Trigonometry
Write the true bearing 300˚ as a compass bearing
N60˚W
A map has a scale of 1:2500. The distance between a house and supermarket on the map is 65mm. Find the actual distance in metres between the house and supermarket.
162.5m
A survey of which of the following would provide data that are both categorical and nominal?
1. Hair colour
Find the simple interest earned if I invest $5200 for 7 months at 6% p.a.
$182
A plane is 7km in the air. The angle of depression to the airport is 15˚. To the nearest kilometre, how far does the plane need to fly to reach the airport?
27km
Vanessa walks 150m in 12 minutes. Find her speed in kilometres per hour.
0.75km/h
List the 5 steps of the Statistical Investigation Process
1. Identify problem and pose question
2. Collect data
3. Represent data
4. Analyse data
5. Interpret and communicate findings
Joan invests $200. She earns interest at 3% per annum, compounded monthly. What is the future value of Joan's investment after 1.5 years?
$209.19
A hiker sets out on a bearing of 210˚. They walk for 5km, then stop for a rest at a picnic ground. How far south are they from their starting point? Answer correct to 2 significant figures.
4.3km
A map has a scale of 1:60 000. In real life, a hospital and school are 3.3km apart. How far apart are they in millimetres on the map?
55mm
Calculate the mean and standard deviation to 1dp of:
8, 6, 9, 11, 3, 5
Mean = 7
SD = 2.6
Tye needs $1000 in 5 years time. He is going to invest some money today in an account earning 3% per annum compounded annually. He will make no further deposits or withdrawals. How much money does he need to invest today?
$862.61
A boat sails from port P to port Q on a bearing of 080˚. What is the bearing of P from Q?
260˚
Mrs Schultz's fuel consumption is 9.2L/100km. She travels 30 000km in a year. If fuel costs 212c/L, how much will she spend on fuel for the year?
$5851.20
The heights, in centimetres, of 10 players on a basketball team are shown.
170, 180, 185, 188, 192, 193, 193, 194, 196, 202
Is the height of the shortest player on the team considered an outlier? Justify your answer with calculations.
Yes since 170 is less than 171.5
Jo has a credit card that has no interest-free period. Interest is charged at 13.65% p.a., compounding daily, on the outstanding balance. How much interest is Jo charged on an outstanding balance of $2400 for 30 days?
$427.07