- 0 lessons
- 0 quizzes
- 10 week duration
Here you'll be introduced to the bare basics of mathematics. Topics include commonly used words and phrases, symbols, and how to follow the order of operations.
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.
Trigonometry with Right Triangles
Here we focus on right angle triangles within quadrant I of an x-y plane. None of the angles we evaluate here are greater than 90°. A unit on trigonometry with oblique triangles is covered later.
Trigonometry with Oblique Triangles
This unit is a continuation of trigonometry with right triangles except we'll extend our understanding to deal with angles *greater* than 90°. Resolving and combining vectors will be covered at the end of this unit.
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
Introduction to Statistics
Factor a Perfect Square Trinomial
In this unit’s final lesson, we’ll learn how to quickly factor general form quadratics that are considered “perfect square trinomials” (PST). In a PST, the first and last term of these trinomials are always perfect squares. If you don’t recognize the pattern of a PST, you could still factor the quadratic normally by trial-and-error or by decomposition. Therefore, remembering this technique isn’t technically required but if you do recognize the pattern, consider it a shortcut.
Examples of a perfect square trinomials are:
- y = x² + 6x + 9
- Here, √x² = x and √9 = 3
- This factors into (x + 3)²
- y = 4x² +28x + 49
- Here, √4x² = 2x and √49 = 7
- This factors into (2x + 7)²
Two more examples of factoring perfect square trinomials are shown in the video below.
You can factor a perfect square trinomial as:
- a² + 2ab + b² = (a + b)²
- a² – 2ab + b² = (a – b)²