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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. Calculating Negative Exponents and Radical Exponents
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
-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.


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

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3. Difference Between a Factor and a Multiple
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
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
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
-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.


4. Multiplying Expressions with Exponents that Have a Common Base
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Use the sum... If the average of 4 numbers is 7 - then the sum of those 4 numbers is 4*7 - or 28. Suppose that 3 of the numbers are 3 -5 - and 9. These 3 numbers add up to 16 of that 28 - 12 is the fourth number.


5. Converting from part-to-part ratios to part-to-whole ratios
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Combine like terms.
Put each number in the original ratio over the sum of the numbers.
Sum: Average x Number of Terms


6. Adding and Subtracting Fractions
Find a common denominator - then add or subtract the numerators.
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.
Cross multiply.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.


7. Finding the Missing Number in a Series When You are Given the Average
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Use the sum... If the average of 4 numbers is 7 - then the sum of those 4 numbers is 4*7 - or 28. Suppose that 3 of the numbers are 3 -5 - and 9. These 3 numbers add up to 16 of that 28 - 12 is the fourth number.


8. Finding the Area of a Circle
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
(pie)r(squared)


9. Finding the Circumference of a Circle
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Find a common denominator - then add or subtract the numerators.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
2(pie)r


10. What types of angles are formed when a transversal cross parallel lines?
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 common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Four equal acute angles and four equal obtuse angles.
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.


11. Finding the Reciprocal of a Fraction
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.
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.
Switch the numerator and denominator.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.


12. Properties of Similar Triangles
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Part=Percent x Whole
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.


13. Finding the Surface Area of a Rectangular Solid
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Find a common denominator - then add or subtract the numerators.
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.


14. What is the value of x(2)+1-y(2) - if x-y=5 and x+y=7?

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15. Finding the Slope of a Line When Given Two Points on the Line
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
If there are m ways one event can happen and n ways a second event can happen - then there are m*n ways for the 2 events to happen.
Slope=change in y/change in x
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value


16. Simplifying a Fraction to Lowest Terms
Factor out and cancel all factors the numerator and denominator have in common.
Part=Percent x Whole
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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.


17. Multiplying and Dividing Roots
Sector is a piece of the area of a circle. Area of a Sector: (n/360)((pie)r2) - n is the degree measure of the sector's central angle
Multiplying: Multiply the numbers under the different radicals. The product goes under one radical - Dividing: The quotient of more than one square root is equal to the square root of their total quotient.
(pie)r(squared)
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.


18. What is the Pythagorean Theorem?
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
A(2)+b(2)=c(2)
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Switch the numerator and denominator.


19. Characteristics of a Parallelogram
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
-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.
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
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7


20. Definition of a Rational Number
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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
Average the smallest and largest number


21. Properties of a 30-60-90 Triangle
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
The value that appears the most often.
Multiply the numerators and multiply the denominators.


22. Multiply and Divide Positive and Negative Numbers
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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


23. Characteristics of a Square
Multiply the numerators and multiply the denominators.
Domain- The domain of a a function is the set of values for which the function is defined - Range- The range of a function is the set of outputs or results of the function.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.


24. Characteristics of a Rectangle
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Use the sum... If the average of 4 numbers is 7 - then the sum of those 4 numbers is 4*7 - or 28. Suppose that 3 of the numbers are 3 -5 - and 9. These 3 numbers add up to 16 of that 28 - 12 is the fourth number.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.


25. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
-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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%


26. Counting Consecutive Integers
Standard function notation is written f(x) and read 'f of x.' To evaluate the function f(x)=2x+3 for f(4) - replace every x with 4 and simplify. f(4)=2(4)+3=11.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
'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


27. Finding the Mode of a Set of Numbers
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Adjacent angles are supplementary - Vertical angles are equal
Get the absolute value equation by itself. Solve.
The value that appears the most often.


28. What types of angles are formed when two lines intersect?
Set the quadratic equation equal to zero with the terms in order of decreasing exponents - and solve for the roots by factoring. Don't forget to then find the difference in the roots by subtracting them. Ans: 2
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Adjacent angles are supplementary - Vertical angles are equal
Use the sum... If the average of 4 numbers is 7 - then the sum of those 4 numbers is 4*7 - or 28. Suppose that 3 of the numbers are 3 -5 - and 9. These 3 numbers add up to 16 of that 28 - 12 is the fourth number.


29. Simplifying an Algebraic Equation
Plug in the given values for the unknowns and calculate according to PEMDAS.
Use the sum... If the average of 4 numbers is 7 - then the sum of those 4 numbers is 4*7 - or 28. Suppose that 3 of the numbers are 3 -5 - and 9. These 3 numbers add up to 16 of that 28 - 12 is the fourth number.
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.
Cancel factors common to the numerator and denominator.


30. Finding the Median of a Set of Numbers
The value that falls in the middle of the set.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Use the sum... If the average of 4 numbers is 7 - then the sum of those 4 numbers is 4*7 - or 28. Suppose that 3 of the numbers are 3 -5 - and 9. These 3 numbers add up to 16 of that 28 - 12 is the fourth number.
Average the smallest and largest number


31. Converting from an Improper Fraction to a Mixed Number
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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
If there are m ways one event can happen and n ways a second event can happen - then there are m*n ways for the 2 events to happen.
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.


32. Dividing Fractions
Find a common denominator - then add or subtract the numerators.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Use the units to keep things straight - Snowfall inches/hours
Change the division sign to a multiplication sign - invert the second fraction - and multiply.


33. Solving an Inequality
Put each number in the original ratio over the sum of the numbers.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
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.
2(pie)r


34. Finding the Area of a Sector

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35. Convert From a Fraction to a Decimal - Vice Versa
Fraction to a Decimal: Divide the Denominator into the numerator - Decimal to a Fraction: Set the decimal over 1 and multiply the numerator and denominator by 10 raised to the number of digits to the right of the decimal point.
Sum: Average x Number of Terms
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Factor out the perfect squares under the radical - take their square roots - and put the result in front.


36. Finding the LCM of Two or More Numbers

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37. Solving a System of Equations
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Multiply the numerators and multiply the denominators.
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.


38. What are Two Special Pythagorean Triples?

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39. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
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.
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.
Use the sum... If the average of 4 numbers is 7 - then the sum of those 4 numbers is 4*7 - or 28. Suppose that 3 of the numbers are 3 -5 - and 9. These 3 numbers add up to 16 of that 28 - 12 is the fourth number.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)


40. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
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.
Put each number in the original ratio over the sum of the numbers.
Standard function notation is written f(x) and read 'f of x.' To evaluate the function f(x)=2x+3 for f(4) - replace every x with 4 and simplify. f(4)=2(4)+3=11.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.


41. Number of Groups - +1 Each Time
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
2(pie)r
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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


42. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Average the smallest and largest number
Standard function notation is written f(x) and read 'f of x.' To evaluate the function f(x)=2x+3 for f(4) - replace every x with 4 and simplify. f(4)=2(4)+3=11.
Express them with a common denominator.


43. Solving a Problem Involving Rates
Use the units to keep things straight - Snowfall inches/hours
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
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.
Slope=change in y/change in x


44. Formula Used to Find Percent
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Average: Sum of the Terms/Number of the Terms
Part=Percent x Whole
Subtract the smallest from the largest and add 1


45. Prime Factorization of a Number
-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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.


46. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
-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.


47. Finding the Volume of a Rectangular Solid
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
Plug in the given values for the unknowns and calculate according to PEMDAS.
VofaRS=lwh
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle


48. Definition of an Irrational Number
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.


49. If 3(3x)=9(x+2) - what is the value of x?
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Get the absolute value equation by itself. Solve.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)


50. 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.
Get the absolute value equation by itself. Solve.
Do whatever is necessary to both sides to isolate the variable.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24