x
x

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.

If you are interested in providing additional content 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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Other Knowledge
Glossary
Complex Numbers
x
complex number - definition|lu069;why do we need complex numbers|lu070
1;500;514;lv023;video part 1
2;600;514;lv024;video part 2
IRoC = Instantaneous Rate of Change
x
instantaneous rate of change|lu019;
1;lu019;166;7;186;15
Real Numbers
x
real number - definition|lu064;rational number - definition|lu065;irrational number - definition|lu066;how to covert decimal number to a rational number|lu067
Tangent to a Curve
x
Grade 9
Types of Triangles
x
Advanced Functions
Functions
Basic Concepts
Definition of a Function
x
domain of a function|lu002;range of a function|lu005
1;lu002;484;6;50;15
2;lu005;111;23;44;15
1;525;75;lv014;vertical line test video
2;490;568;lv005;video 1
3;550;568;lv007;video 2
4;610;568;lv008;video 3
independent variable; dependent variable; function notation; mapping;
function - definition|lu046; relation - definition|lu050; vertical line test|lu049; domain of a function|lu002; range of a function|lu005;
Domain and Range
x
1;625;602;lv016;video
domain of a function|lu002; range of a function|lu005;
Inequality and Interval Notation
x
domain and range of a function|lu054
1;lu054;170;5;110;17
interval notation|lu032;inequality notation|lu031
Intervals of Increase/ Decrease and Local Maximums and Minimums
x
interval notation|lu032;piecewise functions|lu053
1;lu032;517;77;101;15
2;lu053;60;563;120;15
1;770;604;lv017;video
intervals of increase and decrease|lu038; local maximum|lu017; local minimum|lu018
AACQab
Additional Concepts
Even and Odd Functions
x
even/odd DEGREE polynomials|lu042
1;lu042;362;177;180;16
1;625;184;lv003;video
even/odd functions|lu043
AAGQabc
Piecewise Functions
x
1;530;327;lv012;example 1
2;600;327;lv013;example 2
piecewise functions|lu053
Convert Absolute Value Function to Piecewise Function
x
1;625;375;lv015;video
convert absolute value to piecewise function|lu052
Inverse of a Function
x
function|lu046;range|lu005;domain|lu002
1;lu046;216;84;52;15
2;lu005;73;143;39;15
3;lu002;197;143;49;15
1;450;585;lv002;the basics
2;520;585;lv009;example 1
3;590;585;lv010;example 2
4;660;585;lv011;example 3
inverse of a function|lu056; draw/graph the inverse of a function|lu059; find the equation of an inverse|lu060
AAHQa,AAAQa
Average and Instantaneous Rates of Change
x
local maximum|lu017;local minimum|lu018;tangent to a curve|lu058;IRoC|lu057
1;lu017;440;346;92;15
2;lu017;283;383;93;15
3;lu017;490;843;90;15
4;lu018;606;383;89;15
5;lu018;547;346;89;15
6;lu018;587;843;85;15
7;lu058;335;70;122;15
7;lu057;243;346;37;15
average rate of change|lu020; instantaneous rate of change|lu019; difference quotient|lu023; local maximum|lu017; local minimum|lu018
Transformations
Review of Transformation Basics
x
1;lu037;32;350;232;14
1;lu055;32;372;230;14
order of operations for transformations|lu037;image of a point after transformation|lu055
1;630;300;lv022;video (start to 11:05)
#transformations - all topics;
review of transformation basics|lu068; transformation - horizontal stretch/compress|lu034;transformation - vertical stretch/compress|lu033; transformation - vertical translation|lu035; transformation - horizontal translation|lu036
Order of operations for transformations of functions
x
x
1;38;447
#transformations - all topics
order of operations for transformations|lu037
Image of a point after transformation
x
x
1;37;76
image of a point after transformation; #transformations - all topics
Find the Transformation Equation given two graphs
x
#transformations - all topics; find transformation equation;
AACQcd
Problem Solving Methods
Solving linear and double inequalities
x
inequality notation|lu031;interval notation|lu032
1;lu031;133;478;110;15
2;lu032;432;478;96;15
1;637;231;lv018;video
2;637;491;lv019;video
solving linear inequalities; solving double inequalities
Polynomials
Finite Differences for Polynomial Functions
x
degree of a polynomial|lu006;leading coefficient|lu001
1;lu006;313;37;151;14
2a;lu006;413;183;44;14
3;lu006;93;536;140;14
4;lu001;132;53;115;14
5;lu001;218;257;114;;14
6;lu001;92;557;114;14
1;660;369;lv020;video (start to 8:07)
finite differences for polynomials|lu040; find value of leading coefficient from table of values|lu063; find value of leading coefficient using finite differences|lu063
AAEQa
Polynomial Characteristics
Polynomial Definition, Degree and Basic Shapes
x
leading coefficient|lu001;turning point|lu015;direction of opening|lu009;polynomial end behaviour|lu051
1;lu064;5;31;80;14
2;lu001;634;218;113;14
3;lu015;500;255;86;14
4;lu009;431;271;121;14
5;lu051;567;271;194;14
polynomial - definition|lu047; degree of a polynomial|lu006; polynomial shapes for degrees 1 to 5|lu048;basic polynomial shapes|lu048
AADQb
Leading Coefficient, End Behaviour/ Direction of Opening, Domain and Range
x
degree of a polynomial|lu006;turning points|lu015;range|lu005;domain|lu002;basic polynomial shapes|lu048
a;lu006;6;85;43;14
b;lu006;122;150;43;14
c;lu015;432;150;85;14
d;lu005;69;313;36;14
e;lu005;71;450;36;14
f;lu002;53;486;44;14
g;lu015;378;523;85;14
h;lu048;55;558;149;14
even/odd degree polynomial|lu042; direction of opening of a polynomial|lu009;leading coefficient|lu001;end behaviour for a polynomial|lu051
1;620;480;lv021;video
AADQb
Zeros and Roots/ Solutions
x
real numbers|lu064;complex numbers|lu069;degree of a polynomial|lu006;even/odd degree polynomial|lu042;instantaneous rate of change|lu019
1;lu064;145;196;81;13
2;lu069;291;196;108;13
3;lu006;451;246;152;13
4;lu008;5;270;150;15
5;lu007;5;296;154;15
6;lu019;273;496;178;14
7;lu008;66;674;150;15
8;lu007;395;674;154;15
9;lu006;392;692;154;13
10;lu019;312;739;185;15
x
1;37;787
maximum number of real zeros/roots for a polynomial|lu014;order/multiplicity of a zero/root|lu011;even order zeros/roots|lu012;odd order zero/root|lu013; double order zeros/roots|lu041; triple order zeros/roots|lu071;fundamental theorem of algebra|lu072;zeros/roots of a function - definition|lu010
AADQa
Turning Points
x
instantaneous rate of change|lu019;even order zeros|lu012;degree of a polynomial|lu006;local maximum|lu017;local minimum|lu018
1;lu019;30;37;178;16
2;lu012;5;59;105;16
3;lu006;379;153;150;16
4;lu017;120;226;92;16
5;lu018;120;283;88;16
turning points|lu015; maximum number of turning points|lu016; local maximum|lu017; local minimum|lu018
Families of Polynomials
x
zeros/roots of a function|lu010;order/multiplicity of a zero/root of a function|lu011
family of polynomials; same set of zeros/roots
AALQa
Factoring polynomials of degree three or greater
Factoring Theorems
x
remainder theorem; factor theorem; rational zero theorem; factoring
AAIQa,ZAAQab
Polynomial Division (Long and Synthetic)
x
factor theorem|lu004;rational zero theorem|lu003;root of a factor|lu010
polynomial division - long; polynomial division - synthetic; factoring
AAJQabc,ZAAQc
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
1;590;216;lv020;video (8:08 to end)
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 for a rational function; 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
1;152;350
radian; arc length
Converting between degrees and radians
x
unit circle|lu045
converting between degrees and radians; radians to degrees; degrees to radians
Angular velocity
x
1;433;412;lv001;here
2;610;500;lv006;video
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; logarithm - definition
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 of a sum, difference, product or quotient function
domain of a function|lu002
Range
x
range of a sum, difference, product or quotient function
range of a function|lu005
Even/ Odd Nature of Combinations
x
even/odd functions|lu043
1;625;358;lv004;video
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
composite functions; composite functions - domain
domain of a function|lu002;
Range of x
x
composite functions; composite functions - range
range of a function|lu005
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; derivative - definition; 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
BAO
BAO;a;29;4;225;19
domain of a function
BAE
BAE;a;31;6;52;18
rational zero theorem
BAV
BAV;a;4;213;152;19
factor theorem
BAV
BAV;a;4;129;109;19
range of a function
BAE
BAE;a;31;25;44;18
degree of a polynomial
BES
BES;a;29;121;151;19
even degree polynomial
BAO
BAO;a;23;222;165;19
odd degree polynomial
BAO
BAO;a;23;359;160;19
direction of opening of a polynomial
BAO
BAO;a;131;128;245;19
zeros/roots of a function - definition
BAQ
BAQ;a;4;6;605;18;b;4;29;198;18;c;4;55;403;18;d;4;84;763;18
order/multiplicity of a zero/root of a function
BAQ
BAQ;a;10;343;193;19
even order zeros/roots
BAQ
BAQ;a;4;583;116;19
odd order zeros/roots
BAQ
BAQ;a;4;540;109;19
maximum number of real zeros/roots
BAQ
BAQ;a;30;245;308;19
turning points
BAR
BAR;a;4;11;98;18
maximum number of turning points
BAR
BAR;a;31;153;228;19
local maximum
BEO
BEO;a;25;129;101;19
local minimum
BEO
BEO;a;25;270;101;19
instantaneous rate of change (iroc)
BAK
BAK;a;32;69;195;19
average rate of change (aroc)
BAK
BAK;a;32;7;157;19
even function
BAB
BAB;a;13;7;106;20
odd function
BAB
BAB;a;335;6;97;20
difference quotient
BAK
BAK;a;273;235;132;19;b;657;245;123;19
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;4;4;134;19
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;31;69;38;b;129;505;121;19
interval notation
BAD
BAD;a;10;234;61;38;b;460;505;108;19
transformation - vertical stretch/compression
BBW
BBW;a;4;32;230;16
transformation - horizontal stretch/compression
BBW
BBW;a;4;132;281;16
transformation - vertical translation
BBW
BBW;a;4;81;220;16
transformation - horizontal translation
BBW
BBW;a;4;203;242;16
order of operations for transformations
BAF
BAF;a;3;5;256;19
intervals of increase and decrease
BEO
BEO;a;47;4;131;19;b;47;31;131;19
find transformation equations
BEP
finite differences for polynomials
BAM
BAM;a;10;5;221;19
double order zero/root
BAQ
BAQ;a;17;626;116;19
even/odd degree polynomials
BAO
BAO;a;23;222;165;19;b;23;359;160;19
even/odd functions
BAB
BAB;a;13;7;106;20;b;335;6;97;20
right triangle
CAA
CAA;a;449;10;208;112
unit circle
BCN
function - definition
BER
BER;a;175;22;60;18
polynomial - definition
BES
BES;a;16;6;171;19
basic polynomial shapes
BES
BES;a;30;217;185;19
vertical line test
BER
BER;a;517;37;116;18
relation - definition
BER
BER;a;17;5;56;19
polynomial end behaviour
BAO
BAO;a;3;129;101;19;b;270;129;106;19
convert absolute value to piecewise function
BAC
BAC;a;22;5;373;19
piecewise functions
BAI
BAI;a;37;6;123;19
domain and range of a function
BAE
BAE;a;30;5;55;17;b;30;26;44;17
image of a point after transformation
BAG
BAG;a;3;4;249;19
BAG;b;461;30;173;46
inverse of a function
BAH
BAH;a;29;5;137;19
IRoC = Instantaneous Rate of Change
CAB
CAB;a;4;6;35;17
tangent to a curve
CAC
CAC;a;17;6;119;18
draw/graph the inverse of a function
BAH
BAH;a;23;241;108;18
find the equation of an inverse
BAH
BAH;a;139;314;198;18
solving linear inequalities
BAJ
BAH;a;4;8;175;19
solving double inequalities
BAJ
BAH;a;5;268;179;19
leading coefficient formula (using finite differences)
BAM
BAM;a;5;255;182;19
real number - definition
CAD
CAD;a;68;5;92;19
rational number - definition
CAD
CAD;a;5;46;117;19
irrational number - definition
CAD
CAD;a;5;220;123;19
convert decimal number to a rational number
CAD
CAD;a;5;332;416;19
review of transformation basics
BBW
BBW;a;4;5;217;19
complex numbers - definition
CAE
CAE;a;4;6;122;17
why do we need complex numbers
CAE
CAE;a;4;526;238;19
triple order zero/root
BAQ
BAQ;a;394;626;105;19
fundamental theorem of algebra
BAQ
BAQ;a;127;784;218;19
1;625;tba;lv002;video
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
even and odd Functions - examples
frameborder="0" scrolling="no" width="853" height="520" src="https://www.khanacademy.org/embed_video?v=8VgmBe3ulb8" allowfullscreen webkitallowfullscreen mozallowfullscreen
BAB
even/odd nature of combination functions
width="960" height="720" src="//www.youtube.com/embed/uQr6-P5AqkE" frameborder="0" allowfullscreen
The writing in this video is sometimes a bit hard to read but the content is perfect for explaining how to
determine if a combination of even and odd functions is even, odd or not even or odd.
BEE
function - definition showing different mapping models
width="1280" height="720" src="//www.youtube.com/embed/gTqwGuwglwo" frameborder="0" allowfullscreen
BER
angular and linear velocity - example
width="853" height="480" src="//www.youtube.com/embed/bfWkgA5GSE0" frameborder="0" allowfullscreen
BCA
functions - definition and the vertical line test
width="960" height="720" src="//www.youtube.com/embed/OxZ0JL4Bjzk" frameborder="0" allowfullscreen
BER
functions - definition with examples
width="853" height="480" src="//www.youtube.com/embed/UAMf8586G2o" frameborder="0" allowfullscreen
BER
find the inverse of a function - example 1
width="1280" height="720" src="//www.youtube.com/embed/5MigilleeY4" frameborder="0" allowfullscreen
BAH
Warning: If you click on the link for Example 2 that appears in the upper left of this video you will exit High School Math Review
Click here for Example 2 Click here for Example 3
find the inverse of a function - example 2
width="1280" height="720" src="//www.youtube.com/embed/nwNMFaJFFCY" frameborder="0" allowfullscreen
BAH
This is Example 2 of a set of three examples of finding the inverse of a function
Click here for Example 1 Click here for Example 3
find the inverse of a function - example 3
width="1280" height="720" src="//www.youtube.com/embed/8RLvI5Ybz6I" frameborder="0" allowfullscreen
BAH
This is Example 3 of a set of three examples of finding the inverse of a function
Click here for Example 1 Click here for Example 2
piecewise functions - draw graph given equation
width="1280" height="720" src="//www.youtube.com/embed/uu3sjDKvAbw" frameborder="0" allowfullscreen
BAI
piecewise functions - write equation given graph
width="1280" height="720" src="//www.youtube.com/embed/Agc7bhu4oNk" frameborder="0" allowfullscreen
BAI
Writing the equation given the graph starts at 2:12 in the video
vertical line test
width="1280" height="720" src="//www.youtube.com/embed/gO5WN9g1fJo" frameborder="0" allowfullscreen
BER
http://youtu.be/gO5WN9g1fJo
Mathispower4u
convert absolute value function to a piecewise function
width="960" height="720" src="//www.youtube.com/embed/71SfBO-B4dE" frameborder="0" allowfullscreen
BAC
http://youtu.be/71SfBO-B4dE
Daniel Kopsas
introduction to domain and range
width="960" height="720" src="//www.youtube.com/embed/jGxW8qsR_u8" frameborder="0" allowfullscreen
BAE
http://youtu.be/jGxW8qsR_u8
Mathispower4u
increasing/decreasing and local maximums/minimums
width="960" height="720" src="//www.youtube.com/embed/aJuJOB6NTuc" frameborder="0" allowfullscreen
BEO
http://youtu.be/aJuJOB6NTuc
patrickJMT
solving linear inequalities
width="1280" height="720" src="//www.youtube.com/embed/SXrxEmmfp7A" frameborder="0" allowfullscreen
BAJ
x
http://youtu.be/SXrxEmmfp7A
Mathispower4u
solving double linear inequalities
width="1280" height="720" src="//www.youtube.com/embed/lsj-iMM2eXI" frameborder="0" allowfullscreen
BAJ
http://youtu.be/lsj-iMM2eXI
Anil Kumar
use finite differences to find polynomial equation from data points
width="1280" height="720" src="//www.youtube.com/embed/L7sgclzptP8" frameborder="0" allowfullscreen
BAM;BEQ
x
http://youtu.be/L7sgclzptP8
L Wun
end behaviour of a polynomial
width="960" height="720" src="//www.youtube.com/embed/kLLO4xKSlpE" frameborder="0" allowfullscreen
BAO
x
http://youtu.be/kLLO4xKSlpE
Daniel Kopsas
transformation basics using the square root parent function
width="1280" height="720" src="//www.youtube.com/embed/qv8nnGYESmc" frameborder="0" allowfullscreen
BBW
x
http://youtu.be/qv8nnGYESmc
the AllAroundMathGuy
introduction to complex numbers - part 1
width="560" height="315" src="//www.youtube.com/embed/2LgMw_LgTe4" frameborder="0" allowfullscreen
CAE
WARNING: Clicking the link that appears on this video starting at 13:30 will exit High School Math Review.
Click here to view Part 2
http://youtu.be/2LgMw_LgTe4
ProfRobBob
introduction to complex numbers - part 2
width="560" height="315" src="//www.youtube.com/embed/eliOsy3LzAs" frameborder="0" allowfullscreen
CAE
This is part 2 of a two part video.
Click here to view Part 1
http://youtu.be/eliOsy3LzAs
ProfRobBob
https://www.desmos.com/calculator/ufdu4dgfct