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Master Parallel and Perpendicular Lines in Linear Functions

Grade 12 Math: Master Advanced Concepts & Skills

Solve problems that involve measures of central tendency, including mean, median, mode, weighted mean, trimmed mean

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Complex numbers and complex planes

Center of a data set: mean, median, mode

Spread of a data set - standard deviation & variance

Measures of relative standing - z-score, quartiles, percentiles

Critique the viability of small business options by considering expenses, sales, profit or loss

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

Applications of quadratic functions

Demonstrate an understanding of linear relations by recognizing patterns and trends, graphing, creating tables of values, writing equations, interpolating and extrapolating, solving problems

Direct variation

Identifying direct variations

Inverse variation

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Distance formula: <katex>d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}</katex>

Distance formula

Midpoint formula: \(M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)\)

Midpoint formula

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

Slope equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Slope equation: <katex>m = \frac{y_2-y_1}{x_2- x_1}</katex>

Slope intercept form:  y = mx + b

Slope intercept form: y = mx + b

General form:  Ax  + By  + C = 0

General form: Ax + By + C = 0

Point-slope form: y - y_1 = m(x - x_1)

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Word problems of graphing linear functions

Function notation

Rate of change

Parallel and perpendicular lines in linear functions

Applications of linear relations

Analyze and interpret problems that involve probability

Fundamental counting principle

Fundamental Counting Principle Involving Restrictions

Permutations

Combinations

Problems involving both permutations and combinations

Ferris wheel trig problems

Addition rule for "OR"

Addition Rule for "OR"

Multiplication rule for "AND"

Multiplication Rule for "AND"

Conditional probability

Probability involving permutations and combinations

Demonstrate an understanding of the limitations of measuring instruments, including precision, accuracy, uncertainty, tolerance

Upper and lower bound

Upper and Lower Bound

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

Difference quotient: applications of functions

Solve problems by using the sine law and cosine law, excluding the ambiguous case

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Applications of the sine law and cosine law

Solve problems that involve triangles, quadrilaterals, regular polygons

Classifying triangles

Isosceles and equilateral triangles

Demonstrate an understanding of transformations on a 2-D shape or a 3-D object, including translations, rotations, reflections, dilations

Line symmetry

Rotational symmetry and transformations

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Transformations of functions: Horizontal translations

Transformations of functions: Vertical translations

Transformations of functions: Horizontal stretches

Transformations of functions: Vertical stretches

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

Organizing outcomes

Calculating Outcomes

Solve problems that involve the acquisition of a vehicle by buying, leasing, leasing to buy

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

Finance: Compound interest

Finance: Compound Interest

Finance: Future value and present value

We&apos;ve got you covered with our complete help for Grade 12 math, whether it&apos;s Ontario curriculum, <a href="https://www.alberta.ca/writing-diploma-exams.aspx">Diploma exam</a> (Alberta), <a href="http://www.edu.gov.mb.ca/k12/assess/tests/index.html">Provincial test</a> (Manitoba) or <a href="https://www.saskatchewan.ca/residents/education-and-learning/departmental-exams">Departmental exam</a> (Saskatchewan).

Aligned with your class or textbook, you will get grade 12 math help on topics like Trigonometric identities, Vectors, Permutations and Combinations, Matrices, Polynomial functions and so many more. Learn the concepts with our video tutorials that show you step-by-step solutions to even the hardest grade 12 math questions. Then, strengthen your understanding with tons of grade 12 math practice. 

All our lessons are taught by experienced Grade 12 math teachers. Let&apos;s finish your homework in no time, and ACE that final.

Mathematics 30-3

math

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Ex. 1

Ex. 2

Ex. 3

Ex. 4

Ex. 5

Intro

<a href='[[glossary.html|{"keyword":"Parallel Lines"}]]'>Parallel lines</a> are lines with identical slope. In other words, these lines will never cross each other. Perpendicular lines will always pass through each other and form right angles at the interception. In this lesson, we will learn how to use information such as, points in lines and their slopes, to determine whether the lines are parallel, perpendicular or neither.

Parallel or perpendicular lines - Linear function

Point-slope form: \(y - y_1 = m (x - x_1)\)