🔢 Sequences & Growth
An arithmetic sequence begins 8, 13, 18... What is the common difference?
5
What is the purpose of a moving average?
Smooth short-term fluctuations to show the underlying trend
Brisbane is UTC+10. What time is it in Brisbane when it is 12 noon UTC?
10pm
What does p.a. mean?
Per annum / per year
What do we call a point in a network?
Vertex
Find the next term: 3, 6, 12, 24, ...
48
Sales are 20, 24, 28. Find the 3-point moving average.
24
Two locations lie on the same longitude at 20°S and 45°S. Find their angular distance.
25°S
Find the periodic interest rate for 6% p.a. compounded monthly.
0.5% per month
A vertex has 5 edges connected to it. What is its degree?
5
An arithmetic sequence has t1=353 and t3=439. Find d.
43
Actual sales = $6000, seasonal index = 1.2. Find the deseasonalised value.
6000÷1.2= $5000
Brisbane is UTC+10 and Dubai UTC+4. Brisbane time is 6:00 pm. What time is it in Dubai?
12:00 noon
Which has the higher effective rate: 7% quarterly or 6.8% monthly?
7% quarterly; effective ≈ 7.186%, versus ≈ 7.016%
A connected graph has exactly 2 odd vertices. Is it Eulerian, semi-Eulerian or neither?
Semi
A population starts at 500 and decreases 20% per year. Write a geometric model.
500 x 0.8 ^n-1
A least-squares line is y=4.2x+35. Predict y when x=10.
77
Calculate the surface distance for an angular distance of 30°.
111.2 x 30 = 3336km
$10,000 is invested at 5% p.a. compounded annually for 3 years. Find the final balance.
$11,576.25
Activities A and B take 6 and 8 min and must both finish before C begins. What is the earliest C can start?
8 min
Lines have slopes −0.8, 0.4, −0.2, .... Find the slope of Line 5.
-0.05
Quarterly sales are 8, 18, 94, 10 thousand dollars. Find the seasonal index for Q3 if the yearly quarterly average is 32.5.
94÷32.5≈ 2.89
A plane leaves Brisbane at 10:45 pm Monday, flies 14 h 35 min to Dubai. Brisbane UTC+10, Dubai UTC+4. Give Dubai arrival time/day.
7:20am Tuesday
A perpetuity pays $1800 annually and earns 5% p.a. How much must initially be invested?
1800÷0.05= $36,000
A network has source capacities 50, 30 and 40 tonnes, but only 20, 40 and 30 tonnes can enter the sink. What is the maximum possible flow?
90 t