Day 1

Standards 1.0, 2.0, 3.0, 4.0Arithmetic Properties and Operations One Variable Equations Absolute Value Equations

Arithmetic Properties and Operations

• Commutative PropertyAddition-For any numbers a and b, a + b= b +aEx. 21x +7 = 7+ 21xMultiplication-For any numbers a and b, ab =baEx. 3x(5+y) = (5+y) 3xWe can change the order without changing the result

Associative Property

Addition-For any number a,b and c a+(b+c)= (a+b)+cExample: 2x+(3x+4)=(2x+3x)+4Multiplication-For any numbers a, b and cA(bc)=(ab)cExample: 2x(yz)=(2xy)z

Distributive Property

For any numbers a, b and c a(b + c) = ab + ac (b +c) a = ab +acExamples: 5(2x + 3)= 10x + 15 (x + 4) 3= 3x + 12

Identity Property

• Addition-For any number a, a + 0= aExample: 5c + 0= 5c

• MultiplicationFor any number a, a(1)=aExample: 3x(1) = 3x

Inverse Property

• Additive inverse-Two rational numbers whose sum is 0 a+(-a)=0Example: 5 + (-5) = 0

Reciprocal and Inverse

Multiplicative InverseTwo rational numbers whose product is 1Or the multiplication of reciprocals a(1/a)= 1Example 3(1/3)=1The reciprocal of 3/5 is 5/3 because 3/5 (5/3) =1

One Variable Equation• Solve the following equations: 2x + 5 = x - 3 + 3x

3(5-2x) - 4 = -2 (x -3) - 4 + x

Absolute Equations

• Solve the following equations: |3x-2|=7

3|4-2x| = 6

Absolute Value Inequalities

• Solve the following absolute value inequalities:

|3x-4|>2 |5x-10|<20

DAY 2Standards 6.0, 7.0, 8.0

Linear Equations

Does the point (3, -2) lie on the line 3x – 4y = 5 ?

Is (5, -1) a solution to ?

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y =4

5x −5

What are the x and y-intercepts of the graph?1) 3x + 2y = 8

2) y=3x-4

Write an equation for a line that has a slope of ½ and contains the point (4, -3).

Write an equation for a line that has a slope -3 and passes through the point (-1, 2).

Graph each line.

2x-3y=-12

Write an equation for each line.

Extra Practice: http://teachers.henrico.k12.va.us/math/HCPSAlgebra1/Geogebra/LineEqs.html

Are the graphs of the two equations parallel?

Are the graphs of the two equations perpendicular?

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y =4

3x −5

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5x + 4y = 8

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4x −5y =10

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3x + 4y = −20

Write an equation for a line that is perpendicular to 4x-5y=22 and passes through the point (8, -2)

Day 3Systems of EquationsStandards 3.0, 6.0, 9.0

Solve the system of equations using the graphing method

Y=x+16x+3Y=12

Solve the system of equations using the graphing method

y+2x=52y-5x=10

Solve the system of equations by using the substitution method

y=x+54x+2y=16

Solve the system of equations by using the substitution method

y=-3x-5y=x+3

Solve the system of equations by using the addition method

x+y=52x-y=4

Solve the system of equations by using the addition method

3x – 4y = 16 5x + 6y =14

Solve the system of equations by using the addition method

2x – 5y = 8 6x -15y =10

DAY 4 STANDARDS 3.0,6.0,9.0

ONE VARIABLES INEQUALITIESLINEAR INEQUALITIES

SYSTEM OF LINEAR INEQUALITIES

What is the solution to the inequality

-6x – 9 > 27 ?

What is the solution to the inequality

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−6x −10 ≥ −30 −2x

Graph the inequality

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y >3

5x + 2

• Graph the following system of inequalities

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y ≥ −2x −1

y ≥2

5x −2

Graph the following system of inequalities

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3x −2y ≤ 8

2x + y > 6

Day 5Standards 2.0, 10.0, 11.0

Exponents RulesPolynomial OperationsFactoring Polynomials

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Exponents• Simplify(3x2)4= 3(x2)4= 2x3y(4x2y3)=

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9x 4y 3

3x 2y=

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2ab3

8a4b2=

Polynomials

Simplify the following expressions:(5xy + 3x) + (xy + 4x - 4y) =

(2x2 + 5x) - (4x2 - 3x) =

(4x2 - 3y)(2x + 5y)=

(6x - 3)(x - 4) =

(2x - 3)2 =

Factoring

5x - 10x2 = 4a2- 6ac =

9a2- 25 = 16c4 - d2 =

x2 - 7x + 12 = 2x2 - 3x - 5 =

e2 - 4e + 4 = h2 + 12h + 36= 2x2 - 6x - 20 = ad2 - 5dx + 4d =

Day 6Standards: 11.0, 14.0, 19.0, 20.0,

21.0, 22.0, 23.0Quadratic EquationsGraphs of Quadratic EquationsProjectile Motion

Solve the quadratic equations

1) X2-2x-15=0

2) 4x2 – 9 = 0

3) 4y2+3y=7

4) x2-6x=3

Complete the square

2x2+6x+2=0

Determine the number of solutions:3x2+4x+1=0

Determine the number of x-intercepts:y=x2+5x+9

Determine the number of roots:x2+4x+4

Sketch the graph of y=x2+7x+6

X-intercepts:

Opens up/down?

Vertex:

Sketch the graph of f(x) = -3x2+27

X-intercepts:

Opens up/down?

Vertex:

A ball is thrown in the air. The relationshipbetween the time the ball is inthe air in seconds (t) and the height of theball in feet above the ground (h) isrepresented by h=-16t2 + 46t + 6. Howmany seconds will it take for the ball to hitthe ground.