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• Answer 50 questions in 15 minutes.
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• Match each statement with the correct term.
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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 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.
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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
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.


2. 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
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.


3. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.


4. 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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
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.
Just add or subtract the coefficients in front of the radicals.


5. Adding and Subtracting Roots
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.
Do whatever is necessary to both sides to isolate the variable.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Just add or subtract the coefficients in front of the radicals.


6. Finding the Distance Between Two Points on a Coordinate Graph
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 distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)


7. Number of Groups - +1 Each Time
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
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 least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.


8. If 3(3x)=9(x+2) - what is the value of x?
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Use the distributive property then combine the like terms.
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.


9. 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
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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 least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.


10. Raising a Power to a Power
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.
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 the exponents - (x^3)^4=x^3*4=x^12
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.


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

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12. Difference Between a Factor and a Multiple
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
-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.
2(pie)r
Find a common denominator - then add or subtract the numerators.


13. Finding a Term in a Geometric Sequence
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.
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
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I


14. Converting from part-to-part ratios to part-to-whole ratios
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Put each number in the original ratio over the sum of the numbers.
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.
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.


15. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.


16. Definition of a Rational Number
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Use the formula distance=rate*time and its variations to help in this question.


17. Counting Consecutive Integers
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Use the formula distance=rate*time and its variations to help in this question.
Subtract the smallest from the largest and add 1
Put each number in the original ratio over the sum of the numbers.


18. Finding the Length of an Arc in a Circle

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19. Dividing Fractions
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.


20. What value of x is not in the domain of the function f(x)=x-2/x-3?
Just add or subtract the coefficients in front of the radicals.
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.
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
The value that falls in the middle of the set.


21. Calculating Negative Exponents and Radical Exponents
Multiply the numerators and multiply the denominators.
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
Two relatively prime numbers are integers that have no common factor other than 1.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.


22. Properties of a 30-60-90 Triangle
Factor out and cancel all factors the numerator and denominator have in common.
-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.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Isolate the radical expression and use the standard rules of algebra.


23. Multiplying Fractions
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Multiply the numerators and multiply the denominators.
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


24. How do you know if an integer is a multiple of 3 or 9?
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
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.


25. Simplifying an Algebraic Equation
Use the distributive property then combine the like terms.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Cancel factors common to the numerator and denominator.


26. Characteristics of a Rectangle
Average: Sum of the Terms/Number of the Terms
Cancel factors common to the numerator and denominator.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Subtract the smallest from the largest and add 1


27. Properties of Similar Triangles
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.


28. Finding the Midpoint Between Two Points
(x1+x2)/2 -(y1+y2)/2
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
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.
Find a common denominator - then add or subtract the numerators.


29. Converting From a Mixed Number to an Improper Fraction
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
The value that appears the most often.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.


30. Adding and Subtracting Monomials
VofaRS=lwh
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Get the absolute value equation by itself. Solve.


31. Adding and Subtracting Fractions
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.
Put each number in the original ratio over the sum of the numbers.
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.
Find a common denominator - then add or subtract the numerators.


32. Comparing the values of two or more Fractions
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Express them with a common denominator.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
-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.


33. Multiplying and Dividing Roots
-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.
Get the absolute value equation by itself. Solve.
Combine like terms.
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.


34. Finding the Domain and Range of a Function
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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
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.
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.


35. What is the Pythagorean Theorem?
FOIL: First - Outer - Inner - Last... Combine Like Terms
A(2)+b(2)=c(2)
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.


36. Setting Up a Ratio
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.
(pie)r(squared)
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.


37. What Does Solving In Terms of Mean?
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
VofaRS=lwh
Part=Percent x Whole
The value that appears the most often.


38. General Procedure for Multiplying Polynomials
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
Use the distributive property then combine the like terms.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Probability: Number of Favorable Outcomes/Total Possible Outcomes


39. Finding the GCF of Two or More Numbers
Factor out and cancel all factors the numerator and denominator have in common.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
FOIL: First - Outer - Inner - Last... Combine Like Terms


40. 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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
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
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.


41. Finding the Slope of a Line When Given Two Points on the Line
Slope=change in y/change in x
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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.


42. Prime Factorization of a 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.
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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Use simple numbers like 1 and 2 and see what happens.


43. Finding the LCM of Two or More Numbers

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44. What types of angles are formed when a transversal cross parallel lines?
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
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.
Four equal acute angles and four equal obtuse angles.


45. What is the Triangle Inequality Theorem?
Use simple numbers like 1 and 2 and see what happens.
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.
Find a common denominator - then add or subtract the numerators.
Multiply the exponents - (x^3)^4=x^3*4=x^12


46. 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?
Slope=change in y/change in x
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Switch the numerator and denominator.


47. Characteristics of a Parallelogram
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.
Slope=change in y/change in x
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.


48. Finding the Area of a Triangle

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49. What are Two Special Pythagorean Triples?

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50. Finding the Median of a Set of Numbers
Do whatever is necessary to both sides to isolate the variable.
The value that falls in the middle of the set.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.