In math there are 50 multiple choice questions covering a broad range of topics and assessing a wide range of abilities. topics include arithmetic, basic algebra, elementary geometry, probability, and statistics. On the ninth year version of test, there is also some trigonometry.

Many questions assess your knowledge of  basic concepts. Others test your ability to think creatively and apply what you know in what may be new or unfamiliar situations.

The SHSAT does not provide formulas or reference material for use during the test. You must know the formulas and familiar with technical mathematical terms.

This section provides you with brief reference. It is not intended to be a complete list. These, as well as many terms and concepts, are found among the detailed solution to the sample exam.


Integers :

Positive and negative whole numbers together with zero.

........-3, -2, -1, 0, 1, 2, 3, 4, 5................

√9, 0, -12/2, and 2.0 are integers.

√7, 4/3 and 13.3 are not integers.

Even integers :

........-6, -4, -2, 0, 2, 4, 6, 8........

All even integers are multiples of 2. 

Note that 0 is an even integer.

Odd integers :

...........-5, -3, -1, 1, 3, 5, 7,............

All odd integers are 1 more (or less) than even integers.

Consecutive integers :

-1, 0, 1, 2, 3 are five consecutive integers.

-9, -8, -7 are three consecutive integers.

-2, 0, 2, 4, 6 are five consecutive even integers.

3, 5, 7 are three consecutive odd integers.

Operations on Even and odd integers :

Odd ± odd  =  Even

Odd ± Even  =  Odd

Even ± Even  =  Even

Odd x odd  =  Odd

Odd x Even  =  Even

Even x Even  =  Even


A factor of a number is any positive integer that may be divided evenly into the number that is, leaving a remainder of zero.

3 is a factor of 12.

5 is not a factor of 19.

8 is a factor of both 24 and 80 and 8 is called a common factor of 24 and 80.

To know more about finding factors of a number, please visit the page "Finding factors of a number".


If a is factor of b, then b is called a multiple of a.

15 is multiple of 3.

15 is also multiple of 5.

4, 8, 12, 16 area four consecutive multiples of 4.

To know more about the difference between factors and multiples, please visit "Factors and multiples"


A prime(or prime number) is any positive integer having exactly two different integer factors. F

The first five primes are 2, 3, 5, 7 and 11.

  • The number 1 is not a prime number.
  • The only even prime number is 2.
  • There is an infinite number of prime numbers.

Every positive integers be factored into primes.

To know how to write positive numbers into prime factor, please visit the page "How to express a number as the product of its prime factors"


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

GCF, GCD and HCF are same.

The GCF of 24 and 30 is 6.

To know more about finding greatest common factors for two or more numbers, please visit the page "Finding Greatest Common Factor"


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

The LCM of 4 and 6 is 12.

The LCM of 9 and 18 is 18.

To know more about finding least common multiple two or more numbers using different methods, please visit the page "Methods of finding least common multiple"


When 42 is divided by 8, the quotient is 5 and the remainder is 2. The number 42 is called the dividend and 8 is called the divisor.

This can be written as 

42  =  5 x 8 + 2

To know more about division of two numbers, please visit the page "Division algorithm"


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"


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"


  • > 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".


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


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


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%


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


Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

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


Variables and constants

Writing and evaluating expressions

Solving linear equations using elimination method

Solving linear equations using substitution method

Solving linear equations using cross multiplication method

Solving one step equations

Solving quadratic equations by factoring

Solving quadratic equations by quadratic formula

Solving quadratic equations by completing square

Nature of the roots of a quadratic equations

Sum and product of the roots of a quadratic equations 

Algebraic identities

Solving absolute value equations 

Solving Absolute value inequalities

Graphing absolute value equations  

Combining like terms

Square root of polynomials 

HCF and LCM 

Remainder theorem

Synthetic division

Logarithmic problems

Simplifying radical expression

Comparing surds

Simplifying logarithmic expressions

Negative exponents rules

Scientific notations

Exponents and power


Quantitative aptitude

Multiplication tricks


Aptitude test online


Test - I

Test - II


Horizontal translation

Vertical translation

Reflection through x -axis

Reflection through y -axis

Horizontal expansion and compression

Vertical  expansion and compression

Rotation transformation

Geometry transformation

Translation transformation

Dilation transformation matrix

Transformations using matrices





Converting customary units worksheet

Converting metric units worksheet

Decimal representation worksheets

Double facts worksheets

Missing addend worksheets

Mensuration worksheets

Geometry worksheets

Comparing  rates worksheet

Customary units worksheet

Metric units worksheet

Complementary and supplementary worksheet

Complementary and supplementary word problems worksheet

Area and perimeter worksheets

Sum of the angles in a triangle is 180 degree worksheet

Types of angles worksheet

Properties of parallelogram worksheet

Proving triangle congruence worksheet

Special line segments in triangles worksheet

Proving trigonometric identities worksheet

Properties of triangle worksheet

Estimating percent worksheets

Quadratic equations word problems worksheet

Integers and absolute value worksheets

Decimal place value worksheets

Distributive property of multiplication worksheet - I

Distributive property of multiplication worksheet - II

Writing and evaluating expressions worksheet

Nature of the roots of a quadratic equation worksheets

Determine if the relationship is proportional worksheet



Trigonometric ratio table

Problems on trigonometric ratios

Trigonometric ratios of some specific angles

ASTC formula

All silver tea cups

All students take calculus 

All sin tan cos rule

Trigonometric ratios of some negative angles

Trigonometric ratios of 90 degree minus theta

Trigonometric ratios of 90 degree plus theta

Trigonometric ratios of 180 degree plus theta

Trigonometric ratios of 180 degree minus theta

Trigonometric ratios of 180 degree plus theta

Trigonometric ratios of 270 degree minus theta

Trigonometric ratios of 270 degree plus theta

Trigonometric ratios of angles greater than or equal to 360 degree

Trigonometric ratios of complementary angles

Trigonometric ratios of supplementary angles 

Trigonometric identities 

Problems on trigonometric identities 

Trigonometry heights and distances

Domain and range of trigonometric functions 

Domain and range of inverse  trigonometric functions

Solving word problems in trigonometry

Pythagorean theorem


Mensuration formulas

Area and perimeter



Types of angles 

Types of triangles

Properties of triangle

Sum of the angle in a triangle is 180 degree

Properties of parallelogram

Construction of triangles - I 

Construction of triangles - II

Construction of triangles - III

Construction of angles - I 

Construction of angles - II

Construction angle bisector

Construction of perpendicular

Construction of perpendicular bisector

Geometry dictionary

Geometry questions 

Angle bisector theorem

Basic proportionality theorem


Coordinate geometry formulas

Distance between two points

Different forms equations of straight lines

Point of intersection

Slope of the line 

Perpendicular distance


Area of triangle

Area of quadrilateral



Matrix Calculators

Coordinate geometry calculators

Statistics calculators

Mensuration calculators

Algebra calculators

Chemistry periodic calculator


Missing addend 

Double facts 

Doubles word problems


Direct proportion and inverse proportion

Constant of proportionality 

Unitary method direct variation

Unitary method inverse variation

Unitary method time and work


Order of rotational symmetry

Order of rotational symmetry of a circle

Order of rotational symmetry of a square

Lines of symmetry


Converting metric units

Converting customary units


HCF and LCM  word problems

Word problems on simple equations 

Word problems on linear equations 

Word problems on quadratic 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


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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