Index: Algebra I (Offline Edition)
This index lists important terms from the Algebra I offline course.
- Each term (left side) links to the relevant location in this offline course.
- Numbers at the right refer to the corresponding page in the printed Algebra I book (or full-text PDF).
Symbols
A
- absolute value (distance from zero) $331$
- absolute value equations (solving) $336$
- absolute value expressions (determining sign of) $334$
- absolute value notation $\,|x|\,$ (definition) $332$
- absolute value (properties of) $333$
- absolute value sentences (solving, simple) -
- accuracy -
- adding and subtracting fractions with variables -
- adding a negative number $30$
- addition and subtraction (significant figures) -
- Addition Property of Equality (theorem) $277$
- Addition Property of Equality (translation) $279$
- Addition Property of Equality (use in solving equations) $281$
- ad infinitum $19$
- adding numbers with different signs $33$
- adding numbers with the same signs $32$
- Addition Property of Zero $13$
- addition (shorthand for repeated addition) $75$
- additive identity $13$
- additive inverse $21$
- algebra (uses letters to represent numbers) $71$
- and (logical connective) $250$
- assignment (use ‘let’ to give a name to an expression) $60$
- associative laws (meaning) -
- Associative Property of Addition -
- Associative Property of Multiplication -
- at least $117$
- at most $117$
- average (definition) $39$
- average (formula) $39$
- average (halfway between) $39$
- average (lies between least and greatest) $41$
- average of $\,N\,$ numbers $41$
- average of $N$ numbers (definition) $41$
- average (proof it is halfway) $40$
B
- balancing point $41$
- base (grouping) 43
- base (in the expression $\,x^n\,$) $177$
- base ten number system $48$
- base three number system $46$
- big $20$
- bigger $20$
- bigger (not the same as greater) $116$
- binomials (multiplying using FOIL) $237$
- braces $59$
- brackets $59$
C
- canceling common factors (resulting in a puncture point) -
- cat (meaning in title) cover page
- checking a solution (preferred format) $290$
- checking endpoints of a solution interval $354$
- checking solutions (using a calculator) $313$
- clearing decimals (when solving equations) $314$
- clearing fractions (when solving equations) $313$
- coefficient (numerical coefficient) $232$
- coefficient (‘hidden’ when it is $\,1\,$) $232$
- combining like terms $233$
- commas (separate members in list notation) $58$
- common denominator (definition) $105$
- common factors (definition) $263$
- Commutative Property of Addition $72$
- Commutative Property of Multiplication $12$
- commute (definition) $12$
- compound inequalities (proper conventions and pitfalls) $325$
- compound inequality $a \lt x \lt b$ (definition) $324$
- compound fractions (in rate problems) $171$
- compound sentences $244$
- concise $1$
- connectives (for sentences and expressions) $244$
- consecutive whole numbers $20$
- constant terms $232$
- conundrum: equal versus not equal -
- conventions (overriding) $82$
- conventions (practice with) $82$
- cookies, bananas and clocks -
- coordinate plane ($xy$-plane) -
- coordinates (first, second) -
- cube root: definition $196$
D
- dashed vs. solid boundary lines -
- decider digit $157$
- decimal (definition) $51$
- decimal (name versus number) -
- decimal point $51$
- decimal point (inserting, if none is shown) $55$
- decimal point (read as ‘and’) $52$
- decimals (reading aloud) $52$
- decimal to fraction $53$
- decimal to percent $55$
- defined versus not defined (sentences) $253$
- definitions (if versus if and only if) -
- denominator $53$
- density property of the real numbers $23$
- difference of squares (definition) -
- difference of squares (factoring formula) -
- difference of squares (factoring, practice) -
- direct variation -
- distance between two points -
- Distance Formula -
- distance formula (steps) -
- distance from zero (bigger and smaller) $116$
- distributive law $216$
- distributive law (area model) $216$
- distributive law (practice) -
- divide a decimal by powers of ten $54$
- dividing a polynomial by a monomial -
- divisibility equivalences $110$
- divisibility test $13$
- divisible (by $\,1\,$ and itself) -
- divisible by $2$ $13$
- divisibility by $2$ (test) $13$
- divisibility by $3$ (test) $14$
- divisibility by $5$ (test) $14$
- divisibility by $10$ (test) $16$
- divisible by $n$ (meaning) $13$
- division (as multiplication by reciprocal) $98$
- division by zero $93$
- division (ways to denote) $54$
- domain convention -
- domain of a function (definition) -
- downhill lines have negative slope -
- dummy variable -
E
- elements (of a set) $58$
- ellipsis (three lower dots) $19$
- empty parentheses method (for function evaluation) -
- empty set (definition, notation) $62$
- equal $23$
- equal or opposites $228$
- equal versus approximately equal $147$
- equal versus equivalent (distinction) $242$
- equation (definition) -
- equation in two variables -
- equation with an ‘invisible’ variable -
- equivalence of sentences $241$
- equivalence (truth table definition) $246$
- estimating radicals (between consecutive integers) $198$
- estimating square roots (to a decimal place) -
- evaluate (an expression) -
- even numbers $13$
- even roots: definition $202$
- even roots: issues $201$
- exact numbers -
- exact versus approximate $147$
- expanded form (base ten number system) $46$
- exponent (or power) $177$
- exponent law: $\,x^mx^n = x^{m+n}$ $186$
- exponent law: $\displaystyle\frac{x^m}{x^n} = x^{m-n}$ $187$
- exponent law: $\,(x^m)^n = x^{mn}$ $188$
- exponent law: $\displaystyle x^{-p} = \frac{1}{x^p}$ $190$
- exponent law practice: one-step $186$
- exponent law practice: multi-step $186$
- exponents as repeated multiplication -
- expression (definition) $1$
- expression to sequence of operations $76$
- expression (common types) $0$
- extraneous solutions (from multiplying by zero) $296$
F
- factor an expression (definition) $262$
- Factor by Grouping method -
- Factor by Grouping (theorem and proof) -
- factoring a difference of squares -
- factoring a quadratic (application of averaging concepts) -
- factoring out the greatest common factor $271$
- factoring over the integers -
- factoring trinomials ($\,x^2 + bx + c\,,$ $\,c \gt 0\,$) -
- factoring trinomials ($\,x^2 + bx + c\,,$ $\,c \lt 0\,$) -
- factoring trinomials (basic concepts) -
- factoring trinomials (key tool) -
- factoring trinomials (mixed, practice) -
- factoring trinomials of the form $\,ax^2 + bx + c$ -
- factoring (using the distributive law backwards) $262$
- factors $53$
- factors (every number has a factor of $1$) $108$
- factors (in a product) $261$
- factors (listing all factors of a whole number) $268$
- factors (numbers that go in evenly) $107$
- factors (occur in pairs) $107$
- factors of $\,N\,$ (pairs: $\,\lt \sqrt N\,,$ $\,\gt \sqrt N\,$) -
- family of equations -
- filled-in dot $19$
- finger trick (multiply by $9$) $15$
- finite decimal $151$
- finite or infinite repeating decimals $151$
- finite set (definition) $58$
- five-step process (adding signed numbers) $33$
- flip (reciprocal) $183$
- FOIL (First, Outer, Inner, Last) method $236$
- FOIL (practice) -
- ‘for all’ sentences (generalizations) $278$
- forward slash (division symbol) -
- fraction equal to $\,1\,$ $159$
- fractions (adding and subtracting) $105$
- fractions (adding with a common denominator) $105$
- fractions (dividing) $98$
- fractions (locating between two integers) $91$
- fractions (involving zero) $93$
- fractions (multiplying) $96$
- fractions (renaming by multiplying by $1$) $107$
- fractions (renaming with a specified denominator) $107$
- fractions (rewriting as whole number + fraction) $91$
- fraction (with denominator of $\,2\,$) to decimal $40$
- fractions (with zero in denominator) $93$
- fractions (with zero in numerator) $93$
- function as a box -
- function (definition) -
- function name versus function output -
- function notation (definition) -
- function notation (higher-level practice) -
- Fundamental Theorem of Arithmetic -
- $f$ versus $f(x)$ -
- $f(x)$ (reading aloud) -
G
- gcd (greatest common divisor) -
- gcf (greatest common factor) $267$
- graphing a line (intercept method) -
- graphing linear inequalities using the test point method -
- graph of a sentence in two variables -
- greater than $20$
- greatest common divisor (greatest common factor) -
- greatest common factor (definition) $267$
- greatest common factor (efficient algorithm) -
- greatest common factor (practice with variable expressions) $271$
- greatest common factor (using prime factorization) $269$
- Guess-and-Check method (factoring trinomials) -
H
- half-plane -
- hollow dot $19$
- horizontal lines -
- horizontal lines have zero slope -
- hundredths place $51$
- hypotenuse -
I
- identifying common factors (method) $263$
- if and only if (iff) $248$
- Individual Rates Assumption -
- inequalities (multiplying/dividing by negative number, change direction) $320$
- inequalities with variables -
- inequality (definition) -
- inequality symbols -
- infinite repeating decimal $151$
- infinity (symbol $\infty$) $62$
- in (membership symbol $\in$) $59$
- infinite set (definition) $58$
- integers $22$
- INtegers (memory device) $82$
- interval notation (for sets) $62$
- inverse variation -
- irrational numbers $150$
- isolating the absolute value (inequalities) $354$
J
- JSXGraph: adding signed numbers -
- JSXGraph: precision vs accuracy -
- juxtaposition $214$
- juxtaposition (general discussion) $75$
K
L
- large $20$
- Laurel and Yanny -
- lcm (least common multiple) $106$
- leading zero (decimal) $51$
- least common multiple $106$
- least common multiple (finding) $106$
- least common multiple (prime factorization method) $109$
- left/right positioning (greater and lesser) $116$
- legs (of a right triangle) -
- less than $20$
- let (assigning a name to a set) $60$
- Let it be! (memory device) -
- like terms $233$
- linear equation in one variable (definition) $311$
- linear equations in one variable (exactly one solution) $312$
- linear equation in two variables (definition) -
- linear equations (solving, all mixed types, practice) -
- linear equations (solving, basic procedure) $312$
- linear equations (solving, simple practice) -
- linear equations (solving, more complicated practice) -
- linear equations (solving, with fractions) $313$
- linear inequalities in two variables -
- linear inequality in one variable (definition) $318$
- linear inequality in two variables (definition) -
- linear inequalities (tools for solving; theorem) $318$
- line (equivalent forms) -
- line (standard/general form) -
- lines (practice graphing) -
- list notation (sets) $58$
- lives-in -
M
- March of the Multiples (finding the lcm) $106$
- members (of a set) $58$
- membership in a set $59$
- memory device for horizontal lines -
- memory device for vertical lines -
- memory devices (greater versus lesser) $115$
- mental math (addition) -
- Midpoint Formula -
- midpoint of a line segment -
- minus (reading subtraction sign) $36$
- minus (versus negative) $36$
- mixed addition/subtraction of signed numbers -
- mixed arithmetic -
- moncur (imaginary unit of money) -
- movement (interpretation of a number) $30$
- movement in the coordinate plane -
- multiplication and division (significant figures) -
- multiplication as repeated addition -
- multiplication (centered dot notation) $12$
- multiplication (centered dot versus times symbol) -
- Multiplication Property of Equality (theorem) $293$
- Multiplication Property of Equality (translation) $294$
- Multiplication Property of Equality (use in solving equations) $296$
- Multiplication Property of One $12$
- Multiplication Property of Zero $12$
- Multiplication Property of Zero $12$
- multiplication (repeated addition) $12$
- multiplication (ways to denote) $5$
- multiplicative identity $12$
- multiplicative inverse -
- multiply a decimal by powers of ten $53$
- multiply by powers of ten $48$
- multiplying across $96$
- multiplying and dividing fractions with variables -
- multiplying by $\,1\,$ (in an appropriate form) $163$
- multiplying by zero (effect on truth of an equation) $295$
- multiplying trinomial and binomial $238$
N
- names for the number one -
- naming conventions (for variables) $81$
- negative (reading a number) $36$
- negative (versus minus) $22$
- negative real numbers $18$
- neutral status of zero $18$
- no-bias rounding convention -
- nonnegative real numbers $19$
- nonzero real number $19$
- not defined (division by zero) $93$
- not in (symbol $\notin$) $61$
- numbers (different names) $17$
- number (means real number) $24$
- number (name doesn’t affect position on number line) $19$
- numbers (represented by lowercase letters) $81$
- numerator $53$
O
- odd numbers -
- odd roots: definition $199$
- one-step conversion (definition) $161$
- opposite of $x$ (meaning of $-x$) $213$
- opposite reciprocals -
- opposites (a number added to its opposite is zero) $21$
- opposites $21$
- ordered pairs (convention for $x$ and $y$) -
- ordered pair (definition) -
- ordered pairs (equality) -
- order (numbers) $20$
- order of operations $180$
- origin (definition) -
- or (logical connective) $250$
- overlapping -
P
- pairing (of real numbers, points on the number line) $18$
- PANS memory device -
- parallel lines -
- parameters versus variables -
- parentheses (plural form of ‘parenthesis’) $59$
- parenthesis (singular form of ‘parentheses’) $59$
- PEMDAS (common mistake) -
- PEMDAS (Please Excuse My Dear Aunt Sally) $182$
- percent decrease (formula) -
- percent decrease (visualizing, JSXGraph exploration) -
- percent (equals $\frac{1}{100}$) $54$
- percent increase/decrease (find resulting percent change) -
- percent increase/decrease (mixed practice) -
- percent increase/decrease (practice writing expressions) -
- percent increase/decrease (units cancel) -
- percent increase (formula) -
- percent increase (visualizing, JSXGraph exploration) -
- percent (means per one hundred) $54$
- percents (renamed as decimals for computation) $54$
- percent symbol $54$
- percent to decimal $55$
- perfect squares -
- perfect squares (identifying, practice) -
- perfect squares (simplifying $\,(a+b)^2\,$ and $\,(a-b)^2\,$) -
- perpendicular lines -
- place value names (base ten) $46$
- plotting points -
- ‘plus or minus’ notation, $\,\pm$ $335$
- point (reading decimals digit by digit) $53$
- point-slope form (of a line) -
- points (practice with) -
- position (interpretation of a number) $30$
- positive real numbers $18$
- powerful $1$
- power (or exponent) $177$
- powers of one -
- powers of ten ($\,10^n\,$ is $\,1\,$ followed by $\,n\,$ zeroes) $48$
- powers of zero -
- practice with the form $a\cdot\frac bc$ $102$
- precise $1$
- precision -
- prime factorization (conventional form) -
- Prime Factorization Theorem (section) -
- Prime Factorization Theorem (theorem) -
- prime numbers -
- prime numbers ($\,1\,$ is not prime) -
- prime numbers (checking up to square root) -
- prime numbers (definition) -
- prime numbers (efficient method to see if # is prime) -
- prime numbers (ending digits) -
- prime numbers (pile interpretation) -
- prime numbers (why $\,1\,$ is not prime) -
- product (last operation is multiplication) $260$
- products involving signed variables $214$
- PuDdLe DiPpeR (memory device) $55$
- puncture points -
- Pythagorean Theorem -
Q
- quadrants (definition) -
- quadrants (I, II, III, IV) -
- quadratic equation (definition) -
- quadratic equations (identifying, practice) -
- quadratic equations (solving, by factoring) -
- quadratic equations (solving more complicated, by factoring) -
- quadratic equations (writing in standard form) -
R
- radicals: definition $204$
- radicals to rational exponents $207$
- raising opposites to even powers $222$
- raising opposites to odd powers $226$
- range (difference between greatest and least values) -
- range of a function (definition) -
- rate (definition) $170$
- rate problems (solving) $172$
- rates (different names) $171$
- rates (individual versus combined) -
- rates in work problems -
- rates (renaming) $171$
- rates versus times in work problems -
- rational exponents, simplifying (practice) $209$
- rational exponents to radicals $209$
- rational numbers $150$
- reading ‘$\,x\in\mathbb{R}\,$’ $74$
- real number line $17$
- real numbers $18$
- real numbers (two interpretations) $30$
- reciprocal (of $\,\frac ab\,$ is $\,\frac ba\,$) $97$
- reciprocal (of $\,x\,$ is $\,\frac 1x\,$) $97$
- reciprocal (product of # and its reciprocal is $\,1\,$) $97$
- reciprocal ($x^{-1}$) $177$
- recognizing patterns $\,x^n\,$ and $(-x)^n$ $223$
- reflecting about a horizontal line -
- reflecting about a vertical line -
- reflecting about the $x$-axis -
- reflecting about the $y$-axis -
- reflecting a point about a line -
- relatively prime (definition) -
- reliability -
- renaming as $\,kx\,$: sign first, size second $102$
- repeated addition versus repeated multiplication -
- right angle -
- right triangle -
- right triangle ($3{-}4{-}5$) -
- right triangle collage (JSXGraph exploration) -
- rise (definition, in slope of line) -
- roots undo powers $196$
- rounding decimals to a specified number of places $155$
- rounding digit $156$
- rounding digit is $\,9\,$, rounding up $157$
- rounding down $156$
- rounding (significant figures) -
- rounding up $155$
- run (definition, in slope of line) -
S
- (to) satisfy a sentence -
- scientific notation -
- scientific notation (definition) -
- scientific notation (exception for × symbol) -
- scientific notation to standard notation -
- scientific notation (two parts) -
- sentence (definition) $8$
- sentence (truth of) $6$
- sequence of operations to expression $76$
- set (definition) $57$
- set (is a mathematical expression) $58$
- set (must be well-defined; not vague) $57$
- sets can have different names $58$
- sets (represented by uppercase letters) $81$
- significant figures/digits -
- significant figures (rules for determining) -
- sign (of a number) $31$
- signed numbers $30$
- signs (plus or minus) of products $101$
- simplest form of a fraction $148$
- size (of a number, definition) $30$
- size (of a number, bigger/smaller) $20$
- size versus sign $31$
- slope formula -
- slope formula (order is important) -
- slope (gives information about slant) -
- slope-intercept form of a line ($\,y = mx + b\,$) -
- slope of a line (introduction) -
- smaller $20$
- smaller (not the same as lesser) $116$
- solution of a sentence in two variables -
- solution set of an inequality vs equation $322$
- solutions of equations/inequalities in two variables (equivalent statements) -
- solving absolute value equations $341$
- solving absolute value inequalities involving ‘greater than’ $360$
- solving absolute value inequalities involving ‘less than’ $349$
- solving absolute value sentences (mixed, practice) -
- solving a sentence $80$
- solving a sentence (preferred formats) $283$
- solving equations involving perfect squares (more complicated) -
- solving equations involving perfect squares (simple) -
- solving equations involving perfect squares (theorem) -
- solving equations of the form $\,xy = 0$ $121$
- solving linear equations (all mixed types) -
- solving linear inequalities (involving fractions) $323$
- solving linear inequalities (integer coefficients) $322$
- solving linear inequalities (mixed practice) -
- solving for a particular variable -
- solving sentences by inspection -
- solving word problems (two equations, step-by-step method)
- sparse (whole numbers in real numbers) $20$
- speed-it-up trick (divisibility by $3$) -
- square root: definition $202$
- square root (get rid of perfect square factor) -
- square root (naming convention) -
- square root (renaming the square root of a product) -
- square root (simplifying) -
- square roots undo squares (for nonnegative numbers) -
- square root (writing in simplest form) -
- standard notation to scientific notation -
- story problems (practice) -
- strangers -
- subcollections of real numbers $19$
- subscript (definition) $41$
- subscript notation $41$
- subset (definition) $64$
- substitute (numbers for letters) -
- substitution method (informal introduction) -
- subtraction (addition in disguise) $36$
- subtract (add the opposite) $36$
- subtraction (more than two numbers) $37$
- subtraction (reading problems aloud) $36$
- subtraction (three steps in) $37$
- sum (last operation is addition) $261$
- suspect (measurements in science) -
- system of equations (definition) -
T
- tenths place $51$
- term (coefficient and variable part) $232$
- term includes its sign $262$
- terms (conventional way to write) $232$
- terms (in a sum) $261$
- three dots (indicate a pattern is to be repeated) -
- test point method (for graphing linear inequalities in two variables) -
- translating mathematical phrases -
- translating words into equations -
- Trial-and-Error method (factoring trinomials) -
- triangle angle sum -
- triangles (longest side opposite largest angle) -
- truth tables $245$
U
- undoing a sequence of operations -
- undoing a square with a square root (theorem) -
- union symbol ($\,\cup\,$) -
- uniqueness (prime factorization) -
- unit conversion (definition) $163$
- unit conversion information $163$
- unit conversions, one-step $159$
- unit conversions (multi-step) $168$
- units cancel (like numbers) $160$
- units (consistency in equations) -
- universal set (of a variable) $71$
- unlike terms $233$
- uphill lines have positive slope -
- upward bias -
V
- variable (definition) $71$
- variable names (integers) $82$
- variable names (real numbers) $81$
- variables (hand-writing) $83$
- variables (italic style) $83$
- variables versus parameters -
- variable (to represent a sequence of operations) $75$
- variable (to represent an unknown) $77$
- variable (to state a general principle) $72$
- variables follow each other in size -
- variables go in different directions -
- varies directly as -
- varies inversely as -
- verb $1$
- vertical lines -
- vertical lines have no slope -
W
- whole numbers $19$
- word problems (involving perfect squares) -
- word problems (resulting in linear equations) -
- work problems (basic concepts) -
- work problems (guided practice) -
- work problems (quick-and-easy estimates) -
- writing expressions in the form $A^2$ -