General Mathematics

Get Started. It's Free
General Mathematics

1. Functions and Their Graphs

1.9. Asymptotes

1.9.1. vertical - right to left

1.9.2. horizontal- up or down

2. Logic

2.1. Proposition

2.1.1. Complete declarative sentence that is either true or false.

2.2. Connective proposition

2.2.1. Conjunction

2.2.2. Disjunction

2.2.3. Implication

2.2.3.1. Hypothesis and Conclusion

2.2.3.2. logically equivalent to its contrapositive

2.2.4. Biconditional

2.3. Compound proposition

2.3.1. Tautology

2.3.1.1. always true

2.3.2.1. Always false

2.3.3. Contingency

2.4. Valid arguement

2.4.1. Rules of inference

2.5. Fallasies

2.5.1. incorrect reasoning resembling rules of inference.

2.6. Method of proofs

2.6.1. Direct

2.6.2. Indirect

2.6.3. Existence

2.6.4. Nonexistence

3. Exponential and Logarithmic Functions

3.1. Exponential

3.1.1. If f is increasing or decreasing throughout domain, then f is one-to-one

3.1.2. if each horizontal line intersects the graph in at most one point, then the function if one-to-one.

3.1.3. Laws of exponent

3.1.3.1. (a^x)(a^y)=a^x+y

3.1.3.2. (a^x)^Y=a^xy

3.1.3.3. (ab)^x=a^x b^x

3.1.3.4. (a/b)^x= (a^x)/(b^x)

3.1.3.5. (a^x)/(a^y)=a^x-y

3.1.4. A function of f is one-to-one if every number in its range  corresponds to exactly one number i its domain.

3.1.5. If it is not one-to-one, then their is no inverse.

3.1.6. Real Life applications

3.1.6.1. Half-life decay model

3.1.6.2. Compound interest

3.1.6.3. Doubling time growth

3.1.6.4. Population growth

3.2. Logarithmic

3.2.1. Common Log

3.2.1.1. if there is no base, the base will automatically 10

3.2.2. Natural Log

3.2.2.1. it has a base of e written as lnx

4.1. Simple interest

4.1.1. earned when only the original principal earns interest for a duration of the term.

4.1.2. I=Prt

4.2. Maturity value

4.2.1. sum of the principal and interest rate.

4.2.2. F=(1+rt)

4.3. Compound interest

4.3.1. type of interest that results from the periodic addition of simple interest to principal.

4.3.2. F=P(1+i)^n

4.4. Annuity -  sequence of equal payment

4.4.1. Simple - interest period is the same as the payment period.

4.4.2. General - interest period and payment period are not the same.

4.4.3. - the payments are made are made at the end of each interest period.

4.4.4. Deffered - the first payment is not made at the end of the first interest period but later.

4.5. Stocks

4.5.1. shares of ownership in a company

4.6. Bonds

4.6.1. is a loan.

4.6.2. for corporations to raised the necessary funds.

4.7. Amortization

4.7.1. dept-repayment scheme wherein the original amount borrowed is repaid by making equal payments periodically.

4.8. Outstanding principal

4.8.1. dept that are still unpaid.