GRAPHS, FUR1 2014 VCAA 1 MC
GRAPHS, FUR1 2006 VCAA 8 MC
The cost of manufacturing a number of frying pans consists of a fixed cost of $400 plus a cost of $50 per frying pan.
The manufacturer could break even by selling
A. 10 frying pans at $90 each.
B. 10 frying pans at $45 each.
C. 15 frying pans at $60 each.
D. 15 frying pans at $30 each.
E. 20 frying pans at $50 each.
GRAPHS, FUR1 2006 VCAA 9 MC
The four inequalities below were used to construct the feasible region for a linear programming problem.
`x >= 0`
`y >= 0`
`x + y <= 9`
`y <= 1/2 x`
A point that lies within this feasible region is
A. `(4, 4)`
B. `(5, 3)`
C. `(6, 2)`
D. `(6, 4)`
E. `(7, 3)`
GRAPHS, FUR1 2006 VCAA 7 MC
In a linear programming problem involving animal management on a farm
• `x` represents the number of cows on the farm
• `y` represents the number of sheep on the farm.
The feasible region (with boundaries included) for the problem is indicated by the shaded region on the diagram below.
One of the constraints defining the feasible region indicates that
A. there must be 20 cows and 60 sheep.
B. there must be 40 cows and 40 sheep.
C. the number of sheep cannot exceed 40.
D. the number of cows must be at least 60.
E. the total number of cows and sheep cannot exceed 80.
GRAPHS, FUR1 2006 VCAA 6 MC
The point of intersection of two lines is `(2, – 2)`.
One of these two lines could be
A. `x - y = 0`
B. `2x + 2y = 8`
C. `2x + 2y = 0`
D. `2x - 2y = 4`
E. `2x - 2y = 0`
GRAPHS, FUR1 2006 VCAA 5 MC
Which one of the following statements about the line with equation `12x - 4y = 0` is not true?
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 `12x - 4y = 12`
D. the point `(1, 3)` lies on the line
E. for this line, as `x` increases `y` increases
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, `M`, of the gas container (in grams) changes with time, `t` (in hours), over this period.
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. `1.5\ text(hours.)`
B. `3\ text(hours.)`
C. `4.5\ text(hours.)`
D. `6\ text(hours.)`
E. `220\ text(hours.)`
Part 2
Which one of the following rules could be used to describe the graph above?
A. `M={(332.5 − 25t \ \ \ \ \ text( for ) \ \ \ \ \ \ 0 ≤ t ≤ 4.5),(220 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ text(for ) \ \ \ 4.5 < t ≤ 6) :}`
B. `M={(332.5 − 25t \ \ \ \ \ text( for ) \ \ \ \ \ \ 0 ≤ t ≤ 4.5),(220t \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ text( for ) \ \ \ 4.5 < t ≤ 6) :}`
C. `M={(332.5 + 25t \ \ \ \ \ text( for ) \ \ \ \ \ \ 0 ≤ t ≤ 4.5),(220t \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ text( for ) \ \ \ 4.5 < t ≤ 6) :}`
D. `M={(332.5 − 12.5t \ \ text( for ) \ \ \ \ \ \ 0 ≤ t ≤ 4.5),(220t \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ text( for ) \ \ \ 4.5 < t ≤ 6) :}`
E. `M={(332.5 − 12.5t \ \ text( for ) \ \ \ \ \ \ 0 ≤ t ≤ 4.5),(220 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ text(for ) \ \ \ 4.5 < t ≤ 6) :}`
GRAPHS, FUR1 2006 VCAA 2 MC
GRAPHS, FUR1 2006 VCAA 1 MC
GRAPHS, FUR1 2007 VCAA 9 MC
The following five constraints apply to a linear programming problem.
`x>= 0,\ \ y>= 0,\ \ x + y>=50,\ \ x + y<=100,\ \ y<=x`
In the diagram below, the shaded region (with boundaries included) represents the feasible region for this linear programming problem.
The aim is to maximise the objective function `Z = 2x + ky`.
If the maximum value of `Z` occurs only at the point `(100, 0)`, then a possible value for `k` is
A. `1`
B. `2`
C. `3`
D. `4`
E. `5`
GRAPHS, FUR1 2007 VCAA 8 MC
Which one of the following pairs of simultaneous linear equations has no solution?
A. | `3x - y = 5` |
`4x + y = 9` |
B. | `2x−y = 1` |
`4x−2y = 3` |
C. | `x + 3y = 0` |
`2x - y = 7` |
D. | `x - 3y = 10` |
`3x + 2y = 8` |
E. | `4x + y = - 6` |
`2x - y = 0` |
GRAPHS, FUR1 2007 VCAA 7 MC
GRAPHS, FUR1 2007 VCAA 6 MC
Russell is a wine producer. He makes both red and white wine.
Let `x` represent the number of bottles of red wine he makes and `y` represent the number of bottles of white wine he makes.
This year he plans to make at least twice as many bottles of red wine as white wine.
An inequality representing this situation is
A. `y <= x + 2`
B. `y <= 2x`
C. `y >= 2x`
D. `x <= 2y`
E. `x >= 2y`
GRAPHS, FUR1 2007 VCAA 5 MC
The cost of hiring one motorbike for up to 4 hours is shown in the graph above.
Two motorbikes were hired.
The total charge for hiring the two motorbikes was $45.
The time for which each motorbike was hired could have been
A. 1 hour and 2 hours.
B. 1 hour and 3 hours.
C. 1.5 hours and 2 hours.
D. 1.5 hours and 3 hours.
E. 2 hours and 3.5 hours.
GRAPHS, FUR1 2007 VCAA 4 MC
Paul makes rulers. There is a fixed cost of $60 plus a manufacturing cost of $0.20 per ruler.
Last week Paul was able to break even by selling his rulers for $1 each.
The number of rulers Paul sold last week was
A. `50`
B. `75`
C. `90`
D. `120`
E. `150`
GRAPHS, FUR1 2007 VCAA 3 MC
GRAPHS, FUR1 2007 VCAA 2 MC
A builder's fee, `C` dollars, can be determined from the rule `C = 60 + 55n`, where `n` represents the number of hours worked.
According to this rule, the builder's fee will be
A. $60 for 1 hour of work.
B. $110 for 2 hours of work.
C. $500 for 8 hours of work.
D. $550 for 10 hours of work.
E. $1150 for 10 hours of work.
GRAPHS, FUR1 2007 VCAA 1 MC
GRAPHS, FUR1 2008 VCAA 6 MC
At the local bakery, the cost of four donuts and six buns is $14.70.
The cost of three donuts and five buns is $11.90.
At this bakery, the cost of one donut and two buns will be
A. `$2.80`
B. `$3.80`
C. `$3.85`
D. `$4.55`
E. `$4.85`
GRAPHS, FUR1 2008 VCAA 8 MC
A region is defined by the following inequalities
`y >= -4x + 10`
`y - x >= 1`
A point that lies within this region is
A. `(1, 3)`
B. `(2, 1)`
C. `(3, 2)`
D. `(4, 6)`
E. `(5, 1)`
GRAPHS, FUR1 2008 VCAA 7 MC
GRAPHS, FUR1 2008 VCAA 5 MC
A mixture contains two liquids, `A` and `B`.
Liquid `A` costs $2 per litre and liquid `B` costs $3 per litre.
Let `x` be the volume (in litres) of liquid `A` purchased.
Let `y` be the volume (in litres) of liquid `B` purchased.
Which graph below shows all possible volumes of liquid `A` and liquid `B` that can be purchased for exactly $12?
GRAPHS, FUR1 2008 VCAA 4 MC
When shopping, Betty can use either Easypark or Safepark to park her car.
At Easypark, cars can be parked for up to 8 hours per day.
The fee structure is as follows.
`text(Fee)={(text($5.00,), 0 < text(hours) <= 2),(text($8.00,), 2 < text(hours) <= 5),(text($11.00,), 5 < text(hours) <= 8) :}`
Safepark charges fees according to the formula
`text(Fee) = $2.50 xx text(hours)`
Betty wants to park her car for 5 hours on Monday and 3 hours on Tuesday.
The minimum total fee that she can pay for parking for the two days is
A. `$7.50`
B. `$11.00`
C. `$15.50`
D. `$16.00`
E. `$20.00`
GRAPHS, FUR1 2008 VCAA 3 MC
The graph below shows the time `t`, in hours, taken to travel 100 km at an average speed of `s` km/h.
Which statement is false?
- As average speed increases, the time taken to travel 100 km decreases.
- It will take 2 hours to travel 100 km at an average speed of 50 km/h.
- The relationship between time and average speed is linear.
- When travelling at an average speed of 20 km/h, the 100 km journey takes 5 hours to complete.
- A formula that relates `s` and `t` is `t = 100/s, \ s > 0`
GRAPHS, FUR1 2008 VCAA 2 MC
Initially there are 5000 litres of water in a tank. Water starts to flow out of the tank at the constant rate of 2 litres per minute until the tank is empty.
After `t` minutes, the number of litres of water in the tank, `V`, will be
A. `V = 5000 - 2t`
B. `V = 2t - 5000`
C. `V = 5000 + 2t`
D. `V = 2 - 5000t`
E. `V = 5000t - 2`
GRAPHS, FUR1 2008 VCAA 1 MC
The concentration (in mg/L) of a particular chemical in a swimming pool is graphed over a four-week period.
For this four-week period, the concentration of the chemical was greater than 3 mg/L for
A. exactly four weeks.
B. between three and four weeks.
C. exactly two weeks.
D. exactly one week.
E. less than one week.
GRAPHS, FUR1 2009 VCAA 9 MC
GRAPHS, FUR1 2009 VCAA 8 MC
Brian, a landscaping contractor, charges by the hour for his company’s services.
To complete a particular job, he will have to use three workers and pay each of them $20 per hour. The fixed costs for the job are $150 and it will take four hours to complete the job.
To break even on this job, his hourly charge to the client should be
A. `$38.25`
B. `$57.50`
C. `$97.50`
D. `$127.50`
E. `$132.50`
GRAPHS, FUR1 2009 VCAA 7 MC
A school’s squash and volleyball teams plan to enter a sports competition.
A squash team requires at least 4 players.
A volleyball team requires at least 6 players.
No more than 25 students from any one school can enter the competition.
Let `x` be the number of squash players sent by the school to the competition.
Let `y` be the number of volleyball players sent by the school to the competition.
The constraints above define the feasible region shaded in the graph below.
A fee is charged for all players entering the competition. Squash players are charged $5 and volleyball players are charged $4.
Given the above constraints, the maximum cost for the school’s squash and volleyball teams to enter the competition is
A. `$44`
B. `$104`
C. `$119`
D. `$121`
E. `$144`
GRAPHS, FUR1 2009 VCAA 5-6 MC
Kathy is a tutor who offers tutorial sessions for English and History students.
Part 1
An English tutorial session takes 1.5 hours.
A History tutorial session take 30 minutes.
Kathy has no more than 15 hours available in a week for tutorial sessions.
Let `x` represent the number of English tutorial sessions Kathy has each week.
Let `y` represent the number of History tutorial sessions Kathy has each week.
An inequality representing the constraint on Kathy’s tutorial time each week (in hours) is
A. `1.5x + 30y = 15`
B. `1.5x + 30y >= 15`
C. `1.5x + 30y <= 15`
D. `1.5x + 0.5y >= 15`
E. `1.5x + 0.5y <= 15`
Part 2
Kathy prefers to have no more than 18 tutorial sessions in total each week.
She prefers to have at least 4 English tutorial sessions.
She also prefers to have at least as many History tutorial sessions as English tutorial sessions.
Let `x` represent the number of English tutorial sessions Kathy has each week.
Let `y` represent the number of History tutorial sessions Kathy has each week.
The shaded region that satisfies all of these constraints is
GRAPHS, FUR1 2009 VCAA 4 MC
The total playing time of three CDs and four DVDs is 690 minutes.
The total playing time of five CDs and seven DVDs is 1192 minutes.
All of the CDs have the same playing time as each other and all of the DVDs have the same playing time as each other.
Let `x` be the playing time of a CD.
Let `y` be the playing time of a DVD.
The set of simultaneous linear equations that can be solved to find the playing time of a CD and the playing time of a DVD is
A. |
`4x + 3y` | `= 690` |
`7x + 5y` | `= 1192` |
B. | `3x + 4y` | `= 690` |
`5x + 7y` | `= 1192` |
C. | `3x + 5y` | `= 690` |
`4x + 7y` | `= 1192` |
D. | `3x + 4y` | `= 1192` |
`5x + 7y` | `= 690` |
E. | `4x + 3y` | `= 1192` |
`7x + 5y` | `= 690` |
GRAPHS, FUR1 2009 VCAA 1-3 MC
The graph below shows the water temperature in a fish tank over a 12-hour period.
Part 1
Over the 12-hour period, the temperature of the tank is increasing most rapidly
A. during the first 2 hours.
B. from 2 to 4 hours.
C. from 4 to 6 hours.
D. from 6 to 8 hours.
E. from 8 to 10 hours.
Part 2
The fish tank is considered to be a safe environment for a type of fish if the water temperature is maintained between 24°C and 28°C.
Over the 12-hour period, the length of time (in hours) that the environment was safe for this type of fish was closest to
A. `1.5`
B. `5.0`
C. `7.0`
D. `8.5`
E. `10.5`
Part 3
The graph below can be used to determine the cost (in cents) of heating the fish tank during the first five hours of heating.
The cost of heating the tank for one hour is
A. `4\ text(cents.)`
B. `5\ text(cents.)`
C. `15\ text(cents.)`
D. `20\ text(cents.)`
E. `100\ text(cents.)`
GEOMETRY, FUR1 2006 VCAA 7 MC
GEOMETRY, FUR1 2008 VCAA 5 MC
GEOMETRY, FUR1 2006 VCAA 9 MC
Points `M` and `P` are the same distance from a third point `O`.
The bearing of `M` from `O` is 038° and the bearing of `P` from `O` is 152°.
The bearing of `P` from `M` is
A. between 000° and 090°
B. between 090° and 180°
C. exactly 180°
D. between 180° and 270°
E. between 270° and 360°
GEOMETRY, FUR1 2006 VCAA 8 MC
GEOMETRY, FUR1 2006 VCAA 6 MC
GEOMETRY, FUR1 2006 VCAA 5 MC
A block of land is triangular in shape.
The three sides measure 36 m, 58 m and 42 m.
To calculate the area, Heron’s formula is used.
The correct application of Heron’s formula for this triangle is
- `text(Area) = sqrt(136\ (136 − 36) (136 − 58) (136 − 42))`
- `text(Area) =sqrt(136\ (136 −18) (136 − 29) (136 − 21))`
- `text(Area) =sqrt(68\ (68 − 36) (68 − 58) (68 − 42))`
- `text(Area) = sqrt(68\ (68 −18) (68 − 29) (68 − 21))`
- `text(Area) = sqrt(68\ (136 − 36) (136 − 58) (136 − 42))`
GEOMETRY, FUR1 2006 VCAA 4 MC
GEOMETRY, FUR1 2006 VCAA 2 MC
GEOMETRY, FUR1 2006 VCAA 1 MC
GEOMETRY, FUR1 2007 VCAA 9 MC
The points `M`, `N` and `P` form the vertices of a triangular course for a yacht race.
`MN = MP = 4\ text(km.)`
The bearing of `N` from `M` is 070°
The bearing of `P` from `M` is 180°
Three people perform different calculations to determine the length of `NP` in kilometres.
Graeme | `\ \ \ \ \ NP` | `= sqrt(16 + 16 − 2 xx 4 xx 4 xx cos110^@)` |
Shelley | `NP` | `= 2 xx 4 xx cos 35^@` |
Tran | `NP` | `= (4 xx sin110^@)/sin35^@` |
The correct length of `NP` would be found by
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
A closed cubic box of side length 36 cm is to contain a thin straight metal rod.
The maximum possible length of the rod is closest to
A. `36\ text(cm)`
B. `51\ text(cm)`
C. `62\ text(cm)`
D. `108\ text(cm)`
E. `216\ text(cm)`
GEOMETRY, FUR1 2007 VCAA 6 MC
GEOMETRY, FUR1 2007 VCAA 5 MC
A block of land has an area of 4000 m².
When represented on a map, this block of land has an area of 10 cm².
On the map 1 cm would represent an actual distance of
A. `10\ text(m)`
B. `20\ text(m)`
C. `40\ text(m)`
D. `400\ text(m)`
E. `4000\ text(m)`
GEOMETRY, FUR1 2007 VCAA 4 MC
GEOMETRY, FUR1 2007 VCAA 3 MC
A rectangle is 3.79 m wide and has a perimeter of 24.50 m.
Correct to one decimal place, the length of the diagonal of this rectangle is
A. `9.2\ text(m)`
B. `9.3\ text(m)`
C. `12.2\ text(m)`
D. `12.3\ text(m)`
E. `12.5\ text(m)`
GEOMETRY, FUR1 2007 VCAA 2 MC
For an observer on the ground at `A`, the angle of elevation of a weather balloon at `B` is 37°.
`C` is a point on the ground directly under the balloon. The distance `AC` is 2200 m.
To the nearest metre, the height of the weather balloon above the ground is
A. `1324\ text(m)`
B. `1658\ text(m)`
C. `1757\ text(m)`
D. `2919\ text(m)`
E. `3655\ text(m)`
GEOMETRY, FUR1 2007 VCAA 1 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. `063°`
B. `108°`
C. `153°`
D. `162°`
E. `180°`
GEOMETRY, FUR1 2008 VCAA 8 MC
GEOMETRY, FUR1 2008 VCAA 7 MC
Sand is poured out of a truck and forms a pile in the shape of a right circular cone. The diameter of the base of the pile of sand is 2.6 m. The height is 1.2 m.
The volume (in m³) of sand in the pile is closest to
A. `2.1`
B. `3.1`
C. `6.4`
D. `8.5`
E. `25.5`
GEOMETRY, FUR1 2008 VCAA 6 MC
GEOMETRY, FUR1 2008 VCAA 4 MC
GEOMETRY, FUR1 2011 VCAA 3 MC
The radius of a circle is 6.5 centimetres.
A square has the same area as this circle.
The length of each side of the square, in centimetres, is closest to
A. `6.4`
B. `10.2`
C. `11.5`
D. `23.0`
E. `33.2`
GEOMETRY, FUR1 2011 VCAA 2 MC
The point `Q` on building `B` is visible from the point `P` on building `A`, as shown in the diagram above.
Building `A` is 16 metres taller than building `B`.
The horizontal distance between point `P` and point `Q` is 23 metres.
The angle of depression of point `Q` from point `P` is closest to
A. `35°`
B. `41°`
C. `44°`
D. `46°`
E. `55°`
GEOMETRY, FUR1 2011 VCAA 5 MC
GEOMETRY, FUR1 2011 VCAA 6 MC
GEOMETRY, FUR1 2011 VCAA 4 MC
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