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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. 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.
A rational number is a number that can be expressed as a ratio of two numbers or as a terminating or repeating decimal.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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.


2. Characteristics of a Square
Substitute r=4 and t=3 and evaluate the exponents before subtracting the expression.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
Use the units to keep things straight - Snowfall inches/hours
Factor out the perfect squares under the radical - take their square roots - and put the result in front.


3. Properties of Similar Triangles
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
(x1+x2)/2 -(y1+y2)/2


4. Raising a Power to a Power
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Sum: Average x Number of Terms
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Multiply the exponents - (x^3)^4=x^3*4=x^12


5. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)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.
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 simple numbers like 1 and 2 and see what happens.


6. 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.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
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.


7. Finding the Area of a Sector

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8. Finding a Term in a Geometric Sequence
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.
Use simple numbers like 1 and 2 and see what happens.
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.
(x1+x2)/2 -(y1+y2)/2


9. Solving an Inequality
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Average the smallest and largest number
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


10. Simplifying an Algebraic Equation
Cancel factors common to the numerator and denominator.
Do whatever is necessary to both sides to isolate the variable.
(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.


11. Convert From a Fraction to a Decimal - Vice Versa
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
Just add or subtract the coefficients in front of the radicals.
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 number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.


12. If x(2)=7x+18 - what is the positive value of x?
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Average: Sum of the Terms/Number of the Terms
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal


13. Solving a Radical Equation
Plug in the given values for the unknowns and calculate according to PEMDAS.
Isolate the radical expression and use the standard rules of algebra.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)


14. Multiplying Monomials
-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.
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2


15. Formula to Find Average
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Average: Sum of the Terms/Number of the Terms
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a


16. Finding the Domain and Range of a Function
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.
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.
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.


17. Finding the Reciprocal of a Fraction
Switch the numerator and 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.
The whole number left over after division.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.


18. 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.
Multiply the numerators and multiply the denominators.
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Find a common denominator - then add or subtract the numerators.


19. Calculating the Probability that an Event will Take Place
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.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Isolate the radical expression and use the standard rules of algebra.


20. 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.
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
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
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.


21. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
FOIL: First - Outer - Inner - Last... Combine Like Terms
VofaC: (pie)r(2)h


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

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23. Factoring a Polynomial ('FOIL in Reverse')
Multiply the exponents - (x^3)^4=x^3*4=x^12
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5


24. If 4(x(2)-10x+25) - then what is the value of x?
Put the equation into y=mx+b-- in which case b is the y-intercept.
Part=Percent x Whole
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a


25. Solving a Problem Involving Rates
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
-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 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
Use the units to keep things straight - Snowfall inches/hours


26. Finding the Sum of the Average of a Series of Numbers
A(2)+b(2)=c(2)
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.
Sum: Average x Number of Terms
Factor out the perfect squares under the radical - take their square roots - and put the result in front.


27. Direct Variation and Inverse Variation
Use the distributive property then combine the like 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
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time


28. If f(x)=x(1/3)+1/3x - then what is the value of f(27)?
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
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
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
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.


29. Finding the LCM of Two or More Numbers

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30. Dividing Expressions with Exponents that Have a Common Base
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
The whole number left over after division.


31. General Procedure for Multiplying Polynomials
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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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 distributive property then combine the like terms.


32. Setting Up a Ratio
Check the multiples of the larger number until you find one that's also a multiple of the smaller.
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
(x1+x2)/2 -(y1+y2)/2
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.


33. Finding the Area of a Circle
Subtract the smallest from the largest and add 1
(pie)r(squared)
Two pairs of parallel sides. Opposite sides/angles are equal. Any two consecutive angles add up to 180. Area: base*height.
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.


34. Adding and Subtracting Monomials
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.
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7


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

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36. 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.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.


37. Average Rate and How Do You Find It
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
Change the division sign to a multiplication sign - invert the second fraction - and multiply.


38. PEMDAS
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Cross multiply.
A(2)+b(2)=c(2)


39. Multiplying Fractions
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.
Multiply the numerators and multiply the denominators.
Put each number in the original ratio over the sum of the numbers.
-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.


40. Simplifying Square Roots
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.


41. 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
Express them with a common denominator.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
Use simple numbers like 1 and 2 and see what happens.


42. Properties of the Interior and Exterior Angles of a Triangle
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.
-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.
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
The value that appears the most often.


43. Converting from an Improper Fraction to a Mixed Number
Ignore the signs... find the positive difference between the numbers - Then attach the sign of the original number with the larger absolute value
Cross multiply.
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.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I


44. Dividing Fractions
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
-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.
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.


45. Counting Consecutive Integers
Subtract the smallest from the largest and add 1
The whole number left over after division.
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
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a


46. 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 each number in the original ratio over the sum of the numbers.
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.


47. What are Two Special Pythagorean Triples?

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48. What value of x is not in the domain of the function f(x)=x-2/x-3?
(pie)r(squared)
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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
Just add or subtract the coefficients in front of the radicals.


49. Simplifying a Fraction to Lowest Terms
Subtract the smallest from the largest and add 1
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
2(pie)r
Factor out and cancel all factors the numerator and denominator have in common.


50. An Important Property of a Line Tangent to a Circle
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
-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.
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.
Use the formula distance=rate*time and its variations to help in this question.