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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
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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


2. Raising a Power to a Power
Multiply the exponents - (x^3)^4=x^3*4=x^12
FOIL: First - Outer - Inner - Last... Combine Like Terms
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Two relatively prime numbers are integers that have no common factor other than 1.


3. Finding the Area of 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
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
(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.


4. Multiplying Fractions
Factor out and cancel all factors the numerator and denominator have in common.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Multiply the numerators and multiply the denominators.


5. Adding and Subtracting Roots
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
The whole number left over after division.
Just add or subtract the coefficients in front of the radicals.


6. Finding the Area of a Triangle

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7. Definition of Remainder
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
The whole number left over after division.
FOIL: First - Outer - Inner - Last... Combine Like Terms
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.


8. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.


9. If the average of a - b - and 48 is 48 - what is the value of a + b?
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Isolate the radical expression and use the standard rules of algebra.
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.


10. Multiplying Monomials
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.
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.
Find a common denominator - then add or subtract the numerators.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2


11. Converting From a Mixed Number to an Improper Fraction
Combine like terms.
Multiply the numerators and multiply the denominators.
Isolate the radical expression and use the standard rules of algebra.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.


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

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13. Comparing the values of two or more Fractions
Express them with a common denominator.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%


14. Knowing if an Integer is a Multiple of 2 or 4
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Just add or subtract the coefficients in front of the radicals.
-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.
The value that falls in the middle of the set.


15. Solving a Proportion
Cross multiply.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Adjacent angles are supplementary - Vertical angles are equal


16. Number of Groups - +1 Each Time
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.


17. Factoring a Polynomial ('FOIL in Reverse')
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
-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.
Use the distributive property then combine the like terms.
-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.


18. Average Rate and How Do You Find It
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Cancel factors common to the numerator and 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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I


19. Finding the Area of a Sector

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20. What value of x is not in the domain of the function f(x)=x-2/x-3?
Isolate the radical expression and use the standard rules of algebra.
Use the units to keep things straight - Snowfall inches/hours
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
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


21. What types of angles are formed when two lines intersect?
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Adjacent angles are supplementary - Vertical angles are equal
Put each number in the original ratio over the sum of the numbers.


22. Calculating the Probability that an Event will Take Place
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Multiply the exponents - (x^3)^4=x^3*4=x^12
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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


23. Adding and Subtracting Fractions
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)
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Find a common denominator - then add or subtract the numerators.


24. Finding the GCF of Two or More Numbers
Use simple numbers like 1 and 2 and see what happens.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5


25. Finding the Mode of a Set of Numbers
Express them with a common denominator.
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.
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.
The value that appears the most often.


26. Finding the Volume of a Rectangular Solid
Put the equation into y=mx+b-- in which case b is the y-intercept.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
VofaRS=lwh


27. PEMDAS
The whole number left over after division.
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.
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction


28. What is the Triangle Inequality Theorem?
Two relatively prime numbers are integers that have no common factor other than 1.
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
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.


29. Finding the Missing Number in a Series When You are Given the Average
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.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Put each number in the original ratio over the sum of the numbers.


30. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
-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.
A(2)+b(2)=c(2)
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.


31. Simplifying Square Roots
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.


32. If 2+l6-xl=10 and x>0 - what is the value of 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.
Do whatever is necessary to both sides to isolate the variable.
Get the absolute value equation by itself. Solve.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)


33. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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
Express them with a common denominator.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.


34. Simplifying an Algebraic Equation
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Cancel factors common to the numerator and denominator.


35. Solving a Problem Involving Rates
Use the units to keep things straight - Snowfall inches/hours
Use the distributive property then combine the like terms.
Average: Sum of the Terms/Number of the Terms
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.


36. How do you know if an integer is a multiple of 3 or 9?
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.


37. What is the slope of the line perpendicular to the line with linear equation 4x+2y=12?
The value that falls in the middle of the set.
Express them with a common denominator.
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 units to keep things straight - Snowfall inches/hours


38. Convert From a Fraction to a Decimal - Vice Versa
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Cross multiply.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
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.


39. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
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
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Use simple numbers like 1 and 2 and see what happens.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.


40. Formula Used to Find Percent
Part=Percent x Whole
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
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
2(pie)r


41. Properties of the Interior and Exterior Angles of a Triangle
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.


42. Finding the Domain and Range of a Function
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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.
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.
Average the smallest and largest number


43. If x(2)=7x+18 - what is the positive value of x?
Put each number in the original ratio over the sum of the numbers.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
VofaRS=lwh


44. 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?
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Sum: Average x Number of Terms
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.


45. An Important Property of a Line Tangent to a Circle
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.
Part=Percent x Whole
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.
Multiply the exponents - (x^3)^4=x^3*4=x^12


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

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47. Multiplying Binomials
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
FOIL: First - Outer - Inner - Last... Combine Like Terms
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Multiply the exponents - (x^3)^4=x^3*4=x^12


48. Solving a System of Equations
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Find a common denominator - then add or subtract the numerators.
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. Finding the Length of an Arc in a Circle

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50. Finding the Median of a Set of Numbers
Use simple numbers like 1 and 2 and see what happens.
The value that falls in the middle of the set.
FOIL: First - Outer - Inner - Last... Combine Like Terms
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.