 Pre-Kindergarten [5]
Operations with numbers [5]
Addition [4]
Subtraction [3]
Number sense [15]
What numbers mean
Counting [13]
One-to-one [2]
Equivalence
Parts of a whole [4]
Patterns and sequences [10]
Sort and classify [8]
Algebra
Geometry in the plane [9]
Shapes [3]
Geometry in space [3]
Spatial relations
Measurement [7]
Data analysis [2]
Collect data [1]
Organize data
Probability [4]
Kindergarten [15]
Operations with numbers [5]
Addition [8]
Subtraction [5]
Whole numbers [1]
Rounding
Estimation [2]
Number sense [14]
Counting [15]
Patterns [3]
One-to-one [1]
Equivalence (equal shares)
Ordering numbers
Writing numbers [2]
Place value [4]
Ordinal numbers [2]
Fractions [19]
Patterns and sequences [16]
Sort and classify [8]
Algebra
Geometry in the plane [22]
Classify geometric objects [5]
Symmetry [20]
Geometry in space [3]
Recognize shapes in 3-D
Measurement [4]
Time [10]
Calendar
Length/height [8]
Weight/mass [1]
Capacity/volume [2]
Money/coins [3]
Temperature
Metric
Non-standard units
Data analysis [1]
Collect data [2]
Record data [1]
Organize data [1]
Pictographs
Graph real objects
Tally charts
Bar graphs [2]
Probability [3]
Math 1 [24]
Operations with numbers [10]
Addition [23]
Subtraction [12]
Whole numbers [2]
Mental math [9]
Rounding
Estimation [4]
Number sense [19]
Counting [13]
Patterns [5]
Ordering numbers [5]
Writing numbers [1]
Place value [10]
Ordinal numbers [2]
Fractions [26]
Patterns and sequences [17]
Sort and classify [10]
Algebra
Number sentences [3]
Geometry in the plane [25]
Classify geometric objects [5]
Symmetry [22]
Geometry in space [6]
Recognize shapes in 3-D [1]
Measurement [4]
Time [11]
Calendar
Length/height [7]
Weight/mass [1]
Capacity/volume [2]
Money/coins [8]
Temperature [1]
Metric
Non-standard units
Data analysis [2]
Collect data [1]
Record data
Organize data
Pictographs
Tally charts
Bar graphs [2]
Probability [4]
Certain, likely, impossible
Math 2 [25]
Operations with numbers [13]
Addition [29]
Subtraction [18]
Multiplication [14]
Division [8]
Whole numbers [3]
Mental math [13]
Rounding [1]
Estimation [4]
Number sense [17]
Counting [17]
Patterns [12]
Ordering numbers [11]
Writing numbers [2]
Place value [17]
Ordinal numbers [2]
Roman numerals
Fractions [31]
Patterns and sequences [18]
Sort and classify [9]
Algebra [1]
Number sentences [3]
Geometry in the plane [25]
Classify geometric objects [3]
Symmetry [22]
Geometry in space [7]
Recognize shapes in 3-D [1]
Measurement [4]
Time [13]
Calendar
Length/height [7]
Weight/mass [1]
Capacity/volume [2]
Money/coins [9]
Temperature [1]
Standard units [1]
Metric [2]
Non-standard units
Perimeter [1]
Area [1]
Data analysis [2]
Collect data [1]
Record data
Organize data
Pictographs
Tally charts
Bar graphs [1]
Line graphs
Probability [5]
Certain, likely, impossible
Math 3 [34]
Operations with numbers [50]
Addition [35]
Subtraction [22]
Multiplication [19]
Division [13]
Whole numbers [2]
Mental math [19]
Rounding [2]
Estimation [20]
Truncating
Front-end
Number sense [27]
Place value [17]
Roman numerals
Number theory [9]
Prime [2]
Composite [2]
Factor [11]
Prime factorization [1]
Divisibility tests
Greatest common factor [1]
Multiple [6]
Least common multiple [1]
Fractions [18]
Writing fractions [17]
Equivalent fractions [21]
Comparing & ordering [17]
Simplifying fractions [7]
Writing decimals [3]
Comparing & ordering [1]
Rounding decimals [1]
Adding decimals [5]
Subtracting decimals [5]
Percentages [5]
Writing percentages [2]
Algebra [6]
Patterns and sequences [14]
Number sentences [4]
Geometry in the plane [22]
Classify geometric objects [10]
Symmetry [12]
Tessellations [9]
Fractals [1]
Geometry in space [8]
Recognize shapes in 3-D [7]
Measurement [2]
Time [11]
Calendar [5]
Length/height [4]
Weight/mass [9]
Capacity/volume [1]
Money/coins [15]
Temperature [2]
Standard units [1]
Metric [4]
Non-standard units [2]
Perimeter [6]
Area [7]
Data analysis [12]
Collect data [2]
Record data [1]
Organize data [1]
Pictographs
Bar graphs [5]
Line graphs
Probability [5]
Certain, likely, impossible
Math 4 [35]
Operations with numbers [58]
Addition [41]
Subtraction [31]
Multiplication [25]
Division [16]
Whole numbers [2]
Mental math [22]
Rounding [4]
Estimation [20]
Truncating
Front-end
Comparing and ordering [4]
Order of operations [2]
Number sense [29]
Place value [18]
Roman numerals
Large numbers [8]
Very small numbers [2]
Number theory [14]
Prime [4]
Composite [4]
Factor [14]
Prime factorization [2]
Divisibility tests [1]
Greatest common factor [2]
Multiple [10]
Least common multiple [5]
Fractions [32]
Writing fractions [22]
Equivalent fractions [28]
Comparing and ordering [20]
Simplifying fractions [9]
Adding fractions [13]
Subtracting fractions [6]
Writing decimals [7]
Comparing and ordering [5]
Rounding decimals [2]
Adding decimals [7]
Subtracting decimals [7]
Multiplying decimals [5]
Dividing decimals [4]
Fractions <--> decimals [10]
Percentages [8]
Writing percentages [3]
Finding percentages [3]
Integers [17]
Understanding integers [2]
Negative numbers [13]
Algebra [10]
Patterns and sequences [33]
Number sentences [4]
Formulas
Equations and functions [18]
Setting up an equation [1]
Ratio and proportion [11]
Ratios [5]
Rates [4]
Proportions [2]
Geometry in the plane [28]
Classify geometric objects [11]
Triangles [9]
Quadrilateral properties [5]
Symmetry [13]
Similarity [2]
Transformations [8]
Reflections [8]
Rotations [6]
Translations [5]
Tessellations [12]
Fractals [13]
Geometry in space [10]
Recognize shapes in 3-D [6]
Cylinder [1]
Measurement [4]
Time [12]
Calendar [5]
Length/height [7]
Weight/mass [9]
Capacity/volume [6]
Money/coins [11]
Temperature [6]
Standard units [2]
Metric [6]
Non-standard units [2]
Perimeter [12]
Area [15]
Data analysis [12]
Collect data [7]
Record data [6]
Pictographs
Bar graphs [10]
Circle graphs [5]
Line graphs
Misleading graphs [1]
Probability [16]
Certain, likely, impossible [6]
Probability of event [9]
Math 5 [35]
Operations with numbers [57]
Addition [38]
Subtraction [29]
Multiplication [28]
Division [19]
Whole numbers [4]
Mental math [22]
Rounding [4]
Estimation [20]
Truncating
Front-end
Comparing & ordering [5]
Order of operations [5]
Properties of numbers [1]
Identity [1]
Multiplicative [1]
Associative [1]
Commutative [3]
Distributive [1]
Number sense [25]
Base ten, place value [15]
Roman numerals
Large numbers [8]
Very small numbers [2]
Exponents [4]
Powers of ten [2]
Number theory [16]
Prime [6]
Composite [4]
Factor [16]
Prime factorization [4]
Divisibility tests [1]
Greatest common factor [2]
Multiple [13]
Least common multiple [10]
Sequences & series [12]
Pascal's triangle [11]
Fractions [32]
Writing fractions [19]
Equivalent fractions [35]
Comparing & ordering [24]
Simplifying fractions [15]
Adding fractions [17]
Subtracting fractions [9]
Multiplying fractions [11]
Dividing fractions [11]
Writing decimals [5]
Comparing & ordering [6]
Rounding decimals [2]
Adding decimals [6]
Subtracting decimals [7]
Multiplying decimals [7]
Dividing decimals [5]
Fractions <--> decimals [13]
Percentages [15]
Writing percentages [7]
Finding percentages [10]
Integers [19]
Understanding integers [4]
Negative numbers [12]
Modeling integers [1]
Graphing on number line [5]
Algebra and expressions [19]
Patterns and sequences [36]
Variables [4]
Formulas
Equations and functions [22]
Setting up an equation [2]
Representations [6]
Ratio and proportion [16]
Ratios [18]
Rates [10]
Proportions [10]
Geometry in the plane [38]
Triangles [9]
Symmetry [15]
Similarity [8]
Transformations [11]
Reflections [11]
Rotations [8]
Translations [8]
Tessellations [19]
Fractals [16]
Geometry in space [8]
Polyhedra [19]
Cylinder [5]
Surface area [3]
Volume [14]
Measurement [6]
Time [18]
Length/height [8]
Weight/mass [9]
Temperature [6]
Converting between units [4]
Metric [4]
Non-standard units [2]
Perimeter [15]
Area [20]
Data analysis [17]
Data collection [11]
Pictographs
Bar graphs [13]
Circle graphs [6]
Line graphs
Misleading graphs [1]
Probability [25]
Probability of event [17]
Logic and set theory [7]
Venn diagrams [11]
Math 6 [43]
Operations with numbers [53]
Addition [20]
Subtraction [16]
Multiplication [19]
Division [9]
Mental math [18]
Rounding [4]
Estimation [15]
Truncating
Front-end
Comparing & ordering [3]
Order of operations [7]
Properties of numbers [3]
Identity [1]
Multiplicative [1]
Associative [2]
Commutative [1]
Distributive [1]
Number sense [32]
Base ten, place value [12]
Large numbers [5]
Very small numbers
Exponents [7]
Powers of ten [3]
Number theory [13]
Prime [6]
Composite [3]
Factor [16]
Prime factorization [4]
Divisibility tests
Greatest common factor [1]
Multiple [7]
Least common multiple [9]
Sequences & series [16]
Pascal's triangle [11]
Fractions [32]
Writing fractions [11]
Equivalent fractions [23]
Comparing & ordering [22]
Simplifying fractions [13]
Adding fractions [17]
Subtracting fractions [9]
Multiplying fractions [10]
Dividing fractions [10]
Writing decimals [5]
Comparing & ordering [4]
Rounding decimals [3]
Adding decimals [4]
Subtracting decimals [5]
Multiplying decimals [6]
Dividing decimals [4]
Fractions <--> decimals [14]
Percentages [22]
Writing percentages [2]
Finding percentages [7]
Integers [27]
Understanding integers [4]
Negative numbers [4]
Modeling integers
Graphing on number line [2]
Algebra and expressions [25]
Patterns and sequences [33]
Variables [5]
Formulas
Equations and functions [36]
Setting up an equation [6]
Representations [13]
Ratio and proportion [23]
Ratios [20]
Rates [11]
Proportions [12]
Rect coordinate geometry [31]
First quadrant [2]
All quadrants [3]
Geometry in the plane [32]
Triangles [18]
Pythagorean theorem [12]
Symmetry [20]
Similarity [10]
Transformations [13]
Reflections [16]
Rotations [13]
Translations [13]
Tessellations [18]
Intersecting, ||, & perp. [2]
Fractals [21]
Geometry in space [10]
Polyhedra [24]
Cylinder [5]
Surface area [5]
Volume [21]
Perspective (3-D in 2-D) [17]
Measurement [8]
Time [16]
Length/height [8]
Weight/mass [6]
Temperature [1]
Converting between units [6]
Metric [4]
Non-standard units
Perimeter [14]
Area [28]
Data analysis [24]
Data collection [9]
Pictographs
Bar graphs [13]
Line plots
Stem-and-leaf plots [3]
Circle graphs [7]
Line graphs [3]
Scatter plots [5]
Histograms, freq. dist [10]
Box-and-whisker plots [7]
Misleading graphs [5]
Probability [55]
Probability of event [25]
Logic and set theory [10]
Venn diagrams [9]
Math 7 [57]
Operations with numbers [51]
Mental math [16]
Rounding [2]
Estimation [14]
Truncating
Front-end
Order of operations [9]
Properties of numbers [7]
Identity [2]
Multiplicative [3]
Associative [3]
Commutative [3]
Distributive [3]
Number sense [29]
Base ten, place value [9]
Large numbers [6]
Very small numbers
Exponents [9]
Powers of ten [3]
Writing powers [8]
Negative & zero [5]
Exponential growth
Exponential decay
Roots/radicals [5]
Writing square roots [1]
Writing cube roots
Approximating
Rational numbers [3]
Irrational numbers [5]
Orders of magnitude
Scientific notation [2]
Number theory [14]
Prime [8]
Composite [3]
Factor [21]
Prime factorization [4]
Divisibility tests [1]
Greatest common factor [2]
Multiple [6]
Least common multiple [11]
Sequences & series [24]
Pascal's triangle [13]
Fractions [39]
Writing fractions [10]
Equivalent fractions [26]
Comparing & ordering [24]
Simplifying fractions [12]
Adding fractions [20]
Subtracting fractions [12]
Multiplying fractions [11]
Dividing fractions [10]
Writing decimals [7]
Comparing & ordering [4]
Rounding decimals [3]
Adding decimals [4]
Subtracting decimals [4]
Multiplying decimals [5]
Dividing decimals [3]
Fractions <--> decimals [15]
Percentages [29]
Writing percentages [3]
Finding percentages [10]
Percentage increase/decrease [4]
Integers [18]
Understanding integers [6]
Negative numbers [5]
Modeling integers [1]
Graphing on number line [3]
Four quadrant graphing [2]
Comparing & ordering [1]
Integer operations [12]
Adding integers [14]
Subtracting integers [13]
Multiplying integers [18]
Dividing integers [13]
Absolute value [2]
Algebra and expressions [50]
Variables [8]
Visualize [6]
Translate [1]
Simplify [4]
Add like terms [2]
Formulas [4]
Equations and functions [48]
Setting up an equation [9]
Representations [10]
Monomials
Binomials [1]
Polynomials [1]
Mult. polynomials [1]
Squaring binomials [4]
Dividing polynomials [1]
Functions [5]
Deriving a function [10]
Vertical line test [10]
Domain & range [3]
Function notation [5]
1:1 correspondence
Graph functions [7]
Linear relationships [36]
Recognize [1]
Represent [2]
Graph [13]
Find slope [13]
Slope-intercept form [2]
Equation of the line [5]
Distance-rate-time [11]
Ratio and proportion [31]
Ratios [21]
Rates [10]
Proportions [12]
Making comparisons [5]
Proportional reasoning [8]
Scale [8]
Rect coordinate geometry [42]
First quadrant [2]
All quadrants [7]
Geometry in the plane [54]
Angles of polygons [17]
Triangles [38]
Pythagorean theorem [30]
Quadrilateral properties [32]
Symmetry [25]
Similarity [21]
Transformations [24]
Reflections [24]
Rotations [19]
Translations [17]
Tessellations [27]
Intersecting, ||, & perp. [12]
Fractals [49]
Geometry in space [14]
Polyhedra [21]
Platonic solids [12]
Archemedian solids [5]
Prisms [8]
Cylinder [6]
Cone [1]
Sphere [4]
Surface area [11]
Volume [25]
Euler's formula [5]
Perspective (3-D in 2-D) [12]
2-D nets -> 3-D figures [14]
Measurement [14]
Time [15]
Length/height [6]
Weight/mass [9]
Capacity [8]
Temperature [1]
Units
Converting between units [8]
Metric [6]
Perimeter [18]
Area [36]
Data analysis [35]
Data collection [10]
Sample size [3]
Bias
Data displays [4]
Pictographs [1]
Bar graphs [13]
Line plots
Stem-and-leaf plots [3]
Circle graphs [7]
Line graphs [4]
Scatter plots [6]
Histograms, freq. dist [10]
Box-and-whisker plots [6]
Misleading graphs [6]
Mean, median & mode [13]
Variance & range [6]
Probability [78]
Probability of event [34]
Independent events [17]
Conditional probability [14]
Expected value [5]
Making predictions [13]
Simulations [54]
Experimental probability [27]
Theoretical probability [22]
Law of large numbers [16]
Logic and set theory [7]
Venn diagrams [10]
Counting principles [6]
Tree diagrams [2]
Counting principle [1]
Counting techniques [1]
Permutations [2]
Combinations [4]
Geometry [73]
History of geometry [1]
Points and lines [15]
Point [9]
Line [51]
Plane [4]
Space [1]
Coordinate geometry [30]
Cartesian plane [16]
Slope [16]
Midpoint formula [6]
Distance formula [7]
Equations of a line [18]
|
Angles [51]
Obtuse [3]
Acute [3]
Exterior [8]
Interior [10]
Right [6]
Bisectors [13]
Vertical [4]
Perpendicular and parallel lines [13]
Parallel [32]
Perpendicular [15]
Transversals [9]
Alternate interior angles [7]
Alternate exterior angles [7]
Corresponding angles [5]
Logic and proof [15]
Inductive reasoning
If-then statements [2]
Converse, inverse, contrapositive
Postulates and definitions
Triangles [106]
Isosceles [20]
Equilateral [21]
Scalene [11]
Right [21]
Obtuse [8]
Acute [8]
Centers of triangles [31]
Law of sines [7]
Law of cosines [5]
Congruence and similarity [3]
Congruence [28]
Similarity [27]
Right Triangles [11]
Special right triangle [3]
Pythagorean theorem [35]
Trigonometry [14]
Polygons [57]
Quadrilaterals [33]
Square [30]
Rhombus [12]
Rectangle [26]
Parallelogram [27]
Kite [11]
Trapezoid [15]
Regular polygons [14]
Other polygons [5]
Circles [78]
Radius [4]
Diameter [10]
Circumference [5]
Arcs [20]
Angles [16]
Chords [21]
Tangents [18]
Secants [4]
Pi [5]
Perimeter, area, and volume [48]
Quadrilaterals [21]
Regular polygons [9]
Pyramids [10]
Prisms [17]
Cylinders [16]
Spheres [7]
Surface area [10]
Volume [25]
Regular polyhedra [23]
2D pictures of 3D solids [33]
Transformations and symmetry [32]
Reflection [27]
Translation [14]
Rotation [20]
Glide [8]
Dilation [8]
Tessellations [17]
Construction and loci [11]
Straightedge and compass [50]
Paper folding [1]
Modeling and applications [21]
Special topics [6]
Fibonacci sequence and spiral [3]
Golden ratio [7]
Fractals [51]
Spherical geometry [5]
Hyperbolic geometry [4]
Geometric probability [5]
Algebra [86]
Number Systems [4]
Whole [1]
Natural [1]
Integers [4]
Rational [2]
Irrational [5]
Real [3]
Properties of Reals [8]
Commutative [2]
Associative [2]
Distributive [2]
Closure
Identities
Integer Operations [4]
Add / Subtract [6]
Multiply / Divide [4]
Exponents [2]
Order of Operations [4]
Absolute Value [4]
Use of Variables [17]
Sentence as Expression [4]
Expression as Sentence [3]
Evaluating Expressions [2]
Similar Terms [4]
One Variable Equations [22]
Inverse Operations [7]
Equivalent Equations [4]
Applications [1]
Functions / Relations [36]
Domain and Range [2]
Ind / Dep Variables [2]
Vertical Line Test [4]
Notation [2]
Linear Equations [39]
Slope Between Points [25]
Finding Intercepts [19]
Slope - Intercept Form [23]
Point - Slope Form [9]
Graphing [48]
Parallel Lines [6]
Perpendicular Lines [6]
Linear Formulas [9]
Analyzing Linear Data [10]
Is It Linear? [8]
Writing an Equation [8]
Line of Best Fit [12]
Linear Systems [14]
Solve by graphing [15]
Solve by substitution [5]
Solve by combination [4]
Inconsistent System
Applications [3]
Linear Inequalities [11]
Graphing [13]
Linear Programming [4]
Exponents [3]
Basic Rules [8]
Negative [1]
Rational [2]
Polynomials [18]
Add / Subtract [2]
Multiply [8]
Squaring Binomials [4]
Long Division
Synthetic Division
Factoring Polynomials [9]
Common Factors [4]
Difference of Squares
Trinomials [1]
Trinomial Squares [1]
Grouping [1]
Rational Expressions [3]
Simplify [6]
Multiply / Divide [2]
Complex Fractions
Add / Subtract [2]
Rational Equations [3]
Applications
Radicals [2]
Simplify Expressions [2]
Add / Subtract [1]
Multiply / Divide [1]
Equations
Quadratic Equations [18]
Factoring [3]
Completing the Square [8]
Quadratic Formula [7]
Graphing [24]
Applications [2]
Graphing Quadratics [21]
Vertex [1]
Intercepts [1]
Standard Form [7]
Vertex Form [5]
Quadratic Systems [2]
Solve by graphing [7]
Solve by substitution
Solve by combination
Exponential Functions [7]
Growth [4]
Decay [3]
Graphing [20]
Algebra II [77]
Solving systems of equations [14]
Cramer's Rule [1]
Matrices [5]
Elimination
Substitution [1]
Quadratic Equations [5]
Factoring [3]
Completing the square [5]
Standard form [4]
Vertex form [6]
Graphing [20]
Curve of Best Fit [4]
Projectile Motion
Free-fall Motion [1]
Parametric form
Applications [1]
Quadratic Inequalities [5]
Variation [1]
Joint
Direct [2]
Inverse
Combined
Functions / Relations [21]
Domain and Range [3]
Ind / Dep Variables [3]
Vertical Line Test [1]
Notation
Composition of Functions [3]
Parent Functions [8]
Linear [3]
Absolute Value [4]
Quadratic [6]
Square Root [4]
Transformations of functions [11]
Horizontal shift [13]
Vertical shift [13]
Vertical stretch / compression [8]
Horizontal stretch / compression [8]
Polynomials [5]
Factoring [6]
Binomial Expansion [4]
Local min / max [1]
Long Division
Synthetic Division [2]
Factor Theorem
Rational Root Theorem [1]
Rational Expressions [1]
Simplify [4]
Multiply / Divide [2]
Complex Fractions
Add / Subtract [2]
Rational Equations [4]
Graphing [13]
Vertical Asymptotes [1]
Horizontal Asymptotes [1]
Holes [1]
Applications
Radicals [1]
Simplify Expressions [1]
Add / Subtract
Multiply / Divide
Equations
Exponential Functions [8]
Laws of Exponents
Growth and decay applications [9]
Graphing [18]
Curve of Best Fit [5]
Compound Interest [3]
Definition of e [3]
Solving Exponential Equations [2]
Logarithmic Functions [8]
Laws of Logarithms [1]
Common Logarithms [3]
Natural Logarithms [2]
Graphing [14]
Curve of Best Fit [2]
Solving Lograithmic Equations [2]
Applications [2]
Sequences and Series [5]
Arithmetic sequences and series [5]
Geometric sequences and series [9]
Infinite geometric series [2]
Recursion and special sequences [11]
Fractals [10]
Binomial Theorem
Conic sections [13]
Vocabulary [4]
Circles [4]
Parabolas [12]
Ellipses [14]
Hyperbolas [11]
Graph from equation [6]
Equation from graph [2]
Parametric form
Trigonometry [65]
Working with Angles [3]
Definitions [4]
Deg - Rad - Grad [4]
Reference Angles [1]
Right Triangles [5]
30-60-90 and 45-45-90 [1]
sin, cos and tan [23]
Solving Triangles [1]
Applications [1]
Trig Functions [10]
Of Acute Angles [8]
Of Any Angle [3]
The Unit Circle [21]
Graphs of Functions [41]
Transforming Graphs [22]
Applications [6]
Inverse Functions [3]
Finding Angles [10]
Domain and Range [4]
Solving Trig Equations [11]
Identities
Reciprocal [1]
Co-function
Negative Angle
Pythagorean [2]
Sum and Difference [1]
Double Angle
Half Angle
Verifying Identities
Oblique Triangles
Law of Sines [5]
Ambiguous Case [3]
Law of Cosines [4]
Finding Area
Heron's Formula
Applications [2]
Complex Numbers [10]
Rectangular Form [1]
Trig or Polar Form [1]
Operations in Trig Form [2]
DeMoivre?'s Theorem
nth roots
Polar Coordinates [8]
Plotting Points
Polar to Rectangular [1]
Rectangular to Polar [1]
Graphing Equations [10]
Vectors [5]
Component Form & Length [3]
Vector Addition [5]
Scalar Multiplication [1]
Unit Vectors
Dot Product [1]
Angle Between Vectors
Vector Analysis [2]
Applications [2]
Parametric Equations [5]
Hyperbolic Functions [4]
sinh, cosh, tanh [3]
Inverses [1]
Coordinate Systems [2]
Rectangular (2D & 3D) [2]
Spherical [2]
Cylindrical [1]
Distance Formula
Series [1]
Harmonic
Taylor [1]
Fourier [2]
PreCalculus [68]
Functions [23]
linear [23]
quadratic [23]
exponential [35]
logarithmic [15]
absolute value [15]
piecewise [2]
rational [6]
domain and range of functions [14]
graphs and parameters of these functions [42]
set builder notation
interval notation
vertical line test
horizontal line test
composite functions [4]
asymptotes [3]
increasing, decreasing and constant rates of change [14]
continuity [1]
one-to-one [1]
inverse [2]
limits [23]
derivative [5]
tangent line [5]
Properties of Rational Functions [7]
Definition
Difference Quotient
Synthetic Division
Remainder Theorem
Factor Theorem
Rational Zeros Theorem
Fundamental Theorem of Algebra
Number of Zeros Theorem
Conjugate Zeros Theorem
Intermediate Value Theorem [1]
Boundedness Theorem
Graphing [12]
Operations with Logs [1]
properties [3]
base 10 [1]
natural log [2]
change of base theorem [1]
Linear Algebra [4]
solving systems of linear equations [5]
reduced row echelon form [2]
Gauss-Jordan Method [2]
determinants [8]
Cramer's Rule [1]
Linear Programming
operations with matrices [15]
matrix inverses [5]
Partial Fractions [2]
decomposition [1]
Conic Sections [12]
general, standard forms of equations [6]
polar forms
parabolas [8]
directrix
foci [1]
vertex
hyperbolas [6]
foci
asymptotes
fundamental rectangle
circles [2]
ellipses [14]
vertices
major / minor axes [4]
foci [6]
Rotations
Equations
angle of rotation
Sequences and Series [12]
finite [4]
infinite [21]
limit [7]
summation notation [2]
arithmetic [3]
geometric [29]
Factorial Notation [1]
Binomial Coefficient
Binomial Theorem
Binomial Expansion [2]
Mathematical Induction
Variation
direct
inverse
joint
Complex Numbers [15]
Calculus [90]
Functions, Graphs, and Limits [30]
Function graphs [96]
Limits of functions [11]
One-sided limits [5]
Intuitive understanding lims. [10]
Calculating limits [5]
Proving limits [17]
Est. lims. w/ graphs or tables [11]
Asymptotic & Unbounded Behavior [2]
Understanding asymptotes [2]
Asymptotic behavior and limits [13]
Rel. magnitudes of fcn. growth
Param., Polar, & Vector Fcns. [7]
Analysis of parametric curves [11]
Analysis of polar curves [3]
Analysis of vector curves [12]
Continuity [9]
Intuitive understanding [1]
Continuity in terms of limits [8]
Intermediate Value Theorem [2]
Extreme Value Theorem [4]
Concept of the Derivative [8]
Graphical & numerical [3]
Derivatives analytically [4]
And average rate of change [2]
As an instant. rate of change [10]
As the lim. of the diff. quot. [16]
Differentiability & continuity [6]
Leibniz notation [1]
Derivative at a Point [8]
Slope of a curve at a point [9]
Tangent line [40]
Local linearity [14]
Instantaneous rate of change [3]
Approximating rate of change [14]
Derivative as a Function [8]
Graph of f vs. f' [19]
Meaning of the sign of f' [7]
Meaning of critical points [6]
Mean Value Theorem [10]
Equations involving derivs.
Second Derivatives [7]
The graphs of f, f', and f" [14]
Concavity and the sign of f" [1]
Points of inflection [2]
Applications of Derivatives [16]
Monotonicity and concavity [2]
Planar curves - param. form [4]
Planar curves - polar form [3]
Planar curves - vector form
Velocity and accel. vectors [3]
Optimization and extrema [18]
Rates of change
Related rates problems [5]
Implicit differentiation [12]
Derivative of inverse function [18]
Derivative as rate of change [1]
Velocity, speed, accel. [24]
Differential equations [22]
Slope fields [10]
Numerical soln. of diff. eqns. [6]
Euler's Method [5]
L'Hopital's Rule [4]
Newton's Method [15]
Computation of Derivatives [6]
Derivatives of basic functions [31]
Deriv. of sums, prods., quots. [12]
Chain rule and implicit diff. [10]
Param., polar, vector fcns. [6]
Definite Integrals [14]
Interpretations & properties [9]
Summation notation [1]
Riemann sums: L, R, and M. [24]
Riemann sums: int. as lim. [12]
Integral of a rate of change
Additivity and linearity [4]
Applications of Integrals [5]
Integral of a rate of change
Accumulation problems [1]
Riemann sums and integrals [2]
Area of a region [46]
Vol. of a solid of revolution [24]
Solids with known X-sections [9]
Average value of a function [11]
Dist. traveled by a particle [1]
Arc length [10]
Surface area
Work
Fluid pressure and forces
Centers of mass
Fundamental Thrm. of Calculus [7]
To evaluate definite integrals [1]
To represent an antiderivative [5]
Antidifferentiation Techniques [22]
From derives. of basic fcns. [15]
Substitution [36]
Trigonometric substitution [1]
Inverse trig. functions
Improper integrals [49]
Integration by parts [21]
Rational functions [24]
Hyperbolic functions
Apps. of Antidifferentiation [4]
Finding specific antiderivs. [2]
Separable diff. equations
Modeling, including exp. fcns. [11]
Logistic diff. equations
Numeric Approx. to Def. Ints. [5]
Riemann and trapezoidal sums [7]
Simpson's Rule [4]
Polynomial Approxs. and Series [15]
Concept of infinite series [9]
Decimal expansion
Geometric series [4]
The harmonic series [2]
Altern. series, error bound. [2]
The integral test, p-series [16]
Ratio test [3]
Comparison test [21]
Taylor Series [2]
Taylor polynomials [15]
Graphic demo. of convergence [3]
Lagrange error bound.
Taylor and Maclaurin series [2]
Series for common functions [9]
Series substitution
Differentiation and antidiff. [9]
Fcns. defined by power series [2]
Radius and interval of conv. [11]
Probability & Statistics [62]
Data and Distributions [44]
Displaying with Graphs [29]
Describing with Numbers [9]
Density Curves [3]
Normal Distributions [13]
Normal Calculations [2]
Scatterplots [17]
Correlation [12]
Least-Squares Regression [16]
Non-Linear Relationships [8]
Correlation & Regression [14]
Categorical Data Relations [2]
Samples and Experiments [30]
Designing Samples [3]
Designing Experiments [4]
Simulating Experiments [59]
Probability [58]
Randomness [35]
Probability Models [29]
Discrete Random Variables [16]
Continuous Random Vars [3]
Means of Random Variables [3]
Variance of Random Vars [2]
Binomial Distributions [8]
Geometric Distributions [6]
Sampling Distributions [9]
Sample Proportions [4]
Sample Means [4]
Inference [11]
Estimating with Confidence [4]
Tests of Significance [2]
Using Significance Tests [1]
Inference as a Decision [2]
Mean of a Population [1]
Comparing Two Means
Population Proportion [1]
Comparing Two Proportions
Testing Goodness of Fit
Two-Way Tables
Inference and Models [1]
Inference and Predictions [3]
Checking Assumptions [3]
Population Spread
One-Way Variance Analysis [1]
Discrete Math [38]
Logical Form & Equivalence [7]
Statements
Logical connectives
Symbolic notation
Truth tables [6]
Exclusive or
Logical equivalence
De Morgan's laws
Tautologies and contra.
Conditional Statements
Conditional statements
Negation of a conditional
Contrapositive
Converse and inverse
Only if and iff.
Necess. and suff. conds.
Proofs [2]
Techs. of direct proof
Disproof by countereg.
Proof by contradiction
Proof by contraposition
Sequences [4]
Terminology of sequences [2]
Formula for a sequence [4]
Summation notation [2]
Telescoping sums
Change of variable
Product notation
Props. of sums & prods
Factorial notation [1]
Mathematical Induction
Princip. of math. induct.
Strong Math. Induction
Set Theory: Basic Defns.
Definition of subset
Venn diagrams [3]
Rels. among sets of nos.
Equal., union, intersect.
Diffs. and complements [1]
Cartesian products
Properties of Sets
Basic set properties
Proving properties
Deriving set properties
Empty Set, Partits., Power
Counting [1]
Counting lists, sublists
The multiplication rule [1]
Counting possibilities [3]
Permutations [3]
Perms. of selected elements
R-permutations
Proving props. of P(n, r)
Counting Elements of Disj. Sets
The addition rule
Inclusion/exclusion rule
Gen'l inclusion/exclusion
Subsets and Combinations [4]
R-combinations [1]
Ordered and unordered [1]
Permutations vs. combs. [4]
Perms. w. repeated elements
Double counting
R-combs. with repetition
Combinatorial formulas [1]
Pascal's triangle [3]
The binomial theorem
Functions Defined on Sets [1]
Definition of a function
Equality of functions
Examples of functions
Well-defined functions
One-to-one and onto fcns.
One-to-one corresps.
Inverse functions
Pigeonhole principle
Applications [1]
Composition of functions
Comp. of 1-1 & onto fcns.
Recursion [3]
Recurrence relations [11]
Recurs. def. sequences [6]
The towers of Hanoi [3]
The Fibonacci numbers
Solving Recurrence Rels. [1]
Explicit formulas
Arith. & geom. sequences
Does seq. satisf formula?
2nd.order lin. rec. rels.
Technique for solving
Formula for Fib. seq.
Gambler's ruin
Gen'l recursive defns.
Graphs and Trees [3]
Graphs, digraphs
Complete graphs
Bipartite graphs
Sub graphs
Degree
Degree vs. no. of edges
Paths and Circuits [3]
Konigsberg bridges
Walks, paths, circuits [3]
Connectedness
Euler's theorem
Constr. an Euler circuit [2]
Hamiltonian circuits [2]
Traveling salesperson [1]
Matrix Reps. of Graphs [2]
Matrix notation [1]
Adjacency
Matrix multiplication [1]
No. of walks of length n
Isomorphisms of Graphs [2]
Definition
Finding noniso. graphs
Isomorphic invariants
Showing graphs noniso.
Trees [1]
Definition and examples
Characterizations
Rooted trees
Binary trees
Spanning Trees [1]
Definition
Existence
Finding minimal
Social Choice and Voting Theory [1]
Fair division [3]
Voting methods [1]
Apportionment methods [1]
Financial math [1]
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