math reviewer 3rd term

8/2/2019 Math Reviewer 3rd Term

1/4


2/4

The set of natural numbers is all the numbers to the right of zero in the number line (all

of them are positive and symbol is N). The set of whole numbers is the set of natural

numbers including zero (symbol is W).

Set of Integers:

The set of Integers are the set of whole numbers including negative numbers (symbol

is Z or I).

Combined Operations:

This the GEMDAS rule where G stands for groups, E stands for exponents and roots, M

and D stand for multiplication and division and A and S stand for addition and

subtraction.

Set of Rational Numbers and Set of Irrational Numbers:

The set of Rational Numbers are the set of integers including all fractions, decimals and

repeating decimals (symbol is Q). The set of Irrational Numbers is the complement of

the set of Rational Numbers and it contains all decimals that are endless but doesnt

have a repeating block of digits.

Set of Real Numbers:

It contains the set of Rational numbers and the set of Irrational numbers. Its

complement is the set of Imaginary numbers and them combined makes the set ofComplex numbers.

(The points given to this topic will be 0~2 points)

Factoring:

GCF:

Ex. (2x+2) to 2(x+1)

DOTS:

Follow the form: (x^2-y^2) to (x+y)(x-y)

SOTC and DOTC:

Follow the form: (x^3-y^3) to (x-y)(x^2+xy+y^2)


3/4

(x^3+y^3) to (x+y)(x^2-xy+y^2)

PST:

Follow the form: (x^2+2xy+y^2) to (x+y)^2

QT:

There are two types of QT, which have the form x^2+(a+b)x+ab and

acx^2+(ad+bc)x+bd (take note that a, b, c and d are all constants but can be

variables). Make use of the ac test when factoring the second form. The ac test, given

this form ax^2+(a+c)x+c, is basically multiplying a and c then check if then check if

the product of a and c can make the coefficient of the middle term (take note that the

form given for ac test where a is equal to ac and c is equal to bd in the second form.

Ex. x^2+10x+16 to (x+8)(x+2), 4x^2+ 15x+14 to (4x+7)(x+2)

Factoring by grouping:

Apply all the past factoring lessons but you group the terms so as to apply the factoring

techniques.

Ex. x^2+2xy+y^2-16x^4 to (x+y)^2-16x^4 to (x+y+4x^2)(x+y-4x^2)

8xy+4y+16x^2+8x to 4y(2x+1)+8x(2x+1) to (4y+8x)(2x+1)


RAE:

To simplify RAE you will have to make use of factoring. For the operations on RAE and

complex fractions you will have to make use of the rules on the operation on fractions.

For Rational Equations you will have to simple make use of the latter and also make it

into a linear equation but keep in mind that the answer should not make the

denominator equal to zero but if so the answer is called an extraneous root and there is

no answer to the equation.


Statistics:

Measures of Central Tendency:


4/4

Mode is the most popular, Mean is the average, Median is the middle. To get the mode

you just have to get the most frequent and the grouped mode is class mark of the most

frequent class interval. To get the mean you have to add all the values and divide it by

the number of values and the grouped mean you just have to follow the formula (x sub-

1 f sub-1)+(x sub-2 f sub-2)++(x sub-n f sub-n) all over total frequency (x is theclass mark and f is the frequency). To get median you have the arrange the numbers

from lowest to highest then get the central number but if there are two get the mean of

the two numbers and the grouped mean follow the formula L+H/f(N/2-C) (L is lower

boundary before the median class, H is the size/width of the median class, N is the total

frequency, C is the cumulative frequency before the median class, f is the frequency of

the median class and the median class is N/2 but if there is no cumulative frequency

equal to N/2 then get the lowest cumulative frequency greater than N/2. Mean is used

because it uses all the values in the data. Median is preferred over mean when there

are extreme data. Mode is the least use and is only significant in large sets of data.

Measures of Dispersion:

The range is highest value minus lowest value. To get the variance, first, get the mean

of the values. Then, subtract each value from the mean; the difference is called

deviation. Then, square the each deviation. Finally, add the squared deviations then

divide it by n-1 where n is the sample size. To get the standard deviation just get the

square root of the variance and round it to the tenths digit or the lowest place value of

the variance if the variance is a decimal. The variance considers the deviation of each

observation from the mean. The standard deviation represents the variance in the formof raw data. The lower the value of the range, variance and standard deviation the

better because it is less dispersed.

Word Problems:

For number problems always represent the number as 10x+y if it is a two-digit number

or 100x+10y+z if it is a three-digit number. For age problems always represent the

present, past and future. For Geometric Problems always remember the formula for the

shape and represent it using the shape. For investment problems always represent it

with I=PRT where I is the interest, P is the principle or the amount invested, R is therate and T is the time. For mixture problems represent it as Amount of Solvent times

the Concentration is equal to the Amount of Solute. For uniform motion problems

represent it as RT=D and for work problems as RT=W (take note that the work done is

always equal to 1).

math reviewer 3rd term

Documents