CBEST Math Exam with 100% Correct
Solutions
Natural numbers - ANS-The counting numbers: 1,2,3,4...
Whole numbers - ANS-The counting numbers beginning with zero: 0,1,2,3,4...
Integers - ANS-Positive and negative whole numbers and zero.
Odd numbers - ANS-Numbers not divisible by two: 1,3,5,7...
Even numbers - ANS-Numbers divisible by two: 2,4,6,8...
Prime numbers - ANS-Numbers divisible only by 1 and itself: 2,3,5,7,11,13...
Composite number - ANS-Number divisible by more than just 1 and itself:
4,6,8,9,10,12,14,15...
Squares - ANS-The result when the numbers are multiplied by themselves: (2x2 = 4),
(3x3 =9): 1,4,9,16,25,36
Cubes - ANS-The result when numbers are multiplied by themselves, and again by the
original number, raised to the third power. (2x2x2 = 8), (3x3x3 = 27) ; 1,8,27
Difference - ANS-The result of using subtraction.
Product, of, times, at, twice - ANS-The result of using multiplication. Example: The
product of 3 and 6 is 18, 3x6 = 18.
Quotient, divided by, divided into, ratio, half, each - ANS-The result of using division.
Sum, total, plus - ANS-The result of using addition. Example: The sum of 5,6, and 8,
5+6+8 = 19.
Commutative property of addition - ANS-The order does not make any difference. a + b
=b+a
Associative property of addition - ANS-The grouping of the numbers does not make any
difference. (a + b) + c = a + (b + c)
, Identity element for addition is 0 - ANS-Adding any number to 0 gives the original
number. 3 + 0 =3.
Additive inverse property of addition - ANS-Is the opposite (negative) of the number.
Any number plus its additive inverse equals 0. 3 + (-3) = 0.
Commutative property of multiplication - ANS-Order does not make a difference. a x b =
bxa
Associative property of multiplication - ANS-The grouping does not make any
difference. (a x b) x c = a x (b x c)
Identity element for multiplication is 1 - ANS-Multiplying any number by 1 gives the
original number. 3 x 1 = 3
Multiplicative inverse is the reciprocal of the number - ANS-Any number multiplied by its
reciprocal equals 1.
2 x 1/2 = 1 because both 2's cancel out by cross multiplication.
Mean - ANS-How to calculate mean:
1. Add all numbers together
2. Divide by the number of data values given in set
Also known as the average.
Median - ANS-Median is simply the middle number of a list of numbers after it has been
written in order. Arrange them in order from greatest to least.
If the number of data values is even, you add the two middle values and divide the total
by two and you have your median.
Mode - ANS-Mode is simply the number most frequently listed in a group of numbers.
Range - ANS-Is the difference between the largest data value and the smallest data
value. To calculate the range, subtract the smallest number from the largest number.
Probability - ANS-It is the likelihood that a particular event will occur. It is
probability = number of favorable outcomes/
number of possible total outcomes
You use multiplication when calculating.
Counting principles - ANS-If there are a number of successive choices to make and the
choices are independent of each other, the total number of possible choices is the
product of each of the choices at each stage.
Example: How many possible arrangements of shirts and ties are there if there are five
different color shirts and three different color ties?
Multiply them to find the total: 5 x 3 = 15
Solutions
Natural numbers - ANS-The counting numbers: 1,2,3,4...
Whole numbers - ANS-The counting numbers beginning with zero: 0,1,2,3,4...
Integers - ANS-Positive and negative whole numbers and zero.
Odd numbers - ANS-Numbers not divisible by two: 1,3,5,7...
Even numbers - ANS-Numbers divisible by two: 2,4,6,8...
Prime numbers - ANS-Numbers divisible only by 1 and itself: 2,3,5,7,11,13...
Composite number - ANS-Number divisible by more than just 1 and itself:
4,6,8,9,10,12,14,15...
Squares - ANS-The result when the numbers are multiplied by themselves: (2x2 = 4),
(3x3 =9): 1,4,9,16,25,36
Cubes - ANS-The result when numbers are multiplied by themselves, and again by the
original number, raised to the third power. (2x2x2 = 8), (3x3x3 = 27) ; 1,8,27
Difference - ANS-The result of using subtraction.
Product, of, times, at, twice - ANS-The result of using multiplication. Example: The
product of 3 and 6 is 18, 3x6 = 18.
Quotient, divided by, divided into, ratio, half, each - ANS-The result of using division.
Sum, total, plus - ANS-The result of using addition. Example: The sum of 5,6, and 8,
5+6+8 = 19.
Commutative property of addition - ANS-The order does not make any difference. a + b
=b+a
Associative property of addition - ANS-The grouping of the numbers does not make any
difference. (a + b) + c = a + (b + c)
, Identity element for addition is 0 - ANS-Adding any number to 0 gives the original
number. 3 + 0 =3.
Additive inverse property of addition - ANS-Is the opposite (negative) of the number.
Any number plus its additive inverse equals 0. 3 + (-3) = 0.
Commutative property of multiplication - ANS-Order does not make a difference. a x b =
bxa
Associative property of multiplication - ANS-The grouping does not make any
difference. (a x b) x c = a x (b x c)
Identity element for multiplication is 1 - ANS-Multiplying any number by 1 gives the
original number. 3 x 1 = 3
Multiplicative inverse is the reciprocal of the number - ANS-Any number multiplied by its
reciprocal equals 1.
2 x 1/2 = 1 because both 2's cancel out by cross multiplication.
Mean - ANS-How to calculate mean:
1. Add all numbers together
2. Divide by the number of data values given in set
Also known as the average.
Median - ANS-Median is simply the middle number of a list of numbers after it has been
written in order. Arrange them in order from greatest to least.
If the number of data values is even, you add the two middle values and divide the total
by two and you have your median.
Mode - ANS-Mode is simply the number most frequently listed in a group of numbers.
Range - ANS-Is the difference between the largest data value and the smallest data
value. To calculate the range, subtract the smallest number from the largest number.
Probability - ANS-It is the likelihood that a particular event will occur. It is
probability = number of favorable outcomes/
number of possible total outcomes
You use multiplication when calculating.
Counting principles - ANS-If there are a number of successive choices to make and the
choices are independent of each other, the total number of possible choices is the
product of each of the choices at each stage.
Example: How many possible arrangements of shirts and ties are there if there are five
different color shirts and three different color ties?
Multiply them to find the total: 5 x 3 = 15
