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This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.

1. Properties of a 30-60-90 Triangle
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Average the smallest and largest number
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a


2. Definition of Remainder
Isolate the radical expression and use the standard rules of algebra.
The whole number left over after division.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
The union of Set A and Set B is the set of elements that are in either or both Set A and Set B - The intersection of Set A and Set B is the set of elements common to both Set A and Set B


3. Characteristics of a Square
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Sum: Average x Number of Terms
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Values of x the take the denominator of a faction equal to zero - thereby dividing by zero which is not possible - are not in the domain of a function. Set the denominator equal to zero and solve for x. Ans: 3


4. Determining Absolute Value of a Number
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Don't be confused by all the variables. Recall that (x-y)(x+y)=x(2)-y(2). Then - x(2)-y(2)=5*7=35. x(2)+1-y(2)=x(2)-y(2)+1=35+1=36.
Four equal acute angles and four equal obtuse angles.
Plug in the given values for the unknowns and calculate according to PEMDAS.


5. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
Area of a Triangle=1/29(base)(height) - The height is the perpendicular distance between the side that's chosen as the base and the opposite vertex.
Use the formula - a(n)=a(1)r(n-1) - where a(n) is the nth term - a1 is the first term - and r is the ratio between the terms.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Plug in the given values for the unknowns and calculate according to PEMDAS.


6. Factoring a Polynomial ('FOIL in Reverse')
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Two relatively prime numbers are integers that have no common factor other than 1.


7. What Does Solving In Terms of Mean?
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.


8. Finding the Area of a Triangle

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9. Simplifying a Fraction to Lowest Terms
Factor out and cancel all factors the numerator and denominator have in common.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
FOIL: First - Outer - Inner - Last... Combine Like Terms
Remember that any non-zero base to the power of zero is equal to one. Set the exponent equal to zero and solve for x.


10. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
The whole number left over after division.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.


11. What types of angles are formed when a transversal cross parallel lines?
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
(x1+x2)/2 -(y1+y2)/2
Four equal acute angles and four equal obtuse angles.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.


12. Finding the Midpoint Between Two Points
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
-An integer is divisible by 5 if the last digit is 5 or 0. - An integer is divisible by 10 if the last digit is 0.
(x1+x2)/2 -(y1+y2)/2
Subtract the smallest from the largest and add 1


13. Finding the Reciprocal of a Fraction
Switch the numerator and denominator.
Use the distributive property then combine the like terms.
Four equal acute angles and four equal obtuse angles.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.


14. What is the positive difference between the answers to the equation 35+x(2)=12x?

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15. General Procedure for Multiplying Polynomials
Use the distributive property then combine the like terms.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Remember that any non-zero base to the power of zero is equal to one. Set the exponent equal to zero and solve for x.


16. What value of x is not in the domain of the function f(x)=x-2/x-3?
Values of x the take the denominator of a faction equal to zero - thereby dividing by zero which is not possible - are not in the domain of a function. Set the denominator equal to zero and solve for x. Ans: 3
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides


17. Definition of a Rational Number
When a line is tangent to a circle - or touches the circle at just one point - the radius of the circle is perpendicular to the line at the point of contact.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
If a right triangle's leg-to-leg ratio is 3:4 - or if the leg-to-hypotenuse ratio is 3:5 - it's a 3-4-5 triangle and you don't need to use the Pythagorean theorem to find the third side.


18. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Use the units to keep things straight - Snowfall inches/hours
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2


19. If x varies directly with y - and the value of x is 12 when y is 11 - what is the value of y when x is 66?
Factor out and cancel all factors the numerator and denominator have in common.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
An integer is divisible by 3 if the sum of its digits is divisible by 3 - - An integer is divisible by 9 is the sum of its digits is divisible by 9.


20. Comparing the values of two or more Fractions
Values of x the take the denominator of a faction equal to zero - thereby dividing by zero which is not possible - are not in the domain of a function. Set the denominator equal to zero and solve for x. Ans: 3
Scalene- No sides or angles are equal - Isosceles- Have two equal sides. The angles opposite the equal sides are also equal - Equilateral- All three sides and angles are equal.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Express them with a common denominator.


21. Finding the Volume of a Rectangular Solid
Combine like terms.
VofaRS=lwh
The union of Set A and Set B is the set of elements that are in either or both Set A and Set B - The intersection of Set A and Set B is the set of elements common to both Set A and Set B
Divide the denominator into the numerator to get a whole number quotient with a remainder. The quotient becomes the whole number of the mixed number. Remainder becomes the numerator.


22. Formula to Find Average
Average: Sum of the Terms/Number of the Terms
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Use the units to keep things straight - Snowfall inches/hours
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds


23. Properties of the Interior and Exterior Angles of a Triangle
Area of a Triangle=1/29(base)(height) - The height is the perpendicular distance between the side that's chosen as the base and the opposite vertex.
The 3 interior angles of a any triangle add up to 180 degrees. An exterior angle of a triangle is equal to the sum of the remote - that is - non-adjacent - interior angles.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Part=Percent x Whole


24. Definition of an Irrational Number
Average: Sum of the Terms/Number of the Terms
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)


25. Multiplying Expressions with Exponents that Have a Common Base
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
-The Factors of integer n are the positive integers that divide into n with no remainder - The Multiples of n are the positive integers that n divides into with no remainder.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
In a 30-60-90 triangle - the measure of the longer leg is 7(square root: 3) - then the length of the shorter side or shorter leg must be 7.


26. Properties of a 45-45-90 Triangle
Combine like terms.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Values of x the take the denominator of a faction equal to zero - thereby dividing by zero which is not possible - are not in the domain of a function. Set the denominator equal to zero and solve for x. Ans: 3
Consecutive odd integers are odd integers in order in a row - such as 1 - 3 - and 5. The difference between any two consecutive odd integers is 2. Translate the question into an equation that expresses the relationship between the integers.


27. Characteristics of a Rectangle
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
The union of Set A and Set B is the set of elements that are in either or both Set A and Set B - The intersection of Set A and Set B is the set of elements common to both Set A and Set B
Two relatively prime numbers are integers that have no common factor other than 1.


28. An Important Property of a Line Tangent to a Circle
When a line is tangent to a circle - or touches the circle at just one point - the radius of the circle is perpendicular to the line at the point of contact.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Slope=change in y/change in x


29. Solving an Inequality
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Consecutive odd integers are odd integers in order in a row - such as 1 - 3 - and 5. The difference between any two consecutive odd integers is 2. Translate the question into an equation that expresses the relationship between the integers.
Don't be confused by all the variables. Recall that (x-y)(x+y)=x(2)-y(2). Then - x(2)-y(2)=5*7=35. x(2)+1-y(2)=x(2)-y(2)+1=35+1=36.


30. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
Remember that any non-zero base to the power of zero is equal to one. Set the exponent equal to zero and solve for x.
Use the units to keep things straight - Snowfall inches/hours
Express them with a common denominator.
Variables that have an inverse relationship will always have the same product. As one value gets larger - the other gets smaller. Set up and solve the equation 310=6x. Answer: 5


31. Converting from part-to-part ratios to part-to-whole ratios
Combine the equations so that one of the variables cancels out. 4x+3y=8 and x+y=3. Multiply equation 2 by -3... then add the two equations.
Subtract the smallest from the largest and add 1
Find a common denominator - then add or subtract the numerators.
Put each number in the original ratio over the sum of the numbers.


32. Definition of an Integer
-An integer is divisible by 2 if the last digit is even - An integer is divisible by 4 if the last two digits form a multiple of 4.
-An integer is divisible by 5 if the last digit is 5 or 0. - An integer is divisible by 10 if the last digit is 0.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Find a common denominator - then add or subtract the numerators.


33. What are Two Special Pythagorean Triples?

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34. Increasing and Decreasing a Number by a Certain Percentage
Express them with a common denominator.
-Increasing: Add the percent to 100 percent - convert to a decimal - and multiply - Decrease: Subtract the percent from 100 percent - convert to a decimal - and multiply.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Remember that any non-zero base to the power of zero is equal to one. Set the exponent equal to zero and solve for x.


35. Finding the Length of an Arc in a Circle

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36. If 2+l6-xl=10 and x>0 - what is the value of 2x?
Get the absolute value equation by itself. Solve.
VofaRS=lwh
Do whatever is necessary to both sides to isolate the variable.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)


37. What is a Function and how do you Evaluate one?

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38. Adding and Subtracting Monomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Cancel factors common to the numerator and denominator.
Isolate the radical expression and use the standard rules of algebra.
Multiply and/or divide positives and negatives treat the number parts as usual - and attach a negative sign if there is an odd number of negatives


39. Multiply and Divide Positive and Negative Numbers
Combine the equations so that one of the variables cancels out. 4x+3y=8 and x+y=3. Multiply equation 2 by -3... then add the two equations.
Multiply and/or divide positives and negatives treat the number parts as usual - and attach a negative sign if there is an odd number of negatives
A(2)+b(2)=c(2)
The whole number left over after division.


40. Finding the Slope When Given an Equation of a Line
The 3 interior angles of a any triangle add up to 180 degrees. An exterior angle of a triangle is equal to the sum of the remote - that is - non-adjacent - interior angles.
Four equal acute angles and four equal obtuse angles.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.


41. What is the greatest of three consecutive odd integers where the sum of the third and twice the first is equal to nine more than twice the second?
The length of one side of a triangle must be greater than the difference and less of the sum of the lengths of the other two sides.
The 3 interior angles of a any triangle add up to 180 degrees. An exterior angle of a triangle is equal to the sum of the remote - that is - non-adjacent - interior angles.
Consecutive odd integers are odd integers in order in a row - such as 1 - 3 - and 5. The difference between any two consecutive odd integers is 2. Translate the question into an equation that expresses the relationship between the integers.
Sum: Average x Number of Terms


42. Solving a Problem Involving Rates
Adjacent angles are supplementary - Vertical angles are equal
Use the units to keep things straight - Snowfall inches/hours
Get the absolute value equation by itself. Solve.
Slope=change in y/change in x


43. Finding the Area of a Circle
When a line is tangent to a circle - or touches the circle at just one point - the radius of the circle is perpendicular to the line at the point of contact.
(pie)r(squared)
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Divide the denominator into the numerator to get a whole number quotient with a remainder. The quotient becomes the whole number of the mixed number. Remainder becomes the numerator.


44. Prime Factorization of a Number
When a line is tangent to a circle - or touches the circle at just one point - the radius of the circle is perpendicular to the line at the point of contact.
Ue the formula y=mx+b - and remember that the value of m is the slope of the line. The slopes of two perpendicular lines are negative reciprocals of one another.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Remember that any non-zero base to the power of zero is equal to one. Set the exponent equal to zero and solve for x.


45. Finding the Mode of a Set of Numbers
Multiply the numerators and multiply the denominators.
The length of one side of a triangle must be greater than the difference and less of the sum of the lengths of the other two sides.
The value that appears the most often.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.


46. Expressing the Union and Intersection of Sets
The union of Set A and Set B is the set of elements that are in either or both Set A and Set B - The intersection of Set A and Set B is the set of elements common to both Set A and Set B
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Subtract the smallest from the largest and add 1


47. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
Divide the denominator into the numerator to get a whole number quotient with a remainder. The quotient becomes the whole number of the mixed number. Remainder becomes the numerator.
VofaRS=lwh
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
In a 30-60-90 triangle - the measure of the longer leg is 7(square root: 3) - then the length of the shorter side or shorter leg must be 7.


48. Knowing if an Integer is a Multiple of 5 or 10
Slope=change in y/change in x
Area of a Triangle=1/29(base)(height) - The height is the perpendicular distance between the side that's chosen as the base and the opposite vertex.
-An integer is divisible by 5 if the last digit is 5 or 0. - An integer is divisible by 10 if the last digit is 0.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2


49. Identifying Which Number of a Fraction is the Part and Which Number is the Whole

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50. Counting Consecutive Integers
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Subtract the smallest from the largest and add 1
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.