Do Now!!

In your composition notebook THOROUGHLY explain how you would solve the equation below:

-3(x – 3) ≥ 5 – 4x

EOC Review

Objective

SWBAT make connections with content from Chapters 1 – 4.

1-1 Variables and Expressions

A variable is a symbol, usually a letter, that represents values of a variable quantity. For example, d often represents distance. An algebraic expression is a mathematical phrase that includes one or more variables. A numerical expression is a mathematical phrase involving numbers and operations symbols, but no variables.

1-1 Variables and Expressions

What is an algebraic expression for the word phrase 3 less than half a number x?

You can represent “half a number x” as x/2. Then subtract 3 to get: x/2 – 3.

1-4 Properties of Real NumbersYou can use properties such as the ones below to

simplify and evaluate expressions.Commutative Properties: -2 + 7 = 7 + (-2)

3 × 4 = 4×3Associative Properties: 2× (14×3) = (2×14) × 3

3 + (12 + 2)= (3 + 12) + 2 Identity Properties: -6 + 0 = -6

21 × 1 = 21Zero Property of Multiplication: -7 × 0 = 0Multiplication Property of -1: 6 (-1) = -6∙

2-1 and 2-2 Solving One- and Two-Step Equations

To solve an equation, get the variable by itself on one side of the equation. YOU can use properties of equality and inverse operations to isolate the variable. For example, use multiplication to undo its inverse, division.

2-1 and 2-2 Solving One- and Two-Step Equations

What is the solution of _y_ + 5 = 8 2

_y_ + 5 – 5 = 8 – 5 Subtract to undo + 2 _y_ = 3 Simplify 2 2 * _y_ = 3*2 Multiply

2 y = 6 Simplify

2-3 Solving Multi-Step Equations

To solve some equations, you may need to combine like terms or use the Distributive Property to clear fractions or decimals.

2-3 Solving Multi-Step Equations

You do!

What is the solution of 12 = 2x + _4_ – _2x_ ? 3 3

8 = x

2-4 Solving Equations With Variables on Both Sides

When an equation has variables on both sides, you can use properties of equality to isolate the variable on one side. An equation has no solution if no value of the variable makes it true. An equation is an identity if every value of the variable makes it true.

2-4 Solving Equations With Variables on Both Sides

What is the solution of 3x – 7 = 5x + 19 ?3x – 7 – 3x = 5x + 19 – 3x Subtract 3x-7 = 2x + 19 Simplify-7 – 19 = 2x + 19 – 19 Subtract 19-26 = 2x Simplify-26 = 2x Divide by 2 2 2 -13 = x Simplify

2-5 Literal Equations and Formulas

A literal equation is an equation that involves two or more variables. A formula is an equation that states a relationship among quantities. You can use properties of equality to solve a literal equation for one variable in terms of others.

2-5 Literal Equations and Formulas

You Do!What is the width of a rectangle with area 91 ft2 and length 7 ft?

13 = w

3-1 Inequalities and Their Graphs

A solution of an inequality is any number that makes the inequality true. You can indicate all the solutions of an inequality on the graph a closed or dot indicates that the midpoint is a solution. An open dot indicates that the midpoint is not a solution.

3-1 Inequalities and Their Graphs

What is the graph of x ≤ - 4?

-4

3-2 Solving Inequalities Using Addition or Subtraction

You can use the addition and subtraction properties of inequality to transform an inequality into a simpler, equivalent inequality.

3-2 Solving Inequalities Using Addition or Subtraction

What are the solutions of x + 4 ≤ 5 ? x + 4 ≤ 5 x + 4 – 4 ≤ 5 – 4 Subtract 4 x ≤ 1 Simplify

3-3 Solving Inequalities Using Multiplication or Division

You can use the multiplication and division properties of inequality to transform an inequality. When you multiply or divide each side of an inequality by a negative number you have to reverse the inequality symbol.

3-3 Solving Inequalities Using Multiplication or Division

What are the solutions of -3x > 12 ? -3x > 12 -3x < 12 Divide each by -3 -3 -3 Reverse Inequality

Symbol x < -4 Simplify

3-4 Solving Multi-Step Inequalities

When you solve inequalities, sometimes you need to use more than one step. You need to gather the variable terms on one side of the inequality and the constant terms on the other side.

3-4 Solving Multi-Step Inequalites

You do!What are the solutions of 3x + 5 > -1 ?

x > -2

3-5 Working With Sets

The complement of a set A (A’) is the set of all elements in the universal set that are not in A.

3-5 Working With Sets

Suppose U = {1, 2,3,4,5,6} and Y = {2,4,6}. What is Y’?

The elements in U that are not in Y are 1, 3, and 5. So Y’ = {1, 3, 5}

3-8 Unions and Intersections of Sets

The union of 2 or more sets is the set that contains all elements of the sets. The intersection of 2 or more sets is the set of elements that are common to all the sets. Disjoint sets have no elements in common.

4-4 Graphing a Function Rule

A continuous graph is a graph that is unbroken. A discrete graph is composed of distinct, isolated points. In real-world graph, show only points that make sense.

4-4 Graphing a Function Rule

The total height h of a stack of cans is a function of the number n of layers of 4.5-in. cans used. This situation is represented by h = 4.5n. Graph the function.

4-5 Writing a Function Rule

To write a function rule describing a real-world situation, it is often helpful to start with a verbal model of the situation.

4-5 Writing a Function Rule

At a bicycle motocross (BMX) track, you pay $40 for a racing license plus $15 per race. What is the function rule that represents your total cost?

Total cost = license fee + fee per race # of ∙races

C = 40 + 15 r∙

A function rule is C = 40 + 15r

4-6 Formalizing Relations and Functions

A relation pairs numbers in the domain with numbers in the range. A relation may or may not be a function.

4-6 Formalizing Relations and Functions

Is the relation [(0,1), (3,3), (4,4), (0,0)] a function?The x-values of the ordered pairs form the domain, and the y-values form the range. The domain value 0 is paired with two range values, 1 and 0. So the relation is not a function.

4-7 Sequences and Functions

A sequence is an ordered list of numbers, called terms, that often forms a pattern. In an arithmetic sequence, there is a common difference between consecutive terms.

4-7 Sequences and Functions

Tell whether the sequence is arithmetic.

5 2 -1 -4…… -3 -3 -3

The sequence has a common difference of -3, so it is arithmetic

Summary

Our Objectives were that:SWBAT make connections with content from

Chapters 1 – 4.

HomeworkIn TEXTbook

NC EOC Test PracticeChapter 1 pg. 74 – 76 Problems 1 – 20

evenChapter 2 pg. 158-160 Problems 1 – 18 evenChapter 3 pg. 228 – 230 Problems 1 – 20 evenChapter 4 pg. 286-288 Problems 1 – 14 even

Class AssignmentIn the paper back NC Algebra 1 EOC Test

WorkbookComplete Problems:1-9; 11-12; 14-22; 24-26; 28-29; 31 – 34 On pages 1-7SHOW ALL WORK If there is no computation to answer the

question, EXPLAIN your reasoning for getting your answer choice.

YOU MAY write in the text book.

EARLY BIRDS

Review Released EOC test booklet and choose questions from the booklet you need to go over. Have these questions ready for Thursday’s review.

Objective

SWBAT make connections with content from Chapters 5 – 8.

Do Now!!

Factor each expression:1) h2 + 8h + 162) d2 – 20d + 1003) m2 + 18m + 81

5-1 Rate of Change and SlopeRate of change shows the relationship between

two changing quantities. The slope of a line is the ratio of the vertical change (the rise) to the horizontal change (the run).slope = rise = y2 – y1

run x2 – x1

The slope of a horizontal line is 0, and the slope of a vertical line is undefined.

5-1 Rate of Change and SlopeWhat is the slope of the line that passes through

the points (1, 12) and (6, 22)?

Slope = y2-y1 = 22 – 12 = 10 = 2

x2-x1 6 – 1 5

5-2 Direct Variation

A function represent a direct variation a direct variation if it has the form y = kx, where k ≠0. The coefficient k is the constant of variation.

5-2 Direct VariationSuppose y varies directly with x, and y = 15 when x = 5. Write a direct variation equation that relates x and y. What is the value of y when x = 9?

y = kx 15 = k(5) 3 = k y = 3xThe equation y = 3x relates x and y. When x = 9, y =

27

5-3, 5-4, and 5-5 Forms of Linear Equations

The graph of a linear equation is a line. You can write a linear equation in different forms.

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-

intercept.The point-slope form of a linear equation is y – y1 = m(x – x1), where m is the slope and (x1,y1) is a

point on the line.The standard form of a linear equation is Ax+By = C,

where A, B, and C are real numbers, and A and B are not both zeros.

5-6 Parallel and Perpendicular Lines

Parallel lines are lines in the same plane that never intersect. Two lines are perpendicular if they intersect to form right angles.

5-6 Parallel and Perpendicular Lines

Are the graphs of y = 4/3 x + 5 and y = -3/4x + 2 parallel, perpendicular, or neither? Explain.

The slope of the graph of y = 4/3x + 5 is 4/3The slope of the graph of y = -3/4x + 2 is -3/4

(4/3) (-3/4) = -1∙The slopes are opposite reciprocals, so the graphs are

perpendicular.What type of slopes do parallel lines have?The same slope

5-7 Scatter Plots and Trend Lines

A scatter plot displays two sets of data as ordered pairs. A trend line for a scatter plot shows the correlation between the two sets of data. The most accurate trend line is the line of best fit. To estimate or predict values on a scatter plot, you can use interpolation or extrapolation.

6-1 Solving Systems by Graphing

One way to solve a system of linear equations is by graphing each equation and finding the intersection point of the graph, if one exists.

6-1 Solving Systems by Graphing

What is the solution of the system? y = -2x + 2 y = -0.5x – 3

The solution is (2, -2)

6-2 Solving Systems Using Substitution6-3 Solving Systems Using Elimination

• You can solve a system of equations by solving one equation for one variable and then substituting the expression for that variable into the other equation.

• You can add or subtract equations in a system to eliminate a variable. Before you add or subtract, you may have to multiply one or both equations by a constant to make eliminating a variable possible.

6-5 and 6-6 Linear Inequalities and Systems of Inequalities

A linear Inequality describes a region of the coordinate plane with a boundary line. Two or more inequalities form a system of inequality. The system’s solutions lie where the graphs of the inequalities overlap.

6-5 and 6-6 Linear Inequalities and Systems of Inequalities

What is the graph of the system?y > 2x – 4

y ≤ -x + 2

7-1 Zero and Negative Exponents

You can use zero and negative integers as exponents. For every nonzero number a, a0 = 1. For every nonzero number a and any integer n, a-n = 1/an. When you evaluate an exponential expression, you, you can simplify the expression before substitution values for the variables.

7-3 and 7-4 Multiplication Properties of Exponents

To multiply powers, with the same bases, add the exponents am a∙ n = am+n, where a≠0 and m and n are integers.

To raise a power to a power, multiply the exponents. (am)n = amn, where a≠0 and m and n are integers.

To raise a product to a power, raise each factor in the product to the power.

(ab)n = anbn, where a≠0, b≠0, and n is an integer

7-5 Division Property of ExponentsTo divide powers with the same base, subtract

the exponents.am = am-n, where a ≠ 0 and m and n are integers

an

To raise a quotient to a power, raise the numerator and the denominator to the power.

_a_ n = _an where a≠0 & b≠0; n is an integer b bn

7-3 and 7-4 Multiplication Properties of Exponents7-5 Division Property of Exponents

You Doa) 310 3∙ 4 b) (x5)7

c) (pq)8

d) 5x4 3

z2

7-6 Exponential FunctionsAn exponential function involves repeated multiplication of an initial amount a by the same positive number b. The general form of an exponential function is y = a b∙ x, where a≠0, b>0, and b≠1.

7-6 Exponential FunctionsWhat is the graph of y = ½ 5∙ x ?Make a table of values. Graph the ordered the pairs.

7-7 Exponential Growth and Decay

When a > 0 and b >1, the function y = a b∙ x

models exponential growth. The base b is called the growth factor. When a >0 and 0<b<1, the function y = a b∙ x models exponential decay. In this case the base b is called the decay factor.

7-7 Exponential Growth and Decay

You Do!The population of a city is 25, 000 and decreases

1% each year. Predict the population after 6 years.

The population will be about 23,537 after 6 years.

Rule for an Arithmetic SequenceThe nth term of an arithmetic sequence with

first term A(1) and common difference d is given by:

A(n) = A(1) + (n – 1)dWhere n = nth termA(1) = the first term n = term number d= common difference

Arithmetic Sequence and Recursive Formula

Arithmetic Sequence:– Sequence with a constant difference between

terms.

Recursive Formula:– Formula where each term is based on the term

before it

Recursive Formula for an Arithmetic Sequence:

2,1

1

ndaa

a

nn

Arithmetic Sequence and Recursive Formula

• If you buy a new car, you might be advised to have an oil change after driving 1000 miles and every 3000 miles thereafter. Then the following sequence gives the mileage when oil changes are required:1000 4000 7000 10000 13000 16000

2;3000

1000

1

1

naa

a

nn

Arithmetic Sequence and Recursive Formula You DO

• Briana borrowed $870 from her parents for airfare to Europe. She will pay them back at the rate of $60.00 per month. Let an be the amount she still owes after n months. Find a recursive formula for this sequence.

2,60

870

1

1

naa

a

nn

8-1 Adding and Subtracting Polynomials

A monomial is a number, a variable, or a product of a number and one or more variables. A polynomial is a monomial or the sum of two or more monomials. The degree of a polynomial in one variable is the same as the degree of the monomial with the greatest exponent. To add 2 polynomials, add the like terms of the polynomials. To subtract a polynomial, add the opposite of the polynomial.

8-1 Adding and Subtracting Polynomials

You Do!What is the difference of 3x3 – 7x2 + 5 and 2x2 – 9x – 1?

3x3 – 9x2 + 9x + 6

8-2 Multiplying and Factoring

You can multiply a monomial and a polynomial using the Distributive Property. You can factor a polynomial by finding the greatest common factor (GCF) of the terms of the polynomial.

8-3 and 8-4 Multiplying Binomials

You can use algebraic tiles, tables, or Distributive Property to multiply polynomials. The FOIL method (First, Outer, Inner, Last) can be used to multiply two binomials. You can also use rules to multiply special case binomials.

8-3 and 8-4 Multiplying Binomials

What is the simplified form of (4x + 3)(3x + 2)?

= 12x2 + 17x + 6

8-5 and 8-6 Factoring Quadratic Trinomials

You can write some quadratic trinomials as the product of two binomials factors. When you factor a polynomial, be sure to factor out the GCF first.

8-5 and 8-6 Factoring Quadratic Trinomials

What is the factored form x2 + 7x + 12?List the pairs of factors of 12. Identify the pair

with a sum of 7.

x2 + 7x + 12 = (x+3)(x+4)

Factors of 12 Sum of Factors

1, 12 13

2, 6 8

3,4 7

8-7 Factoring Special CasesWhen you factor a perfect-square trinomial, the

two binomial factors are the same. a2 + 2ab + b2 = (a+b)(a+b) = (a+b)2

a2 – 2ab + b2 = (a-b)(a-b) = (a-b)2

When you factor a difference of squares of 2 terms, the 2 binomial factors are the sum and the difference of the two terms.

a2 – b2 = (a+b)(a-b)

8-7 Factoring Special Cases

What is the factored form of 81t2 – 90t + 25 ?

(9t – 5)2

Summary

Our objective was: SWBAT make connections with content from

Chapters 5 – 8.

Homework

Chapter 5 EOC pg. 354 – 356 Problems 1- 15Chapter 6 EOC pg. 408 – 410 Problems 1 – 17 Chapter 7 EOC pg. 468 – 470 Problems 1- 19 oddChapter 8 EOC pg. 528 – 530 Problems 1–21 odd

Assignment

Resume yesterday’s assignment:In the paper back NC Algebra 1 EOC Test WorkbookComplete Problems:1-9; 11-12; 14-22; 24-26; 28-29; 31 – 34 On pages 1-7SHOW ALL WORK If there is no computation to answer the question,

EXPLAIN your reasoning for getting your answer choice.

YOU MAY write in the text book.

Do Now

Find the length of the hypotenuse. Write your answer in simplified radical form.

3√2

Objective

SWBAT make connections with the content from Chapters 9 - 12

9-1 and 9-2 Graphing Quadratic Functions

A function of the form y = ax2 + bx + c, where a ≠0, is a quadratic function. Its graph is a parabola. The axis of symmetry of a parabola divides it into two matching halves. The vertex of a parabola is the point at which the parabola line intersects the axis of symmetry.

9-1 and 9-2 Graphing Quadratic Functions

What is the vertex of the graph of y = x2 + 6x – 2?

The vertex is (-3, -11)

9-3 and 9-4 Solving Quadratic Equations

The standard form of a quadratic equation is ax2 + bx + c = 0, where a ≠ 0. Quadratic

equations can have two, one, or no real-number solutions. You can solve a quadratic equations by graphing the related function and finding the x-intercepts . Some quadratic equations can also be solved using square roots. If the left side of ax2+bx+c = 0 can be factored, you can use the Zero-Product Property to solve the equation.

9-3 and 9-4 Solving Quadratic Equations

What are the solutions of 2x2 – 72 = 0 ?

x = + 6

9-5 Completing the Square

You can solve any quadratic equation by writing it in the form x2 + bx = c, completing the square, and finding the square roots of each side of the equations.

9-5 Completing the Square

What are the solutions of x2 + 8x = 513

x = 19 or x = -27

9-6 The Quadratic Formula and the Discriminant

You can solve the quadratic equation ax2+bx+c = 0 where a ≠ 0, by using the quadratic formula

x = -b + √(b2 – 4ac)2a

Discriminant: is the expression under the radical sign in the quadratic formula, it tells how many solutions the equation has.

x = -b + √(b2 – 4ac)2a

The discriminant

9-6 The Quadratic Formula and the Discriminant

• How many real-number solutions does the equation x2 + 3 = 2x have?

Because the discriminant is negative, the equation has no real-number solutions.

9-8 Systems of Linear and Quadratic Equations

Systems of linear and quadratic equations can have 2 solutions, one solution, or no solution. These systems can be solved graphically or algebraically.

9-8 Systems of Linear and Quadratic Equations

What are the solutions of the system? y = x2 – 7x – 40 y = -3x + 37

(11, 4) and (-7, 58)

10-1 The Pythagorean Theorem

Given the lengths of 2 sides of a right triangle, you can use the Pythagorean Theorem to find the length of the third side. Given the lengths of all 3 sides of a triangle, you can determine whether it is a right triangle.

10-2 Simplifying Radicals

A radical expression is simplified if the following statements are true:

• The radicand has no perfect-square factors other than 1

• The radicand contains no fractions• No radicals appear in the denominator of a

fraction

10-2 Simplifying RadicalsWhat is the simplified for of √(3x) ?

√(2)√(3x) = √(3x) ∙ √(2) Multiply by

√2√(2) √(2) √(2)

√2= √(6x) = √(6x) Simplify √(4) 2

10-5 Graphing Square Root Functions

Graph a square root function by plotting points or translating the parent square root function y = √x.

The graph of y = √x + k and y = √x – k are vertical translations of y = √x. The graphs of y = √(x+h) and y = √(x – h) are horizontal translation of

y = √x

10-5 Graphing Square Root Functions

What is the graph of the square root function y = √(x-2) ?

The graph of y = √(x – 2) is the graph of y = √x shifted 2 units to the right.

11-5 Solving Rational Expressions

A rational expression is an expression that can be written in the form: polynomial

polynomialA rationale expression is in simplified form when

the numerator and denominator have no common factors other than 1.

11-5 Solving Rational Expressions

What is the simplified form of x2 – 9 x2 – 2x -15

x2 – 9_ = (x-3)(x+3) Factor numerator x2 – 2x -15 (x+3)(x-5) and denominator(x-3)(x+3) Divide out

common(x-5)(x+3) factor(x- 3) Simplify(x-5)

11-6 Inverse VariationWhen the product of 2 variables is constant, the variables form an inverse variation. You can write an inverse variation in the form xy = k or y = k/x, where k is the constant of variation.

11-6 Inverse VariationSuppose y varies inversely with x, and y = 8

when x = 6. What is an equation for the inverse variation?

xy = k General form of inverse variation 6(8) = k Substitute 48 = k Solve for k xy = 48 Write equation

11-7 Graphing Rational FunctionsA rational function can be written in the form f(x) = polynomial . The graph of a rational

polynomial function in the form y = _a_ + c has a vertical

x – b asymptote at x = b and a horizontal asymptote at y = c. A line is an asymptote of a graph if the graphgets closer to the line as x or y gets larger inabsolute value.

12-2 Frequency and HistogramsThe frequency of an interval is the number of data values in that interval. A histogram is a graph that groups data into intervals and shows the frequency of values in each interval.

12-3 Measures of Central Tendency and Dispersion

The mean of a data set equals: sum of data values

Total number of data values.The median is the middle value in the data set

when the values are arranged in order. The mode is the data item that occurs the most times. The range of set of data is the difference between the greatest and least data values.

12-4 Box-and-Whisker PlotsA box-and-whisker plot organizes data values into four groups using the minimum value, the first quartile, the median, the third quartile, and the maximum value.

1-7 Midpoint and Distance in the Coordinate Plane

You can find the coordinates of the midpoint M of AB with endpoints A(x1,y1) and B(x2,y2) using the Midpoint Formula.

M( x1+x2 , y1+y2)

2 2You can find the distance d between two pointsA(x1,y1) and B(x2,y2) using the Distance

Formula. d = √(x2-x1)2 + (y2-y1)2

1-8 Perimeter, Circumference, and Area

Circles have a circumference C. The area A of a polygon or a circle is the number of square units it encloses.

Circle: Circumference = ∏d or Circumference = 2∏rArea = ∏r2

11-4, 11-5, 11-6 Volumes of Cylinders, Pyramids, Cones, and Spheres

Cylinder: V = Bh or V = ∏r2h

Pyramids: V = 1/3Bh

Cones: V = 1/3Bh; or V = 1/3∏r2h

Spheres: V= 4/3∏r3

Summary

Our objective was:SWBAT make connections with the content from

Chapters 9 - 12

Homework

Chapter 9 EOC Practice pg. 594 – 596 1 – 20 allChapter 10 EOC Practice pg. 646 – 648 1 – 17

oddChapter 11 EOC Practice pg. 708 – 710 1 – 21

odd

Assignment

In TEXTbookPg. 780 – 785 End-Of-Course AssessmentComplete Problems:1 – 47 ALL Do not do problems:3, 27, 45