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Grades 9/10/11 Number Sense and Algebraic Expressions

Exponent laws. Manipulating expressions including polynomials, radical and rational expressions. Investigating prime factorization.

This is one of seven strands of the CEMC Grade 9/10/11 courseware. The other strands and more information about this courseware is available on the Grade 9/10/11 homepage.

Unit 1: Exponents

This lesson will examine the relationship between the exponential representation of length, area, and volume. Algebraic expressions will be represented in both exponential form and expanded form.

This lesson introduces the exponent rules for multiplying and dividing monomials.

In this lesson, we will continue working with operations involving exponents and explore the power of a power rule.

In this lesson, we will examine powers with positive and negative integer bases. We will also explore the exponent rule for an exponent of zero and will examine powers with negative integer exponents.

In this lesson, we will define the \(n\) th root of a number and explore positive rational exponents of the form \(\dfrac{1}{n}\).

In this lesson, we will simplify and evaluate positive rational exponents of the form \(\dfrac{a}{n}\) and negative rational exponents of the form \(\dfrac{-a}{n}\).

This lesson puts together all of the Exponent Rules learned to simplify algebraic expressions. We will also use exponents and exponent rules to evaluate expressions.

All of the pencil and paper practice exercises, answers, and solutions for this unit are reproduced here.

This is a collection of additional, and sometimes challenging, problems that extend the material covered in this unit, connect material from different lessons, and further explore real-world applications.

Unit 2: Manipulating Algebraic Expressions

Unit 3: Radicals and Rational Functions

Unit 4: Prime Factorization