Important Concepts for This Unit
We will review the real numbers, equations, and the coordinate plane. you are probably already familiar with these concepts but it is helpful to get a fresh look at how these ideas work together to solve problems and model realworld situations. The standards that will be assessed in this chapter are
1.2 Can simplify expressions using properties of exponents
1.3 Can simplify expressions involving factoring and expanding
1.4 Can combine and simplify rational expressions
1.5 Can solve equations involving exponents, algebraic expressions, and rational expressions.
Topic, Focus, and Exercises

Khan Academy Videos

Khan Academy Homework (KHW)

u1.1  Real Numbers
· The various subsets of the real
number line.
· The algebraic properties of real
numbers.
· Closed and open intervals of real
numbers, and their unions and intersections.
· Absolute value and distance.
Core Exercises: 1, 28, 31, 41,
44, 55, 64, 70, 76
Recommended: 1, 13, 18, 22,
28, 31, 32, 33, 40, 41, 44, 45, 48, 55, 59, 64, 70, 76, 87

Algebraic
expressions with fractions.
Absolute value equations.

KHW:
Practice with nested fractions.
KHW: Absolute Value Equations

u1.2  Exponent and Radicals
 The definition
of a^{n} in the case where n is
rational, and where n negative.
 Algebraic
properties of exponents.
 Rationalizing
denominators.
 Scientific
notation and significant figures.
Core Exercises: 3, 44, 67, 70, 76, 86, 88, 100
Recommended: 1, 3, 6, 15, 40, 44, 45, 48, 62, 67, 70, 74, 76, 83,
86, 88, 89, 90, 95, 100

Properties of exponents
Exponent properties examples with
variables
Fractional exponents
Simplifying
radical expressions
Solving equations with radicals

KHW:
Practice simplifying expressions with exponents
KHW:
Manipulating fractional exponents
KHW: Fractional exponent practice
KHW:
Simplifying square roots
KHW: Adding and subtracting
radicals
KHW: Solve equations containing
square roots of variables
KHW: Extraneous solutions to
radical equations

u1.3  Algebraic Expressions
 Definition of
and algebraic operations with polynomials.
 Special product
formulas.
 Factoring
expressions by finding common factors and recognition of special cases.
 Factoring
quadratics by trial and error.
Core Exercises: 2, 18, 27, 42,
51, 60, 72, 94, 136
Recommended: 2, 4, 13, 18,
20, 24, 27, 29, 33, 42, 46, 51, 55, 60, 68, 72, 78, 85, 94, 124, 136

Adding and multiplying
polynomials
Factoring quadratics

KHW: Adding and subtracting
polynomials
KHW: Multiplying binomials by
polynomials
KHW: Factoring quadratics with
leading coefficient of 1
KHW: Factoring polynomials using
quadratic methods
KHW: Factoring difference of
squares
KHW: Factoring polynomials with
special product forms

u1.4 Rational Expressions
 Finding the
domain of an algebraic expression.
 Simplifying,
adding, and subtracting rational expressions, including compound
fractions.
 Rationalizing
numerators and denominators.
Core Exercises: 4, 6, 15, 24,
48, 65, 83, 98
Recommended: 1, 4, 6, 10,
12, 15, 18, 24, 25, 31, 39, 48, 54, 65, 83, 86, 98, 99, 25

Rational Expressions
Domain and range
Simplifying rational expressions
Adding and subtracting rational
expressions
Multiplying and dividing rational
expressions
Solving rational equations

KHW: Domain of a function
KHW: Dividing polynomials by
binomials
KHW: Simplifying rational
expressions
KHW: Adding and subtracting
rational expressions
KHW: Multiplying and dividing
rational expressions
KHW: Solving rational equations

u1.5  Equations
 Solving
equations using the techniques of adding constants to both sides of the
equation, multiplying both sides of the equation by a constant, and
raising both sides of the equation to the same nonzero power.
 Avoiding the
pitfalls of accidentally multiplying or dividing by zero, or introducing
extraneous solutions.
 Solving
quadratic equations using the techniques of factoring, completing the
square, and the quadratic formula, and the use of the discriminant
to determine the nature of the solutions to a quadratic equation.
 Solving
generalized quadratic equations.
 Solving
equations involving fractional expressions.
Core Exercises: 1, 13, 32, 45,
58, 70, 80, 90, 123, 129
Recommended: 1, 5, 10, 12,
13, 20, 30, 32, 41, 45, 51, 58, 64, 70, 73, 80, 81, 87, 90, 123, 129, 139



u1.7  Modeling with equations
 Solving applied problems
described verbally (word problems)
 Presenting the solution
process in a clear, organized way.
Core Exercises: 3, 7, 20, 37,
42, 46, 56, 70, 85
Recommended: 3, 6, 7, 15,
18, 20, 23, 29, 37, 42, 46, 48, 51, 56, 61, 66, 70, 77, 82, 85



u1.9  The Coordinate Plane
 The distance and midpoint formulas.
 The relationship between a twovariable equation and
its graph. (This is the most crucial concept.)
 Sketching graphs by plotting points, using intercepts
and symmetry.
 Equations of circles and their graphs, including the
technique of completing the square.
Core Exercises: 2, 10, 25, 35, 50, 60, 71, 92, 98, 115
Recommended : 2, 6, 8, 10, 14, 17, 25, 35, 38, 45, 50, 56,
60, 65, 71, 76, 87, 92, 98, 106, 115, 127



u1.12  Modeling Variation
 Direct variation and
proportionality
 inverse variation
 Combinations of direct and
inverse variation
Core
Exercises: 3, 7, 34, 39, 47, 49, 74, 79, 96
Recommended: 3, 4, 7, 13, 18, 24, 31, 34, 39, 46, 47, 49, 50,
62, 71, 74, 79, 86, 92, 96




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