PSAT MATH PREPARATION

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.

• Writing a number in scientific notation
• Convert between standard and scientific notation
• Operations with scientific notation

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, D -----> Division

A -----> Addition, S -----> Subtraction

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.

A 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"

• How to Find GCF and LCM easily

OPERATIONS ON EVEN AND ODD INTEGERS

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.

• Factors and Multiples
• Factors and Multiples worksheet

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, D -----> Division

A -----> Addition, S -----> Subtraction

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

DIVISIBILITY RULES

A 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

• Divisibility Rules
• Divisibility rules worksheet

FRACTIONS AND DECIMALS

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

To know about adding, subtracting, multiplying and dividing fractions, please visit the page "Operations with fractions."

• Comparing and ordering fractions
• Writing equivalent fractions
• Word problems on fractions and decimals

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%

• Percentage of a Number
• Converting fraction into percentage
• Compare percents to fractions and decimals

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

To know more about exponents, please visit "Exponents"

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"

• Operations with radicals
• Comparing radicals

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

• Arithmetic mean of ungrouped data
• How to find the missing number of arithmetic mean

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.

• Median of ungrouped data
• How to find median of grouped data

Mode :

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

• How to find mode of ungrouped data
• How to find the mode of the data
• Finding mode of ungrouped data worksheet
• Find mean median and mode of grouped data

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.

To know more about ratio and proportion, please visit the page

• Ratio and proportion
• How to solve ratio word problems
• Ratio and Proportion Worksheet
• Ratio and Proportion in Geometry

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

• Finding probability
• Finding experimental probability
• Using experimental probability to make predictions