Quantitative Reasoning Flashcards
Percentage Change
new value = original value x base value * base value represents % change i.e. 1 +/- increase/decrease e.g. 10% increase = 1.10 110% increase = 2.10 20% decrease = 0.8
Compound Interest accumulated interest. interest on interest –> overall money owed
FV = PV(1+r)n
FV = Full Value
PV = Present Value
r = Annual Interest
n = Number of Periods
Simple Interest interest value owed separated from initial amount * typically an undervalue of compound interest
I = PRT I = Interest P = Initial amount R = Annual rate T = Time (years)
kilometres to metres
x 1000
hours to minutes
x 60
Temperature in F
(temperature in C *1.8) +32
Example Question (conversion) : Thermometer is not always accurate, as temperature can be +/- 2 C. What is the maximum temperature difference between 2 countries in Fahrenheit F = ( 1. deduce the countries with the maximum temperature difference - country #1 38C - country #2 22 C
- To get the maximum difference, add 2 C to the higher value and minus 2 C from lowest and then convert
Example Question (conversion) : Thermometer is not always accurate, as temperature can be +/- 2 C. What is the maximum temperature difference between 2 countries in Fahrenheit F = ( C x 1.8) + 32 A) 60.8 B) 64.4 C) 36.0 D) 82.5 1. deduce the countries with the maximum temperature difference - country #1 38C - country #2 22 C
- To get the maximum difference, add 2 C to the higher value and minus 2 C from lowest and then convert (40 x 1.8) + 32 = 104 (20 x 1.8) + 32 = 68 104 - 68 = 36 answer is C (I may do this mentally and round the numbers up, e.g. 112 -72)
Weighted Mean
= sum of (each value x individual weight) for example find the value of the mean of the values 1 2 3 4 where 3 has a weighting of 70% = (1 x 0.3) + (2 x 0.3) + (3 x 0.7) + (4 x 0.1) = 2.8 NOTE: if there is a significant weighting on a value in comparison to other values, it is fair to estimate the average to be closest to that value.
Example Question (weighted mean): There are 10 boys and 20 girls. The average age for boys in 19 years and the average age for girls is 20. What is the average for the class? a) 18 b) 18.5 c) 19 d) 19.5
(1/3 x 10) + (2/3 x 20) = 19 answer is c
Metres to feet
1 metre - 3.3 feet
Question example (conversion): What is the total difference in price of painting a room floor of 5 x 3 metres between using + labour per metre squared a) cream - cost of using $20 - labour $8 b) - cost of using $40 - labour $6 A)270 B)300 C)450
- difference of cost per metre squared 46 - 28 = $18 per metre squared 2. area = 5 x 3 = 15 metres squared 3. difference in saving in 15 metres squared $18 x 15 metres squared = 270 The answer is A
centimetres to metres
/ 100
area of a circle
πr2
area of a square
a2
