Solutions can be found by pressing ‘hint’
0 of 4 Questions completed
Questions:
You have already completed the quiz before. Hence you can not start it again.
Quiz is loading…
You must sign in or sign up to start the quiz.
You must first complete the following:
0 of 4 Questions answered correctly
Your time:
Time has elapsed
You have reached 0 of 0 point(s), (0)
Earned Point(s): 0 of 0, (0)
0 Essay(s) Pending (Possible Point(s): 0)
Average score |
|
Your score |
|
Pos. | Name | Entered on | Points | Result |
---|---|---|---|---|
Table is loading | ||||
No data available | ||||
The air pressure, P, in a bubble varies inversely with the volume, V, of the bubble.
(i) Write an equation relating P, V and a, where a is a constant. (1 mark)
(ii) It is known that P=3 when V=2.
By finding the value of the constant, a, find the value of P when V=4. (2 marks)
(iii) Sketch a graph to show how P varies for different values of V.
Use the horizontal axis to represent volume and the vertical axis to represent air pressure. (2 marks)
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
(i) P ∝ 1/V
= a/V
(ii) When P = 3, V = 2
⇒3 = a/2
a = 6
Need to find P when V = 4
P =6/4
=1 1/2
(iii)
When people walk in snow, the depth (D cm) of each footprint depends on both the area (A cm²) of the shoe sole and the weight of the person. The graph shows the relationship between the area of the shoe sole and the depth of the footprint in snow, for a group of people of the same weight.
(i) The graph is a hyperbola because D is inversely proportional to A. The point P lies on the hyperbola.
Find the equation relating D and A. (2 marks)
(ii) A man from this group walks in snow and the depth of his footprint is 4 cm.
Use your equation from part (i) to calculate the area of his shoe sole. (1 mark)
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
i. D ∝1/A ⇒ D=k/A
When D=15,A=300
15 =k/300
∴k =4500
ii. 4 =4500/A
∴A =4500/4
=1125 cm²
The cost of hiring an open space for a music festival is $120 000. The cost will be shared equally by the people attending the festival, so that C (in dollars) is the cost per person when n people attend the festival.
(i) Complete the table below by filling in the THREE missing values. (1 mark)
(ii) Using the values from the table, draw the graph showing the relationship between n and C. (2 marks)
(iii) What equation represents the relationship between n and C? (1 mark)
(iv) Give ONE limitation of this equation in relation to this context. (1 mark)
(v) Is it possible for the cost per person to be $94? Support your answer with appropriate calculations. (1 mark)
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
(i)
(ii)
(iii) C=120 000/n
(iv) Limitations can include:
• n must be a whole number
• C>0
(v) If C=94
⇒94 =120 000/n
94n =120 000
n =120 000/94
=1276.595…♦ Mean mark 38%
∴ Cost cannot be $94 per person,
because n isn’t a whole number.
A health rating, R, is calculated by dividing a person’s weight, w, in kilograms by the square of the person’s height, h, in metres.
(i) Fred is 150 cm and weighs 72 kg. Calculate Fred’s health rating. (1 mark)
(ii) Over several years, Fred expects to grow 10 cm taller. By this time he wants his health rating to be 25. How much weight should he gain or lose to achieve his aim? Justify your answer with mathematical calculations. (2 marks)
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
(i) R=w/h^2
When w=72 and h=1.5 m
R =72/1.5^2
=32
(ii) Find w if R=25 and h=1.6
25 =w/1.6^2
w =25×1.6^2
=64 kg
∴ Weight Fred should lose
=72−64
=8 kg