A coordinate plane - Slope of a line - IntoMath
In this lesson you will learn about a coordinate plane (Cartesian Plane). You will learn how to plot a point and record its coordinates – an ordered pair (x, y).
You will discover how to determine the relationship between two quantities. One of those quantities is dependent on another like distance and time or like the circumference of a circle and its diameter.
You will also learn how to graph the relationship.
You will learn about the rate of change (slope of a line) and how to calculate it using the coordinates of the two points. When the relationship is linear, the rate of change is constant.
You will see how the slope of a line (linear relationship) depends on the change in the x and y coordinates.
Additional practice will help you master the skills.
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Square root - Converting between decimal, fraction, percent - IntoMath
In this lesson we are discussing two topics: square root of a number and percent.
A square root of a number is a number that has been squared to get the number under the square root.
For example, the √4 is 2, because 2 x 2 = 4.
Watch the video lesson to see the examples and learn why we cannot take a square root of a negative number.
We have already discussed the concept of percent in our previous lessons. However, since it is a very commonly used concept, we will go over it again in more detail.
In this lesson you will learn the general formula for finding the percent of a number. You will see how to use proportions in order to calculate percent.
Together, we will go over some real life problems with percentages.
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Solving linear equations - Pythagorean theorem - IntoMath
In this lesson you will learn how to solve one step and multi step linear equations.
For example, x – 3 = 10 or 2h + 1 = – 9.
The lesson demonstrates how to solve linear equations with brackets.
For example, 2(x – 1) = 16.
Such equations are solved using inverse operations and reverse BEDMAS. The first step is always expanding the expression with brackets using the distributive multiplication property.
You will also discover the Pythagorean Theorem.
You will learn when and why to use it, how to set it up and solve the equation.
The challenge of using a Pythagorean Theorem is that it involves squares (multiplying the number by itself) and it is important to follow the BEDMAS and equation solving algorithm carefully in order to avoid mistakes. For example, the quantities should always be squared first, then added.
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Circle - Volume of Cylinder - Scientific Notation - IntoMath
In this lesson you will learn about scientific notation and its significance when working with very large and very small numbers.
Scientific notation is widely used in Physics, Astronomy and Chemistry. For example, it could be used to express the volume of water in a large lake. Instead of writing all the zeros we multiply the number by a certain power of 10.
You will also learn how to calculate area and circumference of a circle.
You will discover the importance of the Pi number. Here are the first 100,000 digits of Pi.
The lesson teaches you how to determine the volume of a cylinder (a 3D shape with circular bases and a rectangular lateral part). You will also learn what calculating the volume means and what units should be used.
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Proportions - IntoMath
In this lesson you will learn about proportions, their importance, how to set them up and how to solve them.
A proportion is an equivalent relationship of quantities. It is a name we give to a statement that two ratios are equal. It can be represented in two ways: two equal fractions or as a : b = c : d. We can determine whether a proportion is true or false. We can also find an unknown in a proportion or solve real life problems using proportions.
We often use proportions to convert to or from percentages.
For example, what is 10% of 45?
We can set up a proportion: 45 corresponds to 100%, then what corresponds to 10%?
10 : 100 = n : 45
n = (45 x 10)/100
n = 4.5
There are many examples in math in which the exact answer is required.
For example, if a doctor prescribed to a patient a drug requiring a specific measure, the doctor would have to prescribe the exact amount; if the doctor simply estimated the amount, a patient could have severe side effects or it could even lead to a fatal outcome. Thus, understanding proportions could save lives!
Proportions can be solved using visual models. However, it is important to understand and learn how to quickly set them up and solve algebraically.
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Multiplication properties - Simplifying algebraic expressions - IntoMath
In this lesson you will learn about multiplication properties and their significance.
For example, that a × b = b × a or that a(b + c) = ab + bc.
You will learn how distributive property is used to simplify algebraic expressions. This property is also often used to solve equations. For example, when solving an equation 2(3x – 1) = 10 the first step would be to expand the expression with brackets. It would become 6x – 2 = 10. Then the equation could be solved using inverse operations and reverse BEDMAS.
The lesson covers simplifying algebraic expressions by collecting like terms.
Algebraic expressions are symbols or combinations of symbols used in algebra, containing one or more numbers, variables, and arithmetic operations.
Like terms are terms that have the same variables with the same exponents or no variables – constants (4n and 5n, 6 and 89).
Additional practice will help you master the skills.
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Mean - Pie Graph - Bar Graph - IntoMath
In this lesson you will learn what a mean is.
You will discover how the mean is related to the average.
For example, given a set of numbers: 2, 5, 7, 7, 8 the mean is calculated by first finding the sum of all numbers and dividing the sum by how many numbers there are in a set: (2 + 5 + 7 + 7 + 8)/ 5.
The mean is often used in research, academics and in sports.
You often see these graphs used by media to show the relationships between various quantities ( for example, during the elections, bar or pie graphs are used to show the ratings of the candidates.
You will learn how to use bar graphs when representing the relationships between quantities that are not dependent on each other.
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