 42 lessons
 0 quizzes
 10 week duration

Measurements
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

Factoring

Solving Equations

Functions and Graphs

Geometry
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
Solving Second Degree Equations by the Quadratics Formula
A seconddegree equation (also known as a quadratic equation) is one whose highestdegree term is of second degree. Generally, the highest degree in any equation dictates the maximum possible number of solutions. Thus a quadratic equation, being of degree 2, has up to two solutions or roots. This is the same reason why all the firstdegree equations we solved in the previous lesson always had a single solution.
Solving quadratic equations is definitely an art form. There are many things you need to look out for before devising a plan to solve. The first thing you need to determine is whether the quadratic is pure, incomplete, or complete. Examples of each type is shown below:
 x² = 4 [pure]
 9x² – 5x = 0 [incomplete]
 4x² – 5x + 2 = 0 [complete]
Pure quadratics are the easiest to solve. They contain an x² term and a constant only; no firstdegree term exists. To solve pure quadratics, you isolate for x similar to the way you solve firstdegree equations. Incomplete quadratics possess a 2^{nd} and 1^{st} degree term – solving these require a special technique called factoring that’ll be introduced in a later unit. Our main focus in this lesson is to solve complete quadratics, which contain a 1^{st}, 2^{nd}, and constant term, using the quadratic formula and electronically using a calculator. All complete quadratics follow the general form: y = ax² + bx + c. Take example 3, for instance, 4 presents a, –5 presents b, and +2 represents c.
The formula looks like this:
… and can be used to solve basically any quadratic equation, including pure and incomplete quadratics. Notice that the formula contains the same letters found in the general form, y = ax² + bx + c. So to use it correctly, you have to identify the a, b, and c coefficients in a quadratic trinomial and substitute them into the formula. Let’s see this in action:
A slightly more complicated question is provided underneath. Notice that quadratics with noninteger coefficients are ideal for the quadratic formula.
Unlike firstdegree equations which form a straight line when graphed, quadratics form a parabola (∪ or ∩). Therefore, depending on the equation, not all parabolas pass through the xaxis (left). If that’s the case, the quadratic formula will give you an error when calculating the squareroot part. In other words, sometimes given the way a quadratic is positioned on an xy plane, it will not yield any solutions. We consider these roots as nonreal roots. For example, try using the quadratic formula for the equation:
x² + 2x + 5 = 0
You’ll notice that the radicand (the number under a radical symbol) is 16. Any time your radicand is less than zero, your parabola doesn’t cross the xaxis (shown in figure).
Guidelines to determine the number of roots
The discriminant is the part of the quadratic formula underneath the square root symbol: b² − 4ac. The discriminant tells us whether there are two solutions, one solution, or no solutions.
If b²−4ac = 0 (1 real root)
If b²−4ac > 0 (2 real root)
If b²−4ac < 0 (0 real root)
More on this is explained in the video below:
Finally, a major part of this section is your ability to use technology (your calculator) to solve quadratics rather than waste time doing it manually using the formula. The video below explains how to use your Casio fx991ES Plus to find the roots of any quadratic.