# PSAT MATH PREPARATION

The PSAT Math section is composed of two sub-sections: a 45-minute calculator-optional section, and a 25-minute no-calculator section. These sections include a total of 48 questions: 40 multiple-choice questions and 8 student-produced response.

In this section, we are going to cover the math topics and skills required to answer PSAT Math questions.

## ARITHMETIC

Integer :

Whole numbers that are positive or negative and included zero.

Examples :

-1, 0, 1, 4.0, -20/2 are all integers.

Consecutive integer :

1, 2, 3, 4 are consecutive integers.

2, 4, 6, 8, ... are consecutive even integers

1, 3, 5, 7, .........are consecutive odd integers.

Whole numbers :

These are counting numbers, including 0. There are no negative in whole numbers.

Example 0, 1, 2, 3, ...........

Rational numbers :

All integers, fractions, decimals, repeating decimals and terminating decimals.

Example 1, 0.121212, 1/8, 19.01

Irrational numbers :

These numbers cannot be written as fractions. These are non repeating  decimals.

Example : 0.162728..........., √2, π

## SCIENTIFIC NOTATION

To write a number which is greater than 1 in scientific notation, move the decimal point left and use a positive exponent.

To write a number which is less than 1 in scientific notation, move the decimal point right and use a negative exponent

To know more about writing a number in scientific notation, please visit the pages.

## PEMDAS

This rule can be used to simplify or evaluate complicated numerical expressions with more than one binary operation easily.

Very simply way to remember  PEMDAS rule :

P -----> Parenthesis, E -----> Exponents

M -----> Multiplication, -----> Division

To look into example problems based on this topic, please visit "PEMDAS Rule"

## PRIME OR COMPOSITE

A prime number is a whole number that only has two factors which are itself and one. 2 is the only even prime number.

composite number has factors in addition to one and itself. The numbers 0 and 1 are neither prime nor composite. All even numbers are divisible by two and so all even numbers greater than two are composite numbers.

To know more about prime or composite numbers, please visit the page "Prime or composite"

## GCF and LCM

GCF :

The greatest common factor of two numbers is the largest positive integer that is factor of both numbers.

To know more about GCF, please visit the page "Greatest common factor"

LCM :

The smallest among the common multiples of two or more numbers is called their least common multiple ( LCM)

To know more about LCM, please visit the page "Least Common Multiple"

## OPERATIONS ON EVEN AND ODD INTEGERS

 Odd ± odd  =  EvenOdd ± Even  =  OddEven ± Even  =  Even Odd x odd  =  OddOdd x Even  =  EvenEven x Even  =  Even

## FACTORS AND MULTIPLES

Factor :

A factor is a positive integer that divides evenly into a given number with no remainder.

Multiple :

A multiple is a number that a given number will divide into with no remainder.

## THE ORDER OF OPERATIONS

This rule can be used to simplify or evaluate complicated numerical expressions with more than one binary operation easily.

Very simply way to remember  PEMDAS rule :

P -----> Parenthesis, E -----> Exponents

M -----> Multiplication, -----> Division

To look into example problems based on this topic, please visit "PEMDAS Rule"

## DIVISIBILITY RULES

divisibility test is a rule for determining whether one whole number is divisible by another. It is a quick way to find factors of large numbers.

To know the shortcuts of divisibility test, please look into the page

## FRACTIONS AND DECIMALS

fraction represents a part of a whole or, more generally, any number of equal parts.

## PERCENTS

To convert a fraction or decimal to a percent, multiply by 100%. To convert a percent to a fraction or decimal, divide by 100%

## EXPONENTS AND SQUARE ROOTS

Exponents :

3 x 3 is written as 32

The base is 3 and exponent is 2.

54  =  5 ⋅ 5 ⋅ 5 ⋅ 5

In general, if n is any nonzero numbers, then n0  = 1

Square roots :

Since 62  =  36, 6 is the square root of 36.

The square root of 64 is 8.

To know more about square roots, please visit the page "Square Roots"

## INEQUALITY SYMBOLS

• > means "is greater than" (5 > 3)
• < means is less than (3 < 5)
• ≥ means greater than or equal to.
• ≤ means is less than or equal to.

To know more about writing linear inequality from word problems, pleased visit the page "Write a linear inequality word problems".

## MEAN, MEDIAN AND MODE

Mean :

Average  =  Sum of terms/Number of the terms

Median :

The median of a group of terms is the value of the middle term with the terms arranged in increasing order.

When there is an even numbers of terms, the median is the average of the two middle terms with the terms arranged in increasing order.

Mode :

The mode is the value of the terms that occurs most.

## RATIO AND PROPORTION

Ratio :

The comparison of 2 quantities of the same kind by means of division is termed as ratio.

Proportion :

An equality of two ratios is called a proportion.

Four quantities a, b, c, d are said to be in proportion if a : b = c : d (also written as a : b :: c : d). That is, if a/b = c/d.

## PROBABILITY

An event is a collection or set of outcome.

The sample space is a set of all possible outcomes for an event. A sample space can be small, such as the 2 outcomes when a coin is flipped. Or a sample space can be large, such as the possible number of Texas Classic automobile license plates.

Probability  =  Number of desirable outcomes/Total number of possible outcomes

## PSAT MATH ONLINE WORKSHEETS

PSAT online practice test math - Paper 1

PSAT online practice test math - Paper 2

PSAT online practice test math - Paper 3

PSAT online practice test math - Paper 5

PSAT online practice test math - Paper 6

PSAT online practice test math - Paper 7

PSAT online practice test math - Paper 8

PSAT online practice test math - Paper 9

PSAT online practice test math - Paper 10

PSAT online practice test math - Paper 11 Apart from the stuff given aboveif you need any other stuff in math, please use our google custom search here.

If you have any feedback about our math content, please mail us :

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You can also visit the following web pages on different stuff in math.

WORD PROBLEMS

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6

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