a holiday in Seatown (`S`).
- Bai considers travelling by bus along the route Northend (`N`) – Opera (`O`) – Seatown (`S`).
How much would Bai have to pay? (1 mark)
- If Bai takes the cheapest route from Northend (`N`) to Seatown (`S`), which other town(s) will he pass through? (1 mark)
- Euler’s formula, `v + f = e + 2`, holds for this graph.
Complete the formula by writing the appropriate numbers in the boxes provided below. (1 mark)
MATRICES, FUR2 2017 VCAA 2
Junior students at a school must choose one elective activity in each of the four terms in 2018.
Students can choose from the areas of performance (`P`), sport (`S`) and technology (`T`).
The transition diagram below shows the way in which junior students are expected to change their choice of elective activity from term to term.
- Of the junior students who choose performance (`P`) in one term, what percentage are expected to choose sport (`S`) the next term? (1 mark)
Matrix `J_1` lists the number of junior students who will be in each elective activity in Term 1.
`J_1 = [(300),(240),(210)]{:(P),(S),(T):}`
- 306 junior students are expected to choose sport (`S`) in Term 2.
Complete the calculation below to show this. (1 mark)
- In Term 4, how many junior students in total are expected to participate in performance (`P`) or sport (`S`) or technology (`T`)? (1 mark)
CORE, FUR2 2017 VCAA 5
Alex is a mobile mechanic.
He uses a van to travel to his customers to repair their cars.
The value of Alex’s van is depreciated using the flat rate method of depreciation.
The value of the van, in dollars, after `n` years, `V_n`, can be modelled by the recurrence relation shown below.
`V_0 = 75\ 000 qquad V_(n + 1) = V_n - 3375`
- Recursion can be used to calculate the value of the van after two years.
Complete the calculations below by writing the appropriate numbers in the boxes provided. (2 marks)
- By how many dollars is the value of the van depreciated each year? (1 mark)
- Calculate the annual flat rate of depreciation in the value of the van.
Write your answer as a percentage. (1 mark)
- The value of Alex’s van could also be depreciated using the reducing balance method of depreciation.
The value of the van, in dollars, after `n` years, `R_n`, can be modelled by the recurrence relation shown below.
`R_0 = 75\ 000 qquad R_(n + 1) = 0.943R_n`
At what annual percentage rate is the value of the van depreciated each year? (1 mark)
Algebra, MET2 2017 VCAA 2
Sammy visits a giant Ferris wheel. Sammy enters a capsule on the Ferris wheel from a platform above the ground. The Ferris wheel is rotating anticlockwise. The capsule is attached to the Ferris wheel at point `P`. The height of `P` above the ground, `h`, is modelled by `h(t) = 65 - 55cos((pit)/15)`, where `t` is the time in minutes after Sammy enters the capsule and `h` is measured in metres.
Sammy exits the capsule after one complete rotation of the Ferris wheel.
- State the minimum and maximum heights of `P` above the ground. (1 mark)
- For how much time is Sammy in the capsule? (1 mark)
- Find the rate of change of `h` with respect to `t` and, hence, state the value of `t` at which the rate of change of `h` is at its maximum. (2 marks)
As the Ferris wheel rotates, a stationary boat at `B`, on a nearby river, first becomes visible at point `P_1`. `B` is 500 m horizontally from the vertical axis through the centre `C` of the Ferris wheel and angle `CBO = theta`, as shown below.
- Find `theta` in degrees, correct to two decimal places. (1 mark)
Part of the path of `P` is given by `y = sqrt(3025 - x^2) + 65, x ∈ [−55,55]`, where `x` and `y` are in metres.
- Find `(dy)/(dx)`. (1 mark)
As the Ferris wheel continues to rotate, the boat at `B` is no longer visible from the point `P_2(u, v)` onwards. The line through `B` and `P_2` is tangent to the path of `P`, where angle `OBP_2 = alpha`.
- Find the gradient of the line segment `P_2B` in terms of `u` and, hence, find the coordinates of `P_2`, correct to two decimal places. (3 marks)
- Find `alpha` in degrees, correct to two decimal places. (1 mark)
- Hence or otherwise, find the length of time, to the nearest minute, during which the boat at `B` is visible. (2 marks)
Graphs, MET2 2017 VCAA 1 MC
Let `f : R → R, \ f (x) = 5sin(2x) - 1`.
The period and range of this function are respectively
- `π\ text(and)\ [−1, 4]`
- `2π\ text(and)\ [−1, 5]`
- `π\ text(and)\ [−6, 4]`
- `2π\ text(and)\ [−6, 4]`
- `4π\ text(and)\ [−6, 4]`
Harder Ext1 Topics, EXT2 2017 HSC 14b
Two circles, `cc"C"_1` and `cc"C"_2`, intersect at the points `A` and `B`. Point `C` is chosen on the arc `AB` of `cc"C"_2` as shown in the diagram.
The line segment `AC` produced meets `cc"C"_1` at `D`.
The line segment `BC` produced meets `cc"C"_1` at `E`.
The line segment `EA` produced meets `cc"C"_2` at `F`.
The line segment `FC` produced meets the line segment `ED` at `G`.
Copy or trace the diagram into your writing booklet.
- State why `/_ EAD = /_ EBD`. (1 mark)
- Show that `/_ EDA = /_ AFC`. (1 mark)
- Hence, or otherwise, show that `B, C, G` and `D` are concyclic points. (3 marks)
CORE, FUR2 2017 VCAA 2
The back-to-back stem plot below displays the wingspan, in millimetres, of 32 moths and their place of capture (forest or grassland).
- Which variable, wingspan or place of capture, is a categorical variable? (1 mark)
- Write down the modal wingspan, in millimetres, of the moths captured in the forest. (1 mark)
- Use the information in the back-to-back stem plot to complete the table below. (2 marks)
- Show that the moth captured in the forest that had a wingspan of 52 mm is an outlier. (2 marks)
- The back-to-back stem plot suggests that wingspan is associated with place of capture.
Explain why, quoting the values of an appropriate statistic. (2 marks)
Graphs, EXT2 2017 HSC 4 MC
CORE, FUR1 2017 VCAA 1-3 MC
The boxplot below shows the distribution of the forearm circumference, in centimetres, of 252 people.
Part 1
The percentage of these 252 people with a forearm circumference of less than 30 cm is closest to
- `text(15%)`
- `text(25%)`
- `text(50%)`
- `text(75%)`
- `text(100%)`
Part 2
The five-number summary for the forearm circumference of these 252 people is closest to
- `\ \ \ 21,\ 27.4,\ 28.7,\ 30,\ 34`
- `\ \ \ 21,\ 27.4,\ 28.7,\ 30,\ 35.9`
- `24.5,\ 27.4,\ 28.7,\ 30,\ 34`
- `24.5,\ 27.4,\ 28.7,\ 30,\ 35.9`
- `24.5,\ 27.4,\ 28.7,\ 30,\ 36`
Part 3
The table below shows the forearm circumference, in centimetres, of a sample of 10 people selected from this group of 252 people.
The mean, `barx`, and the standard deviation, `s_x`, of the forearm circumference for this sample of people are closest to
- `barx = 1.58qquads_x = 27.8`
- `barx = 1.66qquads_x = 27.8`
- `barx = 27.8qquads_x = 1.58`
- `barx = 27.8qquads_x = 1.66`
- `barx = 27.8qquads_x = 2.30`
Functions, EXT1 F2 2017 HSC 1 MC
Which polynomial is a factor of `x^3-5x^2 + 11x-10`?
- `x-2`
- `x + 2`
- `11x-10`
- `x^2-5x + 11`
Statistics, 2ADV 2017 HSC 12e
A spinner is marked with the numbers 1, 2, 3, 4 and 5. When it is spun, each of the five numbers is equally likely to occur.
The spinner is spun three times.
- What is the probability that an even number occurs on the first spin? (1 mark)
- What is the probability that an even number occurs on at least one of the three spins? (1 mark)
- What is the probability that an even number occurs on the first spin and odd numbers occur on the second and third spins? (1 mark)
- What is the probability that an even number occurs on exactly one of the three spins? (1 mark)
Algebra, STD2 A1 2017 HSC 7 MC
It is given that `I = 3/2 MR^2`.
What is the value of `I` when `M = 26.55` and `R = 3.07`, correct to two decimal places?
A. `375.35`
B. `3246.08`
C. `9965.45`
D. `14\ 948.18`
Statistics, STD2 S1 2017 HSC 1 MC
Probability, NAP-J2-02
Graphs, MET2 2007 VCAA 15 MC
The graph of the function `f: [0, oo) -> R` where `f(x) = 3x^(5/2)` is reflected in the `x`-axis and then translated 3 units to the right and 4 units down.
The equation of the new graph is
`y = 3(x - 3)^(5/2) + 4`
`y = -3 (x - 3)^(5/2) - 4`
`y = -3 (x + 3)^(5/2) - 1`
`y = -3 (x - 4)^(5/2) + 3`
`y = 3(x - 4)^(5/2) + 3`
Calculus, MET2 2009 VCAA 2 MC
At the point `(1, 1)` on the graph of the function with rule `y = (x - 1)^3 + 1`
- there is a local maximum.
- there is a local minimum.
- there is a stationary point of inflection.
- the gradient is not defined.
- there is a point of discontinuity.
Calculus, MET2 2011 VCAA 3
- Consider the function `f: R -> R, f(x) = 4x^3 + 5x - 9`.
- Find `f′(x)` (1 mark)
- Explain why `f′(x) >= 5` for all `x`. (1 mark)
- The cubic function `p` is defined by `p: R -> R, p(x) = ax^3 + bx^2 + cx + k`, where `a`, `b`, `c` and `k` are real numbers.
- If `p` has `m` stationary points, what possible values can `m` have? (1 mark)
- If `p` has an inverse function, what possible values can `m` have? (1 mark)
- The cubic function `q` is defined by `q:R -> R, q(x) = 3 - 2x^3`.
- Write down a expression for `q^(−1)(x)`. (2 marks)
- Determine the coordinates of the point(s) of intersection of the graphs of `y = q(x)` and `y = q^(−1)(x)`. (2 marks)
- The cubic function `g` is defined by `g: R -> R, g(x) = x^3 + 2x^2 + cx + k`, where `c` and `k` are real numbers.
- If `g` has exactly one stationary point, find the value of `c`. (3 marks)
- If this stationary point occurs at a point of intersection of `y = g(x)` and `g^(−1)(x)`, find the value of `k`. (3 marks)
Calculus, MET2 2016 VCAA 4 MC
The average rate of change of the function `f` with rule `f(x) = 3x^2 - 2 sqrt(x + 1)`, between `x = 0 and x = 3`, is
A. `8`
B. `25`
C. `53/9`
D. `25/3`
E. `13/9`
Graphs, MET2 2016 VCAA 2 MC
Let `f: R -> R,\ f(x) = 1 - 2 cos ({pi x}/2).`
The period and range of this function are respectively
- `4 and [−2, 2]`
- `4 and [−1, 3]`
- `1 and [−1, 3]`
- `4 pi and [−1, 3]`
- `4 pi and [−2, 2]`
Graphs, MET2 2016 VCAA 1 MC
The linear function `f: D -> R,\ f(x) = 5 - x` has range `[−4, 5).`
The domain `D` is
- `(0, 9]`
- `(0, 1]`
- `[5, −4)`
- `[−9, 0)`
- `[1, 9)`
Algebra, MET2 2012 VCAA 1 MC
The function with rule `f(x) = −3sin((pix)/5)` has period
- `3`
- `5`
- `10`
- `pi/5`
- `pi/10`
NETWORKS, FUR2 2016 VCAA 1
A map of the roads connecting five suburbs of a city, Alooma (`A`), Beachton (`B`), Campville (`C`), Dovenest (`D`) and Easyside (`E`), is shown below.
- Starting at Beachton, which two suburbs can be driven to using only one road? (1 mark)
A graph that represents the map of the roads is shown below.
One of the edges that connects to vertex `E` is missing from the graph.
-
- Add the missing edge to the graph above. (1 mark)
(Answer on the graph above.)
- Explain what the loop at `D` represents in terms of a driver who is departing from Dovenest. (1 mark)
- Add the missing edge to the graph above. (1 mark)
GRAPHS, FUR2 2016 VCAA 1
Maria is a hockey player. She is paid a bonus that depends on the number of goals that she scores in a season.
The graph below shows the value of Maria’s bonus against the number of goals that she scores in a season.
- What is the value of Maria’s bonus if she scores seven goals in a season? (1 mark)
- What is the least number of goals that Maria must score in a season to receive a bonus of $2500? (1 mark)
Another player, Bianca, is paid a bonus of $125 for every goal that she scores in a season.
- What is the value of Bianca’s bonus if she scores eight goals in a season? (1 mark)
- At the end of the season, both players have scored the same number of goals and receive the same bonus amount.
How many goals did Maria and Bianca each score in the season? (1 mark)
MATRICES, FUR2 2016 VCAA 3
A travel company is studying the choice between air (`A`), land (`L`), sea (`S`) or no (`N`) travel by some of its customers each year.
Matrix `T`, shown below, contains the percentages of customers who are expected to change their choice of travel from year to year.
`{:(qquadqquadqquadqquadqquadquadtext(this year)),(qquadqquadqquadquadAqquadqquadLqquadqquadSqquadquadN),(T = [(0.65,0.25,0.25,0.50),(0.15,0.60,0.20,0.15),(0.05,0.10,0.25,0.20),(0.15,0.05,0.30,0.15)]{:(A),(L),(S),(N):}text(next year)):}`
Let `S_n` be the matrix that shows the number of customers who choose each type of travel `n` years after 2014.
Matrix `S_0` below shows the number of customers who chose each type of travel in 2014.
`S_0 = [(520),(320),(80),(80)]{:(A),(L),(S),(N):}`
Matrix `S_1` below shows the number of customers who chose each type of travel in 2015.
`S_1 = TS_0 = [(478),(d),(e),(f)]{:(A),(L),(S),(N):}`
- Find the values missing from matrix `S_1 (d, e, f )`. (1 mark)
- Write a calculation that shows that 478 customers were expected to choose air travel in 2015. (1 mark)
- Consider the customers who chose sea travel in 2014.
How many of these customers were expected to choose sea travel in 2015? (1 mark)
- Consider the customers who were expected to choose air travel in 2015.
What percentage of these customers had also chosen air travel in 2014?
Round your answer to the nearest whole number. (1 mark)
In 2016, the number of customers studied was increased to 1360.
Matrix `R_2016`, shown below, contains the number of these customers who chose each type of travel in 2016.
`R_2016 = [(646),(465),(164),(85)]{:(A),(L),(S),(N):}`
The company intends to increase the number of customers in the study in 2017 and in 2018.
The matrix that contains the number of customers who are expected to choose each type of travel in
2017 (`R_2017`) and 2018 (`R_2018`) can be determined using the matrix equations shown below.
`R_2017 = TR_2016 + BqquadqquadqquadR_2018 = TR_2017 + B`
`{:(qquadqquadqquadqquadqquadquadtext(this year)),(qquadqquadqquadquadAqquadqquadLqquadqquadSqquadquadN),(T = [(0.65,0.25,0.25,0.50),(0.15,0.60,0.20,0.15),(0.05,0.10,0.25,0.20),(0.15,0.05,0.30,0.15)]{:(A),(L),(S),(N):}text(next year)):}qquadqquad{:(),(),(B = [(80),(80),(40),(−80)]{:(A),(L),(S),(N):}):}`
-
- The element in the fourth row of matrix `B` is – 80.
Explain this number in the context of selecting customers for the studies in 2017 and 2018. (1 mark)
- Determine the number of customers who are expected to choose sea travel in 2018.
Round your answer to the nearest whole number. (2 marks)
- The element in the fourth row of matrix `B` is – 80.
MATRICES, FUR2 2016 VCAA 2
A travel company has five employees, Amara (`A`), Ben (`B`), Cheng (`C`), Dana (`D`) and Elka (`E`).
The company allows each employee to send a direct message to another employee only as shown in the communication matrix `G` below.
The matrix `G^2` is also shown below.
`{:(),(),(G = text(sender)):}{:(qquadqquadqquad\ text(receiver)),(qquadqquadAquadBquadCquadDquadE),({:(A),(B),(C),(D),(E):}[(0,1,1,1,1),(1,0,1,0,0),(1,1,0,1,0),(0,1,0,0,1),(0,0,0,1,0)]):}qquad{:(),(),(G^2 = text(sender)):}{:(qquadqquadqquad\ text(receiver)),(qquadqquadAquadBquadCquadDquadE),({:(A),(B),(C),(D),(E):}[(2,2,1,2,1),(1,2,1,2,1),(1,2,2,1,2),(1,0,1,1,0),(0,1,0,0,1)]):}`
The 1 in row `E`, column `D` of matrix `G` indicates that Elka (sender) can send a direct message to Dana (receiver).
The 0 in row `E`, column `C` of matrix `G` indicates that Elka cannot send a direct message to Cheng.
- To whom can Dana send a direct message? (1 mark)
- Cheng needs to send a message to Elka, but cannot do this directly.
Write down the names of the employees who can send the message from Cheng directly to Elka. (1 mark)
MATRICES, FUR2 2016 VCAA 1
A travel company arranges flight (`F`), hotel (`H`), performance (`P`) and tour (`T`) bookings.
Matrix `C` contains the number of each type of booking for a month.
`C = [(85),(38),(24),(43)]{:(F),(H),(P),(T):}`
- Write down the order of matrix `C`. (1 mark)
A booking fee, per person, is collected by the travel company for each type of booking.
Matrix `G` contains the booking fees, in dollars, per booking.
`{:((qquadqquadquadF,\ H,\ P,\ T)),(G = [(40,25,15,30)]):}`
-
- Calculate the matrix product `J = G × C`. (1 mark)
- What does matrix `J` represent? (1 mark)
CORE, FUR2 2016 VCAA 5
Ken has opened a savings account to save money to buy a new caravan.
The amount of money in the savings account after `n` years, `V_n`, can be modelled by the recurrence relation shown below.
`V_0 = 15000, qquad qquad qquad V_(n + 1) = 1.04 xx V_n`
- How much money did Ken initially deposit into the savings account? (1 mark)
- Use recursion to write down calculations that show that the amount of money in Ken’s savings account after two years, `V_2`, will be $16 224. (1 mark)
- What is the annual percentage compound interest rate for this savings account? (1 mark)
- The amount of money in the account after `n` years, `Vn` , can also be determined using a rule.
- Complete the rule below by writing the appropriate numbers in the boxes provided. (1 mark)
`V_n =` `^n xx` - How much money will be in Ken’s savings account after 10 years? (1 mark)
- Complete the rule below by writing the appropriate numbers in the boxes provided. (1 mark)
CORE, FUR2 2016 VCAA 2
A weather station records daily maximum temperatures
- The five-number summary for the distribution of maximum temperatures for the month of February is displayed in the table below.
- The boxplots below display the distribution of maximum daily temperature for the months of May and July.
- Describe the shapes of the distributions of daily temperature (including outliers) for July and for May. (1 mark)
- Determine the value of the upper fence for the July boxplot. (1 mark)
- Using the information from the boxplots, explain why the maximum daily temperature is associated with the month of the year. Quote the values of appropriate statistics in your response. (1 mark)
- Describe the shapes of the distributions of daily temperature (including outliers) for July and for May. (1 mark)
CORE, FUR2 2016 VCAA 1
The dot plot below shows the distribution of daily rainfall, in millimetres, at a weather station for 30 days in September.
- Write down the
- range (1 mark)
- median. (1 mark)
- Circle the data point on the dot plot above that corresponds to the third quartile `(Q_3).` (1 mark)
- Write down the
- the number of days on which no rainfall was recorded (1 mark)
- the percentage of days on which the daily rainfall exceeded 12 mm. (1 mark)
- Use the grid below to construct a histogram that displays the distribution of daily rainfall for the month of September. Use interval widths of two with the first interval starting at 0. (2 marks)
NETWORKS, FUR1 2016 VCAA 1 MC
Lee, Mandy, Nola, Oscar and Pieter are each to be allocated one particular task at work.
The bipartite graph below shows which task(s), 1–5, each person is able to complete.
Each person completes a different task.
Task 4 must be completed by
- `text(Lee.)`
- `text(Mandy.)`
- `text(Nola.)`
- `text(Oscar.)`
- `text(Pieter.)`
GRAPHS, FUR1 2016 VCAA 2 MC
A phone company charges a fixed, monthly line rental fee of $28 and $0.25 per call.
Let `n` be the number of calls that are made in a month.
Let `C` be the monthly phone bill, in dollars.
The equation for the relationship between the monthly phone bill, in dollars, and the number of calls is
- `C = 28 + 0.25n`
- `C = 28n + 0.25`
- `C = n + 28.25`
- `C = 28(n + 0.25)`
- `C = 0.25(n + 28)`
GRAPHS, FUR1 2016 VCAA 1 MC
GEOMETRY, FUR1 2016 VCAA 2 MC
Number and Algebra, NAP-B1-07
Moe has 22 first cousins and Homer has 28.
Barney has more first cousins than Moe but less than Homer.
How many first cousins could Barney have?
`19` | `21` | `24` | `29` |
|
|
|
|
Measurement, NAP-B1-06
Number and Algebra, NAP-B1-05 SA
Write seven hundred and fifty-six as a number.
Geometry, NAP-B1-04
Statistics, NAP-B1-03
Number and Algebra, NAP-C1-05
Geometry, NAP-C1-04
Number and Algebra, NAP-C1-03
Statistics, NAP-D1-07
Number and Algebra, NAP-D1-06
Geometry, NAP-D1-03
Probability, NAP-E1-07
Fiona plays netball tomorrow.
Today is Tuesday.
Which of these is certain?
|
Fiona's team will lose. |
|
Fiona's team trains on Monday. |
|
It will be sunny during the game. |
|
Tomorrow is Wednesday. |
Number and Algebra, NAP-D1-02
Number and Algebra, NAP-F1-09
Statistics, NAP-F1-06
Measurement, NAP-F1-05
Number and Algebra, NAP-G1-08
Number and Algebra, NAP-G1-07
Milly walked 13 kilometres to get to town and then travelled 38 kilometres by bus.
How many kilometres did she travel altogether?
`25` | `41` | `45` | `51` |
|
|
|
|
Geometry, NAP-F1-03
Geometry, NAP-F1-02
Measurement, NAP-H1-05
Number and Algebra, NAP-H1-03
Number and Algebra, NAP-I1-08 SA
Geometry, NAP-I1-05
- « Previous Page
- 1
- 2
- 3
- 4
- 5
- 6
- …
- 8
- Next Page »