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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 a Term in a Geometric Sequence
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
FOIL: First - Outer - Inner - Last... Combine Like Terms
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.


2. Adding and Subtracting Monomials
Average the smallest and largest number
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
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
FOIL: First - Outer - Inner - Last... Combine Like Terms


3. Finding the Volume of a Cylinder
VofaC: (pie)r(2)h
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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
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.


4. Adding a Positive Number to a Negative Number
Average the smallest and largest number
Multiply the exponents - (x^3)^4=x^3*4=x^12
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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


5. Converting from part-to-part ratios to part-to-whole ratios
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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.
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.


6. Prime Factorization of a Number
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Sum: Average x Number of Terms
-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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.


7. Determining Absolute Value of a Number
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.
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.
2(pie)r


8. If x(2)=7x+18 - what is the positive value of x?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Average the smallest and largest number
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)


9. Knowing if an Integer is a Multiple of 2 or 4
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Use the formula distance=rate*time and its variations to help in this question.
-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.
Just add or subtract the coefficients in front of the radicals.


10. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Cross multiply.
Use the formula distance=rate*time and its variations to help in this question.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Average: Sum of the Terms/Number of the Terms


11. Finding the Slope When Given an Equation of a Line
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Use the units to keep things straight - Snowfall inches/hours
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.


12. Properties of a 45-45-90 Triangle
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
The value that falls in the middle of the set.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%


13. 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
Put the equation into y=mx+b-- in which case b is the y-intercept.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.


14. Finding the Reciprocal of a Fraction
2(pie)r
Switch the numerator and denominator.
Just add or subtract the coefficients in front of the radicals.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time


15. Finding the Slope of a Line When Given Two Points on the Line
Slope=change in y/change in x
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Average: Sum of the Terms/Number of the 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.


16. Properties of Similar Triangles
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%.
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.


17. PEMDAS
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.
-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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Get the absolute value equation by itself. Solve.


18. Definition of a Rational Number
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.
Isolate the radical expression and use the standard rules of algebra.
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 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.


19. Finding the Sum of the Interior Angles of a Polygon
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
The whole number left over after division.
-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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides


20. 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.
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
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.


21. If (Square Root: x-1)+5=12 - what is the value of x/2?
Combine like terms.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Express them with a common denominator.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25


22. What are Two Special Pythagorean Triples?

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23. Difference Between a Factor and a Multiple
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
-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.
Express them with a common denominator.
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.


24. Knowing if an Integer is a Multiple of 5 or 10
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Factor out and cancel all factors the numerator and denominator have in common.
A(2)+b(2)=c(2)
-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.


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

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26. If the average of a - b - and 48 is 48 - what is the value of a + b?
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Factor out and cancel all factors the numerator and denominator have in common.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
-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.


27. Finding the LCM of Two or More Numbers

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28. Setting Up a Ratio
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
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.


29. Finding the Mode of a Set of Numbers
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Find a common denominator - then add or subtract the numerators.
The value that appears the most often.
Cancel factors common to the numerator and denominator.


30. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
VofaC: (pie)r(2)h
Do whatever is necessary to both sides to isolate the variable.
Average the smallest and largest number


31. Finding the Length of an Arc in a Circle

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32. Calculating the Probability that an Event will Take Place
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
(x1+x2)/2 -(y1+y2)/2
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Probability: Number of Favorable Outcomes/Total Possible Outcomes


33. Solving a Proportion
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
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.
Cross multiply.
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.


34. Finding the GCF of Two or More Numbers
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Plug in the given values for the unknowns and calculate according to PEMDAS.


35. What Does Solving In Terms of Mean?
Combine like terms.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Do whatever is necessary to both sides to isolate the variable.
FOIL: First - Outer - Inner - Last... Combine Like Terms


36. Number of Groups - +1 Each Time
Adjacent angles are supplementary - Vertical angles are equal
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
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.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.


37. If 3(3x)=9(x+2) - what is the value of x?
Switch the numerator and denominator.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I


38. Adding and Subtracting Fractions
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 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Find a common denominator - then add or subtract the numerators.
Plug in the given values for the unknowns and calculate according to PEMDAS.


39. 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.
Adjacent angles are supplementary - Vertical angles are equal
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.


40. Multiplying Fractions
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.
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.
Multiply the numerators and multiply the denominators.
Factor out and cancel all factors the numerator and denominator have in common.


41. Adding and Subtracting Polynomials
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.
Combine like terms.
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.
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.


42. 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?
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/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.


43. Expressing the Union and Intersection of Sets
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Just add or subtract the coefficients in front of the radicals.
Average: Sum of the Terms/Number of the Terms
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


44. Finding the Surface Area of a Rectangular Solid
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72


45. Raising a Power to a Power
Subtract the smallest from the largest and add 1
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Multiply the exponents - (x^3)^4=x^3*4=x^12


46. 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.
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 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
The value that falls in the middle of the set.


47. What is the length of the shorter leg of a right triangle whose other leg measures 7(square root: 3)?
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2


48. Finding the Area of a Sector

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49. Finding the Volume of a Rectangular Solid
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Multiply the numerators and multiply the denominators.
VofaRS=lwh


50. 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?
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.
Cancel factors common to the numerator and denominator.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Multiply the numerators and multiply the denominators.