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1

Simple Interest 1.1

- I = PRN
- Total owing = principal + interest

Interest: money earned on investment/charged on loan
Simple interest: (flat rate) interest calculated as a percentage of principal (amount invested/borrowed)

2

Compound Interest 1.2

- FV = PV(1+R)^2
- I = FV - PV

Compound Interest: interest added to principal + reinvested

3

Inflation and Appreciation 1.3

- FV = PV(1+R)^n

Inflation: increase in price of goods/services
appreciation: increase in value of an item

4

Investing in Shares 1.4

- DIVIDEND YIELD = dividend per share ÷ market price per share X 100
- DIVIDEND = dividend yield X market price

Share: part ownership in a company
Dividend: type of interest earned by share holders
Dividend yield: percentage of market price of share
Brokerage: commission charged by stockbrokers

5

Share tables and graphs 1.5

LAST SALE = market price at end of day
+ OR - = change in price from previous day
NO. SOLD (100s) = no. shares sold (100s)
52 WEEK HIGH/LOW = maximum and minimum price in 52 weeks

Share tables: daily information about shares

6

Straight Line Depreciation 1.6

- S = Vo-Dn

s - salvage
Vo - initial value
D - depreciation
n - no.periods

Depreciation: loss in value of asset over time
Straight line: item value decreases by same each time

7

Declining Balance Depreciation 1.7

- S = Vo(1-r)^n

s - salvage (current value)
Vo - initial value
r = depreciation rate
n = number of periods

Declining balance: item value decreased by some percentage each period

8

Ration problems 2.1

Ratio: compares two or more parts of the same type

*simplify ratio, divide both parts by the HCF

105 : 75 (÷ by 15)
7 : 5

0.04 : 0.4 (x100 to make integers)
4 : 40 (÷ by 4)
1 : 10

45cm : 3m (convert to cm)
45cm : 300cm (÷ by 15)
3 : 20

A jar of jellybeans contains one yellow, white + green in ratio 12 : 11 : 22. if there are 600g of yellow, what is the mass of white jellybeans and all jellybeans.
12 : 11 : 22
Y : W : G
Y = 12 parts, 12p=600g
1p= 50g

since white=11p
11p = 50g X 11 = 550g
all parts= 12+11+22=45p
45p = 50g X 45=2250g

9

Dividing quantity in Ratio 2.2

1. Find total number of parts by adding
2. Find the size of one part by dividing
3. Find size of each term of ratio by multiplying
4. Check answers add to original quantity

Tim pays 30% of his weekly income of $1080 in tax. The remaining income is divided into savings + living expenses in the ratio 2:5. How much does Tim use for living expenses?

Saves 100-30=70% X 1080= $756
2 : 5 - total parts = 2+5=7p
7p = $756 (÷ by 7)
1p = $108
living expenses = 5p = 5 X $108 - $540

10

Rate problems 2.3

- Rate rule
write unit as fraction and solve using X/÷

e.g. beats/min = beats÷min

11

Unit Pricing 2.4

- UNIT PRICE = price ÷ no. items/units

Unit price: price of one item or unit

Small can:
$2.85/375g (divide)
$0.0076/g = 0.76c/g

Large can:
$5.85/750g (÷)
$0.0078/g = 0.78c/g
i.e. small can is best buy

12

Solving Equations 3.1

1. keep equation balanced by performing same on both sides
2. Aim to have variable on one side of equation + a number on the other side

Equation: contains algebraic expression and equals sign

solve: 5-x÷2 = 2
10-x = 4
-x = -6
x = 6

13

Formulas and Equations 3.2

M = x+y+z÷3

M=22, x=25, y=26

22= 25+26+z÷3
66=51+z
z=15

14

Changing the subject 3.3

y = mx+c
mx+c = y
c = y-mx

15

Linear Functions 3.4

- Form y=mx+c
- Gradient: rate of change y relative to x - m= rise÷run
- y-intercept = value of y when x = 0

Function: relationship between 2 variables

y= -2x+10
-2 is coefficient of x
10 is constant term

16

Direct Linear Variation 3.5

- y = kx

y - directly proportional to x
k - constant

solving a linear variation problem
1. identify 2 variables and form variation equation
2. substitute values for x and y to find k
3. Rewrite y=kx using value of k
4. Substitute a value for x or y into y=kx

17

Intersection of Lines 3.6

Simultaneous equations: equations solved same time
Break even point: when revenue covers the cost exactly

18

Reducing Balance Loan 2.1

- TOTAL PAID = loan repayment X no. repayment
- TOTAL PAID = principal + interest

Reducing balance loan: calculated on balance owing on loan original principal borrowed

19

Credit Cards 4.2

- DAILY INTEREST RATE = annual interest rate ÷ 365
- FV = PV(1+R)^N
- I = FV-PV

Credit cards: used to buy goods/services and pay for them later, interest can be flat/compound.
- if payment not received, interest charged from purchase date
- Interest usually charged daily using compound interest
- Monthly statement provides record of spending

20

Annuities 4.3

Using Table
1. Determine time period and rate of interest
2. Find intersection of time/rate of interest
3. Multiply number w/ money contributed

Annuity: form of an investment involving regular contributions e.g. investment into super
- made at end of compound period
- earns more interest because regular/equal payments made

Future value: total value at end of term, sum of all contributions plus interest

21

Loan repayment tables 4.4

Loan repayment tables: enable repayments for reducing balance loans to be easily calculated

22

Repaying Home loans 4.5

$560000 purchase price with a $150 000 deposit over 30yrs compounding monthly at 7.2%p.a. with these fees:
- $600 loan establishment fee
- 1.4c per $1000 borrowed per month
- $3.80 per month management fee
- $720 mortgage discharge fee

Total cost of loan
P = 560 000 - 150 000 = 410 000
therefore PV = 410 000

Monthly repayments
monthly rate = 7.2÷12=0.6%/month, n=30X12 = 360 months

23

Scatter Plots 5.1

Scatterplot: graph of points on plane
- represents bivariate data (2 variables)

24

Correlation 5.2

Correlation: measure of strength of linear association or relationship between 2 variables.

Pearson's correlation co-efficient: r, is a number between -1, +1 measuring correlation of 2 units

25

Line of Best fit 5.3

Line of best fit: the straight line drawn through the centre of dots with an equal number of dots above and below lone.
- The line can be used to predict values given one variable.

LINE OF BEST FIT - REGRESSION LINE (least squares line of best fit)

26

Speed + fuel consumption 2.5

AVERAGE SPEED = Distance travelled ÷ time taken

Speed: rate at which something is moving/changing

Fuel consumption: Rate at which a vehicle uses fuel measured in L/100km
- depends on: driving urban, towing, using A/C

27

Converting Rates 2.6

- express as fraction, then divide

A car travels at 75km/h, how far to the nearest 0.1m will it travel in 5sec

28

Least Squares regression 5.4

- y = mx+c
- m = r X standard deviation of y-scores ÷ standard deviation of x-scores
- c = mean of y-scores - mean of x-scores

Regression line: line of best fit, representing all points (gradient/y-intercept calculated using formula)

29

Life Expectancy 5.5

Life expectancy: average number of years of life remaining to a person of specific age

30

Networks 6.1

Graph = diagram of a network, containing vertices (points), joined by lines called edges (arcs)

Loop = edge connecting a vertex to itself

Directed network = arrows on edges, indicate direction

Weighted network = numbers/weights on edges, distance same
- WEIGHT = SUM OF ALL EDGES

Degree: number of edges connected to vertices can be odd/even
- SUM OF ALL DEGREES = TWICE NUMBER OF EDGES

Walk: any route along edges that includes repeat vertexes/edges

Closed: starts/ends at same vertex

Trail: walk with no repeat edges, vertices may be reused

Circuit: Closed trail with no repeat edges

Path: no repeat vertices/edges

Cycle: Closed path with no repeat vertices/edges

Connected network: connected if path between 2 vertices

Networks/tables: networks can be represented using matrix/table