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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 f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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
First - substitute for the variable. Then evaluate the expression using the correct order of operations.


2. Finding the Length of an Arc in a Circle

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3. Finding the Area of a Triangle

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4. Difference Between a Factor and a Multiple
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
-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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.


5. Formula Used to Find Percent
Part=Percent x Whole
The whole number left over after division.
Subtract the smallest from the largest and add 1
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.


6. Finding a Term in a Geometric Sequence
Express them with a common denominator.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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
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.


7. Convert From a Fraction to a Decimal - Vice Versa
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 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%
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.


8. Finding the Slope of a Line When Given Two Points on the Line
Slope=change in y/change in x
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal


9. Definition of an Irrational Number
Switch the numerator and 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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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


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

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11. Formula to Find Average
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Average: Sum of the Terms/Number of the Terms


12. Factoring the Difference of Two Squares
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Multiply the numerators and multiply the denominators.


13. Adding and Subtracting Roots
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.
Part=Percent x Whole
Just add or subtract the coefficients in front of the radicals.
A(2)+b(2)=c(2)


14. What value of x is not in the domain of the function f(x)=x-2/x-3?
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the 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.
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
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction


15. 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?
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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
-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 number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.


16. Scalene - Isosceles - and Equilateral Triangles
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.
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.
Average the smallest and largest number


17. What Does Solving In Terms of Mean?
Factor out and cancel all factors the numerator and denominator have in common.
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.
Multiply the whole number part by the denominator - then add the numerator. Keep the same 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.


18. Factoring a Polynomial ('FOIL in Reverse')
Multiply the whole number part by the denominator - then add the numerator. Keep the same 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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.


19. 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?
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.


20. 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.
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
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


21. Properties of a 30-60-90 Triangle
-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.
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 sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Average: Sum of the Terms/Number of the Terms


22. Finding the Surface Area of a Rectangular Solid
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
VofaC: (pie)r(2)h


23. Expressing the Union and Intersection of Sets
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Multiply the numerators and multiply the denominators.
Plug in the given values for the unknowns and calculate according to PEMDAS.
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


24. Finding the Distance Between Two Points on a Coordinate Graph
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
The value that appears the most often.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24


25. An Important Property of a Line Tangent to a Circle
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
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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.
(x1+x2)/2 -(y1+y2)/2


26. Finding the Reciprocal of a Fraction
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Switch the numerator and denominator.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
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


27. Solving a Problem Involving Rates
Use the units to keep things straight - Snowfall inches/hours
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
(pie)r(squared)


28. Multiplying Binomials
Use simple numbers like 1 and 2 and see what happens.
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.
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.
FOIL: First - Outer - Inner - Last... Combine Like Terms


29. Calculating the Probability that an Event will Take Place
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.


30. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.


31. Dividing 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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Sum: Average x Number of Terms
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value


32. Finding the Volume of a Rectangular Solid
VofaRS=lwh
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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


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

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34. Adding a Positive Number to a Negative Number
Subtract the smallest from the largest and add 1
Average the smallest and largest number
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.


35. Finding the Rate of Speed
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Use the formula distance=rate*time and its variations to help in this question.
Average: Sum of the Terms/Number of the Terms
Plug in the given values for the unknowns and calculate according to PEMDAS.


36. Finding the LCM of Two or More Numbers

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37. Definition of Remainder
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
The whole number left over after division.


38. If 2+l6-xl=10 and x>0 - what is the value of 2x?
-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.
Get the absolute value equation by itself. Solve.
Cross multiply.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.


39. What types of angles are formed when a transversal cross parallel lines?
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Four equal acute angles and four equal obtuse angles.
(x1+x2)/2 -(y1+y2)/2
Put the equation into the slope-intercept form: y=mx+b. The slope is m.


40. Number of Groups - +1 Each Time
Adjacent angles are supplementary - Vertical angles are equal
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 the distributive property then combine the like 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.


41. Multiply and Divide Positive and Negative Numbers
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
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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.
A(2)+b(2)=c(2)


42. Simplifying a Fraction to Lowest Terms
The whole number left over after division.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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.
Factor out and cancel all factors the numerator and denominator have in common.


43. Finding the Area of a Circle
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)
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Express them with a common denominator.


44. Multiplying and Dividing Roots
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Plug in the given values for the unknowns and calculate according to PEMDAS.
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.
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.


45. Definition of a Rational Number
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
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
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.


46. Solving a Linear Equation
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.
Slope=change in y/change in x
Do whatever is necessary to both sides to isolate the variable.
Find a common denominator - then add or subtract the numerators.


47. Finding the Sum of the Average of a Series of Numbers
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Sum: Average x Number of Terms
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.
Cross multiply.


48. How do you know if an integer is a multiple of 3 or 9?
Standard function notation is written f(x) and read 'f of x.' To evaluate the function f(x)=2x+3 for f(4) - replace every x with 4 and simplify. f(4)=2(4)+3=11.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/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.
Use the units to keep things straight - Snowfall inches/hours


49. Finding the Domain and Range of a Function
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
Part=Percent x Whole
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.
Put each number in the original ratio over the sum of the numbers.


50. Numbers that are Relatively Prime
Two relatively prime numbers are integers that have no common factor other than 1.
(x1+x2)/2 -(y1+y2)/2
The value that appears the most often.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.