- 0 lessons
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- 10 week duration
An introduction to numerical computation. Emphasis is placed on scientific and engineering notation, the rule of significant figures, and converting between SI and Imperial units.
Fractions, Percentage, Ratios and Proportion
Emphasis here is placed on understanding fractions, percent, and using ratios to compare quantities and set up proportions to solve problems.
Introduction to Algebra
Functions and Graphs
This unit focuses on analyzing and understand the characteristics of various shapes, both 2D and 3D.
- Identify, measure, and calculate different types of straight lines and angles
- Calculate the interior angles of polygons
- Solve problems involving a variety of different types of triangles
- Calculate the area of a variety of different types of quadrilaterals
- Solve problems involving circles
- Calculate the areas and volumes of different solids
Factor Quadratics by Trial-and-Error
For the first time in this course, you’ll learn how to convert a quadratic that’s in its general form to a quadratic in factored form.
General form: y = ax² + bx + c → Factored form: y = a(x – r)(x – s) where r and s represent the x coordinates of the roots.
The first technique you can try is trial-and-error.
Take, for example, the quadratic equation:
x² – x – 6 = 0
First, identify the c constant and b coefficients. The c constant is -6, the b coefficient it -1. You have to do this all the time.
Next, you need to find two factors of -6 that multiply to it, and those same two factors add to -1.
The only possibility that words is -3 and +2.
-3 × (+2) = -6
-3 + 2 = -1
You then rewrite your equation as two factors: y = (x – 6)(x – 1).
Pointers to keep in mind:
- Always begin the process of factoring a quadratic by common factoring if possible. In the example shown above, nothing could be common factored.
- This technique can only be tried if the a coefficient is 1. Otherwise, another technique known as factoring by decomposition is used (next lesson).
- Many quadratic expressions, such as x² + 3x + 5, cannot be factored over the integers. No two integers have a product of 5 and a sum of 3. In that case, we’ll use the quadratic formula (more to come on this later on).
Now let’s see this in action.