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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. Adding and Subtracting Polynomials
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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
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.
Combine like terms.


2. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Sum: Average x Number of Terms
Plug in the given values for the unknowns and calculate according to PEMDAS.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
First - substitute for the variable. Then evaluate the expression using the correct order of operations.


3. Finding the Area of a Circle
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Sum: Average x Number of Terms
(pie)r(squared)


4. Solving an Inequality
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Sum: Average x Number of Terms
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. Properties of a 45-45-90 Triangle
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.


6. Numbers that are Relatively Prime
The value that appears the most often.
The value that falls in the middle of the set.
Two relatively prime numbers are integers that have no common factor other than 1.
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.


7. Finding the GCF of Two or More Numbers
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.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
The value that appears the most often.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.


8. Characteristics of a Parallelogram
Plug in the given values for the unknowns and calculate according to PEMDAS.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
VofaRS=lwh


9. Properties of Similar Triangles
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side 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.


10. Finding the Distance Between Two Points on a Coordinate Graph
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
(pie)r(squared)
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.


11. PEMDAS
VofaC: (pie)r(2)h
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Use the formula distance=rate*time and its variations to help in this question.


12. Finding the Volume of a Rectangular Solid
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 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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
VofaRS=lwh


13. Finding the Median of a Set of Numbers
The value that falls in the middle of the set.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
-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.
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.


14. Counting Consecutive Integers
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Subtract the smallest from the largest and add 1
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.


15. Finding the Surface Area of a Rectangular Solid
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
VofaRS=lwh
Factor out and cancel all factors the numerator and denominator have in common.
Multiply the exponents - (x^3)^4=x^3*4=x^12


16. Finding the Length of an Arc in a Circle

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17. Quickly Finding the Average of a Series of Evenly Spaced Numbers
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
The value that appears the most often.
Average the smallest and largest number
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.


18. Knowing if an Integer is a Multiple of 5 or 10
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.
-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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Plug in the given values for the unknowns and calculate according to PEMDAS.


19. Finding the Volume of a Cylinder
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Put each number in the original ratio over the sum of the numbers.
VofaC: (pie)r(2)h
Combine like terms.


20. An Important Property of a Line Tangent to a Circle
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
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Part=Percent x Whole


21. Finding the LCM of Two or More Numbers

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22. Multiplying Binomials
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle


23. Multiplying Fractions
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.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Multiply the numerators and multiply the denominators.


24. Raising a Power to a Power
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
Multiply the numerators and multiply the denominators.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Plug in the given values for the unknowns and calculate according to PEMDAS.


25. Finding the Rate of Speed
Use the formula distance=rate*time and its variations to help in this question.
Four equal acute angles and four equal obtuse angles.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.


26. Solving a Radical Equation
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Average: Sum of the Terms/Number of the Terms
Isolate the radical expression and use the standard rules of algebra.
2(pie)r


27. Finding the Circumference of a Circle
Use the units to keep things straight - Snowfall inches/hours
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.
2(pie)r
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.


28. What is the Triangle Inequality Theorem?
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.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal


29. Finding the Missing Number in a Series When You are Given the Average
Put each number in the original ratio over the sum of the numbers.
The value that appears the most often.
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.
Get the absolute value equation by itself. Solve.


30. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
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.
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Express them with a common denominator.


31. Simplifying Square Roots
-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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.


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

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33. Evaluating an Algebraic Expression
Plug in the given values for the unknowns and calculate according to PEMDAS.
Subtract the smallest from the largest and add 1
-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 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%


34. Finding the Area of a Triangle

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35. Finding the Reciprocal of a Fraction
VofaRS=lwh
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Switch the numerator and denominator.
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


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

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37. 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?
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
The value that falls in the middle of the set.
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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.


38. Formula Used to Find Percent
Use the distributive property then combine the like terms.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Part=Percent x Whole
Plug in the given values for the unknowns and calculate according to PEMDAS.


39. Finding the Slope of a Line When Given Two Points on the Line
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.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Slope=change in y/change in x


40. 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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.


41. Adding and Subtracting Monomials
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
-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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.


42. Properties of the Interior and Exterior Angles of a Triangle
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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(2)+b(2)=c(2)
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.


43. Convert From a Fraction to a Decimal - Vice Versa
Get the absolute value equation by itself. Solve.
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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2


44. Finding the Slope When Given an Equation of a Line
Find a common denominator - then add or subtract the numerators.
Switch the numerator and denominator.
Slope=change in y/change in x
Put the equation into the slope-intercept form: y=mx+b. The slope is m.


45. If the average of a - b - and 48 is 48 - what is the value of a + b?
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
VofaC: (pie)r(2)h
Change the division sign to a multiplication sign - invert the second fraction - and multiply.


46. Converting from part-to-part ratios to part-to-whole ratios
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Put each number in the original ratio over the sum of the numbers.
FOIL: First - Outer - Inner - Last... Combine Like Terms


47. Finding the Sum of the Interior Angles of a Polygon
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.
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
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides


48. Finding the Domain and Range of a Function
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.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
Subtract the smallest from the largest and add 1


49. Calculating Negative Exponents and Radical Exponents
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.


50. Finding the Midpoint Between Two Points
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.
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
(x1+x2)/2 -(y1+y2)/2