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Comparing Theoretical and Experimental Probability: Key Insights

Analyze objects shapes and processes to solve cost and design problems

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Surface area of 3-dimensional shapes

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Conics - Parabola

Conics - Circle

Conics - Ellipse

Conics - Hyperbola

Even and odd functions

Difference quotient: applications of functions

Solve problems that involve compound interest in financial decision making

Simple interest

Simple Interest — Word Problem

Basic Concepts of Simple Interest – Word Problem

Borrowing Money for More Than One Year  – Word Problem

Investigate the Advantages of Borrowing Money  – Word Problem

Exponential growth and decay by a factor

Exponential growth and decay by percentage

Finance: Compound interest

Finance: Compound Interest

Logarithmic scale: Richter scale (earthquake)

Logarithmic scale: pH scale

Logarithmic scale: dB scale

Finance: Future value and present value

Analyze costs and benefits of renting, leasing and buying

Taxes, discounts, tips and more

Discounts — Word Problem

Taxes — Word Problem

Percentage - Applying a Discount Price– Word Problem

Percentage - Applying a Discount Percent – Word Problem

Percentage - Applying a Tax Total – Word Problem

Percentage - Applying a tax Percent – Word Problem

Geometric series

Geometric Series

Infinite geometric series

Analyze an investment portfolio in terms of interest rate, rate of return, and total return

Applications of rational equations

Continuous growth and decay

Applications of inequalities

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

Direct variation

Identifying direct variations

Evaluating piecewise functions

Graphing piecewise linear functions

Graphing piecewise non-linear functions

Solve problems that involve the application of set theory

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

Solve problems that involve conditional statements

Solving rational inequalities

Solving Rational Inequalities With Two Fractions

Graphing linear inequalities in two variables

Inequalities of combined functions

Inequalities of Combined Functions

Graphing systems of linear inequalities

Reading and drawing Venn diagrams

Probability with Venn diagrams

Interpret and assess the validity of odds and probability statements

Inverse variation

Joint and combined variation

Introduction to probability

Identify the Probability — Word Problem

Compound Probability

Reading Probability Models

Probability

Organizing outcomes

Calculating Outcomes

Comparing experimental and theoretical probability

comparing experimental and theoretical probability

Solve problems that involve the probability of mutually exclusive and non-mutually exclusive events

Arithmetic series

Arithmetic series formula

Addition rule for 

Addition Rule for "OR"

Addition rule for "OR"

Multiplication rule for 

Multiplication rule for "AND"

Multiplication Rule for "AND"

Solve problems that involve the probability of independent and dependent events

Geometric sequences

Permutation vs. Combination

Probability of independent events

Conditional probability

Solve problems that involve the fundamental counting principle

Fundamental counting principle

Fundamental Counting Principle Involving Restrictions

Solve problems that involve permutations

Factorial notation

Path counting problems

Permutations

Solve problems that involve combinations

Combinations

Problems involving both permutations and combinations

Pascal's triangle

Pascal's Triangle

Pascal"s Triangle

Pascal"s triangle

Binomial theorem

Represent data using polynomial functions of degree ≤ 3 to solve problems

Descartes' rule of signs

Descartes' Rule of Signs

Descartes" rule of signs

Polynomial functions

Recognizing a Polynomial Function

Characteristics of polynomial graphs

Determining the equation of a polynomial function

Applications of polynomial functions

Solving polynomial inequalities

Fundamental theorem of algebra

Represent data using exponential and logarithmic functions to solve problems

Solving logarithmic equations

Graphing exponential functions

Graphing transformations of exponential functions

Finding an exponential function given its graph

What is a logarithm?

Logarithms and Exponential Growth

Understanding Logarithms through Exponential Growth

Understanding Logarithms

Quotient rule of logarithms

Combining product rule and quotient rule in logarithms

Evaluating logarithms using logarithm rules

Graphing logarithmic functions

Finding a logarithmic function given its graph

Represent data using sinusoidal functions to solve problems

Sine graph: y = sin x

Cosine graph: y = cos x

Tangent graph: y = tan x

Cotangent graph: y = cot x

Secant graph: y = sec x

Cosecant graph: y = csc x

Graphing transformations of trigonometric functions

Determining trigonometric functions given their graphs

Ferris wheel trig problems

Tides and water depth trig problems

Spring (simple harmonic motion) trig problems

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

Reading and drawing bar graphs

read and draw bar graphs

Reading Bar Graphs

Reading and drawing histograms

Reading and drawing line graphs

Reading Line Graphs

Box-and-whisker plots and scatter plots

Grade 12 Applied Mathematics (40S)

Develop critical thinking skills related to measurement design

Develop number sense in financial applications

Develop logical reasoning

Develop critical thinking skills related to uncertainty

Develop algebraic and graphical reasoning through the study of relations

Develop an appreciation of the role of mathematics in society

math

Ex.1

Ex.2

Intro

In this section, we compare experimental probability and theoretical probability. Experimental probability is the probability of an event occurring based on experimental results. In contrast, theoretical probability is the expected probability of an event occurring. In previous sections, we practiced calculating theoretical probability. In this section, we examine a given chart to determine whether it provides information about experimental or theoretical probability. Also, we practice interpreting tables of experimental results and using these tables to calculate the experimental and theoretical probabilities of outcomes occurring.  

Comparing theoretical and experimental probabilities

Theoretical vs. experimental probability

Introduction to probability 