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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. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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.
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
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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.


2. Scalene - Isosceles - and Equilateral Triangles
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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.


3. Factoring the Difference of Two Squares
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.


4. Finding the Volume of a Rectangular Solid
VofaRS=lwh
Average: Sum of the Terms/Number of the Terms
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.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.


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

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6. Finding the Circumference of a Circle
Average: Sum of the Terms/Number of the 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.
A(2)+b(2)=c(2)
2(pie)r


7. Numbers that are Relatively Prime
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Two relatively prime numbers are integers that have no common factor other than 1.
Get the absolute value equation by itself. Solve.
(x1+x2)/2 -(y1+y2)/2


8. If (Square Root: x-1)+5=12 - what is the value of x/2?
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
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
Multiply the numerators and multiply the denominators.
-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.


9. Finding the Surface Area of a Rectangular Solid
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 coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2


10. Finding the Slope When Given an Equation of a Line
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
A(2)+b(2)=c(2)
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a


11. Adding a Positive Number to a Negative Number
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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
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.
(pie)r(squared)


12. Finding the Length of an Arc in a Circle

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13. Calculating Negative Exponents and Radical Exponents
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 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
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.


14. PEMDAS
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Find a common denominator - then add or subtract the numerators.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.


15. 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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.


16. Counting the Total Number of Possibilities for Several Events to Occur
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.
Use the units to keep things straight - Snowfall inches/hours
Isolate the radical expression and use the standard rules of algebra.
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.


17. 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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Use simple numbers like 1 and 2 and see what happens.
Sum: Average x Number of Terms


18. Finding the Missing Number in a Series When You are Given the Average
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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.
Plug in the given values for the unknowns and calculate according to 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.


19. Simplifying a Fraction to Lowest Terms
Factor out and cancel all factors the numerator and denominator have in common.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.


20. Multiplying Binomials
FOIL: First - Outer - Inner - Last... Combine Like Terms
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
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.


21. Properties of Similar Triangles
Cancel factors common to the numerator and denominator.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.


22. Finding the Rate of Speed
Use the formula distance=rate*time and its variations to help in this question.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction


23. Dividing Expressions with Exponents that Have a Common Base
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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5


24. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Use the formula distance=rate*time and its variations to help in this question.


25. Knowing if an Integer is a Multiple of 2 or 4
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
-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.
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.
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.


26. Direct Variation and Inverse Variation
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
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.
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
-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.


27. Converting from part-to-part ratios to part-to-whole ratios
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
-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.
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.
Put each number in the original ratio over the sum of the numbers.


28. Finding the Domain and Range of a Function
Switch the numerator and denominator.
Use simple numbers like 1 and 2 and see what happens.
(x1+x2)/2 -(y1+y2)/2
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.


29. If 2+l6-xl=10 and x>0 - what is the value of 2x?
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
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
Get the absolute value equation by itself. Solve.
Combine like terms.


30. What is the Triangle Inequality Theorem?
-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.
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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.
2(pie)r


31. Determining Absolute Value of a Number
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Use simple numbers like 1 and 2 and see what happens.
Part=Percent x Whole
The value that appears the most often.


32. Definition of an Irrational Number
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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


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

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34. Solving a Linear Equation
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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.
Do whatever is necessary to both sides to isolate the variable.
(x1+x2)/2 -(y1+y2)/2


35. Characteristics of a Square
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
VofaC: (pie)r(2)h
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.


36. Definition of Remainder
The whole number left over after division.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
-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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides


37. Expressing the Union and Intersection of Sets
Slope=change in y/change in x
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
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.
Multiply the exponents - (x^3)^4=x^3*4=x^12


38. Sale Price of a Jacket Marked Down 30% Each Week for 3 Weeks - What % of the Original Price is the Cost of the Jacket After the 3 Week Sale Period
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.
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%


39. 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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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 distance formula: d=(square root over) (x2-x2)2+(y1-y2)2


40. Finding the Area of a Triangle

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41. Properties of a 45-45-90 Triangle
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.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.


42. Characteristics of a Parallelogram
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.
The value that appears the most often.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Two relatively prime numbers are integers that have no common factor other than 1.


43. How do you know if an integer is a multiple of 3 or 9?
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.
VofaRS=lwh
Average: Sum of the Terms/Number of the Terms
Put the equation into the slope-intercept form: y=mx+b. The slope is m.


44. Simplifying Square Roots
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.
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides


45. Convert From a Fraction to a Decimal - Vice Versa
Subtract the smallest from the largest and add 1
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.
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.


46. Finding the y-intercept When Given an Equation of a Line
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Cross multiply.
Put the equation into y=mx+b-- in which case b is the y-intercept.


47. Finding the Sum of the Interior Angles of a Polygon
Isolate the radical expression and use the standard rules of algebra.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
(pie)r(squared)
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides


48. Formula to Find Average
Do whatever is necessary to both sides to isolate the variable.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Plug in the given values for the unknowns and calculate according to PEMDAS.
Average: Sum of the Terms/Number of the Terms


49. Finding the LCM of Two or More Numbers

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50. What types of angles are formed when a transversal cross parallel lines?
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Four equal acute angles and four equal obtuse angles.
Use the units to keep things straight - Snowfall inches/hours
Cross multiply.