graphs 2002. question one the teachers at valley high want to know the cost of hiring a bus to...
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![Page 1: Graphs 2002. Question One The teachers at Valley High want to know the cost of hiring a bus to travel to the interschool sports day. Betta Buses has two](https://reader035.vdocument.in/reader035/viewer/2022070413/5697bff11a28abf838cbb0ce/html5/thumbnails/1.jpg)
Graphs
2002
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Question One
• The teachers at Valley High want to know the cost of hiring a bus to travel to the interschool sports day.
• Betta Buses has two prices for hiring buses: one for a 45-seat bus and one for a 60-seat bus.
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The graph below shows the cost for distances travelled up to 100
kilometres.
![Page 4: Graphs 2002. Question One The teachers at Valley High want to know the cost of hiring a bus to travel to the interschool sports day. Betta Buses has two](https://reader035.vdocument.in/reader035/viewer/2022070413/5697bff11a28abf838cbb0ce/html5/thumbnails/4.jpg)
Another bus company, Cheap Coaches, gives the teachers an equation to work out the cost of their bus: C = 2d + 200where C is the cost to run the bus for a given distance (in dollars)
and d is the distance travelled by the bus (in kilometres).
Draw the graph for the Cheap Coaches bus on the axes above. You should show costs for distances up to 100 kilometres.
![Page 5: Graphs 2002. Question One The teachers at Valley High want to know the cost of hiring a bus to travel to the interschool sports day. Betta Buses has two](https://reader035.vdocument.in/reader035/viewer/2022070413/5697bff11a28abf838cbb0ce/html5/thumbnails/5.jpg)
Another bus company, Cheap Coaches, gives the teachers an equation to work out the cost of their bus: C = 2d + 200where C is the cost to run the bus for a given distance (in dollars)
and d is the distance travelled by the bus (in kilometres).
Draw the graph for the Cheap Coaches bus on the axes above. You should show costs for distances up to 100 kilometres.
![Page 6: Graphs 2002. Question One The teachers at Valley High want to know the cost of hiring a bus to travel to the interschool sports day. Betta Buses has two](https://reader035.vdocument.in/reader035/viewer/2022070413/5697bff11a28abf838cbb0ce/html5/thumbnails/6.jpg)
For what distance is it the same price to hire a 60-seat Betta Buses bus and a Cheap Coaches bus?
![Page 7: Graphs 2002. Question One The teachers at Valley High want to know the cost of hiring a bus to travel to the interschool sports day. Betta Buses has two](https://reader035.vdocument.in/reader035/viewer/2022070413/5697bff11a28abf838cbb0ce/html5/thumbnails/7.jpg)
For what distance is it the same price to hire a 60-seat Betta Buses bus and a Cheap Coaches bus?
50 km
![Page 8: Graphs 2002. Question One The teachers at Valley High want to know the cost of hiring a bus to travel to the interschool sports day. Betta Buses has two](https://reader035.vdocument.in/reader035/viewer/2022070413/5697bff11a28abf838cbb0ce/html5/thumbnails/8.jpg)
How is this shown by the graphs?
![Page 9: Graphs 2002. Question One The teachers at Valley High want to know the cost of hiring a bus to travel to the interschool sports day. Betta Buses has two](https://reader035.vdocument.in/reader035/viewer/2022070413/5697bff11a28abf838cbb0ce/html5/thumbnails/9.jpg)
How is this shown by the graphs?
The intersection point of the lines
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Which TWO buses cost the same to hire per kilometre?
![Page 11: Graphs 2002. Question One The teachers at Valley High want to know the cost of hiring a bus to travel to the interschool sports day. Betta Buses has two](https://reader035.vdocument.in/reader035/viewer/2022070413/5697bff11a28abf838cbb0ce/html5/thumbnails/11.jpg)
Which TWO buses cost the same to hire per kilometre?
The cheap Coaches and the 45 seat bus
![Page 12: Graphs 2002. Question One The teachers at Valley High want to know the cost of hiring a bus to travel to the interschool sports day. Betta Buses has two](https://reader035.vdocument.in/reader035/viewer/2022070413/5697bff11a28abf838cbb0ce/html5/thumbnails/12.jpg)
How is this shown by the graphs?
The cheap Coaches and the 45 seat bus
![Page 13: Graphs 2002. Question One The teachers at Valley High want to know the cost of hiring a bus to travel to the interschool sports day. Betta Buses has two](https://reader035.vdocument.in/reader035/viewer/2022070413/5697bff11a28abf838cbb0ce/html5/thumbnails/13.jpg)
How is this shown by the graphs?
The gradients of the lines are the same.
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What is the cost per kilometre to hire the 60-seat Betta Buses bus?
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What is the cost per kilometre to hire the 60-seat Betta Buses bus?
300/100=$3 per km
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How is this shown by the graphs
![Page 17: Graphs 2002. Question One The teachers at Valley High want to know the cost of hiring a bus to travel to the interschool sports day. Betta Buses has two](https://reader035.vdocument.in/reader035/viewer/2022070413/5697bff11a28abf838cbb0ce/html5/thumbnails/17.jpg)
What is the cost per kilometre to hire the 60-seat Betta Buses bus?
The gradient of the line.
300/100=$3 per km
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Use the graph to write the equation for the 45-seat Betta Buses bus. (C = …)
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Use the graph to write the equation for the 45-seat Betta Buses bus. (C = …)
C =2d+100
![Page 20: Graphs 2002. Question One The teachers at Valley High want to know the cost of hiring a bus to travel to the interschool sports day. Betta Buses has two](https://reader035.vdocument.in/reader035/viewer/2022070413/5697bff11a28abf838cbb0ce/html5/thumbnails/20.jpg)
Use the graph to write the equation for the 60-seat Betta Buses bus. (C = …)
![Page 21: Graphs 2002. Question One The teachers at Valley High want to know the cost of hiring a bus to travel to the interschool sports day. Betta Buses has two](https://reader035.vdocument.in/reader035/viewer/2022070413/5697bff11a28abf838cbb0ce/html5/thumbnails/21.jpg)
Use the graph to write the equation for the 60-seat Betta Buses bus. (C = …)
C =3d+150
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Question Two
• Tom is designing a logo for the Valley High sports jacket. Part of the logo is shown on the axes below.
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Write the equation of the line labelled AB on the axes below.
−
−
−
−
−
−
−
−
−
− − − − −
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The line passes through -2 on the y-axis and gradient is negative 1/2
−
−
−
−
−
−
−
−
−
− − − − −
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The line passes through -2 on the y-axis and gradient is negative 1/2
−
−
−
−
−
−
−
−
−
− − − − −
y =−12
x−2
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The logo design also has two parabolas.
• On the axes above, draw the graph of y = (x + 4)(x – 1).
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On the axes above, draw the graph of y =
(x + 4)(x – 1).
-9-8-7-6-5-4-3-2-1012
-5 -4 -3 -2 -1 0 1 2 3 4 5
![Page 28: Graphs 2002. Question One The teachers at Valley High want to know the cost of hiring a bus to travel to the interschool sports day. Betta Buses has two](https://reader035.vdocument.in/reader035/viewer/2022070413/5697bff11a28abf838cbb0ce/html5/thumbnails/28.jpg)
On the axes above, draw the graph of y =
(x + 4)(x – 1).
-9-8-7-6-5-4-3-2-1012
-5 -4 -3 -2 -1 0 1 2 3 4 5
![Page 29: Graphs 2002. Question One The teachers at Valley High want to know the cost of hiring a bus to travel to the interschool sports day. Betta Buses has two](https://reader035.vdocument.in/reader035/viewer/2022070413/5697bff11a28abf838cbb0ce/html5/thumbnails/29.jpg)
On the axes above, draw the graph of y =
(x + 4)(x – 1).
-9-8-7-6-5-4-3-2-1012
-5 -4 -3 -2 -1 0 1 2 3 4 5
21
2⎛⎝⎜
⎞⎠⎟
2
=614
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On the axes above, draw the graph of y =
(x + 4)(x – 1).
-9-8-7-6-5-4-3-2-1012
-5 -4 -3 -2 -1 0 1 2 3 4 5
21
2⎛⎝⎜
⎞⎠⎟
2
=614
![Page 31: Graphs 2002. Question One The teachers at Valley High want to know the cost of hiring a bus to travel to the interschool sports day. Betta Buses has two](https://reader035.vdocument.in/reader035/viewer/2022070413/5697bff11a28abf838cbb0ce/html5/thumbnails/31.jpg)
On the axes above, draw the graph of y =
2x 2 – 8
-9-8-7-6-5-4-3-2-1012
-5 -4 -3 -2 -1 0 1 2 3 4 5
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On the axes above, draw the graph of y =
2x 2 – 8
-9-8-7-6-5-4-3-2-1012
-5 -4 -3 -2 -1 0 1 2 3 4 5
![Page 33: Graphs 2002. Question One The teachers at Valley High want to know the cost of hiring a bus to travel to the interschool sports day. Betta Buses has two](https://reader035.vdocument.in/reader035/viewer/2022070413/5697bff11a28abf838cbb0ce/html5/thumbnails/33.jpg)
The part of the graph that is below the x-axis shows the logo for the sports jacket.
x and y are both measured in centimetres.
-9-8-7-6-5-4-3-2-1012
-5 -4 -3 -2 -1 0 1 2 3 4 5
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What is the height of the logo?
-9-8-7-6-5-4-3-2-1012
-5 -4 -3 -2 -1 0 1 2 3 4 5
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What is the height of the graph?
-9-8-7-6-5-4-3-2-1012
-5 -4 -3 -2 -1 0 1 2 3 4 5
8cm
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How is this shown by the graphs?
-9-8-7-6-5-4-3-2-1012
-5 -4 -3 -2 -1 0 1 2 3 4 5
8cm
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How is this shown by the graphs?
-9-8-7-6-5-4-3-2-1012
-5 -4 -3 -2 -1 0 1 2 3 4 5
The distance from the vertex to the x-axis
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What is the width of the logo?
-9-8-7-6-5-4-3-2-1012
-5 -4 -3 -2 -1 0 1 2 3 4 5
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What is the width of the logo?
-9-8-7-6-5-4-3-2-1012
-5 -4 -3 -2 -1 0 1 2 3 4 5
6 cm
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How is this shown by the graphs?
-9-8-7-6-5-4-3-2-1012
-5 -4 -3 -2 -1 0 1 2 3 4 5
The distance between the outer intercepts on the x -axis (-4 and 2)
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Question Three
• Maria won the javelin field event on the sports day.• Her coach recorded the heights of the javelin during her
winning throw.• The javelin is 2 metres above the ground when it is released.• During the first 10 seconds of the javelin’s flight, its height
increases at a constant rate. The rate is 3 metres per second.• The remainder of the javelin’s flight can be modelled by a
parabola.• The javelin reaches a maximum height of 36 metres after 12
seconds.
The coach’s data is graphed on the set of axes below.
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Write TWO equations to model the flight of Maria’s winning
javelin throw.
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The javelin is 2 metres above the ground when it is released.
2
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During the first 10 seconds of the javelin’s flight, its height increases at a constant rate. The rate is
3 metres per second.
2
H =3t+ 2
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The remainder of the javelin’s flight can be modelled
by a parabola.
2
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The javelin reaches a maximum height of 36 metres
after 12 seconds.
2
12
36
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The javelin reaches a maximum height of 36 metres
after 12 seconds.
2
12
36
H =−k t−12( )2 + 36
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Now find a point on the graph you are certain of.
2
12
36
H =−k t−12( )2 + 36
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We know that H = 32 when t = 10
2
12
36
H =−k t−12( )2 + 36
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Substitute H = 32 and t = 10
2
12
36
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Video cameras were placed 27 metres above the ground.
Calculate the TWO times when the javelin was level with the video cameras.
Show all working.
2
12
36
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Substitute 27 for H
2
12
36
H =− t−12( )2 + 36
27 =− t−12( )2 + 36
9 = t−12( )2
t−12 =±3t=15, 9
It wasn’t a parabola at t = 9, so we can only use 15
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Substitute 27 for H in the first equation
2
12
36
H =3t+ 227 =3t+ 225 =3t
t=813
It wasn’t a parabola at t = 9, so we can only use 15