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Understanding natural logarithms

Grade 12 Math: Master Advanced Concepts & Skills

12CT.A1.1

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Graphing exponential functions

Graphing transformations of exponential functions

12CT.A1.2

Solving exponential equations with logarithms

12CT.A1.4

Exponential growth and decay by a factor

Exponential decay: Half-life

Exponential growth and decay by percentage

Finance: Compound interest

Finance: Compound Interest

Continuous growth and decay

12CT.A2.1

Product rule of exponents

Exponents: Product rule (a^x)(a^y) = a^(x+y)

Exponents: Division rule: a^x / a^y = a^(x-y)

Exponents: Power rule: (a^x)^y = a^(xy)

Exponents: Power rule

Quotient rule of exponents

Power of a product rule

Power of a quotient rule

Power of a power rule

Simplify the power

Negative exponent rule

Combining the exponent rules

12CT.A2.2

Solving exponential equations using exponent rules

12CT.A2.3

What is a logarithm?

Logarithms and Exponential Growth

Understanding Logarithms through Exponential Growth

Understanding Logarithms

Converting from logarithmic form to exponential form

Evaluating logarithms without a calculator

12CT.A2.4

Common logarithms

Natural log: ln

12CT.A2.5

Evaluating logarithms using change-of-base formula

Converting from exponential form to logarithmic form

Product rule of logarithms

12CT.A2.6

Logarithmic scale: Richter scale (earthquake)

Logarithmic scale: pH scale

Logarithmic scale: dB scale

12CT.B1.1

What is a polynomial?

Classifying Polynomials

Polynomial components

12CT.B1.2

Polynomial functions

Recognizing a Polynomial Function

12CT.B1.3

Characteristics of polynomial graphs

Determining the equation of a polynomial function

12CT.B1.4

Applications of polynomial functions

12CT.B1.5

Function notation

Function notation (advanced)

12CT.B1.6

Applications of polynomials

12CT.B1.7

Domain and range of a function

12CT.B2.1

Factoring difference of cubes

Factoring sum of cubes

Factor by taking out the greatest common factor

Factor by taking out GCF

Factor by grouping

Factoring difference of squares: \(x^2 - y^2\)

Factoring difference of squares: <katex>x^2 - y^2</katex>

Factoring difference of squares: x^2 - y^2

Factoring trinomials

Factoring Trinomials

12CT.B2.2

Factor theorem

Using the Factor Theorem to Test For Factors of a Polynomial

Multiplicities of polynomials

Imaginary zeros of polynomials

12CT.B2.3

Fundamental theorem of algebra

12CT.B3.1

Descartes' rule of signs

Descartes' Rule of Signs

Descartes" rule of signs

12CT.B3.2

Solving polynomial inequalities

12CT.B3.3

Applications of linear equations

Evaluating algebraic expressions

Evaluating Algebraic Expressions

12CT.B3.4

Multiplying monomial by monomial

Multiply a Monomial by a Monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

12CT.B3.5

Exponents: Rational exponents

Convert between radicals and rational exponents

12CT.B3.6

Solving literal equations

12CT.B3.7

Relationship between two variables

12CT.B3.8

Understand relations between x- and y-intercepts

12CT.C1.1

Find the exact value of trigonometric ratios

12CT.C1.2

ASTC rule in trigonometry (All Students Take Calculus)

ASTC rule in trigonometry

12CT.C1.3

Unit circle

12CT.C1.4

Use sine ratio to calculate angles and sides (Sin = o / h)

Use cosine ratio to calculate angles and sides (Cos = a / h)

Combination of SohCahToa questions

Use tangent ratio to calculate angles and sides (Tan = o / a)

12CT.C1.5

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

12CT.C2.1

Sine graph: y = sin x

Cosine graph: y = cos x

12CT.C2.3

Graphing transformations of trigonometric functions

12CT.C2.6

Determining trigonometric functions given their graphs

12CT.C3.1

Ferris wheel trig problems

Tides and water depth trig problems

Spring (simple harmonic motion) trig problems

12CT.D1.1

Introduction to vectors

12CT.D1.2

Magnitude of a vector

12CT.D1.3

Direction angle of a vector

12CT.D1.4

Scalar multiplication of vectors

12CT.D1.5

Equivalent vectors

Adding and subtracting vectors in component form

Operations on vectors in magnitude and direction form

12CT.D1.6

Word problems on vectors

Unit vector

12CT.D2.2

Conversions between metric and imperial systems

Metric to Imperial Conversions

Imperial to Metric Conversions

Conversions Between Metric and Imperial Systems Speed KM to MI

Conversions Between Metric and Imperial Systems Speed  MI to M

Metric-Imperial Length Conversion Inch To Cm

Metric-Imperial Length Conversion MM/CM/M/KM To FT

Metric-Imperial Length Conversion MM/CM/M/KM To MI

Conversions involving squares and cubic

Imperial to Metric Conversions — Squares and Cubes

Imperial Conversion — Squares and Cubes

Metric to Imperial Conversion — Squares and Cubes

Metric Area Conversion FT to CM

Metric Area Conversion Foot to Inch

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Grade 12 Mathematics for College Technology, College Preparation (MCT4C)

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