CSET Multiple Subjects: Subtest 2 - Math Exam
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Dividing decimals - ✔✔-The same as dividing other numbers, except that if the divisor (the number
you're dividing by) has a decimal, move it to the right as many places as necessary until it is a whole
number
-Move the decimal point in the dividend (the number being divided into) into the same number of
places
-Sometimes you may have to add zeroes to the dividend (the number inside the division sign)
Example: 5 ÷ 1.25 = 500 ÷ 125
Dividing fractions - ✔✔Invert (turn upside down) the second fraction and multiply; reduce if
necessary.
Example: 1/6 ÷ 1/5 = 1/6 x 5/1 = 5/6
Equation - ✔✔-A relationship between numbers and/or symbols that says two expressions have the
same value
-Solving an equation for a variable requires that you find a value or an expression that has the desired
variable on one side of the equation and everything else on the other side of the equation
-By doing the same arithmetic to each side of the equation, you eventually can isolate the desired
variable
Example: x-5 = 23. Solve for x.
Add 5 to each side of the equation
x = 28
Replace the original x with 28 and check to see if the resulting sentence is true.
28 - 5 = 23
23 = 23
Equiangular triangle - ✔✔-Has all of its angles of equal measure
-Thus, each angle has a measure of 60°
-An equiangular triangle is also equilateral
Equilateral triangle - ✔✔-Has all three of its sides of equal length, which in turn make each of the
three angles equal in measure
-Therefore, each angle in an equilateral triangle has a measure of 60° since the sum of the angles in
any triangle is 180°
Evaluating expressions - ✔✔Insert the value(s) given for the unknown(s) and do the arithmetic,
making sure to follow the rules for the order of operations.
Example: Evaluate 2x² - 4y + 11 if x = 3 and y = -5.
2(3)² - 4(-5)+ 11
2(9) - (-20) + 11
18 + 20 + 11
38 + 11
49
Exponent - ✔✔Any exponent means to multiply by itself that many times
,Example: 5³ = 5 x 5 x 5 = 125
x¹ = x and x^0 = 1 when x is any number other than 0
Factoring - ✔✔Finding two or more quantities whose product equals the original quantity
Factoring out a common factor - ✔✔-Find the largest common monomial factor of each term
-Divide the original polynomial by this factor to obtain the second factor (the second factor will be a
polynomial)
Example: Factor completely 2y³ - 6y
2y³ - 6y = 2y(y² -3)
Factoring polynomials that have three terms: Ax² + Bx + C - ✔✔-Check to see if you can monomial
factor (factor out common terms). Then, if A = 1 (the first term is simply x²), use double parentheses
and factor the first term. Place these factors in the left sides of the parenthesis. For example, (x )(x )
-Factor the last term, and place the factors in the right side of the parentheses
To decide on the signs of the numbers, do the following. If the sign of the last term is negative:
-Find two numbers whose product is the last term and whose difference is the coefficient (number in
front) of the middle term
-Give the larger of the two numbers the sign of the middle term, and give the opposite sign to the
other factor
If the sign of the last term is positive:
-Find two numbers whose product is the last term and whose sum is the coefficient of the middle
term
-Give both factors the sign of the middle term
If A ≠ 1 (if the first term has a coefficient different than 1 — for example, 4x² + 5x + 1), then additional
trial and error will be necessary
Factoring the difference between two squares - ✔✔-Find the square root of the first term and the
square root of the second term
-Express your answer as the product of the sum of the quantities from step 1 times the difference of
those quantities
Example: x² - 144
x² - 144 = (x + 12)(x - 12)
Finding percent of a number - ✔✔Change the percent to a fraction or decimal and multiply
Example: What is 20% of 80?
20/100 x 80 = 1600/100 = 16
or .20 x 80 = 16.00 = 16
Fractions - ✔✔Consist of two numbers separated by a bar which indicates division: the numerator is
above the bar and the denominator is below the bar.
Denominator: Tells you into how many equal parts something has been divided.
Numerator: Tells you how many of those parts are being considered.
Example: 3/5 (something has been divided into 5 equal parts, and 3 of those parts are being used)
Graphing equations - ✔✔Graphs of equations in two variables (usually x and y) can be formed by
finding ordered pairs that make the equation true, and then connecting these points
Example: Make a graph of the equation 2x + y = 6
, One way to do this is to set up a table of values with the x-values first, and then the y-values. You then
replace one of the variables with values and find what the other variable would have to be for each
replacement. If the x's were replaced with -2, -1, 0, 1, and 2, then find the corresponding y-values
If x = -2, then 2(-2) + y = 6 --> -4 + y = 6 --> y = 10
Make a table, plot the points
Horizontal axis - ✔✔-x-axis or abscissa
-Numbers to the right of 0 are positive and to the left of 0 are negative
Identity number - ✔✔A value that, when added to another number or multiplied with another
number, does not change the value of that number
Identity number for addition - ✔✔0. Any number added to 0 gives that number
0+a=a+0=a
Example of using the additive identity:
0+3=3+0=3
0+3=3
Identity number for multiplication - ✔✔1. Any number multiplied by 1 gives that number.
1(a) = a(1) = 1
Example of using the multiplicative identity:
1(3) = 3(1) = 3
1(3) = 3
Improper fraction - ✔✔A fraction whose numerator is the same or more than the denominator; has
a value equal to 1 or more than 1.
Examples: 6/6 and 5/4
Incomplete quadratic - ✔✔A quadratic with a term missing
Example: Solve for x. x² - 16 = 0
Factoring, (x + 4)(x - 4) = 0
x + 4 = 0 --> x = -4
or x - 4 = 0 --> x = 4
Inequality - ✔✔-A statement in which the relationships are not equal
-Instead of using an equal sign (=) as in an equation, we use > (greater than) and < (less than), or ≥
(greater than or equal to) and ≤ (less than or equal to).
-When working with inequalities, treat them exactly like equations, EXCEPT: If you multiply or divide
both sides by a negative number, you must reverse the direction of the sign.
Example: Solve for x: -7x > 14
Divide by -7 and reverse the sign
x < -2
Integers - ✔✔...-3, -2, -1, 0, 1, 2, 3... all the whole numbers together with their opposites
Intersecting lines - ✔✔-Two or more lines that cross each other at a point
-That point would be on each of those lines
Irrational numbers - ✔✔Any value that exists but is not rational
Questions and Correct Answers (100%COMPLETE
ANSWERS) ALREADY GRADED A+ 100%
satisfaction guaranteed
Dividing decimals - ✔✔-The same as dividing other numbers, except that if the divisor (the number
you're dividing by) has a decimal, move it to the right as many places as necessary until it is a whole
number
-Move the decimal point in the dividend (the number being divided into) into the same number of
places
-Sometimes you may have to add zeroes to the dividend (the number inside the division sign)
Example: 5 ÷ 1.25 = 500 ÷ 125
Dividing fractions - ✔✔Invert (turn upside down) the second fraction and multiply; reduce if
necessary.
Example: 1/6 ÷ 1/5 = 1/6 x 5/1 = 5/6
Equation - ✔✔-A relationship between numbers and/or symbols that says two expressions have the
same value
-Solving an equation for a variable requires that you find a value or an expression that has the desired
variable on one side of the equation and everything else on the other side of the equation
-By doing the same arithmetic to each side of the equation, you eventually can isolate the desired
variable
Example: x-5 = 23. Solve for x.
Add 5 to each side of the equation
x = 28
Replace the original x with 28 and check to see if the resulting sentence is true.
28 - 5 = 23
23 = 23
Equiangular triangle - ✔✔-Has all of its angles of equal measure
-Thus, each angle has a measure of 60°
-An equiangular triangle is also equilateral
Equilateral triangle - ✔✔-Has all three of its sides of equal length, which in turn make each of the
three angles equal in measure
-Therefore, each angle in an equilateral triangle has a measure of 60° since the sum of the angles in
any triangle is 180°
Evaluating expressions - ✔✔Insert the value(s) given for the unknown(s) and do the arithmetic,
making sure to follow the rules for the order of operations.
Example: Evaluate 2x² - 4y + 11 if x = 3 and y = -5.
2(3)² - 4(-5)+ 11
2(9) - (-20) + 11
18 + 20 + 11
38 + 11
49
Exponent - ✔✔Any exponent means to multiply by itself that many times
,Example: 5³ = 5 x 5 x 5 = 125
x¹ = x and x^0 = 1 when x is any number other than 0
Factoring - ✔✔Finding two or more quantities whose product equals the original quantity
Factoring out a common factor - ✔✔-Find the largest common monomial factor of each term
-Divide the original polynomial by this factor to obtain the second factor (the second factor will be a
polynomial)
Example: Factor completely 2y³ - 6y
2y³ - 6y = 2y(y² -3)
Factoring polynomials that have three terms: Ax² + Bx + C - ✔✔-Check to see if you can monomial
factor (factor out common terms). Then, if A = 1 (the first term is simply x²), use double parentheses
and factor the first term. Place these factors in the left sides of the parenthesis. For example, (x )(x )
-Factor the last term, and place the factors in the right side of the parentheses
To decide on the signs of the numbers, do the following. If the sign of the last term is negative:
-Find two numbers whose product is the last term and whose difference is the coefficient (number in
front) of the middle term
-Give the larger of the two numbers the sign of the middle term, and give the opposite sign to the
other factor
If the sign of the last term is positive:
-Find two numbers whose product is the last term and whose sum is the coefficient of the middle
term
-Give both factors the sign of the middle term
If A ≠ 1 (if the first term has a coefficient different than 1 — for example, 4x² + 5x + 1), then additional
trial and error will be necessary
Factoring the difference between two squares - ✔✔-Find the square root of the first term and the
square root of the second term
-Express your answer as the product of the sum of the quantities from step 1 times the difference of
those quantities
Example: x² - 144
x² - 144 = (x + 12)(x - 12)
Finding percent of a number - ✔✔Change the percent to a fraction or decimal and multiply
Example: What is 20% of 80?
20/100 x 80 = 1600/100 = 16
or .20 x 80 = 16.00 = 16
Fractions - ✔✔Consist of two numbers separated by a bar which indicates division: the numerator is
above the bar and the denominator is below the bar.
Denominator: Tells you into how many equal parts something has been divided.
Numerator: Tells you how many of those parts are being considered.
Example: 3/5 (something has been divided into 5 equal parts, and 3 of those parts are being used)
Graphing equations - ✔✔Graphs of equations in two variables (usually x and y) can be formed by
finding ordered pairs that make the equation true, and then connecting these points
Example: Make a graph of the equation 2x + y = 6
, One way to do this is to set up a table of values with the x-values first, and then the y-values. You then
replace one of the variables with values and find what the other variable would have to be for each
replacement. If the x's were replaced with -2, -1, 0, 1, and 2, then find the corresponding y-values
If x = -2, then 2(-2) + y = 6 --> -4 + y = 6 --> y = 10
Make a table, plot the points
Horizontal axis - ✔✔-x-axis or abscissa
-Numbers to the right of 0 are positive and to the left of 0 are negative
Identity number - ✔✔A value that, when added to another number or multiplied with another
number, does not change the value of that number
Identity number for addition - ✔✔0. Any number added to 0 gives that number
0+a=a+0=a
Example of using the additive identity:
0+3=3+0=3
0+3=3
Identity number for multiplication - ✔✔1. Any number multiplied by 1 gives that number.
1(a) = a(1) = 1
Example of using the multiplicative identity:
1(3) = 3(1) = 3
1(3) = 3
Improper fraction - ✔✔A fraction whose numerator is the same or more than the denominator; has
a value equal to 1 or more than 1.
Examples: 6/6 and 5/4
Incomplete quadratic - ✔✔A quadratic with a term missing
Example: Solve for x. x² - 16 = 0
Factoring, (x + 4)(x - 4) = 0
x + 4 = 0 --> x = -4
or x - 4 = 0 --> x = 4
Inequality - ✔✔-A statement in which the relationships are not equal
-Instead of using an equal sign (=) as in an equation, we use > (greater than) and < (less than), or ≥
(greater than or equal to) and ≤ (less than or equal to).
-When working with inequalities, treat them exactly like equations, EXCEPT: If you multiply or divide
both sides by a negative number, you must reverse the direction of the sign.
Example: Solve for x: -7x > 14
Divide by -7 and reverse the sign
x < -2
Integers - ✔✔...-3, -2, -1, 0, 1, 2, 3... all the whole numbers together with their opposites
Intersecting lines - ✔✔-Two or more lines that cross each other at a point
-That point would be on each of those lines
Irrational numbers - ✔✔Any value that exists but is not rational
