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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. Evaluating an Algebraic Expression
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Use the formula distance=rate*time and its variations to help in this question.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Subtract the smallest from the largest and add 1


2. Finding the LCM of Two or More Numbers

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3. Simplifying a Fraction to Lowest Terms
Factor out and cancel all factors the numerator and denominator have in common.
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.
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 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.


4. Increasing and Decreasing a Number by a Certain Percentage
FOIL: First - Outer - Inner - Last... Combine Like Terms
-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.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Use the formula distance=rate*time and its variations to help in this question.


5. Adding and Subtracting Monomials
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a


6. Knowing Whether the Sum - Difference - or Product of Several Numbers will be Even/Odd
-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.
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
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.


7. Properties of a 30-60-90 Triangle
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
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)


8. Number of Groups - +1 Each Time
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
VofaRS=lwh
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.


9. 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?
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Adjacent angles are supplementary - Vertical angles are equal
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


10. Solving a Proportion
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Cross multiply.
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.
-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. 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.
Cross multiply.
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.
Adjacent angles are supplementary - Vertical angles are equal


12. What is the Pythagorean Theorem?
Factor out and cancel all factors the numerator and denominator have in common.
-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
A(2)+b(2)=c(2)


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

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14. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
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
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.
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.


15. What is the length of a leg of an isosceles rich triangle who's hypotenuse measures 24(square root: 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
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of 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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24


16. If the average of a - b - and 48 is 48 - what is the value of a + b?
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
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.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96


17. Simplifying Square Roots
Put the equation into y=mx+b-- in which case b is the y-intercept.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.


18. Finding the Midpoint Between Two Points
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.
(x1+x2)/2 -(y1+y2)/2
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Get the absolute value equation by itself. Solve.


19. PEMDAS
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Multiply the exponents - (x^3)^4=x^3*4=x^12
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.
Use the distributive property then combine the like terms.


20. 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
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24
Put the equation into y=mx+b-- in which case b is the y-intercept.
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


21. Formula to Find Average
Adjacent angles are supplementary - Vertical angles are equal
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.
Average: Sum of the Terms/Number of the Terms
Factor out and cancel all factors the numerator and denominator have in common.


22. Numbers that are Relatively Prime
Sum: Average x Number of Terms
Two relatively prime numbers are integers that have no common factor other than 1.
First - substitute for the variable. Then evaluate the expression using the correct order of operations.
Multiply the numerators and multiply the denominators.


23. Finding the Surface Area of a Rectangular Solid
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Put each number in the original ratio over the sum of the numbers.
Do whatever is necessary to both sides to isolate the variable.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)


24. 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.
Find a common denominator - then add or subtract the numerators.
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
Cross multiply.


25. Finding a Term in a Geometric Sequence
Four equal acute angles and four equal obtuse angles.
Use the units to keep things straight - Snowfall inches/hours
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.
Just add or subtract the coefficients in front of the radicals.


26. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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.
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
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.


27. Adding and Subtracting Polynomials
Get the absolute value equation by itself. Solve.
Real numbers - Have locations on the number line - Cannot be expressed precisely as a fraction/decimal
Find a common denominator - then add or subtract the numerators.
Combine like terms.


28. Finding the Slope of a Line When Given Two Points on the Line
Slope=change in y/change in x
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
Cross multiply.


29. Solving a System of Equations
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)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.
Put each number in the original ratio over the sum of the numbers.


30. 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.
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 the slope-intercept form: y=mx+b. The slope is m.
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.


31. Finding the Domain and Range of a Function
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
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.
x(2)-5x+6 - What factors of +6 also have a sum of -5? (x-2)(x-3)
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4


32. Dividing Fractions
Change the division sign to a multiplication sign - invert the second fraction - and multiply.
VofaRS=lwh
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
Average: Sum of the Terms/Number of the Terms


33. 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
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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.


34. Identifying Which Number of a Fraction is the Part and Which Number is the Whole

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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.
Use the distributive property then combine the like terms.
Average: Sum of the Terms/Number of the Terms
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides


36. 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.
Factor out the perfect squares under the radical - take their square roots - and put the result in front.
Find a common denominator - then add or subtract the numerators.
2(pie)r


37. Counting Consecutive Integers
VofaC: (pie)r(2)h
Subtract the smallest from the largest and add 1
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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.


38. Solving an Inequality
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
(x1+x2)/2 -(y1+y2)/2
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.


39. Calculating the Probability that an Event will Take Place
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Probability: Number of Favorable Outcomes/Total Possible Outcomes
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Cancel factors common to the numerator and denominator.


40. Finding the Rate of Speed
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2


41. If (Square Root: x-1)+5=12 - what is the value of x/2?
Sum: Average x Number of Terms
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Put each number in the original ratio over the sum of the numbers.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.


42. Finding the Mode of a Set of Numbers
Do whatever is necessary to both sides to isolate the variable.
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
The value that appears the most often.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)


43. Multiplying Fractions
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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2
Multiply the numerators and multiply the denominators.
Switch the numerator and denominator.


44. Factoring the Difference of Two Squares
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)
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.
-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.


45. Finding the Circumference of a Circle
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds
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
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.
2(pie)r


46. Finding the Length of an Arc in a Circle

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47. Finding the Distance Between Two Points on a Coordinate Graph
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
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.
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.


48. Quickly Finding the Average of a Series of Evenly Spaced Numbers
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Average the smallest and largest number
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2


49. Finding the Sum of the Average of a Series of Numbers
Sum: Average x Number of Terms
VofaC: (pie)r(2)h
Use the formula distance=rate*time and its variations to help in this question.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.


50. Finding the Area of a Triangle

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