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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
Combine like terms.
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
The whole number left over after division.


2. Solving a System of Equations
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
FOIL: First - Outer - Inner - Last... Combine Like Terms


3. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 2)?
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
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. Solving an Inequality
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
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.


5. Knowing if an Integer is a Multiple of 5 or 10
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
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.
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.


6. Finding the Sum of the Interior Angles of a Polygon
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.


7. Adding a Positive Number to a Negative Number
-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.
Two relatively prime numbers are integers that have no common factor other than 1.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value


8. Finding the Sum of the Average of a Series of Numbers
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.
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Sum: Average x Number of Terms


9. Multiplying Binomials
FOIL: First - Outer - Inner - Last... Combine Like Terms
A(2)+b(2)=c(2)
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
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.


10. Finding the Rate of Speed
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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 distance=rate*time and its variations to help in this question.
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.


11. Formula Used to Find Percent
Part=Percent x Whole
Subtract the smallest from the largest and add 1
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.


12. If r#t=t(r)-r(t) - then what is 4#3?
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
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.
(pie)r(squared)
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal


13. Properties of a 45-45-90 Triangle
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
FOIL: First - Outer - Inner - Last... Combine Like Terms


14. Finding the Volume of a Cylinder
Slope=change in y/change in 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.
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


15. Prime Factorization of a Number
FOIL: First - Outer - Inner - Last... Combine Like 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.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.


16. Multiplying and Dividing Roots
Get the absolute value equation by itself. Solve.
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.
Average the smallest and largest number
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.


17. Setting Up a Ratio
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24


18. Finding the Circumference of a Circle
Use the units to keep things straight - Snowfall inches/hours
2(pie)r
Two relatively prime numbers are integers that have no common factor other than 1.
Part=Percent x Whole


19. Solving a Radical Equation
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.
The whole number left over after division.
Isolate the radical expression and use the standard rules of algebra.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction


20. Finding the Area of a Triangle

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21. Dividing Expressions with Exponents that Have a Common Base
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.
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.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.


22. Finding the Area of a Sector

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23. Adding and Subtracting Roots
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Just add or subtract the coefficients in front of the radicals.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Adjacent angles are supplementary - Vertical angles are equal


24. Adding and Subtracting Polynomials
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Multiply the exponents - (x^3)^4=x^3*4=x^12
Combine like terms.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72


25. Simplifying an Algebraic Equation
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 the equation into y=mx+b-- in which case b is the y-intercept.
Two relatively prime numbers are integers that have no common factor other than 1.
Cancel factors common to the numerator and denominator.


26. Calculating Negative Exponents and Radical Exponents
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
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.
Get the absolute value equation by itself. Solve.


27. Adding and Subtracting Fractions
Find a common denominator - then add or subtract the numerators.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
The whole number left over after division.


28. Finding the Midpoint Between Two Points
Find a common denominator - then add or subtract the numerators.
(x1+x2)/2 -(y1+y2)/2
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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.


29. Characteristics of a Rectangle
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Use the distributive property then combine the like terms.


30. Raising a Power to a Power
Multiply the exponents - (x^3)^4=x^3*4=x^12
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.


31. Expressing the Union and Intersection of Sets
Slope=change in y/change in x
VofaC: (pie)r(2)h
FOIL: First - Outer - Inner - Last... Combine Like Terms
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


32. Solving a Proportion
Cross multiply.
(x1+x2)/2 -(y1+y2)/2
-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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2


33. Multiplying Fractions
Multiply the numerators and multiply the denominators.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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.


34. Finding the Original Value Before it was Increased or Decreased by a Certain Percentage
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
-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.
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.


35. 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.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.


36. Knowing if an Integer is a Multiple of 2 or 4
Average the smallest and largest number
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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.
-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.


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

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38. What are Two Special Pythagorean Triples?

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

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40. Multiplying Monomials
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
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.
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.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.


41. 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?
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
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 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
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.


42. General Procedure for Multiplying Polynomials
Use the distributive property then combine the like terms.
Average: Sum of the Terms/Number of the Terms
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
VofaRS=lwh


43. Solving a Problem Involving Rates
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Use the units to keep things straight - Snowfall inches/hours
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.


44. Scalene - Isosceles - and Equilateral Triangles
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Do whatever is necessary to both sides to isolate the variable.
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.
Put the equation into the slope-intercept form: y=mx+b. The slope is m.


45. What Does Solving In Terms of Mean?
FOIL: First - Outer - Inner - Last... Combine Like Terms
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
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
Find a common denominator - then add or subtract the numerators.


46. Characteristics of a Square
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7
Cancel factors common to the numerator and denominator.


47. Finding the Area of a Circle
Use simple numbers like 1 and 2 and see what happens.
(pie)r(squared)
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96


48. Finding the Slope of a Line When Given Two Points on the Line
Slope=change in y/change in x
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
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.
Four equal acute angles and four equal obtuse angles.


49. Finding the Missing Number in a Series When You are Given the Average
Part=Percent x Whole
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.
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.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2


50. 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
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Do whatever is necessary to both sides to isolate the variable.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time