Graphs and Networks
Finance
Sequences
Earth Geometry
Bivariate Data
100
For a planar connected graph, find f if v=8 and e=10.
f=4
100
Craig has won $1 000 000 in a lottery and has decided to invest this money in a perpetuity that pays interest at the annual percentage rate of interest of 5.75%, compounding monthly.
What is the monthly payment that Craig can withdraw from his investment?
$4791.67
100
An arithmetic sequence is defined by:
tn+1=tn - 4 t1=6
Find the first five terms.
6 2 -2 -6 -10
100
How many degrees of longitude are equal to 1 hour of time difference?
15
100
Suppose the variance of X is 5, the variance of Y is 6 and the covariance of X and Y is 3. Find the value of r, the correlation between X and Y.
0.5477
200
Describe the following graph as a trail, path, closed trail, cycle, open walk only or closed walk only.
Path
200
An annuity can be modelled by the recurrence relation:
A0=5000, An+1=1.01 x An - 1030
Determine the amount left in the annuity after three payments have been received.
$2030.50
200
What are the next three terms of the following geometric sequence?
2, 18, 108, 648
3888, 23328, 139968,
200
How far apart are Esperance (34oS, 122oE) and Broome (18oS, 122oE)? Round your answer to the nearest kilometer.
1779km
200
If r=0.75, sx=0.85 and sy=0.45, what is the covariance of X and Y?
0.2869
300
Write the adjacency matrix for the following directed graph.
300
Nomsa has borrowed $8000 at an interest rate of 11.28% per annum, compounding monthly. If she makes monthly repayments of $500, what will be the balance of the loan after one year? Round your answer to the nearest cent.
$2630.42
300
In an arithmetic sequence, the second term is 17 and the ninth term is 59. Write down the rule for the sequence and find the first four terms.
tn+1=tn+6 t1=11 t2=17 t3=23 t4=29
300
The longitude of Hanoi is 105oE, while the longitude of Cape Howe is 150oE. When the time in Hanoi is 2:30pm, what is the time in Cape Howe?
5:30pm
300
For the relationship described by the scatterplot shown, the coefficient of determination, R2=0.8215. Determine the value of the correlation coefficient, r (correct to three decimal places).
r=0.906
400
Find the shortest time it would take to start at A, finish at E and visit every town exactly once.
36 mins A-B-C-D-E
400
A building society offers $240000 home loans at an interest rate of 10.25% per annum, compounding monthly. Chelsea would like to pay off this loan over 15 years with monthly repayments.
Determine the repayment amount. Round your answer to the nearest dollar.
$2616
400
An investment of $6000 earns compounding interest at a rate of 4.2% per annum. Write down the value of the investment after n years
A = 6000 x (1.042)n
400
Dimitri is in Athens, which is two hours ahead of Greenwich Mean Time. Allan is in New York, which is five hours behind Greenwich Mean Time. Dimitri is going to ring Allan at 10am on Wednesday, Athens time. What day and time will it be in New York when he rings?
3am the same day
400
For the relationship described by the scatter plot shown, the coefficient of determination R2=0.1243. Determine the value of the correlation coefficient, r(correct to three decimal places).
r=-0.353
500
A housing estate has large open parklands that contain seven large trees. The trees are denoted as vertices A to G on the graph below.
A new track is to be made between two trees. This track will mean that you can start at any vertex, walk along each of the tracks only once and return to your starting point. Between which two vertices should the new track be made?
C and G
500
Kathy is a fan of the Brisbane Broncos. Her annual club membership costs $350. Kathy invests some money and intends to use the interest to pay her membership every year in perpetuity. Assume that the membership fee remains the same from year to year.
If Kathy can invest her money to earn interest at the rate of 3.5% per annum, compounding annually, what principal amount will she need? Round your answer to the nearest cent.
$10 000
500
A simple interest investment of $7000 has an interest rate of 7.4% per annum.
Write down the rule for the value of the simple interest investment An in terms of n. Use the rule to determine how many years it takes for the value of the investment to be more than $10000.
A = 7000+518n
6 years
500
An aircraft flies from Bairnsdale (38oS, 148oE) due north to Grenfell (34oS, 148oE). It then flies due west to Renmark (34oS, 141oE). What is the total distance the aircraft flies?
1090km
500
A study was conducted where a group of 100 adults were asked to record their weekly income, their weekly expenditure on food, and their weekly expenditure on leisure. The researcher determinded the following correlation coefficients:
rincome, food=0.6 rincome, leisure=0.5
Calculate the coefficients of determination relating to income and expenditure on food, and income and expenditure on leisure. Write a sentence that details what the results explain about income and its effect on expenditure.
R2=36%, thus the variation in the weekly expenditure on food can be explained by the variation in income.
R2=25%, thus the variarion in the weeklu expenditure on leisure can be explained by the variation in income.