Number and Algebra, NAP-E2-01
Kylie had 11 balloons. She gave 4 away to her friends and 2 burst.
How many balloons does Kylie have left?
`5` | `6` | `7` | `17` |
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Statistics, NAP-H2-02
Number and Algebra, NAP-G2-01
Barnaby writes a number pattern where each number is four more than the previous number.
`5, 9, 13, 17,` |
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What number should Barnaby write next?
`18` | `20` | `21` | `22` |
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Functions, EXT1 F1 2016 HSC 11a
Find the inverse of the function `y = x^3 - 2`. (2 marks)
Functions, EXT1 F2 2016 HSC 2 MC
What is the remainder when `2x^3-10x^2 + 6x + 2` is divided by `x-2`?
- `-66`
- `-10`
- `-x^3 + 5x^2-3x-1`
- `x^3-5x^2 + 3x + 1`
Calculus, 2ADV C4 2016 HSC 16a
A particle moves in a straight line. Its velocity `v\ text(ms)^-1` at time `t` seconds is given by
`v = 2 - 4/(t + 1).`
- Find the initial velocity. (1 mark)
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- Find the acceleration of the particle when the particle is stationary. (2 marks)
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- By considering the behaviour of `v` for large `t`, sketch a graph of `v` against `t` for `t >= 0`, showing any intercepts. (2 marks)
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- Find the exact distance travelled by the particle in the first 7 seconds. (3 marks)
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Integration, EXT2 2016 HSC 14a
- Show that `int sin^3 x\ dx = 1/3 cos^3 x - cos x + C.` (1 mark)
- Using a graphical approach, or otherwise, explain why
`int_0^pi cos^(2n - 1) x\ dx = 0`, for all positive integers `n.` (1 mark)
- The diagram shows the region `R` enclosed by `y = sin^3 x` and the `x`-axis for `0 <= x <= pi.`
Using the method of cylindrical shells and the results in parts (i) and (ii), find the exact volume of the solid formed when `R` is rotated about the `y`-axis. (3 marks)
Functions, 2ADV F1 2016 HSC 12a
Conics, EXT2 2016 HSC 12d
- Show that the equation of the normal to the hyperbola `xy = c^2,\ \ c != 0`, at `P (cp, c/p)` is given by `px - y/p = c (p^2 - 1/p^2).` (2 marks)
- The normal at `P` meets the hyperbola again at `Q (cq, c/q).`
Show that `q = -1/p^3.` (3 marks)
Complex Numbers, EXT2 N2 2016 HSC 12c
Let `z = cos theta + i sin theta.`
- By considering the real part of `z^4`, show that `cos 4 theta` is
`qquad cos^4 theta - 6 cos^2 theta sin^2 theta + sin^4 theta.` (2 marks)
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- Hence, or otherwise, find an expression for `cos 4 theta` involving only powers of `cos theta.` (1 mark)
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Conics, EXT2 2016 HSC 12a
Graphs, EXT2 2016 HSC 11c
Find `(dy)/(dx)` for the curve given by `x^3 + y^3 = 2xy`, leaving your answer in terms of `x` and `y.` (2 marks)
Complex Numbers, EXT2 N1 2016 HSC 11a
Let `z = sqrt 3 - i.`
- Express `z` in modulus-argument form. (2 marks)
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- Show that `z^6` is real. (1 mark)
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- Find a positive integer `n` such that `z^n` is purely imaginary. (1 mark)
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Measurement, STD2 M1 2016 HSC 26a
Algebra, STD2 A1 2016 HSC 2 MC
Which of the following equations has `x = 5` as the solution?
(A) `x - 5 = 10`
(B) `5 - x = 10`
(C) `x/2 = 10`
(D) `2x = 10`
Calculus, 2ADV C1 2016 HSC 11b
Differentiate `(x + 2)/(3x - 4).` (2 marks)
Functions, MET1 2006 VCAA 4
For the function `f: [– pi, pi] -> R, f(x) = 5 cos (2 (x + pi/3))`
- write down the amplitude and period of the function (2 marks)
- sketch the graph of the function `f` on the set of axes below. Label axes intercepts with their coordinates.
Label endpoints of the graph with their coordinates. (3 marks)
Functions, MET1 2006 VCAA 1
Let `f(x) = x^2 + 1 and g(x) = 2x + 1.` Write down the rule of `f(g(x)).` (1 mark)
Calculus, MET1 2014 VCAA 1a
If `y = x^2sin(x)`, find `(dy)/(dx)`. (2 marks)
CORE*, FUR2 2007 VCAA 1
Khan wants to buy some office furniture that is valued at $7000.
- i. A store requires 25% deposit. Calculate the deposit. (1 mark)
The balance is to be paid in 24 equal monthly instalments. No interest is charged.
- ii. Determine the amount of each instalment. Write your answer in dollars and cents. (1 mark)
Another store offers the same $7000 office furniture for $500 deposit and 36 monthly instalments of $220.
- i. Determine the total amount paid for the furniture at this store. (1 mark)
- ii. Calculate the annual flat rate of interest charged by this store.
Write your answer as a percentage correct to one decimal place. (2 marks)
A third store has the office furniture marked at $7000 but will give 15% discount if payment is made in cash at the time of sale.
- Calculate the cash price paid for the furniture after the discount is applied. (1 mark)
GRAPHS, FUR2 2007 VCAA 1
The Goldsmith family are going on a driving holiday in Western Australia.
On the first day, they leave home at 8 am and drive to Watheroo then Geraldton.
The distance–time graph below shows their journey to Geraldton.
At 9.30 am the Goldsmiths arrive at Watheroo.
They stop for a period of time.
- For how many minutes did they stop at Watheroo? (1 mark)
After leaving Watheroo, the Goldsmiths continue their journey and arrive in Geraldton at 12 pm.
- What distance (in kilometres) do they travel between Watheroo and Geraldton? (1 mark)
- Calculate the Goldsmiths' average speed (in km/h) when travelling between Watheroo and Geraldton. (1 mark)
The Goldsmiths leave Geraldton at 1 pm and drive to Hamelin. They travel at a constant speed of 80 km/h for three hours. They do not make any stops.
- On the graph above, draw a line segment representing their journey from Geraldton to Hamelin. (1 mark)
GRAPHS, FUR2 2008 VCAA 1
Tiffany’s pulse rate (in beats/minute) during the first 60 minutes of a long-distance run is shown in the graph below.
- What was Tiffany’s pulse rate (in beats/minute) 15 minutes after she started her run? (1 mark)
- By how much did Tiffany’s pulse rate increase over the first 60 minutes of her run?
Write your answer in beats/minute. (1 mark)
- The recommended maximum pulse rate for adults during exercise is determinded by subtracting the person’s age in years from 220.
- Write an equation in terms of the variables maximum pulse rate and age that can be used to determine a person’s recommended maximum pulse rate from his or her age. (1 mark)
The target zone for aerobic exercise is between 60% and 75% of a person’s maximum pulse rate.
Tiffany is 20 years of age.
- Determine the values between which Tiffany’s pulse rate should remain so that she exercises within her target zone.
Write your answers correct to the nearest whole number. (1 mark)
CORE*, FUR2 2009 VCAA 1
The recommended retail price of a golf bag is $500. Rebecca sees the bag discounted by $120 at a sale.
- What is the price of the golf bag after the $120 discount has been applied? (1 mark)
- Find the discount as a percentage of the recommended retail price. ( 1 mark)
GRAPHS, FUR2 2009 VCAA 1
Fair Go Airlines offers air travel between destinations in regional Victoria.
Table 1 shows the fares for some distances travelled.
- What is the maximum distance a passenger could travel for $160? (1 mark)
The fares for the distances travelled in Table 1 are graphed below.
- The fare for a distance longer than 400 km, but not longer than 550 km, is $280.
Draw this information on the graph above. (1 mark)
Fair Go Airlines is planning to change its fares.
A new fare will include a service fee of $40, plus 50 cents per kilometre travelled.
An equation used to determine this new fare is given by
fare = `40 + 0.5` × distance.
- A passenger travels 300 km.
How much will this passenger save on the fare calculated using the equation above compared to the fare shown in Table 1? (1 mark)
- At a certain distance between 250 km and 400 km, the fare, when calculated using either the new equation or Table 1, is the same.
What is this distance? (2 marks)
- An equation connecting the maximum distance that may be travelled for each fare in Table 1 on page 16 can be written as
fare = `a` + `b` × maximum distance.
Determine `a` and `b`. (2 marks)
GEOMETRY, FUR2 2010 VCAA 1
In the plan below, the entry gate of an adventure park is located at point `G`.
A canoeing activity is located at point `C`.
The straight path `GC` is 40 metres long.
The bearing of `C` from `G` is 060°.
- Write down the size of the angle that is marked `x^@` in the plan above. (1 mark)
- What is the bearing of the entry gate from the canoeing activity? (1 mark)
- How many metres north of the entry gate is the canoeing activity? (1 mark)
`CW` is a 90 metre straight path between the canoeing activity and a water slide located at point `W`.
`GW` is a straight path between the entry gate and the water slide.
The angle `GCW` is 120°.
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- Find the area that is enclosed by the three paths, `GC`, `CW` and `GW`.
Write your answer in square metres, correct to one decimal place. (1 mark)
- Show that the length of path `GW` is 115.3 metres, correct to one decimal place. (1 mark)
- Find the area that is enclosed by the three paths, `GC`, `CW` and `GW`.
Straight paths `CK` and `WK` lead to the kiosk located at point `K`.
These two paths are of equal length.
The angle `KCW` is 10°.
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- Find the size of the angle `CKW`. (1 mark)
- Find the length of path `CK`, in metres, correct to one decimal place. (1 mark)
CORE*, FUR2 2011 VCAA 1
Tony plans to take his family on a holiday.
The total cost of $3630 includes a 10% Goods and Services Tax (GST).
- Determine the amount of GST that is included in the total cost. (1 mark)
During the holiday, the family plans to visit some theme parks.
The prices of family tickets for three theme parks are shown in the table below.
- What is the total cost for the family if it visits all three theme parks? (1 mark)
If Tony purchases the Movie Journey family ticket online, the cost is discounted to $202.40
- Determine the percentage discount. (1 mark)
CORE*, FUR2 2012 VCAA 1
A club purchased new equipment priced at $8360. A 15% deposit was paid.
- Calculate the deposit. (1 mark)
- i. Determine the amount of money that the club still owes on the equipment after the deposit is paid. (1 mark)
The amount owing will be fully repaid in 12 instalments of $650.
- ii. Determine the total interest paid. (1 mark)
NETWORKS, FUR1 2007 VCAA 3 MC
Consider the following graph.
An adjacency matrix that could be used to represent this graph is
A. | `[(0,2,0,1), (2,0,1,1), (0,1,0,1), (1,1,1,0)]` | B. | `[(0,2,0,1), (0,0,1,1), (0,0,0,1), (0,0,0,0)]` |
C. | `[(0,1,0,1), (2,0,0,1), (0,1,0,1), (1,1,1,0)]` | D. | `[(0,2,0,1), (0,1,1,1), (0,1,1,1), (0,1,1,1)]` |
E. | `[(1,2,0,1), (2,1,0,1), (0,1,1,0), (0,0,1,1)]` |
NETWORKS, FUR1 2010 VCAA 3 MC
NETWORKS, FUR1 2010 VCAA 2 MC
NETWORKS, FUR1 2010 VCAA 1 MC
NETWORKS, FUR1 2006 VCAA 2 MC
NETWORKS, FUR1 2009 VCAA 2 MC
NETWORKS, FUR1 2013 VCAA 1 MC
NETWORKS, FUR2 2006 VCAA 1
George, Harriet, Ian, Josie and Keith are a group of five musicians.
They are forming a band where each musician will fill one position only.
The following bipartite graph illustrates the positions that each is able to fill.
NETWORKS, FUR1 2015 VCAA 5 MC
The graph below represents a friendship network. The vertices represent the four people in the friendship network: Kwan (`K`), Louise (`L`), Milly (`M`) and Narelle (`N`).
An edge represents the presence of a friendship between a pair of these people. For example, the edge connecting `K` and `L` shows that Kwan and Louise are friends.
Which one of the following graphs does not contain the same information?
NETWORKS, FUR2 2009 VCAA 3
The city of Robville contains eight landmarks denoted as vertices `N` to `U` on the network diagram below. The edges on this network represent the roads that link the eight landmarks.
- Write down the degree of vertex `U`. (1 mark)
- Steven wants to visit each landmark, but drive along each road only once. He will begin his journey at landmark `N`.
- At which landmark must he finish his journey? (1 mark)
- Regardless of which route Steven decides to take, how many of the landmarks (including those at the start and finish) will he see on exactly two occasions? (1 mark)
- Cathy decides to visit each landmark only once.
- Suppose she starts at `S`, then visits `R` and finishes at `T`.
Write down the order Cathy will visit the landmarks. (1 mark)
- Suppose Cathy starts at `S`, then visits `R` but does not finish at `T`.
List three different ways that she can visit the landmarks. (1 mark)
- Suppose she starts at `S`, then visits `R` and finishes at `T`.
NETWORKS, FUR2 2011 VCAA 1
Aden, Bredon, Carrie, Dunlop, Enwin and Farnham are six towns.
The network shows the road connections and distances between these towns in kilometres.
- In kilometres, what is the shortest distance between Farnham and Carrie? (1 mark)
- How many different ways are there to travel from Farnham to Carrie without passing through any town more than once? (1 mark)
An engineer plans to inspect all of the roads in this network.
He will start at Dunlop and inspect each road only once.
- At which town will the inspection finish? (1 mark)
Another engineer decides to start and finish her road inspection at Dunlop.
If an assistant inspects two of the roads, this engineer can inspect the remaining six roads and visit each of the other five towns only once.
- How many kilometres of road will the assistant need to inspect? (1 mark)
NETWORKS, FUR2 2013 VCAA 1
The vertices in the network diagram below show the entrance to a wildlife park and six picnic areas in the park: `P1`, `P2`, `P3`, `P4`, `P5` and `P6`.
The numbers on the edges represent the lengths, in metres, of the roads joining these locations.
- In this graph, what is the degree of the vertex at the entrance to the wildlife park? (1 mark)
- What is the shortest distance, in metres, from the entrance to picnic area `P3`? (1 mark)
- A park ranger starts at the entrance and drives along every road in the park once.
- At which picnic area will the park ranger finish? (1 mark)
- What mathematical term is used to describe the route the park ranger takes? (1 mark)
- A park cleaner follows a route that starts at the entrance and passes through each picnic area once, ending at picnic area `P1`.
Write down the order in which the park cleaner will visit the six picnic areas. (1 mark)
NETWORKS, FUR2 2015 VCAA 1
A factory requires seven computer servers to communicate with each other through a connected network of cables.
The servers, `J`, `K`, `L`, `M`, `N`, `O` and `P`, are shown as vertices on the graph below.
The edges on the graph represent the cables that could connect adjacent computer servers.
The numbers on the edges show the cost, in dollars, of installing each cable.
- What is the cost, in dollars, of installing the cable between server `L` and server `M`? (1 mark)
- What is the cheapest cost, in dollars, of installing cables between server `K` and server `N`? (1 mark)
- An inspector checks the cables by walking along the length of each cable in one continuous path.
To avoid walking along any of the cables more than once, at which vertex should the inspector start and where would the inspector finish? (1 mark)
- The computer servers will be able to communicate with all the other servers as long as each server is connected by cable to at least one other server.
- The cheapest installation that will join the seven computer servers by cable in a connected network follows a minimum spanning tree.
- The factory’s manager has decided that only six connected computer servers will be needed, rather than seven.
How much would be saved in installation costs if the factory removed computer server `P` from its minimum spanning tree network?
A copy of the graph above is provided below to assist with your working. (1 mark)
- The cheapest installation that will join the seven computer servers by cable in a connected network follows a minimum spanning tree.
MATRICES, FUR2 2006 VCAA 1
A manufacturer sells three products, `A`, `B` and `C`, through outlets at two shopping centres, Eastown (`E`) and Noxland (`N`).
The number of units of each product sold per month through each shop is given by the matrix `Q`, where
`{:((qquadqquadqquad\ A,qquadquadB,qquad\ C)),(Q=[(2500,3400,1890),(1765,4588,2456)]{:(E),(N):}):}`
- Write down the order of matrix `Q`. (1 mark)
The matrix `P`, shown below, gives the selling price, in dollars, of products `A`, `B`, `C`.
`P = [(14.50),(21.60),(19.20)]{:(A),(B),(C):}`
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- Evaluate the matrix `M`, where `M = QP`. (1 mark)
- What information does the elements of matrix `M` provide? (1 mark)
- Explain why the matrix `PQ` is not defined. (1 mark)
NETWORKS, FUR2 2010 VCAA 1
The members of one team are Kristy (`K`), Lyn (`L`), Mike (`M`) and Neil (`N`).
In one of the challenges, these four team members are only allowed to communicate directly with each other as indicated by the edges of the following network.
The adjacency matrix below also shows the allowed lines of communication.
`{:(quadKquadLquadMquadN),([(0,1,0,0),(1,0,1,0),(0,f,0,1),(0,g,1,0)]{:(K),(L),(M),(N):}):}`
- Explain the meaning of a zero in the adjacency matrix. (1 mark)
- Write down the values of `f` and `g` in the adjacency matrix. (1 mark)
MATRICES, FUR2 2009 VCAA 1
Three types of cheese, Cheddar (`C`), Gouda (`G`) and Blue (`B`), will be bought for a school function.
The cost matrix `P` lists the prices of these cheeses, in dollars, at two stores, Foodway and Safeworth.
`P = [(6.80, 5.30, 6.20),(7.30, 4.90, 6.15)]{:(text(Foodway)),(text(Safeworth)):}`
- What is the order of matrix `P`? (1 mark)
The number of packets of each type of cheese needed is listed in the quantity matrix `Q`.
`Q = [(8),(11),(3)]{:(C),(G),(B):}`
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- Evaluate the matrix `W = PQ`. (1 mark)
- At which store will the total cost of the cheese be lower? (1 mark)
MATRICES, FUR2 2010 VCAA 1
In a game of basketball, a successful shot for goal scores one point, two points, or three points, depending on the position from which the shot is thrown.
`G` is a column matrix that lists the number of points scored for each type of successful shot.
`G = [(1),(2),(3)]`
In one game, Oscar was successful with
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- 4 one-point shots for goal
- 8 two-point shots for goal
- 2 three-point shots for goal.
- Write a row matrix, `N`, that shows the number of each type of successful shot for goal that Oscar had in that game. (1 mark)
- Matrix `P` is found by multiplying matrix `N` with matrix `G` so that `P = N xx G`
Evaluate matrix `P`. (1 mark)
- In this context, what does the information in matrix `P` provide? (1 mark)
MATRICES, FUR2 2011 VCAA 1
The diagram below shows the feeding paths for insects (`I`), birds (`B`) and lizards (`L`). The matrix `E` has been constructed to represent the information in this diagram. In matrix `E`, a 1 is read as "eat" and a 0 is read as "do not eat".
- Referring to insects, birds or lizards
- what does the 1 in column `B`, row `L`, of matrix `E` indicate? (1 mark)
- what does the row of zeros in matrix `E` indicate? (1 mark)
The diagram below shows the feeding paths for insects (`I`), birds (`B`), lizards (`L`) and frogs (`F`).
The matrix `Z` has been set up to represent the information in this diagram.
Matrix `Z` has not been completed.
- Complete the matrix `Z` above by writing in the seven missing elements. (1 mark)
MATRICES, FUR2 2013 VCAA 1
Five trout-breeding ponds, `P`, `Q`, `R`, `X` and `V`, are connected by pipes, as shown in the diagram below.
The matrix `W` is used to represent the information in this diagram.
`{:({:\ qquadqquadqquadPquadQquad\ Rquad\ Xquad\ V:}),(W = [(0,1,1,1,0), (1,0,0,1,0),(1,0,0,1,0),(1,1,1,0,1),(0,0,0,1,0)]):}{:(),(P),(Q),(R),(X),(V):}`
In matrix `W`
• the 1 in column 1, row 2, for example, indicates that a pipe directly connects pond `P` and pond `Q`
• the 0 in column 1, row 5, for example, indicates that pond `P` and pond `V` are not directly connected by a pipe.
- Find the sum of the elements in row 3 of matrix `W`. (1 mark)
- In terms of the breeding ponds described, what does the sum of the elements in row 3 of matrix `W` represent? (1 mark)
The pipes connecting pond `P` to pond `R` and pond `P` to pond `X` are removed.
Matrix `N` will be used to show this situation. However, it has missing elements.
MATRICES, FUR1 2009 VCAA 1 MC
`3[[2,1],[0,3]] + 2[[−1,0],[2,−7]]` equals
A. `[[4,3],[4,−5]]`
B. `6[[1,1],[2,−4]]`
C. `[[4,3],[4,2]]`
D. `5[[1,1],[2,−4]]`
E. `[[3,6],[7,4]]`
MATRICES, FUR1 2010 VCAA 1 MC
The order of the matrix `[(2, 2), (2, 2), (2, 2)]` is
A. `2 xx 2`
B. `2 xx 3`
C. `3 xx 2`
D. `4`
E. `6`
MATRICES, FUR1 2013 VCAA 1 MC
MATRICES, FUR1 2007 VCAA 2 MC
The number of tourists visiting three towns, Oldtown, Newtown and Twixtown, was recorded for three years.
The data is summarised in the table below.
The `3 xx 1` matrix that could be used to show the number of tourists visiting the three towns in the year 2005 is
A. `[(975, 1002, 1390)]` | B. `[(1002, 1081, 1095)]` |
C. `[(975), (1002), (1390)]` | D. `[(1002), (1081), (1095)]` |
E. `[(975, 1002, 1390), (2105, 1081, 1228), (610, 1095, 1380)]` |
MATRICES, FUR1 2011 VCAA 2 MC
If `A=[(0,1),(1,0)],\ B=[(1),(0)]` and `C= [(0),(1)]`, then `AB + 2C` equals
A. `[(0),(3)]`
B. `[(3),(0)]`
C. `[(1),(2)]`
D. `[(2),(0)]`
E. `[(2),(3)]`
MATRICES, FUR1 2011 VCAA 1 MC
The matrix below shows the airfares (in dollars) that are charged by Zeniff Airlines to fly between Adelaide (`A`), Melbourne (`M`) and Sydney (`S`).
`{:(qquadqquadquadtext(from)),({:(qquadA,\ M,\ S):}),([(0,85,89),(85,0,99),(97,101,0)]):}{:(),(),(A),(M),(S):}{:(),(),(),(qquadtext(to)),():}`
The cost to fly from Melbourne to Sydney with Zeniff Airlines is
A. `$85`
B. `$89`
C. `$97`
D. `$99`
E. `$101`
MATRICES, FUR1 2014 VCAA 1 MC
GRAPHS, FUR2 2012 VCAA 1
The cost, `C`, in dollars, of making `n` phones, is shown by the line in the graph below.
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- Calculate the gradient of the line, `C`, drawn above. (1 mark)
- Write an equation for the cost, `C`, in dollars, of making `n` phones. (1 mark)
- The revenue, `R`, in dollars, obtained from selling `n` phones is given by `R = 150n`.
- Draw this line on the graph above. (1 mark)
- How many phones would need to be sold to obtain $54 000 in revenue? (1 mark)
- Determine the number of phones that would need to be made and sold to break even. (1 mark)
CORE*, FUR2 2013 VCAA 1
Hugo is a professional bike rider.
The value of his bike will be depreciated over time using the flat rate method of depreciation.
The graph below shows his bike’s initial purchase price and its value at the end of each year for a period of three years.
- What was the initial purchase price of the bike? (1 mark)
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- Show that the bike depreciates in value by $1500 each year. (1 mark)
- Assume that the bike’s value continues to depreciate by $1500 each year.
Determine its value five years after it was purchased. (1 mark)
The unit cost method of depreciation can also be used to depreciate the value of the bike.
In a two-year period, the total depreciation calculated at $0.25 per kilometre travelled will equal the depreciation calculated using the flat rate method of depreciation as described above.
- Determine the number of kilometres the bike travels in the two-year period. (1 mark)
GRAPHS, FUR2 2013 VCAA 2
Students at the camp can participate in two different watersport activities: canoeing and surfing.
The cost of canoeing is $30 per hour and the cost of surfing is $20 per hour.
The budget allows each student to spend up to $200, in total, on watersport activities.
The way in which a student decides to spend the $200 is described by the following inequality.
30 × hours canoeing + 20 × hours surfing ≤ 200
- Hillary wants to spend exactly two hours canoeing during the camp.
Calculate the maximum number of hours she could spend surfing. (1 mark)
- Dennis would like to spend an equal amount of time canoeing and surfing.
If he spent a total of $200 on these activities, determine the maximum number of hours he could spend on each activity. (1 mark)
GRAPHS, FUR2 2013 VCAA 1
The distance-time graph below shows the first two stages of a bus journey from a school to a camp.
- At what constant speed, in kilometres per hour, did the bus travel during stage 1 of the journey? (1 mark)
- For how many minutes did the bus stop during stage 2 of the journey? (1 mark)
The third stage of the journey is missing from the graph.
During stage 3, the bus continued its journey to the camp and travelled at a constant speed of 60 km/h for one hour.
- Draw a line segment on the graph above to represent stage 3 of the journey. (1 mark)
- Find the average speed of the bus over the three hours.
Write your answer in kilometres per hour. (1 mark)
The distance, `D` km, of the bus from the school, `t` hours after departure is given by
`D = {(100t 0 ≤ t ≤ 1.5), (150 1.5 ≤ t ≤ 2), (60t + k 2≤ t ≤ 3):}`
- Determine the value of `k`. (1 mark)
GRAPHS, FUR2 2015 VCAA 1
Ben is flying to Japan for a school cultural exchange program.
The graph below shows the cost of a particular flight to Japan, in dollars, on each day in February.
- What is the cost, in dollars, of this flight to Japan on 19 February? (1 mark)
- On how many days in February is the cost of this flight to Japan more than $1000? (1 mark)
Algebra, MET2 2014 VCAA 1
The population of wombats in a particular location varies according to the rule `n(t) = 1200 + 400 cos ((pi t)/3)`, where `n` is the number of wombats and `t` is the number of months after 1 March 2013.
- Find the period and amplitude of the function `n`. (2 marks)
- Find the maximum and minimum populations of wombats in this location. (2 marks)
- Find `n(10)`. (1 mark)
- Over the 12 months from 1 March 2013, find the fraction of time when the population of wombats in this location was less than `n(10)`. (2 marks)
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