x
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High School Math Review

A comprehensive summary of the Ontario Grade 12
Advanced Functions (MHF4U) and Calculus and Vectors (MCV4U) courses.


Special note to MHF4U and MCV4U teachers

I am looking for Ontario high school teachers interested in collaborating to create a website
that will be a valuable resource for Advanced Functions and Calculus and Vectors students.

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or have ideas that could improve this site please use [Submit Questions or Comments] below to contact me.

The content of this site can be reorganized to meet the needs of specific schools.

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Previous Grade Knowledge
Grade 9
Types of Triangles
x
CAA;1;lu002;485;6;49;15
Advanced Functions
Functions
Definition of a Function
x
function definition; relation; vertical line test; independent variable; dependent variable; function notation; mapping; domain; range;
BER;1;lu002;485;6;49;15
BER;2;lu005;110;22;43;15
Even and Odd Functions
x
even/odd functions
AAGQabc
Absolute Value
x
absolute value
Inequality and Interval Notation
x
interval notation;inequality notation
Domain and Range
x
domain; range; domain of a function; range of a function
Intervals of Increase/Decrease and Turning Points
x
intervals of increase and decrease; turning points
AACQab
Review of Transformation Basics
x
#transformations - all topics; transformation basics; horizontal stretch/compress; vertical stretch/compress; vertical translation; horizontal translation; transformation formula
Order of operations for transformations of functions
x
x
BAF;1;39;361
#transformations - all topics; order of operations for transformations; stretch/compress/reflect/translate
Image of a point after transformation
x
x
BAG;1;286;40
image of a point after transformation; #transformations - all topics
Find the Transformation Equation given two graphs
x
#transformations - all topics; find transformation equation;
AACQcd
Inverse of a Function
x
BAH;1;20;20;lv002
inverse of a function; draw/graph/sketch the inverse of a function; find the equation of an inverse
AAHQa,AAAQa
Piecewise Functions
x
piecewise functions
Solving linear inequalities
x
solving linear inequalities; solving double inequalities
Average and Instantaneous Rates of Change
x
average rate of change; instantaneous rate of change; difference quotient; local maximum; local minimum
BAK;1;lu017;465;332;93;13
BAK;2;lu017;238;392;92;14
BAK;3;lu017;493;584;90;13
BAK;4a;lu018;602;332;31;13
BAK;4b;lu018;6;356;56;13
BAK;5;lu018;346;392;87;13
BAK;6a;lu018;589;584;32;13
BAK;6b;lu018;68;600;56;13
Polynomials
Finite Differences for Polynomial Functions
x
finite differences; find value of leading coefficient from table of values; find leading coefficient using finite differences
AAEQa
BAM;1;lu001;32;68;111;14
BAM;2;lu001;70;162;119;14
Polynomial Characteristics
Degree and Direction of Opening
x
degree of a polynomial; even/odd degree polynomial; direction of opening of a polynomial
AADQb
BAO;1;lu001;132;124;110;14
BAO;2;lu001;135;148;112;14
BAO;3;lu001;136;247;109;14
BAO;4;lu001;136;272;112;14
BAO;5;lu002;32;339;46;13
BAO;6;lu005;69;175;37;13
BAO;7;lu005;69;299;37;13
Leading Coefficient
x
leading coefficient; direction of opening of a polynomial
AADQc
BAP;1;lu009;300;34;119;13
BAP;2;lu009;334;65;119;13
Zeros and Roots/Solutions
x
x
BAQ;1;39;481
maximum number of real zeros/roots; number of zeros/roots; order of a zero/root; even/odd order zeros/roots; double/triple order zeros/roots; complex zeros/roots; fundamental theorem of algebra
AADQa
BAQ;1;lu006;480;162;149;15
BAQ;2;lu006;394;384;151;15
BAQ;3;lu007;7;214;150;14
BAQ;5;lu007;397;346;76;13
BAQ;6;lu008;6;189;146;14
BAQ;7;lu008;68;344;146;15
Turning Points
x
turning points; maximum number of turning points; local maximum; local minimum
BAR;1;lu006;6;26;150;13
BAR;2;lu006;79;176;127;13
BAR;3;lu012;68;207;100;14
BAR;4;lu019;184;26;176;13
BAR;5;lu019;245;64;174;13
BAR;6;lu019;241;120;173;13
End Behaviour
x
end behaviour; even/odd degree polynomial
BAS;1;lu001;280;7;113;14
BAS;2;lu001;110;85;113;14
BAS;3;lu001;115;113;113;14
BAS;4;lu001;115;164;113;14
BAS;5;lu001;115;192;113;14
BAS;6;lu001;514;342;113;14
BAS;7;lu007;29;62;154;14
BAS;8;lu008;29;141;154;14
BAS;9;lu042;99;295;135;14
BAS;10;lu043;336;295;151;14
Families of Polynomials
x
families of polynomials; same set of zeros/roots
AALQa
BAT;1;lu010;157;26;34;13
BAT;2;lu010;93;154;33;13
BAT;3;lu010;34;200;34;13
BAT;4;lu010;443;317;33;13
BAT;5;lu010;422;349;34;13
BAT;6;lu011;34;56;105;13
BAT;7;lu011;216;154;33;13
BAT;8;lu011;538;317;96;13
Factoring polynomials of degree three or greater
Factoring Theorems
x
remainder theorem; factor theorem; rational zero test theorem; factoring
AAIQa,ZAAQab
Polynomial Division (Long and Synthetic)
x
polynomial long division; polynomial synthetic division; polynomial division - long; polynomial division - synthetic; factoring
AAJQabc,ZAAQc
BAW;1;lu003;55;75;151;15
BAW;2;lu004;259;75;86;15
BAW;3;lu004;27;131;90;15
BAW;4;lu004;455;132;88;14
BAW;5;lu004;422;284;87;14
BAW;6a;lu003;537;284;102;14
BAW;6b;lu003;91;300;52;14
BAW;7;lu010;282;107;28;13
BAW;8;lu010;191;285;26;13
BAW;9;lu010;149;327;28;13
Sum and Difference of Cubes
x
sum of cubes; difference of cubes; factoring
Solving Polynomial Equations and Inequalities
Solving Polynomial Equations
x
solving polynomial equations
Solving factorable polynomial inequalities
x
solving factorable polynomial inequalities
Solving non factorable polynomial inequalities
x
solving non factorable polynomial inequalities
Working with Polynomials
Finding the equation of polynomial given zeros/roots and a point
x
finding the equation of a polynomial given zeros/roots and a point
AALQa
Finding the equation of a polynomial given a set of data points
x
finding the equation of a polynomial given a set of data points;find value of leading coefficient from table of values
AAEQa
Transformations of Polynomial Functions
x
#transformations - all topics; transformations of polynomial functions
Graphing Polynomial Functions
x
Average and instantaneous rates of change
x
average rate of change; instantaneous rate of change; difference quotient
Rational Functions
Graphs of reciprocal functions
x
graphs of reciprocal functions; vertical asymptotes
Discontinuities - vertical asymptotes and holes
x
discontinuities; asymptotes; holes
End Behaviour - Horizontal, oblique and curved asymptotes
x
end behaviour; horizontal asymptotes; oblique asymptotes; curved asymptotes
Finding equations of rational expressions given the graph
Zeros/Roots
x
finding the equation of a rational expression given a graph
Vertical Asymptotes
x
finding the equation of a rational expression given a graph
Holes
x
finding the equation of a rational expression given a graph
Horizontal Asymptotes
x
finding the equation of a rational expression given a graph
Oblique Asymptotes
x
finding the equation of a rational expression given a graph
Solving Rational Equations and Inequalities
Solving Rational Equations
x
solving rational equations
Solving Rational Inequalities Graphically
x
solving rational inequalities graphically
Solving Rational Inequalities Algebraically
x
solving rational inequalities algebraically
Average and instantaneous rates of change
x
average rate of change; instantaneous rate of change;difference quotient
Trigonometry
Radian Measure
Definition of radian
x
x
BBY;1;152;350
radian; arc length
Converting between degrees and radians
x
BBZ;1;lu045;161;11;58;13
converting between degrees and radians; radians to degrees; degrees to radians
Angular velocity
x
BCA;1;435;414;lv001
angular velocity
Finding Equations of Trig Functions given graph or data
Period of sine, cosine, tangent and their reciprocals
x
finding equations of trig functions; trig functions - period; sine; cosine; tangent; secant; cosecant; cotangent; sin; cos; tan; sec; csc; cot
Stretch/Compression Factor of a Periodic Function
x
finding equations of trig functions; sine and cosine - period; sine and cosine - stretch/compression; sine; cosine; sin; cos
Phase Shift of a Periodic Function
x
finding equations of trig functions; phase shift; sine; cosine; sin; cos
Amplitude of a Sine or Cosine Curve
x
finding equations of trig functions; sine and cosine - amplitude; sine; cosine; sin; cos
Axis of a Sine or Cosine Curve
x
finding equations of trig functions; sine and cosine - axis; sine; cosine; sin; cos
Solving Equations involving mixed trig functions
Cofunction Identities
x
cofunction identities
Identities involving x
x
cofunction identities
Working with angles
Primary trig ratios
x
primary trig ratios; sohcahtoa; right angle triangles; sine; cosine; tangent; sin; cos; tan
Trig Ratios for Points on the Cartesian Plane
x
trig ratios for points on the cartesian plane; find angles given (x,y) coordinates; sine; cosine; tangent; sin; cos; tan
Unit Circle
x
unit circle; sine; cosine; sin; cos
Finding all the solutions in a given domain
x
finding all solutions to trig equations
The domain of inverse trig functions on your calculator
x
inverse trig functions on a calculator; domain of inverse trig functions on a calculator
Working with compound angles
Compound Angle Formulas
x
compound angle formulas; sin(a+b); sin(a-b); cos(a+b);cos(a-b); sin(x+y); sin(x-y); cos(x+y); cos(x-y)
Double Angle Formulas
x
double angle formula; sin(2x); cos(2x)
Problems involving multiples of x
x
finding exact values of angles involving pi/12
Trigonometric Identities and Equations
Proving Trigonometric Identities
x
proving trig identities; pythagorean identities; quotient identities
Solving Linear Trigonometric Equations
x
solving linear trig equations
Solving Quadratic Trigonometric Equations
x
solving quadratic trig equations
Exponential and Logarithmic Functions
Finite Differences for Exponential and Logarithmic Functions
x
#logarithmic functions - all topics; #exponential functions - all topics; finite differences; finite differences for exponential and logarithmic functions
Definition of a Logarithm
x
#logarithmic functions - all topics; definition of a logarithm
Properties of Logarithms
x
#logarithmic functions - all topics; properties of logarithms
Laws of Logarithms
x
#logarithmic functions - all topics; laws of logarithms; rules of logarithms
Graphs of Exponential and Logarithmic Functions
x
#logarithmic functions - all topics; #exponential functions - all topics; graphing exponential and logarithmic functions
Transformations of Exponential and Logarithmic Functions
y = a(bk(x - d)) + c, y = a(logb(k(x - d))) + c
x
#logarithmic functions - all topics; #exponential functions - all topics; #transformations - all topics; transformations of exponential and logarithmic functions
Vertical stretch can be expressed as a horizontal translation
x
#transformations - all topics; transformations of exponential and logarithmic functions
Horizontal translation of exponential same as vertical translation of log
x
#transformations - all topics; transformations of exponential and logarithmic functions
Vertical translation of exponential same as horizontal translation of log
x
#transformations - all topics; transformations of exponential and logarithmic functions
Solving Exponential Equations
Solving by changing the base and equating exponents
x
#exponential functions - all topics; solving exponential equations
Solving by rewriting with a common exponent
x
#exponential functions - all topics; solving exponential equations
Solving by taking logarithms of both sides
x
#logarithmic functions - all topics; #exponential functions - all topics; solving exponential equations
Solving quadratic exponential equations
x
#exponential functions - all topics; solving exponential equations; solving quadratic exponential equations;
Solving Logarithmic Equations
Solve by Using Definition of a Logarithm
x
#logarithmic functions - all topics; solving logarithmic equations
Solve by taking logarithms of both sides
x
#logarithmic functions - all topics; solving logarithmic equations
Solve by Equating Logarithmic Arguments
x
#logarithmic functions - all topics; solving logarithmic equations
Comparing Intensities/Concentrations
x
compare intensities or concentrations for richter, ph or decibel (db) scale; earthquake intensities; acid/base intensities
Finding Exponential and Logarithmic Equations
Establish base from two points and asymptote
x
#logarithmic functions - all topics; #exponential functions - all topics; finding exponential and logarithmic equations
Establish base from three equally spaced points
x
#logarithmic functions - all topics; #exponential functions - all topics; finding exponential and logarithmic equations
Problem Solving Tools
Finding Doubling Time
x
finding doubling time
Change of Base Formula
x
change of base formula
Four ways to write loga x
x
#logarithmic functions - all topics; four ways to write loga(x)
Combination Functions
Sum, Difference, Product and Quotient Function
Domain
x
domain; domain of a sum, difference, product or quotient function
Range
x
range; range of a sum, difference, product or quotient function
Even/Odd Nature of Combinations
x
even/odd functions; even/odd nature of sum, difference, product and quotient functions
AAGQdef
Graphing Sum and Difference Functions
x
graphing or sketching sum and difference functions
Graphing Product Functions
x
graphing or sketching product functions
Graphing Quotient Functions
x
graphing or sketching quotient functions
Composite Functions
Definition
x
composite functions; composite functions - definition
Equation of a Composite Function
x
composite functions; composite functions - equation
Domain of x
x
domain; composite functions; composite functions - domain
Range of x
x
range; composite functions; composite functions - range
Even/Odd Nature of Composite Functions
x
even/odd functions; even/odd nature of composite functions; composite functions; composite functions - even/odd nature
Calculus and Vectors
Limits and Continuity
Requirements for Existence of a Limit at a Point
x
requirements for existence of a limit at a point; limit from the left; limit from the right; left limit; right limit
Requirements for Continuity at a Point
x
requirements for continuity at a point; limit from the left; limit from the right; left limit; right limit; continuity; piecewise functions
Existence of Limits as x
x
existence of limits as x approaches infinity; horizontal asymptote
Types of Discontinuities
Holes
x
continuity; discontinuity; removable discontinuity; holes
Jumps
x
continuity; discontinuity; jump discontinuity
Vertical Asymptotes
x
continuity; discontinuity; vertical asymptotes
Methods of Finding Limits as x
Direct Substitution
x
finding limits; finding limits - direct substitution
Factoring
x
finding limits; finding limits - factoring; factoring; limits as x approaches a
Multiply by conjugate (for square root limits)
x
finding limits; finding limits - multiply by conjugate; square root limits; limits as x approaches a
Difference of Cubes or Cube Roots (u substitutions)
x
finding limits; finding limits - difference of cubes; cube root limits; limits as x approaches a
Methods of Finding Limits as x
Degree of NumeratorxDegree of Denominator
x
finding limits; finding limits - horizontal asymptotes; limits as x approaches infinity
Degree of Numerator > Degree of Denominator
x
finding limits; finding limits - oblique asymptotes or curved asymptotes; limits as x approaches infinity
Derivatives
Definition of Derivative
x
#derivatives - all topics; definition of derivative; instantaneous rate of change; slope of the tangent to the curve
Finding Derivatives from First Principles
For a specific point
x
#derivatives - all topics; finding the derivative from first principles - for a specific point
For any point
x
#derivatives - all topics; finding the derivative from first principles - for any point
Requirements for Differentiability
x
#derivatives - all topics; requirements for differentiability; differentiable
Differentiation Rules
Derivative of a Constant
x
#derivatives - all topics; differentiation rules; differentiation rules - derivative of a constant
Power Rule
x
#derivatives - all topics; differentiation rules; differentiation - power rule
Constant Multiple Rule
x
#derivatives - all topics; differentiation rules; differentiation - constant multiple rule
Sum and Difference Rule
x
#derivatives - all topics; differentiation rules; differentiation - sum and difference rule
Product Rule
x
#derivatives - all topics; differentiation rules; differentiation - product rule
Quotient Rule
x
#derivatives - all topics; differentiation rules; differentiation - quotient rule
Chain Rule
x
#derivatives - all topics; differentiation rules; differentiation - chain rule
Exponential and Logarithmic Formulas
Exponential Formula
x
#derivatives - all topics; #exponential functions - all topics; exponential derivative formulas; derivative of e^x, e^f(x), a^x and a^f(x)
Logarithmic Formula
x
#derivatives - all topics; #logarithmic functions - all topics; logarithmic derivative formulas; derivative of ln(x), ln(f(x)), log[a](x) and log[a](f(x))
Trigonometric Formulas
Sine, Cosine, Tangent
x
#derivatives - all topics; trig derivative formulas; sine; cosine; tangent; sin; cos; tan
Secant, Cosecant, Cotangent
x
#derivatives - all topics; trig derivative formulas; secant; cosecant; cotangent; sec; csc; cot
Implicit Differentiation
x
implicit differentiation
Curve Sketching
Find Critical Points
x
find critical points
Find Vertical Asymptotes and Holes
x
find vertical asymptotes and holes
Establish End Behaviour
Horizontal Asymptotes
x
end behaviour - horizontal asymptotes
Oblique Asymptotes
x
end behaviour - oblique asymptotes
Use First Derivative Test to Find Turning Points
x
#derivatives - all topics; use first derivative test to find turning points
Use Second Derivative Test to Classify Turning Points
x
#derivatives - all topics; use second derivative test to classify turning points
Use Second Derivative Test to find POI and Concavity
x
#derivatives - all topics; use second derivative test to find poi and concavity; points of inflection
Calculus Applications
Finding Maximum and Minimum of an Interval
x
finding maximum and minimum of an interval; absolute extrema
Equations of Tangents and Normals
Find Equation through a point on the curve
x
find the equation of the tangent to a curve through a point on the curve; find the equation of the tangent to a curve
Find the Equation of a tangent line with a given slope
x
find the equation of the tangent to a curve with a given slope; find the equation of the tangent to a curve
Find Equation through a point not on the curve
x
find the equation of the tangent to a curve through a point NOT on the curve; find the equation of the tangent to a curve
Motion on a Straight Line
Position
x
motion on a straight line - position function
Velocity
x
motion on a straight line - velocity function
Acceleration
x
motion on a straight line - acceleration function
Financial Applications
Revenue, Profit and Cost
x
financial applications - all; financial applications - revenue; profit and cost
Demand and Price Functions
x
financial applications - all; financial applications - demand function; price function; revenue
Marginal Revenue, Profit and Cost
x
financial applications - all; financial applications - marginal revenue; marginal profit; marginal cost

Basic Vector Operations
Add, Subtract, Scalar Multiplication
x
basic vector operations; adding vectors; subtracting vectors; vector addition; vector subtraction
Modelling - Ground Speed, Tension, Friction
Ground Speed and Direction
x
modelling with vectors; ground speed; air speed; wind speed; tension; friction
Tension is Supporting Cables
x
modelling with vectors; tension in supporting cables
Friction Acting on Objects on Ramps
x
modelling with vectors; friction on a ramp
Dot Product (Geometric and Cartesian)
x
dot product - geometric and cartesian/algebraic; vector product; vector product - scalar
Cross Product (Geometric and Cartesian)
x
cross product; cross product - geometric and cartesian/algebraic; vector product; right hand rule
Direction Angles
x
direction angles; coordinate axis/axes angles
Angle Between Two Vectors
x
angle between 2 vectors; dot product
Projection of one Vector onto Another
x
projection of one vector onto another vector; dot product
Working with Lines and Planes in 3 space
Equations of Lines
Vector Equation of a Line
x
vector equation of a line
Parametric Equations for a Line
x
parametric equations for a line; parameter
Symmetric Equations for a Line
x
symmetric equations for a line
Scalar/Cartesian Equation for a Line
x
scalar equation of a line; cartesian equation of a line
Equations of Planes
Vector Equation of a Plane
x
vector equation of a plane
Parametric Equations for a Plane
x
parametric equations for a plane; parameter
Scalar/Cartesian Equation of a Plane
x
scalar equation of a plane; cartesian equation of a plane
Planes Parallel to Coordinate System
Planes Parallel to Coordinate Planes
x
planes parallel to coordinate planes
Planes Parallel to Coordinate Axes
x
planes parallel to coordinate axes
Angles Between Lines and Planes
Angle Between a Line and a Plane
x
angle between a line and a plane
Angle Between Two Planes
x
angle between 2 planes
Testing for Collinear and Coplanar Vectors
Test for Collinear Vectors
x
test for collinear vectors; scalar multiple
Test for Coplanar Vectors (linear combination)
x
test for coplanar vectors; linear combination
Test for Coplanar Vectors (scalar triple product)
x
test for coplanar vectors; scalar triple product
Test for Perpendicular Vectors
x
test for perpendicular vectors; dot product
Distance between Points and Lines
Distance Between a Point and a Line
In 2D (using dot product and normal)
x
distance between a point and a line - in 2d; dot product
In 3D (using cross product and direction)
x
distance between a point and a line - in 3d; cross product
In 3D (using dot product and direction)
x
distance between a point and a line - in 3d; dot product
Distance Between a Point and a Plane
x
distance between a point and a plane; dot product
Distance Between Parallel Lines
x
distance between parallel lines; cross product
Distance Between Skew Lines
x
distance between skew lines; dot product
Intersections of Lines and Planes
Intersection of Lines with Lines
x
intersection of lines with lines
Intersection of Lines with Planes
x
intersection of lines with planes
Intersection of 3 Planes
Unique Solution (non coplanar normals)
x
intersection of 3 planes; intersection of 3 planes - unique solution; matrix analysis for intersection of 3 planes
Non Unique Solution (coplanar normals)
x
intersection of 3 planes; intersection of 3 planes - non unique solution; coplanar normals; matrix analysis for intersection of 3 planes
No Solution (coplanar normals, 2 or 3 non coincident parallel planes or no parallel planes)
x
intersection of 3 planes; intersection of 3 planes - no solution; coplanar normals; matrix analysis for intersection of 3 planes
1;89;81
a;3;69;295;29
a;3;69;295;29
xxx
5;298;200
a;3;19;13;16
b;3;80;13;16
c;3;152;13;16
d;3;209;13;16
e;3;256;13;16
xx xxxxx
5
a;3;32;304;19;b;3;55;304;19;c;3;79;304;19;d;3;103;304;37;z;3;156;304;18
none
a;3;35;304;20
b;3;59;304;19
c;3;82;304;19
d;3;106;304;34
z;3;154;304;18
AACQaSoln;1;lu032;42;7;98;13
AACQaSoln;2;lu031;43;27;110;13
AACQbSoln;1;lu015;6;7;87;13
AACQbSoln;2a;lu017;566;7;30;13
AACQbSoln;2b;lu017;6;24;60;12
AACQbSoln;3;lu018;319;24;87;12
AACQcSoln;1;lu033;490;6;129;13
AACQcSoln;2;lu034;53;21;143;13
AACQzSoln;1;lu038;258;35;207;14
AACQzSoln;2;lu015;444;65;86;15
AACQzSoln;3;lu039;32;300;177;15
xx xxxx xx
4
a;4;46;248;19;b;4;71;248;19;c;4;94;248;19;z;4;123;248;19
a;4;46;248;19
b;4;71;248;19
c;4;94;248;19
z;4;123;248;19
AADQaSoln;1;lu010;72;7;36;13
AADQbSoln;1;lu006;73;6;132;14
AADQcSoln;1;lu001;72;6;113;14
AADQzSoln;1;lu010;32;8;36;13
AADQzSoln;2;lu010;538;8;33;13
AADQzSoln;3;lu006;32;50;140;14
AADQzSoln;4;lu001;32;82;113;13
xx xxxx
3
a;4;12;296;50;b;4;72;296;53;z;4;134;296;18
a;4;217;296;50
b;4;278;296;53
z;4;339;296;18
AAEQbSoln;1a;lu011;580;8;36;14
AAEQbSoln;1b;lu011;6;26;67;13
AAEQaSoln;2a;lu011;580;294;37;13
AAEQaSoln;2b;lu011;5;310;68;13
AAEQzSoln;1;lu040;108;31;99;13
AAEQzSoln;2;lu006;442;50;149;13
AAEQzSoln;3;lu001;32;96;111;13
AAEQzSoln;4;lu041;67;255;110;13
xx xx xx
7;358;312
a;3;5;298;89;z;3;131;298;22
b;3;8;298;54;c;3;71;298;53
d;3;4;298;37;e;3;53;298;38;f;3;104;298;53
a;3;8;298;89
b;3;108;298;51
c;3;171;298;50
d;3;235;298;36
e;3;286;298;37
f;3;335;298;52
z;3;400;298;20
xx xxxxxx xxx
1;95;115
a;84;26;185;27
a;84;26;185;27
xxx
2
a;4;4;300;97;z;4;110;300;19
a;4;4;300;97
z;4;110;300;19
AAIQaSoln;1;lu026;107;6;122;14
AAIQzSoln;1;lu026;107;6;122;14
xx x x
3;215;165
a;5;7;300;63;b;5;81;300;58;c;5;152;300;74
a;5;7;300;63
b;5;81;300;58
c;5;152;300;74
xx xxx x
1;359;127
a;307;335;53;17
xx x
2
a;4;10;297;33;z;4;247;297;17
a;4;10;297;33
z;4;247;297;17
xx xx
3;150;235
a;5;12;297;57;b;5;78;297;37;c;5;121;297;55
a;5;12;297;57
b;5;78;297;37
c;5;121;297;55
ZAAQaSoln;1;lu026;33;6;113;14
ZAAQbSoln;1;lu004;33;8;88;14
ZAAQcSoln;1;lu025;51;12;104;14
ZAAQcSoln;2;lu028;228;51;42;14
ZAAQcSoln;3;lu029;419;80;48;14
xx xxx x
leading coefficient
BAP
BAP;a;421;8;121;17;b;96;31;112;17;c;129;62;113;17
domain
BAE
BAE;a;31;3;50;16;b;375;111;53;13;c;375;221;53;13;d;375;356;53;13;e;375;423;53;13;f;518;58;46;12;g;551;73;46;13;h;386;174;47;13;i;429;284;45;13;j;371;314;45;13;k;482;498;46;13;l;467;649;45;13
rational zero test theorem
BAV
BAV;a;4;64;113;14;b;111;165;114;14
factor theorem
BAV
BAV;a;4;33;101;14
range
BAE
BAE;a;497;3;39;15;b;384;134;41;15;c;594;174;41;15;d;384;244;41;15;e;503;286;34;12;f;445;316;35;13;g;384;388;41;15;h;384;456;41;15;i;561;500;34;13
degree of a polynomial
BAO
BAO;a;32;8;138;18;b;70;369;138;18
even degree polynomial
BAO
BAO;a;24;99;153;18
odd degree polynomial
BAO
BAO;a;24;223;148;18
direction of opening of a polynomial
BAO
BAO;a;5;76;222;18
zeros/roots of a function
BAQ
BAQ;a;31;90;35;15;b;220;90;34;15
order/multiplicity of a zero/root of a function
BAQ
BAQ;a;183;282;64;15;b;262;282;99;15
even order zeros/roots
BAQ
BAQ;a;366;280;104;15;b;67;409;103;14
odd order zeros/roots
BAQ
BAQ;a;36;297;95;15;b;375;408;94;15
maximum number of real zeros/roots
BAQ
BAQ;a;179;162;185;15;b;93;384;186;15
turning points
BAR
BAR;a;5;8;87;16;b;386;26;79;15;c;17;63;77;15;d;17;119;76;15;e;328;176;83;14;f;293;192;78;14;g;234;208;84;15
maximum number of turning points
BAR
BAR;a;324;9;211;15;b;249;175;164;15
local maximum
BAR
BAR;a;117;62;93;15
local minimum
BAR
BAR;a;117;118;89;15
instantaneous rate of change (iroc)
BAK
BAK;a;30;108;183;17;b;6;133;180;16;c;64;331;177;16;d;426;513;183;16;e;129;542;182;16;f;127;583;176;16
average rate of change (aroc)
BAK
BAK;a;30;2;150;17;b;372;134;141;16;c;350;513;49;16;d;515;513;93;16
even function
BAB
BAB;a;28;3;96;15;b;204;4;91;14;c;265;81;41;15
odd function
BAB
BAB;a;28;31;84;15;b;201;31;84;14;c;564;77;32;15
difference quotient
BAK
BAK;a;237;74;121;16;b;209;179;121;16;c;347;219;123;14;d;226;480;120;16;e;92;512;119;15;f;64;566;121;15
family of polynomials
BAT
BAT;a;210;55;130;16;b;91;137;128;14;c;429;244;131;15;d;117;333;129;15
synthetic division
BAW
BAW;a;79;106;103;14;b;315;170;104;14;c;257;237;105;14;d;79;270;106;14;e;540;355;105;13
remainder theorem
BAV
BAV;a;5;3;125;15
dividend
BAW
BAW;a;7;31;58;15;b;238;39;48;15
divisor
BAW
BAW;a;12;51;45;15;b;154;51;44;15;c;297;40;38;14
quotient
BAW
BAW;a;79;39;51;16;b;350;40;47;15
remainder
BAW
BAW;a;143;31;68;15;b;407;40;58;14
inequality notation
BAD
BAD;a;10;29;63;33;b;131;496;113;17
interval notation
BAD
BAD;a;9;234;56;32;b;464;496;99;16
transformation - vertical stretch/compression
BBW
BBW;a;50;31;182;16
transformation - horizontal stretch/compression
BBW
BBW;a;50;73;200;16
transformation - vertical translation
BBW
BBW;a;50;134;122;16
transformation - horizontal translation
BBW
BBW;a;50;174;139;16
order of operations for transformations
BAF
intervals of increase and decrease
BEO
find transformation equations
BEP
finite differences
BAM
double order zero/root
BAQ
BAQ;a;439;298;114;15
even/odd degree polynomials
BAO
BAO;a;24;99;153;18;b;24;223;148;18
even/odd functions
BAB
BAB;a;28;3;96;15;b;204;4;91;14;c;265;81;41;15;d;28;31;84;15;e;201;31;84;14;f;564;77;32;15
right triangle
CAA
CAA;a;449;10;208;112
unit circle
BCN
Angular Velocity - Dimension Analysis
width="1280" height="720" src="//www.youtube.com/embed/LdZ00OFAfaQ" frameborder="0" allowfullscreen
BCA
Inverse Functions - The Basics
width="960" height="720" src="//www.youtube.com/embed/nSmFzOpxhbY" frameborder="0" allowfullscreen
BAH
average rate of change;
BAK
a;31;3;150;17;b;349;514;52;16;c;514;514;97;16
BBG
a;52;73;145;17
BBV
a;5;70;148;16
complex zeros/roots;
BAQ
a;195;479;89;17
degree of a polynomial;
BAO
a;33;9;137;16
difference quotient;
BAK
a;238;75;120;15;b;211;179;120;16;c;347;218;125;16;d;227;482;120;15;e;93;513;118;15;f;67;567;119;16
BBG
a;5;29;121;15
BBV
a;5;29;121;15
double/triple order zeros/roots;
BAQ
a;440;298;114;15;b;127;314;104;15
even/odd degree polynomial;
BAO
a;24;99;153;18;b;23;224;150;16
BAS
a;29;62;154;14;b;29;141;154;14;c;100;296;208;14
even/odd order zeros/roots;
BAQ
a;367;282;104;15;b;37;298;95;15;c;66;409;106;15;d;375;409;95;15
families of polynomials;
BAT
a;210;55;132;16;b;429;243;132;16;c;116;333;131;15
fundamental theorem of algebra;
BAQ
a;36;478;33;19
instantaneous rate of change;
BAK
a;30;108;184;17;b;4;134;183;16;c;65;331;177;15;d;428;513;183;16;e;130;542;182;17;f;128;584;176;15
BBG
a;84;2;186;16;b;31;117;177;16;c;93;187;175;15
BBV
a;84;2;186;16;b;246;69;178;17;c;88;192;182;16
ABC
a;128;3;176;16
local maximum;
BAR
a;118;63;93;15
BAK
a;465;332;94;16;b;237;392;92;16;c;492;583;92;16
local minimum;
BAK
a;602;331;32;16;b;6;356;58;15;c;345;391;89;16;d;589;583;32;15;e;67;600;58;15
BAR
a;118;119;88;14
maximum number of real zeros/roots;
BAQ
a;180;162;186;19
maximum number of turning points;
BAR
a;326;10;209;14;b;249;176;166;14
number of zeros/roots;
BAQ
a;240;162;126;19
order of a zero/root;
BAQ
a;182;282;184;16
same set of zeros/roots;
BAT
a;83;26;109;15;b;184;41;109;15;c;370;318;109;16
turning points;
BEO
a;6;53;89;16
BAR
a;6;9;87;16;b;386;26;79;14;c;18;63;77;15;d;18;120;77;14;e;328;176;86;14;f;295;192;78;14;g;240;209;83;14
ACC
ACD