Unit 2 - Quadratics, Radicals and Rational Expressions
***
Unit 2 - Quadratics, Radicals and Rational Expressions ***
Lesson 2.1
In this lesson we review terminology surrounding polynomials as well as the mechanics around simplifying expressions involving exponents, multiplying fractions, and the expansion and collection of like terms. An essential skill heading into the review of quadratics from grade 10.
Blank Lesson
Lesson Video - Part 1
Lesson Video - Part 2
Homework Solutions
Lesson 2.2
In this lesson students build upon their exponential power laws from grade 9 to simplify radicals (specifically ones with an index of two - square roots). Students are shown, and encouraged to simplify without the use of a calculator by implementing skills they have acquired in the past like multiplying and simplifying fractions.
Blank Lesson
Lesson 2.2 Video
Homework Sheet (with answers)
Homework Solutions
Lesson 2.3
In this lesson students build on grade 10 skills around expansion and collection of like terms as well as their new knowledge around simplifying radicals. We learn that radicals with the same radicand can be treated as like terms and subsequently combined (added or subtracted together).
Formative 3
This formative targets students ability to simplify radical expressions as discussed in Lesson 2.2 and Lesson 2.3.
Blank Formative
Formative Video
Lesson 2.4
In this lesson we revisit the process known as completing the square and how we can use it to identify the vertex. We extend by solving for the roots of the quadratic, which will ultimately allow us to produce the graph. Students will encounter the applicability of radicals in this lesson when solving for the roots.
Blank Lesson
Lesson 2.4 Video - Part 1
Lesson 2.4 Video - Part 2
Lesson 2.4 Video - Part 3
Lesson 2.5
In this lesson we look at an alternative to the completing the square process in order to find the vertex of a quadratic. Partial Factoring allows us to identify the axis of symmetry, quickly and reliably. We are then able to find the vertex by evaluating the function at the axis of symmetry value.
Blank Lesson
Lesson 2.5 Video
Homework #1 a
Lesson 2.6
In this lesson students revisit a few concepts from grade 10 in order to solve for the Point(s) of Intersection between a quadratic and a line. We revisit the concept of the discriminant to determine, before solving, the number of intersections points we should expect. Students will be expected to apply their solving by factoring skills, as well as the quadratic equation in the event that the quadratic we arrive at does not factor.
Here are videos pertaining to the Discriminant and solving using the Quadratic Equation for review if needed.
Blank Lesson
Lesson 2.6 Video
Lesson 2.6 #4 Video
Formative 4
This formative encompasses content from Lesson 2.4 where we reviewed completing the square, and then solved for the roots directly.
Blank Formative
Formative Video
Formative 5
This formative looks at finding an equation of a quadratic in vertex form from standard using partial factoring. It also covers optimization of revenue and the intersection of a line and a quadratic.
Mid Unit
Test Review
This test will consist of all content from Lesson 2.1-2.6.
- Vocabulary, Expansion + Collecting Like Terms, Multiplying Fractions
- Simplifying Radicals (2.2-2.3)
- Completing the Square + Solving for Roots
- Partial Factoring and Producing the Graph of a Quadratic
- Linear/Quadratic Systems
Radicals Review Sheet - # 1, 2, 3 (a-c), (d-f), (g-i), (j-l), (m-o)
(p-r), (s-u)
Nelson Textbook:
Page 202-203
# 3, 4, 5, 12, 14, 15, 16, 17, 21, 22, 23
Lesson 2.7
In this lesson we begin looking in more depth at the rational graph - y=1/x. We begin by exploring what it means to simplify a rational expression and the major limitation (restriction) that having an x in the denominator can have on an expression. We will explore in later lessons how these restrictions affect the graph.
Blank Lesson
Lesson 2.7 Video
Homework 2.7 Solutions -Page 112-113 #4-9
Page 112-113 #2c, 5c
Lesson 2.8
In this lesson we look at applying our skills to rational expressions involving multiplication and division. Again, we state restrictions on the function based on the original function and not the final simplified expressions. Being able to factor a variety of quadratics becomes imperative moving forward.
Blank Lesson
Lesson 2.8 Video
Homework 2.8 Solutions (#1-9 even)
Formative 6
This formative looks at lessons 2.7 and 2.8 where we simplified rational expressions involving multiplication and division.
Blank Formative
Formative 6 Video
Lesson 2.9
In this lesson we look at adding and subtracting rational expressions. This will require factoring to simplify the numerators and denominators in the rational expressions, as well as identifying, and subsequently creating, common denominators in order to add and subtract the rational expressions.
Blank Lesson
Lesson 2.9 Video
Homework 2.9 Solutions
In this lesson we look at applying our skills from simplifying rational expressions to produce the graph of the expressions. We will look at how to identify vertical and horizontal asymptotes, holes in the graph, x and y intercepts, and end behaviour.
Blank Lesson
Lesson 2.10 Video
Homework 2.10 Solutions
