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Master the Law of Sines: Solve Triangle Problems with Ease

Derive proofs that involve the properties of angles and triangles

Pairs of lines and angles

Parallel lines and transversals

Parallel line proofs

Perpendicular line proofs

Solve problems that involve the properties of angles and triangles

Classifying triangles

Isosceles and equilateral triangles

Solve problems that involve the cosine law and the sine law including the ambiguous case

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Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

Analyze and prove conjectures using inductive and deductive reasoning to solve problems

Set notation

Understanding How to Use Set Notation

Set builder notation

Intersection and union of 2 sets

Intersection and Union of 2 Sets

Intersection and union of 3 sets

Intersection and Union of 3 Sets

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

Analyze puzzles and games that involve spatial reasoning using problem-solving strategies

Line symmetry

Rotational symmetry and transformations

Surface area of 3-dimensional shapes

Arithmetic mean vs. Geometric mean

Solve problems that involve the application of rates

Applications of rational equations

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

Metric systems

Add and Subtract Mixed Units

Metric Length Conversion

Add or Subtract Different Metric Units Convert to CM

Add or Subtract Different Metric Units Convert to M

Add or Subtract Different Metric Units Convert to MM

Imperial systems

Imperial Length Conversion

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

Metric Area Conversion M/CM to Inch

Solve problems that involve scale diagrams using proportional reasoning

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Simplifying rational expressions and restrictions

Adding and subtracting rational expressions

Adding and Subtracting Rational Expressions

Multiplying rational expressions

Multiplying Rational Expressions

Multiplying Rational Expressions in Factored Form

Dividing rational expressions

Dividing Rational Expressions

Dividing Rational Expressions in Factored Form

Simplifying complex fractions

Demonstrate understanding of relationships among scale factors areas surface areas and volumes

Quadratic function in vertex form: y = a(x-p)^2 + q

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

Model and solve problems that involve systems of linear inequalities in two variables

Graphing linear inequalities in two variables

Graphing quadratic inequalities in two variables

Graphing systems of quadratic inequalities

Graphing systems of linear inequalities

Applications of inequalities

Demonstrate understanding of characteristics of quadratic functions

Introduction to quadratic functions

Characteristics of quadratic functions

Transformations of quadratic functions

Quadratic function in general form: y = ax^2 + bx + c

Converting from general to vertex form by completing the square

Shortcut: Vertex formula

Converting general form into vertex form by applying the vertex formula

Vertex Formula Application

Graphing quadratic functions: General form VS. Vertex form

Finding the quadratic functions for given parabolas

Applications of quadratic functions

Completing the square

Completing the Square

Research and give a presentation on a historical event or area of interest that involves mathematics

What is linear programming?

Finding Optimal Values Given Constraints In Slope-Intercept Form

Finding Optimal Values Given Constraints In Standard Form

Linear programming word problems

Arithmetic sequences

Arithmetic series

Arithmetic series formula

Geometric sequences

Geometric series

Geometric Series

Infinite geometric series

Demonstrate understanding of normal distribution including standard deviation and z-scores

Introduction to normal distribution

The Normal Distribution and the 68-95-99.7 Rule

Using "invNorm" to Solve Normal Distribution Problems

Normal distribution and continuous random variable

Z-scores and random continuous variables

Interpret statistical data using confidence intervals confidence levels and margin of error

Point estimates

Confidence levels and critical values

Margin of error

Margin of Error

Making a confidence interval

Grade 11 Applied Mathematics (30S)

Develop spatial sense

Develop logical reasoning

Develop spatial sense and proportional reasoning

Develop algebraic and graphical reasoning through the study of relations

Develop an appreciation of the role of mathematics in society

Develop statistical reasoning

math

Ex.1

Ex.2

Ex.3

intro

In this section, we will learn about the Law of Sines, also known as the Sines Rule. The Law of Sines is a formula that models the relationship between the sides and the angles of any triangle, be it a right-angled triangle, an obtuse triangle, or an acute triangle. In order to use the Law of Sines, we need to satisfy the "one pair, one additional information" condition (i.e. Angle-Angle-Side abbreviated as AAS, and Angle-Side-Angle abbreviated as ASA). We will also explore the concept of the Ambiguous Case of the Law of Sines.