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Nick’s height, ‘h’ cm, over his first 20 years can be modelled by the formula h = 5.5a + 68
Where a is his age in years. At what age did Nick’s height reach 170 cm? (1 mark)
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
170=5.5a+68
5.5a=102
a=18.5
The relationship between the rate of increase (R) in the temperature of water being heated by a coil as a current (I) passes through it is given by the equation R = kI^2.
Where R is measured in C (degrees Celcius) per minute, I is measured in amps and is positive, and k is a constant.
(i) It is found that the water temperature rises by 3.5°C per minute when the current is 1.5 amps. Find k correct to 3 significant figure. (1 mark)
(ii) What current would raise the temperature of the water by 2°C per minute? Answer correct to 2 significant figures. (1 mark)
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
(i) 3.5=k(1.5)^2
k=1.56
(ii) 2=1.56×l^2
l=1.1amps
A manufacturer of mobile phones uses the following two equations relating the cost C of manufacture, and the income I, received from the sale of x phones to retail outlets.
$C = 1,500 + 20x
$I = 80x
Use the two equations to answer the following:
(i) What are the fixed costs if there are NO phones manufactured? (1 mark)
(ii) What is the income from selling 5,000 phones to retail outlets? (1 mark)
(iii) What is the cost of manufacturing these 5,000 phones? (1 mark)
(iv) What profit does the manufacturer make if 5,000 phones are sold? (1 mark)
(v) What is the minimum number of phones that must be sold in order that the manufacturer makes a profit? (1 mark)
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
(i) when x=0 C= $1500
(ii) I=80×5000 =$400 000
(iii) C=1500+20×5000 = $101 500
(iv) P = 400 000 – 101 500 = $298 500
(v) 80x=1500+20x
X=25
phones
Solve for d,
54 = 2(d^3). (2 marks)
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
d^3=27
d = 3
Rearrange the equation to make y the subject of the equation
k = 4π + (2/3)y. (2 marks)
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
(3(k-4π))/2=y
The function for calculating the rectangular area that can be enclosed by a 56 m wire fence is given by A = 28x – x^2 where x is the width of the enclosure in metres.
Would the graph of this function be concave up or concave down? (1 mark)
Complete this table of values and hence sketch the function on the axes below. (3 marks)
What is the maximum area of the enclosure? (1 mark)
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
(i) Concave down
(ii)
(iii) A=28×14-14^2= 196 m
The graph shows the number of bacteria B, present in a culture at any time, t hours.
What was the initial population in the culture? (1 mark)
What is the increase in the number of bacteria in the culture in the third second? (1 mark)
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
(i) 100
(ii) 400 – 250 = 150
At a speed of 120km/h it takes Ken 3 hours to drive to Penville. How fast does he need to drive to reach Penville in 4 hours? (2 marks)
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
The number of tables in a revolving restaurant varies inversely with the distance between them. When they are 15m apart, the restaurant an accommodate 42 tables. If the distance between the tables is 20 m, how many tables can be accommodated? (2 marks)
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
N=k/d
42=k/15
k = 630
N= 630/20
N=31 .5 31 tables
Meryl is organising a social function for her classmates. The cost of the hall is $900 and refreshments cost $18 per person. Meryl charges her classmates $33 per ticket for the function.
How many people have to attend for Meryl to break even? (1 mark)
What is the profit or loss if 92 people attend the function? (1 mark)
This response will be awarded full points automatically, but it can be reviewed and adjusted after submission.
33N=18N+900
15N=900
N=60
(ii) P=33×92-(18×92+900)
P=$480