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.