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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. Finding the Volume of a Rectangular Solid
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
VofaRS=lwh
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.
Find a common denominator - then add or subtract the numerators.


2. Finding the Missing Number in a Series When You are Given the Average
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.
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.


3. Characteristics of a Rectangle
A(2)+b(2)=c(2)
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.


4. Finding the Area of a Triangle

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5. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
Use the units to keep things straight - Snowfall inches/hours
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
(pie)r(squared)


6. Solving an Inequality
Get the absolute value equation by itself. Solve.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Part=Percent x Whole


7. Evaluating an Algebraic Expression
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.
(pie)r(squared)
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.


8. Finding the Area of a Circle
Slope=change in y/change in x
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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
(pie)r(squared)


9. Comparing the values of two or more Fractions
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.
Part=Percent x Whole
Plug in the given values for the unknowns and calculate according to PEMDAS.
Express them with a common denominator.


10. Converting from an Improper Fraction to a Mixed Number
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.
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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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.


11. Counting the Total Number of Possibilities for Several Events to Occur
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
A(2)+b(2)=c(2)
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.


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

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13. Simplifying an Algebraic Equation
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Cancel factors common to the numerator and denominator.
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.


14. 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 value that appears the most often.
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.
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
Average: Sum of the Terms/Number of the Terms


15. Definition of a Rational Number
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Four equal acute angles and four equal obtuse angles.


16. Finding the Median of a Set of 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.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
The value that falls in the middle of the set.


17. Counting Consecutive Integers
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Subtract the smallest from the largest and add 1
Combine like terms.
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.


18. Finding the Distance Between Two Points on a Coordinate Graph
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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
The value that appears the most often.


19. Let N represent the smallest positive integer that is a multiple of 6 and 8 - but leaves a remainder of 2 when divided by 7. What is the value of N?
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.


20. Numbers that are Relatively Prime
-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.
Use the formula distance=rate*time and its variations to help in this question.
Cancel factors common to the numerator and denominator.
Two relatively prime numbers are integers that have no common factor other than 1.


21. Finding the Volume of a Cylinder
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Four equal acute angles and four equal obtuse angles.
VofaC: (pie)r(2)h
Adjacent angles are supplementary - Vertical angles are equal


22. Finding the y-intercept When Given an Equation of a Line
Put the equation into y=mx+b-- in which case b is the y-intercept.
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
Just add or subtract the coefficients in front of the radicals.
-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.


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

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24. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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
Use the units to keep things straight - Snowfall inches/hours


25. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Average the smallest and largest number
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Use the units to keep things straight - Snowfall inches/hours
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction


26. What are Two Special Pythagorean Triples?

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27. PEMDAS
-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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Cross multiply.


28. Multiplying Expressions with Exponents that Have a Common Base
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
Use simple numbers like 1 and 2 and see what happens.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7


29. Converting from part-to-part ratios to part-to-whole ratios
Two relatively prime numbers are integers that have no common factor other than 1.
Use the formula distance=rate*time and its variations to help in this question.
Put each number in the original ratio over the sum of the numbers.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time


30. Finding the Domain and Range of a Function
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Four equal acute angles and four equal obtuse angles.
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.
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


31. Knowing if an Integer is a Multiple of 2 or 4
-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.
Switch the numerator and denominator.
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.
Average the smallest and largest number


32. Simplifying Square Roots
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
The value that falls in the middle of the set.


33. What types of angles are formed when a transversal cross parallel lines?
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.
Four equal acute angles and four equal obtuse angles.
FOIL: First - Outer - Inner - Last... Combine Like Terms


34. Multiplying and Dividing Roots
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.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Get the absolute value equation by itself. 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.


35. Finding the Circumference of a Circle
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
2(pie)r
Express them with a common denominator.
(x1+x2)/2 -(y1+y2)/2


36. Calculating Negative Exponents and Radical Exponents
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
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.


37. Definition of an Integer
Put each number in the original ratio over the sum of the numbers.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.


38. Difference Between a Factor and a Multiple
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
-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.
Two relatively prime numbers are integers that have no common factor other than 1.
Average: Sum of the Terms/Number of the Terms


39. Number of Groups - +1 Each Time
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Do whatever is necessary to both sides to isolate the variable.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.


40. Multiplying Monomials
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Get the absolute value equation by itself. Solve.
Combine like terms.
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.


41. General Procedure for Multiplying Polynomials
Isolate the radical expression and use the standard rules of algebra.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Use the distributive property then combine the like terms.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7


42. Properties of the Interior and Exterior Angles of a Triangle
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.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Put each number in the original ratio over the sum of the numbers.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25


43. 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.
2(pie)r
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.


44. Convert From a Fraction to a Decimal - Vice Versa
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.
The value that appears the most often.
Average: Sum of the Terms/Number of the Terms


45. Finding the Sum of the Average of a Series of Numbers
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Adjacent angles are supplementary - Vertical angles are equal
Sum: Average x Number of Terms
Use the distributive property then combine the like terms.


46. Multiplying Fractions
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
Multiply the numerators and multiply the denominators.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
VofaC: (pie)r(2)h


47. Finding the Area of a Sector

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48. Adding and Subtracting Polynomials
Combine like terms.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Direct Variation- y=kx - where k is constant. As x gets larger - y gets larger. If the number of units of B were to double - the number of units of A would double - Inverse Variation- xy=k - where k is a constant. As x gets larger - y gets smaller. A
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.


49. Direct Variation and Inverse Variation
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Direct Variation- y=kx - where k is constant. As x gets larger - y gets larger. If the number of units of B were to double - the number of units of A would double - Inverse Variation- xy=k - where k is a constant. As x gets larger - y gets smaller. A


50. Increasing and Decreasing a Number by a Certain Percentage
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Multiply the numerators and multiply the denominators.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
-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.