BASIC MATH TERMS FOR SHSAT
SPECIALIZED HIGH SCHOOLS ADMISSION TEST
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.
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"
GREATEST COMMON 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"
LEAST COMMON MULTIPLE
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".
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
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."
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 MEDIAN AND MODE
Average = Sum of terms/Number of the terms
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.
The mode is the value of the terms that occurs most.
RATIO AND PROPORTION
The comparison of 2 quantities of the same kind by means of division is termed as ratio.
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
SHSAT MATH ONLINE WORKSHEETS
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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
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