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How to find the rate of change in math

Grade 11 Math: Master Advanced Concepts & Skills

Solve problems involving SI and imperial units in surface area measurements and verify the solutions

Surface area of 3-dimensional shapes

Enlargements and reductions with scale factors

Scale diagrams

Solve problems requiring manipulation and application of formulas related to volume, capacity, surface area, slope, rate of change, simple interest, and finance charges

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Rate of change

Solving literal equations

Demonstrate understanding of slope as rise over run, rate of change, and by solving problems

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>

Parallel and perpendicular lines in linear functions

Applications of linear relations

Solve problems involving SI and imperial units in volume and capacity measurements

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

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

Solve problems involving two and three right triangles

Angle of elevation and depression

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

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

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

Solve problems involving scale

Bearings and direction word problems

Bearings and Direction Word Problems

Similar triangles

Similar polygons

Analyze puzzles and games involving numerical reasoning using problem-solving strategies

Addition rule for "OR"

Addition Rule for "OR"

Multiplication rule for "AND"

Multiplication Rule for "AND"

Conditional probability

Probability involving permutations and combinations

Solve problems involving personal budgets

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

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

Demonstrate understanding of compound interest

Finance: Compound interest

Finance: Compound Interest

Continuous growth and decay

Finance: Future value and present value

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Mathematics 20-3

math

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https://dmn92m25mtw4z.cloudfront.net/img/textbook/textbook-grade11math.png

Ex. 1

<p>- Hi. Welcome to this question right here. So sometimes in this chapter we've got a little bit of a word problems we need to figure out. So, try to use your common sense and logic, okay? So, we're here to draw a graph. So we're gonna start off by saying that there's a graph over here. Roughly, okay? Let's make it a little longer if you need it. Describe a fare charged by a taxi with an initial cost of<br />
$10.5 plus 2.5 per kilometer traveled. So, by looking at the question right here, it sounds like that there's money over here, which is dollar sign on the y-axis, and there should be a kilometer down here, okay? Which is the distance of travel. So let's go ahead and actually figure this out. You see, there's an initial cost. For example, you go into the taxi. Even though the taxi hasn't driven yet it's gonna cost you $10.50 to start off. So, right here, at the zero kilometer, they haven't even started yet, you're already paying them $10.50. That's how much you're paying. Let's not worry about the scale for now. Let's just use the number right there. So that is your initial spot right there on the graph. But every kilometer you traveled...so let's go ahead and put down 1 kilometer, and let's do down 2 right there, and put a 3 there. You're gonna be adding another 2.50 on top of that, okay? So if that's 10... Let's just go ahead and put a couple of dots right here. So 10.50, if I add 2.50 to that it would be $13, okay? And then if I add another 2.50, it will be 15.50 right there, okay. And if I add another 2.50 it will be $18 over here, okay? So those are the money I assign over there, okay? So what happened is for every kilometer you travel, starting from here actually, every kilometer you travel you had to pay in another 2.50. Another kilometer over, you pay in another 2.50 Another kilometer over, you pay in another 2.50 right there. So, guess what will happen? You're actually have a straight line coming up this way. And then it goes on infinity depending on how far you've driven. So, this is a graph that describes the fare charge to you if you take the taxi with an initial cost of 10.50 right here if you start off at zero kilometer, and for every kilometer the graph will go up by $2.50, okay? $2.50 sorry. Okay?<br />
Thanks for watching.</p>


Ex. 2

Ex. 3

Ex. 4

Rate of change is all around us. For example, we express the speed of a car as Kilometer per hour (km/hr), the wage in a fast food restaurant as dollar per hour, and taxi fare as dollar per meter or kilometer. Let's solve some word problems on rate of change.

Slope intercept form: y = mx + b

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