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Master Arc Length: Calculus Concepts & Real-World Applications

Demonstrate an understanding of the meaning and uses of accuracy and precision

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Upper and lower bound

Upper and Lower Bound

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

Use a measuring tape to measure tactile items in both imperial and SI units

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

Identify the difference between length, area, and volume

Surface area of 3-dimensional shapes

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

Difference quotient: applications of functions

Demonstrate an understanding of the meaning and uses of significant figures

Place value

Comparing and ordering numbers

Comparing Integers

Comparing Numbers

Comparing Fractions

Rounding numbers

Rounding Decimals

Rounding Integers — Up to 9999

Identify, use, and convert among and between SI units and imperial units

Find the exact value of trigonometric ratios

Demonstrate an understanding of and be able to solve problems using the Pythagorean theorem

Pythagorean theorem

Pythagorean Theorem

Using the pythagorean relationship

Applications of pythagorean theorem

Demonstrate mathematical knowledge required for various career choices

Finance: Compound interest

Finance: Compound Interest

Continuous growth and decay

Finance: Future value and present value

Demonstrate entry-level competence in mathematics for specific career choice

Fundamental counting principle

Fundamental Counting Principle Involving Restrictions

Center of a data set: mean, median, mode

Probability distribution - histogram, mean, variance & standard deviation

Sketch and construct a model to show mathematics involved in a career interest

Applications of polynomial functions

Ferris wheel trig problems

Calculate dimensions of actual objects using blueprints with various scales

Combining transformations of functions

Enlargements and reductions with scale factors

Scale diagrams

Sketch and build representations of three-dimensional objects

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

Illustrate and express ratios, fractions, decimals, and percentages in alternative forms

Direct variation

Identifying direct variations

Inverse variation

Ratios

Ratios - Find The Missing Value LHS

Ratios - Find The Missing Value RHS

Equivalent Ratios

Rates

Find the Biggest Rate 

Find the Unit Price 

Unit Rate Fill in Box

Find the Quickest Rate 

Unit Rate

Proportions

Proportions — Missing Denominator

Proportions — Missing Numerator

Proportions - Find the Missing Denominator LHS

Proportions - Find the Missing Denominator RHS

Proportions - Find the Missing Numerator LHS

Proportions - Find the Missing Numerator RHS

Representing percents

Representing Percents

Representing Percents — Word Problem

Representing Percents Two Graphs – Word Problem

Percents, fractions, and decimals

Conversion — Decimal to Fraction

Conversion — Decimal to Percent

Conversion — Fraction to Decimal

Conversion — Fraction to Percent

Conversion — Percent to Decimal

Conversion — Percent to Fraction

Percents – Word Problem

Convert a Decimal to a Fraction

Convert a Decimal to a Percent

Convert a Fraction to a Decimal

Convert a Fraction to a Percent

Convert a Percent  to a Decimal

Convert a Percent to a Fraction

Percents Fractions And Decimals – Word Problem

Percent of a number

Percent of a Number

percent of a number – Word Problem

Percent of a Number  Fraction Percent

Percent of a Number Integer Percent 

Percent of a number number With Decimal Percent 

Percent of a Number  Three Digits Number Percent

Rational vs. Irrational numbers

Converting repeating decimals to fractions

Find and calculate rates in practical applications such as pulse rate

Rate of change

Arc length

Estimate and calculate deductions from a pay stub as percentages of gross earnings

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

Adding and multiplying percents

Add and Multiply Percents — Word Problem

Add and Multiply Percents – Word Problem

Sketch enlargements and reductions of objects using various scales

Transformations of functions: Horizontal stretches

Transformations of functions: Vertical stretches

Use the slope formula to solve trigonometric problems commonly found in industry

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>

Mathematics Essentials 12

Measurement

Mathematics in the Workplace Investigation

Ratio, Rate, and Proportion

Major Project: Math Preparation for the Workplace

math

Intro

Instead of finding the area under the curve, we are going to be the length of the curve between a and b. Now we know we can find the length of a line using the distance formula, but what about the length of the curve? In the intro video, we will learn that we can find the length of the curve by manipulating the distance formula into an integral. After, we will be applying the formula that we've found by finding the arc length of functions in terms of x. We will then look at some advanced questions where we will find the arc length of functions in terms of y, as well as finding the arc length function with an initial point.

How to find arc length in calculus