Algebraic ExpressionsWriting Equations

Pythagorean Theorem

How do I use what I learned about algebraic expressions and equations in different real life situations?

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in

repeated reasoning.

What is an algebraic expression? How do I evaluate an expression? What is a variable? Why do I have to use opposite operation

in an equation? Why do we solve equations?

An algebraic expression is a mathematical expression that consists of variables, numbers and operations. The value of this expression can change.

Calculating the value of an expression is called ‘evaluating’ the expression.

A variable is a symbol used to represent a number in an expression or an equation. The value of this number can change.

The goal in solving an equation is to get the variable by itself on one side of the equation and a number on the other side of the equation.

To isolate the variable, we must reverse the operations acting on the variable. We do this by performing the inverse of each operation on both sides of the equation. Performing the same operation on both sides of an equation does not change the validity of the equation, or the value of the variable that satisfies it.

The process of finding out the variable value that makes the equation true is called ‘solving’ the equation.

Write and solve an equation to find the measure of angle x.

Find the measure of angle b.

A triangle has an area of 6 square feet. The height is four feet. What is the length of the base?

The surface area of a cube is 96 in2. What is the volume of the cube?

The distance from Jonestown to Maryville is 180 miles, the distance from Maryville to Elm City is 300 miles, and the distance from Elm City to Jonestown is 240 miles. Do the three towns form a right triangle? Why or why not?

The Irrational Club wants to build a tree house. They have a 9-foot ladder that must be propped diagonally against the tree. If the base of the ladder is 5 feet from the bottom of the tree, how high will the tree house be off the ground?

Find the length of segment AB

The expression 20(4x) + 500 represents the cost in dollars of the materials and labor needed to build a square fence with side length x feet around a playground. Interpret the constants and coefficients of the expression in context.

 

The Tindell household contains three people of different generations. The total of the ages of the three family members is 85.

Find reasonable ages for the three Tindells. Find another reasonable set of ages for them. One student, in solving this problem, wrote C + (C+20)+ (C+56) = 85 What does C represent in this equation? What do you think the student had in mind

when using the numbers 20 and 56? What set of ages do you think the student

came up with?

Simplify the following.

a.

b.

REVIEW: Algebra Competency

How do I use what I learned on Unit 2 on problem solving?

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in

repeated reasoning.

Simplify the following: 1(x + 3) + (x + 5) 2. (2x + 1) -

(3x – 4) 3. 2)14( x 4. )653)(1( 2 xxx

Which of the following expressions are equivalent to (2x+3)2 ; Choose all that apply

A) 4x2 +12x + 9 B) (2x+3)(2x+3) C) 4x2 + 9 D) (2x)2 + 2(6x) + 32

Express 2(x3 – 3x2 + x – 6) – (x – 3)(x + 4) in factored form and use your answer to say for what values of x the expression is zero.

Given that (2^x)^2 + (2^x) −12 can be written as (2^x + a)(2^x + b), where a, b are integers, find the value of a and of b.

 

Simplify the following expressions

1. 2

82

16

452

2

2

2

xx

xx

x

xx 2. 4

3

2

32

2

x

x

x

x

3. 28

3

4

1

aa 4.

1

4

4

4

x

x

x

x 5.

103

4

5

122

xxx

x

6.

11

1

y

y

x

x 7.

4

31

24

2

x

x

Express in the form , where a(x) and b(x) are polynomials

Rewrite the rational exponents as a radical; Rewrite the radicals with rational exponents.

1. 3

2

8 2. 4 381 3.. 3

1

216 4. 5 2a

5. 5

3

)32( 6. 9 5310 yx 7. Rewrite 2

x

xin at least three alternate forms.

: Simplify:

1) 3 9125x 2. 4 25810 yx 3. Rewrite 3 3 23 3 1x x x in simplest form.

Review: UNIT 2

Introduction to geometry

How do I use definitions, postulates to write a proof?

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in

repeated reasoning.

Identify and describe the basic undefined terms of geometry.

Represent and analyze angles and angle relationships including vertical, adjacent,

complementary, supplementary, obtuse, acute, right, interior, and exterior.

Represent and analyze line/segment/plane relationships including parallel, perpendicular, intersecting, bisecting, and midpoint.

Represent and analyze point relationships including collinear

Construct a simple formal deductive proof using properties of equality and congruence.

If 3x + 28 = 58, then x = 10. Write the correct statements and

reasons in the flowchart ( and two-column proof) to prove the conditional above.

Proving Statements about segments Proving statements about angles Proving vertical angles theorem