M_Bank\YR11-gen\Algebra02.HSC
Modelling Linear Relationships
1)! ¥MIS85-A3ii¥
In a measurement experiment, students poured measured volumes of water into a container partially full of water and recorded the total depth of water in the container. The results are shown in the following table:
Total number of litres added / 0 / 2 / 4 / 6 / 8 / 10Depth of water (millimetres) / 120 / 155 / 175 / 210 / 235 / 270
These results were then plotted as points on a graph, as shown below.
a. What was the depth of water in the container at the start of the experiment before additional water was added?
b. How many litres of water did the students add to bring the depth to 175millimetres?
c. One of the points was plotted incorrectly. Plot this point correctly on the graph and mark it with a cross (X).
d. Draw a straight line of good fit through the correctly plotted points.
e. From your graph, estimate the rate at which the depth increases for each litre added. (Give your answer in millimetres per litre.)¤
«® a)120mm b)4L c) d)e)13mm/L»
2)! ¥MIS86-A5i¥
A certain beer contains 5% alcohol by volume.
a. Find the amount of alcohol in a 286 millilitre glass of this beer.
b. When alcohol is consumed over a period of one hour, the blood alcohol level Bof an average person can be calculated from the formula B=0·0012´a´n, where nis the number of drinks consumed and ais the number of millilitres of alcohol per drink. Use your answer from part (a) to calculate the blood alcohol level of an average person who drinks four 285millilitre glasses of beer in one hour.¤
«® a)14·25 mL b)0·0684 »
3)! ¥MIS91-A5b¥
In a science experiment, Angela collected the results shown in the table. The value ofK for d=15 has been omitted from the table.
d / 5 / 10 / 15 / 20 / 25 / 30K / 2·6 / 4·1 / 7·6 / 9·0 / 10·4
Angela plotted her results on the graph paper below.
i. Read from the graph the value ofK when d=15.
ii. On the graph draw a straight line which is a good fit for Angela's results.
iii. Use the line you have drawn to find the value of d when K=12·0.
iv. Angela's teacher says that the formula forK in terms ofd is
K=0·32d+b.
Find an approximate value forb.¤
«® i)5·9 ii) iii)34 iv)1·0 »
4)! ¥MIS94-A8¥
There are twenty-seven times as many cars in Australia as motorcycles. Cstands for the number of cars and Mfor the number of motorcycles. Which equation correctly describes the relationship between the number of cars and motorcycles?
(A)M=27C (B)C= (C)C=27M (D)M=27+C¤
«® C »
5)! ¥MIS95-B27d¥
The solid line on the graph shows the tax payable on taxable incomes up to $50000 in Australia in 1993. The broken line shows a possible 25% flat tax rate.
i. What was the tax payable on an income of $4000 in 1993?
ii. Bernie's taxable income in 1993 was $15000. What was the tax payable on his income?
iii. Kerry's taxable income in 1993 was $5000 more than Bernie's. How much more tax did Kerry pay than Bernie?
iv. How many cents in the dollar did Kerry pay in tax on the $5000?
v. The broken line on the graph represents a flat tax rate of 25%. Suppose that the taxation system changed to a flat tax rate of 25%. In what range of incomes would more tax be paid under this new system?¤
«® i) Zero ii) $1800 iii) $1200 iv)24cents in the dollar v) All incomes less than $37000 »
6)! ¥MIS97-A3¥
The graph shows the cost of sending parcels of different masses.
Eloise wants to send four parcels each weighing 400g to her friend. How much would be saved by sending them together as one parcel, rather than separately?
(A)$1·00 (B)$3·00 (C)$3·50 (D)$4·50¤
«® C »
7)! ¥MIS98-6¥
The following table shows ordered pairs for the equation y=2x+4.
x / –1 / 0 / 1y / 2 / 4 / 6
Which of the following graphs represents the equation y=2x+4?
¤
«® A »
8)! ¥SPC01-5¥
The graph shows tax payable against taxable income, in thousands of dollars.
¥
Using the graph, the tax payable against taxable income of $36000 is closest to
(A)$8000 (B)$8100 (C)$8200 (D)$8300¤
«® C »
9)! ¥SPC01-6¥
The graph shows the cost of sending parcels of different masses.
¥
Eloise wants to send four parcels each weighing 400g to her friend. How much would be saved by sending them together as one parcel, rather than separately?
(A)$1·00 (B)$3·00 (C)$3·50 (D)$4·50¤
«® C »
10)! ¥GEN01-13¥
What is the equation of the linel?
(A)y=6x+2 (B)y=x+2 (C)y=3x+2 (D)¤
«® D »
11)! ¥GEN01-17¥
The distance-time graph for a moving object is shown.
What is the speed of the object in kilometres per hour?
(A)3km/h (B)14km/h (C)50km/h (D)180km/h¤
«® D »
12)! ¥GEN01-23a¥
The 11 people in Sam’s cricket team always bat in the same order. Sam recorded the batting order and the average number of runs scored by each player during the season.
Batting order / Average number of runs1 / 16
2 / 10
3 / 11
4 / 8
5 / 7
6 / 4
7 / 4
8 / 5
9 / 3
10 / 1
11 / 1
i. Display the data as a scatterplot on the graph paper provided. Make sure that you have labelled the axes.
ii. Draw a line of fit on your scatterplot on the graph paper provided. (No calculations are necessary.)
iii. Using your scatterplot, describe the correlation between the batting order and the average number of runs. ¤
«® i)ii) iii)There is a strong negative correlation »
13)! ¥GEN01-26a¥
Otto is a manager of a weekend market in which there are 220stalls for rent. From past experience, Otto knows that if he charges ddollars to rent a stall, then the number of stalls,s, that will be rented is given by: s=220–4d.
i. How many stalls will be rented if Otto charges $7·50 per stall?
ii. Copy and complete the following table for the function s=220–4d.
d / 10 / 30 / 50s
iii. Draw a graph of the function s=220–4d. Use your ruler to draw axes. Label each axis, and mark a scale on each axis.
iv. Does it make sense to use the formula s=220–4d to calculate the number of stalls rented if Otto charges $60 per stall? Explain your answer. ¤
«® i)190 ii)
d / 10 / 30 / 50s / 180 / 100 / 20
iii) iv)No, when d=60, s=–20. The formula is only valid for 0£d£55 »
14)! ¥GEN02-6¥
Which one of the following could be the graph of y=3x+1?
¤
«® A »
15)! ¥GEN02-22¥
The graph shows the tax payable for taxable incomes up to $60000 in a proposed tax system.
How much of each dollar earned over $30000 is payable in tax?
(A)10cents (B)12cents (C)20cents (D)23cents¤
«® C »
16)! ¥GEN02-26c¥
A class of 30students sat for an algebra test and a geometry test. The results were displayed in a scatterplot, and a line of fit was drawn, as shown.
i. How many students scored less than 30on the algebra test?
ii. Calculate the gradient of the line of fit drawn.
iii. What is the equation of the line of fit drawn?
iv. Describe the correlation between geometry test results and algebra test results.
v. Mitchell looked at the scatterplot and said: ‘In this class, all students who are near the top in algebra are also near the top in geometry’. Explain why his statement is incorrect. ¤
«® i)3 ii) iii) iv)A strong positive correlation v)The statement is only true for some students »
17)! ¥GEN03-7¥
At the same time, Alex and Bryan start riding towards each other along a road. The graph shows their distances (in kilometres) from town after t minutes.
How many kilometres has Alex travelled when they meet?
(A)4 (B)8 (C)12 (D)20¤
«® B »
18)! ¥GEN03-25a¥
A census was conducted of the 33171 households in Sunnytown. Each household was asked to indicate the number of cars registered to that household. The results are summarised in the following table.
Number of cars / Frequency0 / 2735
1 / 12305
2 / 13918
3 / 3980
4 / 233
Total / 33171
i. 1. Determine the mode number of cars in a household.
2. Explain what is meant by “the mode number of cars in a household”.
ii. Sunnytown Council issued a ‘free parking’ sticker for each car registered to
a household in Sunnytown. How many parking stickers were issued?
- The council represented the results of the census in a sector graph. What is the angle in the sector representing the households with no cars? Give your answer to the nearest degree.
- Visitors to Sunnytown Airport have to pay for parking. The following step graph shows the cost of parking for t hours.
What is the cost for a car that is parked one evening from 6pm to 8:30pm? ¤
«® i)1)2 2)The most common number of cars per household ii)53013 iii)30° iv)$10 »
19)! ¥GEN03-26a¥
At a World Cup rugby match, the stadium was filled to capacity for the entire game. At the end of the game, people left the stadium at a constant rate. The graph shows the number of people (N) in the stadium t minutes after the end of the game.
The equation of the line is of the form N=a–bt, where a and b are constants.
- Write down the value ofa, and give an explanation of its meaning.
- 1. Calculate the value b.
2. What does the value of b represent in this situation?
- Rearrange the formula N=a–bt to make t the subject.
- How long did it take 10000 people to leave the stadium?
- Copy or trace the graph of N against t shown above into your answer booklet. Suppose that 15minutes after the end of the game, several of the exits had been closed, reducing the rate which people left. On the same axes, carefully draw another graph of N against t that could represent this new situation. Your new graph should show N from t=15 until all the people had left the stadium. ¤
«® i)a=60000. ais the number of people in the stadium immediately at the end of the game. ii)1)2000 2)bis the rate (people/minute) at which people are leaving the stadium iii) iv)5minutes v) »
20)! ¥GEN03-28c¥
i. While Sandra is on holiday she visits countries where the Fahrenheit temperature scale is used. She knows that the correct way to convert from Celsius to Fahrenheit is: ‘Multiply the Celsius temperature by 1×8, then add 32’. Find the value ofA in the following table.
Celsius / Fahrenheit5 / 41
15 / 59
A / 77
ii. Peter uses the following method to approximate the conversion from Celsius to Fahrenheit: ‘Add 12 to the Celsius temperature, then double your result.’ Express Peter’s rule as an algebraic equation. Use C for the Celsius temperature and F for the approximate Fahrenheit temperature. ¤
«® i)25 ii)F=2(C+12) »
21)! ¥GEN04-2¥
Susan drew a graph of the height of a plant.
What is the gradient of the line?
(A) 1 (B) 5 (C) 7×5 (D) 10¤
«® B »
22)! ¥Gen06-7¥
Which equation represents the relationship between xandy in this table?
(A)y=2x+1 (B)y=2x–2 (C) (D)¤
«® D »
¤©Board of Studies NSW 1984 - 2006
©EduData Software Pty Ltd: Data Ver5.0 2006
239