Mathematics help

Question 1

What is the symbol for a power?

Question 2

What is the symbol for a root?

Answer 2

x√

Question 3

How do you convert decimals to percentages?

Answer 3

Multiply by 100

Question 4

How do you convert percentages to decimals?

Answer 4

Divide by 100

Question 5

Are percentages multiplicative or additive?

Answer 5

Multiplicative.

E.g. Increase 50 by 20% then decrease 20% = 1.2 x 0.8 x 50.

Question 6

How do you calculate the simple averages? (The mean)

Answer 6

Sum (Σ) a series of values and divide by the number of values

E.g. mean of 2 & 10 => (2 + 10) ÷ 2 => 12 ÷ 2 = 6

E.g. mean of 4, 8, 12 & 16 => (4 + 8 + 12 + 16) ÷ 4 => 40 ÷ 4 = 10

Question 7

How do you calculate weighted averages?

Answer 7

When the values in the series have different weights (“level of importance”) which are determined by another factor

Weights must sum to 100%

E.g. weighted average of 2 (40% weight) and 10 (60% weight)
(2 x 40%) + (10 x 60%) => 0.8 + 6 = 6.8

Question 8

How do you calculate powers?

Answer 8

Multiplying a number by itself a number of times

Use the ^ button on your calculator

E.g. 1.1 ^ 4 (1.1 to the power of 4) = 1.4641

Question 9

How do you calculate roots?

Answer 9

The inverse of a power

Use the x√ button on your calculator or ^1/x

E.g. 4 x√ 1.4641 (the fourth root of 1.4641) = 1.1

Question 10

How do we calculate algebra (slide 7)?

Answer 10

Rearrange the formula by doing the same thing to both sides so that the unknown variable is on its own on one side of the = sign;

replace the known variables on the other side of the = sign with their values; then

solve the other side of the = sign using the BODMAS rule

Question 11

What is BODMAS in algebra?

Answer 11

1. Brackets
2. Order (powers and roots)
3. Division
4. Multiplication
5. Addition
6. Subtraction

(Example on slide 9).

Question 12

What is compounding??

Answer 12

INFLATION

Inflating a number from its present value (PV) to a future value (FV) at a constant percentage rate (r) for a given number of years (t)

Formula: FV = PV (1 + r)t

E.g. Compound 100 by 20% per annum for 2 years
FV = 100 x (1 + 0.2) 2
FV = 100 x (1.2) 2
FV = 100 x 1.44
FV = 144

Question 13

What is it known as when you rearrange the compounding formula to solve for the constant percentage rate (r) or a given number of years (t)?

Answer 13

GEOMETRIC PROGRESSION

Rearrange FV = PV (1 + r)t

1. Divide both sides by PV FV ÷ PV = PV x (1 + r)t ÷ PV
2. Which becomes FV ÷ PV = (1 + r)t
3. Take the tth root of both sides t√(FV ÷ PV) = t√(1 + r)t
4. Which becomes t√(FV ÷ PV) = 1 + r.
5. Deduct 1 from both sides t√(FV ÷ PV) – 1 = 1 + r – 1
6. Which becomes r = t√(FV ÷ PV) – 1

Question 14

What is discounting?

Answer 14

A.K.A Deflation

Deflating a number from a future value (FV) to its present value (PV) at a constant percentage rate (r) for a given number of years (t)

Formula: PV = FV ÷ (1 + r)t

E.g. Discount 144 by 20% per annum for 2 years
PV = 144 ÷ (1 + 0.2) 2
PV = 144 ÷ (1.2) 2
PV = 144 ÷ 1.44
PV = 100

Question 15

What is Linear Regression?

Answer 15

The “optimal” relationship between two variables (x & y)

Defined by the formula of the line of best fit (y = ax + b)

Question 16

What is Linear Correlation?

Answer 16

Strength and direction of the relationship between two variables

Measured by a correlation coefficient ρ (rho):

Perfect positive correlation 		ρ = +1
Strong positive correlation		ρ ≥ +0.6
Weak correlation			+0.6 > ρ > -0.6
Strong negative correlation		ρ ≤ -0.6
Perfect negativ§ correlation		ρ = -1

Question 17

What can the normal distribution be used for?

slide 19.

Answer 17

Calculating Probabilities

An actual outcome within μ +/- 1σ is expected 68% of the time (likely)
An actual outcome within μ +/- 2σ is expected 96% of the time (highly likely)