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What is the difference between a unive…

What is the difference between a unive…

What is the difference between an exis…

What is a set?

A universal statement is like all apples are fruits. A condit…

A universal conditional statement is a statement both univers…

An existential universal statement is a statement that is exi…

A set is like this {1,2,3...}. It was introduced by Geog Cant…

What is the difference between a unive…

A universal statement is like all apples are fruits. A condit…

What is the difference between a unive…

A universal conditional statement is a statement both univers…

Expression

Multiple

Place Value

Rectangular Array

A combination of individual terms separated by plus or minus…

The product of a whole number and any other nonzero whole num…

The number assigned to each place that a digit occupies.

An arrangement that can represent a whole number in rows and…

Expression

A combination of individual terms separated by plus or minus…

Multiple

The product of a whole number and any other nonzero whole num…

preference ballot

linear ballot

preference schedule

transitive

a ballot in which the voters are asked to rank the candidates…

a ballot in which ties are not allowed

neatly organized groups of preference ballots of similar rank…

a voter who prefers candidate A over B and prefers candidate…

preference ballot

a ballot in which the voters are asked to rank the candidates…

linear ballot

a ballot in which ties are not allowed

proposition

Conjunction

Disjunction

Exclusive or

A proposition is a declarative sentencethat is either true or…

p∧q= "p and q" = proposition that is true when ... both p and q…

p∨q= "p or q" = proposition that is false when both ... p and q…

p ⊕q = "only p or only q" = proposition that is true ... when ex…

proposition

A proposition is a declarative sentencethat is either true or…

Conjunction

p∧q= "p and q" = proposition that is true when ... both p and q…

The Most Common Mistakes

Strategies for the Mathematics Section

Go Back to the Basics

Don't Rely on Mental Math

People make mistakes all the time -- but during a test, those…

1. Go Back to the Basics... 2. Don't Rely on Mental Math... 3. The…

First and foremost, practice your basic skills: sign changes,…

Using mental math is great for eliminating answer choices, bu…

The Most Common Mistakes

People make mistakes all the time -- but during a test, those…

Strategies for the Mathematics Section

1. Go Back to the Basics... 2. Don't Rely on Mental Math... 3. The…

Natural Number

Integer

Prime Number

Symbol

A whole number from 1 to infinity, sometimes called "counting…

Any of the negative and positive whole numbers including 0.

A whole number greater than 1 which has only two factors: the…

A short way of writing mathematical information, such as "="…

Natural Number

A whole number from 1 to infinity, sometimes called "counting…

Integer

Any of the negative and positive whole numbers including 0.

Effective Annual Rate of Interest earn…

Equivalent Rates

'a(t)'

Accumulation Factor

Two Rates of Interest which result in the same accumulated va…

...is the accumulated value at time 't' of an investment of '…

'a(t)' is the _____ from time '0' to time 't'.

Effective Annual Rate of Interest earn…

Equivalent Rates

Two Rates of Interest which result in the same accumulated va…

Constant

Coefficient

Variable

Equation

Is a number whos value never changes. Example 3, 4, 5

Is a number that is being multiplied by a variable example 4XY

Is a letter that represents a number example m,n

Two mathematical equations that are set equal to each other e…

Constant

Is a number whos value never changes. Example 3, 4, 5

Coefficient

Is a number that is being multiplied by a variable example 4XY

absolute value

constant

equation

inequality

the distance from zero on a number line; shown by // ... (pg. 19)

a value that does not change ... (pg. 6)

a mathematical sentence that shows that two expressions are e…

a mathematical sentence that shows the relationship between q…

absolute value

the distance from zero on a number line; shown by // ... (pg. 19)

constant

a value that does not change ... (pg. 6)

Chinese Postman Problem

Circut

Connected Graph

Digraph

The problem of finding a circuit on a graph that covers every…

A path that starts and ends at the same vertex.

A graph is connected if it is possible to reach any vertex fr…

A graph in which each edge has an arrow indicating the direct…

Chinese Postman Problem

The problem of finding a circuit on a graph that covers every…

Circut

A path that starts and ends at the same vertex.

Plurality method

Pros to plurality

Cons to plurality

Insincere voting

Most common; All that matters is the number of 1st place votes

Simplest method, works perfectly with 2 canidates

If there are more than 2 conidates, the winner may not have t…

When voters don't vote according to their true preferences fo…

Plurality method

Most common; All that matters is the number of 1st place votes

Pros to plurality

Simplest method, works perfectly with 2 canidates

proposition

Propositional variables (or statement…

The truth value of a true proposition,…

The negation of p,

A proposition is a declarative sentencethat is either true or…

Variables that represent propositions, just as letters are us…

denoted by T, if it is a true proposition, and if false, deno…

Denoted by¬p (also denoted by a dash(-) over p), is the state…

proposition

A proposition is a declarative sentencethat is either true or…

Propositional variables (or statement…

Variables that represent propositions, just as letters are us…

Propositions

propositional variables

D1: Negation

Find the negation of the proposition "…

A proposition is a declarative sentence (that is, a sentence…

variables that represent propositions, just as letters are us…

Let p be a proposition. The negation of p, denoted by ¬p (als…

"It is not the case that Michael's PC runs Linux."

Propositions

A proposition is a declarative sentence (that is, a sentence…

propositional variables

variables that represent propositions, just as letters are us…

Describe the result of adding a large…

How do you convert a fraction into a d…

What is the key step that must be perf…

How do you divide one fraction by anot…

The result is a smaller positive number, and is the same as i…

Divide the top number (numerator) by the bottom number (denom…

You must find the lowest (least) common denominator.

You invert the divisor and multiply the numerators together a…

Describe the result of adding a large…

The result is a smaller positive number, and is the same as i…

How do you convert a fraction into a d…

Divide the top number (numerator) by the bottom number (denom…

Squares and Cubes

Lowest Common Denominator

Highest Common Factor

Prime Numbers

axa or axaxa

of two numbers is the smallest multiple shared by both numbers

of two numbers is the largest factor shared by both numbers

Only have two factors; 1 and itself. 1 isn't a prime number

Squares and Cubes

axa or axaxa

Lowest Common Denominator

of two numbers is the smallest multiple shared by both numbers

factor

least common multiple

fraction

quantity

two or more numbers multiplied together to get another number

a number that is a multiple of two or more numbers. Its abbre…

a part of a group or region

anything that can be measured or counted

factor

two or more numbers multiplied together to get another number

least common multiple

a number that is a multiple of two or more numbers. Its abbre…

Variable

Universal Statement

Existential Statement

Conditional Statement

Place holder for a value

A statement which is true for all elements in a set

A statement which asserts that there exists an element in a s…

If one thing is true, than the other thing is true.

Variable

Place holder for a value

Universal Statement

A statement which is true for all elements in a set

Proposition

Propositions

No

propositional variables

A declarative sentence that is either true or false, but not…

Toronto is the capital of Canada... 1 + 1 = 2... 2 + 2 = 3

Is x + 1 = 2 a proposition?

variables used to represent propositions, conventional letter…

Proposition

A declarative sentence that is either true or false, but not…

Propositions

Toronto is the capital of Canada... 1 + 1 = 2... 2 + 2 = 3

Natural numbers

Whole Numbers

Integers

reciprocal / multiplicative inverse of…

N = {1, 2, 3, 4, 5, 6, . . . }

N + 0 or W = {0, 1, 2, 3, 4, 5, 6, . . . }

whole numbers and their opposites; ... Z = {. . ., -3, -2, -1, 0…

- 1/2 is the reciprocal of 2 ... - 1 and -1 are the only integer…

Natural numbers

N = {1, 2, 3, 4, 5, 6, . . . }

Whole Numbers

N + 0 or W = {0, 1, 2, 3, 4, 5, 6, . . . }

Variable

Universal Statement

Existential Statement

Conditional Statement

Place holder for a value

A statement which is true for all elements in a set

A statement which asserts that there exists an element in a s…

If one thing is true, than the other thing is true.

Variable

Place holder for a value

Universal Statement

A statement which is true for all elements in a set

APPROXIMATE

CHART

DIGIT

NUMBER LINE

Not exact, but close enough to be reasonably correct

An arrangement of numbers

The ten number symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9,

A list of numbers arranged in order from left to right on a l…

APPROXIMATE

Not exact, but close enough to be reasonably correct

CHART

An arrangement of numbers

Math Skills Scientists use to collect…

Estimate

Accuracy

Precision

estimation, accuracy and precision, and significant figures.

An approximation of a number based on reasonable assumptions

A measure of how close a measurement comes to the actual or t…

How close a group of measurements are to each other

Math Skills Scientists use to collect…

estimation, accuracy and precision, and significant figures.

Estimate

An approximation of a number based on reasonable assumptions

Describe the result of adding a large…

How do you convert a fraction into a d…

What is the key step in order to add o…

How do you divide one fraction by anot…

The result is smaller positive number.

Divide the top number by bottom number

Finding the lowest common denominator

Invert divisor and multiply both numerators and denominators…

Describe the result of adding a large…

The result is smaller positive number.

How do you convert a fraction into a d…

Divide the top number by bottom number

associative properties

commutative properties

compatible numbers

expanded form

changing the grouping does not change the answer

changing the order of the numbers does not change the answer…

numbers that are easy to compute mentally, especially with pr…

is a sum that shows the place and value of each digit

associative properties

changing the grouping does not change the answer

commutative properties

changing the order of the numbers does not change the answer…

Estimate

Accuracy

Precision

Significant figures

An approximation of a number based on reasonable assumptions

A measure of how close a measurement comes to the actual or t…

How close a group of measurements are to each other

All the digits that are known in a measurement, plus the last…

Estimate

An approximation of a number based on reasonable assumptions

Accuracy

A measure of how close a measurement comes to the actual or t…

Estimate

Compatible Number

Underestimate

Overestimate

Close to the exact answer but are usually easier and faster t…

Close to the numbers in the problem, and they can help you do…

An estimate that is less than the exact answer.

An estimate that is greater than the exact answer.

Estimate

Close to the exact answer but are usually easier and faster t…

Compatible Number

Close to the numbers in the problem, and they can help you do…

Describe the result of adding a large…

How do you convert a fraction into a d…

What is the key step in order to add o…

How do you divide one fraction by anot…

The result is smaller positive number.

Divide the numerator by the denominator.

Finding the lowest common denominator

Invert the denominator of the second fraction and multiply.

Describe the result of adding a large…

The result is smaller positive number.

How do you convert a fraction into a d…

Divide the numerator by the denominator.

Describe the result of adding a large…

How do you convert a fraction into a d…

What is the key step in order to add o…

How do you divide one fraction by anot…

The result is smaller positive number.

Divide the numerator by denominator

Finding the lowest common denominator

Invert the second fraction and multiply both numerators and d…

Describe the result of adding a large…

The result is smaller positive number.

How do you convert a fraction into a d…

Divide the numerator by denominator

Natural numbers

whole numbers

integers

reciprocal

numbers used to count. ex: 1,2,3

natural numbers and 0; 0,1,2,3

whole numbers and their opposites. ex: (-2,-1,0,1,2)

1/number. ex: reciprocal of 8 = 1/8

Natural numbers

numbers used to count. ex: 1,2,3

whole numbers

natural numbers and 0; 0,1,2,3

Significant Figures

Significant Figures in Measurement

Significant Figures in Addition and Su…

Significant Figures in Multiplication…

Include all nonzero digits and any trailing zeros in a number…

Last digit provided is not significant.

Reduce answer to have the same number of decimal places as th…

Reduce the answer to have the same number of significant digi…

Significant Figures

Include all nonzero digits and any trailing zeros in a number…

Significant Figures in Measurement

Last digit provided is not significant.

Period

Base

Distributive property

Exponent

In a large number, periods are groups of 3 digits separated b…

is the number used as the repeated factor.

When one of the factors of a product is a sum, multiplying ea…

The number that tells the number of times the base is multipl…

Period

In a large number, periods are groups of 3 digits separated b…

Base

is the number used as the repeated factor.

Sole Proprietorship

Personally Liable

Shareholders

Trades

A business that is owned by one person.

A business owner who is personally responsible for the debts…

People who own shares of stock in a corporation.

Transactions on the stock market.

Sole Proprietorship

A business that is owned by one person.

Personally Liable

A business owner who is personally responsible for the debts…

Relation: A set of ordered pairs (x,y)

Domain: X values

Range: Y values

Function: special relationship where e…

The relation explained the rate of speed of the car versus ti…

The domain of (2,1) is 2

The range of (2,1) is 1

The function of these ordered pairs is f(x) = x^2

Relation: A set of ordered pairs (x,y)

The relation explained the rate of speed of the car versus ti…

Domain: X values

The domain of (2,1) is 2

absolute value

algebraic expression

coulomb per kilogram

direct variation

the meaning of a number equal to the distance of that number…

a mathematical sentence or term consisting of letters and/or…

an SI unit known as the Roentgen, C/kg... occupational dose.

one quantity is a multiple of a second quantity

absolute value

the meaning of a number equal to the distance of that number…

algebraic expression

a mathematical sentence or term consisting of letters and/or…

Natural numbers

Integers

Rational numbers

rational qualifications

(N) 0, 1, 2, 3, 4, 5)

-4, -3, -2, -1, 0, 1, 2, 3, 4

(p/q where p and q are integers and q equals 0)

-it can be written as a quotient of two integers... -its decimal…

Natural numbers

(N) 0, 1, 2, 3, 4, 5)

Integers

-4, -3, -2, -1, 0, 1, 2, 3, 4

Algorithm

Flow chart

Trace table

Bubble sort

A set of instructions for solving a problem

A way of visually representing an algorithm

A table used to keep track of an algorithm

An algorithm that sorts a list into order by systematically s…

Algorithm

A set of instructions for solving a problem

Flow chart

A way of visually representing an algorithm

3,415,105

3,000; thousand

1, 3, 7,21

1,2,3,4,6,8,12,24

what is the standard form of three million, four hundred and…

what is the value and place value of the digit 3 in 993,891?

write all the factors of 21

write all the factors of 24

3,415,105

what is the standard form of three million, four hundred and…

3,000; thousand

what is the value and place value of the digit 3 in 993,891?

Absolute value

Algebraic expression

Coulomb per kilogram

Direct variation

...... The distance a number is from zero on a number line. ALWA…

...... A mathematical phrase involving at least one variable and…

...... Formerly the Roentgen (R)

one quantity is a multiple of a second quantity

Absolute value

...... The distance a number is from zero on a number line. ALWA…

Algebraic expression

...... A mathematical phrase involving at least one variable and…

Describe the result of adding a large…

How do you convert a fraction into a d…

What is the key step in order to add o…

How do you divide one fraction by anot…

The result is smaller positive number.

Divide the top number by bottom number

Finding the lowest common denominator

Invert divisor and multiply both numerators and denominators…

Describe the result of adding a large…

The result is smaller positive number.

How do you convert a fraction into a d…

Divide the top number by bottom number

single-choice ballot

preference ballot

truncated preference ballot

ranking (full ranking)

a ballot in which a voter only has to choose one candidate

a ballot in which the voter has to rank all candidates in ord…

a ballot in which a voter only has to rank the top k choices…

in an election, an outcome that lists ALL the candidates in o…

single-choice ballot

a ballot in which a voter only has to choose one candidate

preference ballot

a ballot in which the voter has to rank all candidates in ord…

abductive reasoning

AND

axioms

case proof

Usually starts with an incomplete set of observations and adv…

Conjunction.

Self-evident beginnings.

Shows a statement is true by showing all the cases are true.

abductive reasoning

Usually starts with an incomplete set of observations and adv…

AND

Conjunction.

Estimate

Accuracy

Precision

Significant figures

An approximation of a number based on reasonable assumptions

Refers to how close a measurement is to the true or accepted…

Refers to how close a group of measurements are to each other.

Communicate how precise measurements are; ... All the digits tha…

Estimate

An approximation of a number based on reasonable assumptions

Accuracy

Refers to how close a measurement is to the true or accepted…

Scientific notation

Significant figures and what are the r…

Exponents

Logarithms

-A method of writing numbers in a way that improves the ease…

-Include all nonzero digits and any trailing zeroes in a numb…

-A notion for repeated multiplication... -They may be manipulate…

-Inverse of exponents... -Are subject to similar mathematical ma…

Scientific notation

-A method of writing numbers in a way that improves the ease…

Significant figures and what are the r…

-Include all nonzero digits and any trailing zeroes in a numb…

absolute value

additive inverses

Associative Property of Addition

Associative Property of Multiplication

a number's distance from zero on a number line

two numbers whose sum is zero

changing the grouping of the addends does not change the sum

changing the grouping of the factors does not change the prod…

absolute value

a number's distance from zero on a number line

additive inverses

two numbers whose sum is zero