**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.

**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

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.

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"

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 :**

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"

Odd ± odd = Even Odd ± Even = Odd Even ± Even = Even |
Odd x odd = Odd Odd x Even = Even Even x Even = Even |

**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.

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"

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

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."

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 :**

3 x 3 is written as 3^{2}

The base is 3 and exponent is 2.

5^{4} = 5 ⋅ 5 ⋅ 5 ⋅ 5

In general, if n is any nonzero numbers, then n^{0} = 1

To know more about exponents, please visit "Exponents"

**Square roots :**

Since 6^{2} = 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"

- > 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 :**

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 :**

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

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 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 4**

**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**

We hope that the stuff given in this section would have been much useful for the students who are preparing for PSAT exam.

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**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**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**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**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 **

**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 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**