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

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2. Evaluating an Algebraic Expression
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Switch the numerator and denominator.
-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.
Plug in the given values for the unknowns and calculate according to PEMDAS.


3. Finding the Length of an Arc in a Circle

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4. 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.
Just add or subtract the coefficients in front of the radicals.
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of the expression.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.


5. Definition of Remainder
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.
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Check the multiples of the larger number until you find one that's also a multiple of the smaller.


6. How do you know if an integer is a multiple of 3 or 9?
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.
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


7. General Procedure for Multiplying Polynomials
Use the distributive property then combine the like terms.
The sides of a 30-60-90 triangle are in a ratio of x:x(square root)3:2x.
Combine like terms.
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


8. Average Rate and How Do You Find It
Cross multiply.
Put the equation into y=mx+b-- in which case b is the y-intercept.
Average A per B= Total A/Total B so Average Speed = Total Distance/Total Time
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.


9. PEMDAS
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
To solve a quadratic equation - set the equation equal to zero and solve for the numbers of 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.


10. 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.
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.
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.
The whole number left over after division.


11. Factoring the Difference of Two Squares
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.
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.
First - get the base numbers to be the same. Then - set the exponents equal to each other and solve for x. Answer: 4
Factor the expressions to factor is the difference of squares. a^2-b^2=(a+b)(a-b)


12. Knowing if an Integer is a Multiple of 5 or 10
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
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 5 if the last digit is 5 or 0. - An integer is divisible by 10 if the last digit is 0.
Four-sided figure with four right angles. Perimeter: 2(length+width). Area: length*width.


13. If 4(x(2)-10x+25) - then what is the value of x?
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.
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.
Put the equation into y=mx+b-- in which case b is the y-intercept.
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.


14. Numbers that are Relatively Prime
Isolate the one variable on one side of the equation - leaving an expression containing the other variable on the other side of the equation.
First - get the square root by itself on one side of the equation. Then - solve for x by squaring each side. Answer: 25
Two relatively prime numbers are integers that have no common factor other than 1.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds


15. Finding the Sum of the Interior Angles of a Polygon
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.
Do whatever is necessary to both sides to isolate the variable.
Sum of the Angles of a Polygon: (n-2)*180 - n is the number of sides
Sum: Average x Number of Terms


16. Finding the LCM of Two or More Numbers

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17. If y varies inversely with x - and y is 3 when x is 10 - what is the value of x when y is 6?
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
A(2)+b(2)=c(2)
Multiply the whole number part by the denominator - then add the numerator. Keep the same denominator.
2(pie)r


18. Solving a Proportion
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
Cross multiply.
Set up an equation. Think of the result of a 15 percent increase over x as 1.15x.


19. Prime Factorization of a Number
VofaC: (pie)r(2)h
If two values vary directly - the values increase at the same rate. Express the relationship as x/y - and use a proportion to solve.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
Use the units to keep things straight - Snowfall inches/hours


20. Adding and Subtracting Polynomials
The whole number left over after division.
Combine like 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.
The sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.


21. Finding the Slope When Given an Equation of a Line
Put the equation into the slope-intercept form: y=mx+b. The slope is m.
2(pie)r
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
Put the number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.


22. Adding and Subtracting Monomials
Make sure that the terms to be combined have exactly the same variables. 2a+3a=(2+3)a=5a
-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.
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.


23. Calculating the Probability that an Event will Take Place
Probability: Number of Favorable Outcomes/Total Possible Outcomes
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
Do whatever is necessary to both sides to isolate the variable.
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.


24. Solving a System of Equations
Subtract the smallest from the largest and add 1
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.
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
Subtract the exponents and keep the same base.y^13/y^8=y^13-8=y^5


25. Solving an Inequality
Isolate the variable. When you multiply both sides by a negative number - you must reverse the inequality symbol.
Multiply the numerators and multiply the denominators.
Use common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
Use the distance formula: d=(square root over) (x2-x2)2+(y1-y2)2


26. Finding the Slope of a Line When Given Two Points on the Line
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.
Slope=change in y/change in x
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Average the smallest and largest number


27. Knowing if an Integer is a Multiple of 2 or 4
-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.
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 common multiples of 6 and 8 - and divide by 7 to find a remainder of 2. Answer: 72
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.


28. Properties of a 45-45-90 Triangle
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
Break down the integers into their prime factorizations - and multiply all prime factors they have in common.
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 sides of a 45-45-90 triangle are in a ratio of x:x:x(square root)2.


29. Finding the Rate of Speed
Four equal acute angles and four equal obtuse angles.
Parenthesis - Exponents - Multiplication/Division - Addition/Subtraction
Part=Percent x Whole
Use the formula distance=rate*time and its variations to help in this question.


30. Adding and Subtracting Fractions
They have the same shape - but not necessarily the same size. Their corresponding angles are equal and their corresponding sides are proportional.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Find a common denominator - then add or subtract the numerators.
-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.


31. Comparing the values of two or more Fractions
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.
Combine like terms.
Express them with a common denominator.
Use the distributive property then combine the like terms.


32. Finding the Sum of the Average of a Series of 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
Sum: Average x Number of Terms
To find the prime factorization of an integer - keep breaking it up into factors until all the factors are prime numbers.
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.


33. Difference Between a Factor and a Multiple
-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.
Rewrite the number without the negative sign as the bottom of a fraction with 1 as the top.
Plug in the given values for the unknowns and calculate according to PEMDAS.
Distance of the Number from Zero on the Number Line. AV is always positive. AV of 7: I7I


34. What are Two Special Pythagorean Triples?

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35. Finding the Surface Area of a Rectangular Solid
VofaRS=lwh
-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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Cross multiply.


36. When Given a Series of Percent Increases and Decreases - How do you Determine your ending value?
Start with 100%--> 100% + (10 percent of 100) = 110%... 110% + (20 percent of 110) = 132%.
-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.
Cross multiply.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)


37. Finding the Volume of a Cylinder
VofaC: (pie)r(2)h
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.
Probability: Number of Favorable Outcomes/Total Possible Outcomes
Check the multiples of the larger number until you find one that's also a multiple of the smaller.


38. 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
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.
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.
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.


39. Solving a Problem Involving Rates
Do whatever is necessary to both sides to isolate the variable.
-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.
SA=2lw+2wh+2lh (Length: l - Width: w - Height: h)
Use the units to keep things straight - Snowfall inches/hours


40. An Important Property of a Line Tangent to a Circle
VofaC: (pie)r(2)h
Multiply the exponents - (x^3)^4=x^3*4=x^12
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.
Put each number in the original ratio over the sum of the numbers.


41. 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.
The value that falls in the middle of the set.
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.


42. Counting Consecutive Integers
Length of an Arc: (n/360)(2pier) - n is the degree measure of the arc's central angle
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 smallest from the largest and add 1
Probability: Number of Favorable Outcomes/Total Possible Outcomes


43. What is the Triangle Inequality Theorem?
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.
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 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.
Multiply the coefficients and the variables separately. Be sure to add the exponents when multiplying like bases. 2a3a=(23)(a*a)=6a^2


44. Number of Groups - +1 Each Time
Slope=change in y/change in x
The least common multiple of 2 -3 - and 5 is 30. Therefore - the least number of students in the class is 30+1=31.
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.
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%


45. Formula to Find Average
(x1+x2)/2 -(y1+y2)/2
Average: Sum of the Terms/Number of the Terms
-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.
x(2)+x(2)=(24square root: 2)(2)=576*2 2x(2)=1 -152 - x(2)=576 - Square Root 576= 24


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

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47. Simplifying Square Roots
Switch the numerator and denominator.
Use the distributive property then combine the like terms.
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
Factor out the perfect squares under the radical - take their square roots - and put the result in front.


48. Raising a Power to a Power
Multiply 100 by .30 - then that # by .30 - then that # by .30=34.3. The answer is 34.3%
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 number associated with the word of on top and the quantity associated with the word to on the bottom and simplify.
Multiply the exponents - (x^3)^4=x^3*4=x^12


49. Definition of an Integer
Integers are whole numbers and their opposites; they include negatives of whole numbers and zero.
A(2)+b(2)=c(2)
Rectangle with four equal sides. Perimeter: 4x the length of 1 side. area of a square is equal to one side squared.
'In a group of 260 boys - half of the boys are blonds.' 1/2 of 260 boys are blondes--> 130= # of blonds


50. Multiplying Expressions with Exponents that Have a Common Base
(x1+x2)/2 -(y1+y2)/2
Since the average of the three numbers is 48 - then a+b+48=48*3. A+B=96
Average: Sum of the Terms/Number of the Terms
Add the exponents and keep the same base - x^3*x^4=x^3+4=x^7