Download Algebra II – Pre-Requisite Skills

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Algebra II – Pre-Requisite Skills
Topic: Preparing for Algebra II
Welcome to Algebra 2! Today, we will spend just a little bit of time focusing on some skills that you
already need to have mastered prior to the start of this course. After today, we will begin our journey
that will last us until the End of Course of exam (EOC) is taken many months from now. Since this is a
standards-based course, we will focus on the four standards today that should be mastered by the end
of this lesson. The four standards we will focus on today are:
 A.1.a.: I can identify properties of real numbers and use them and the correct order of
operations to simplify expressions.
 A.1.b.: I can multiply monomials and binomials.
 A.1.c.: I can solve single-step and multistep equations and inequalities in one variable.
 A.1.h.: I can find the distance and midpoint between two points in the coordinate plane.
We first want to focus on the first standard:
 A.1.a.: I can identify properties of real numbers and use them and the correct order of
operations to simplify expressions.
There are several properties of Real Numbers. Define and give an example of each:
1. Commutative Property
2. Associative Property
3. Multiplicative Inverse
4. Additive Inverse
5. Multiplicative Identity
6. Additive Identity
7. Distributive Property
8. Closure Property
EXAMPLES: Name the property illustrated by each question.
#1. 5(a + b) = 5a + 5b
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#2. -10 + 4 = 4 + -10
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#3. 4 + 0 = 4
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#4. ½ * 2 = 1
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EXAMPLES: Simplify each expression using the correct order of operations and properties of real
numbers.
#1. 5a – a
#2. 6r + 3s + 2s – 4r
#3. –(3x + 2y) + 5(3x – 6y)
#4. x(3 – y) + y(x + 6)
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EXAMPLES: Evaluate each expression for the given values of the variables.
#1. -2a + 5b + 6a – 2b + a, a = -3 and b = 2
#2. y(3 – x) + 𝑥 2 ; x = 2 and y = 12
Let’s now focus on our second standard:
 A.1.b.: I can multiply monomials and binomials.
We will start with multiplying monomials.
EXAMPLES: Multiply the following
#1. 𝑥 ∗ 𝑥 4
#2. (𝑥 2 )4
#3. 5𝑥 4 ∗ −3𝑥 5
#4. (2𝑥 3 )3
We will also work on multiplying binomials, using what is commonly known as the FOIL method.
#1. (x + 5)(x – 8)
#2. (2a + b)(-3b – 5b)
Let’s now focus on our third standard:
 A.1.c.: I can solve single-step and multistep equations and inequalities in one variable.
Let’s look at some various types of equations that you should now know how to solve.
EXAMPLES: Solve each equation:
#1. 5x + 4 = 2x + 10
#2. 4(d – 3) = 2d
#3. 5w + 8 – 12w = 16 – 15w
#4. The angles of a triangle are in the ratio of 2:12:16. The sum of all the angles in a triangle must equal
180 degrees. What is the degree measures of each angle of the triangle? Let x = the common factor.
Finally, let’s take a quick look at our fourth (and final) standard for the day:
 A.1.h.: I can find the distance and midpoint between two points in the coordinate plane.
EXAMPLE:
Using the appropriate formulas, find the distance AND midpoint for the following coordinates.
Point A(- 5, 7) and Point B(4, 1)
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HOMEWORK – Pre-Requisite Skills
I.
II.
Name the property of real numbers illustrated by each question
#1. 2(3 + √5) = 2·3 + 2·√5
#2. 16 + (-13) = -13 + 16
#3. (x + 37) + (-37) = x + (37 + (-37))
#4. x ·1 = x
#5. x + (37 + (-37)) = x + 0
#6. x + 0 = x
Simplify each expression below:
#1. 10w – 7w
#2. 7t – 5s + 8t + 10s
#3. 5𝑥 − 3𝑥 2 + 16𝑥 2
#4. 4a – 5(a + 1)
#5. x(x – y) + y(y – x)
III.
Evaluate each expression for the given values of the variables.
#1. -4v + 3(w + 2v) – 5w; v = -2 and w = 4
#2. 𝑐(3 − 𝑎) − 𝑐 2 ; a = 4 and c = -1
IV.
Multiply the following
#1. 𝑦 ∗ 𝑦 8
#2. (𝑡 3 )7
#3. 6𝑥 5 ∗ −4𝑥 2
#5. (w – 6)(w + 3)
#2. (-3z + y)(-4z – 5y)
Solve the following
#1. 9(z – 3) = 12z
#2. 7y + 5 = 6y + 11
#3. 5w + 8 – 12w = 16 – 15w
#4. 3(x + 1) = 2(x + 11)
V.
#4. (2𝑥 4 )4
#5. The sides of a triangle are in the ratio of 5:12:13. What is the length of each side of the
triangle if the perimeter of the triangle is 15 inches?
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VI.
Distance & Midpoint
#1. Find the distance between X(5, 6) and Y(-4, 9)
#2. Find the midpoint of segment MN if M(5, 3) and N(-4, 7).
VII.
MULTIPLE CHOICE
Try the following multiple choice questions and choose the correct answer
1. Standard A.1.a.: Which expression best represents a simpler form of 4m + 3(m + n)?
a. 7m + 3n
b. 4m + 3mn
c. 3m + 4n
d. 7𝑚2 + 3𝑛
2. Standard A.1.a : What is the value of ‘r’ when s = -1, t = 4, and u = 1/5?
a. 7
b. 15
c. 21
d. 22 1/5
For the next TWO questions, what property of real numbers is illustrated by the equation?
3. Standard A.1.a: -6 + (6 + 5) = (-6 + 6) + 5
a. Identity property of addition
b. Inverse property of addition
c. Commutative property of addition
d. Associative property of addition
4. Standard A.1.a: 2(-4 + x ) = 2(-4) + 2 · x
a. Associative property of multiplication
b. Distributive property
c. Associative property of addition
d. Closure property of multiplication
5. Standard A.1.a: The price of a discount airline ticket starts at $150 and increases by $30 each
week. Which algebraic expression models this situation?
a. 30 + 150 w
b. 150 – 30w
c. 30 – 150w
d. 150 + 30w
6. Standard A.1.c.: What is the solution of 12 + y = 18?
a. -6
b. 12
c. 6
d. 30