Transcript ALGEBRA I Tips, Tricks and TI-Calculator

ALGEBRA I
Tips, Tricks and TICalculator
By: Alycia DiPinto
Algebra I
• Pre-Algebra topics but deeper
• Important Topics include:
• Solving Equations (multi step, variables on both
sides, no solution, infinitely many solutions)
• Solving inequalities
• Solving systems of equations graphically and
algebraically
• Slope-intercept form
• Scatter Plots
Solving Equations
• Basic 2x + 5 = 12
• Intermediate 2(x+5)=6x+2
• Advanced ½(x + 5 + 6x) = 3(x + ½)
Solving Equations
• Special Solutions
• 5x + 5 = 3(5x-4)-10x
• 3(2b-1)-7=6b-10
Solving Inequalities
• Solve same way as equations but with
inequality sign.
• Remember: When multiplying or dividing by a
negative number, the inequality sign changes
• Examples
• 2x + 11 < 5x - 10
• -2(4b+1) < -2b + 8
• -12y – 24 > 42
Solving Systems of
Equations
•3 Methods
•Graphing
•Substitution
•Elimination
Solving Systems of
Equations
• Graphic Organizer
Solving Systems of
Equations
• Method 1
• Graphing
• Best used when
both equations can
be easily solved for y
• Example 1:
y = 2x + 3
y = -2x – 5
Solving Systems of
Equations
• Method 1
• Graphing
• Best used when
both equations can
be easily solved for y
• Example 2:
2x – y = -1
4x – 2y = 6
Solving Systems of
Equations
• Method 2
• Substitution
• Best used when one system is easily solved for
y or x
• Example 3:
y = 5x + 1
4x + y = 10
Solving Systems of
Equations
• Method 3
• Elimination
• Addition- when coefficients are opposite
• Example 4:
4x + 6y = 32
3x – 6y = 3
Solving Systems of
Equations
• Method 3
• Elimination
• Subtraction- when coefficients are the same
• Example 5:
5m – p = 7
7m – p = 11
Solving Systems of
Equations
• Method 3
• Elimination
• Multiplication- when coefficients are different
• Example 6:
5x + 6y = -8
2x + 3y = -5
Solving Systems of
Equations
• Special Solutions
• No solution
• Example 7:
-3x + 3y = 4
-x + y = 3
• Infinitely many solutions
• Example 8:
2x + 8y = 6
-5x – 20y = -15
Solving Systems of
Equations
• Tool: Graphing Calculator
Example 1:
Example 2:
Example 3:
Example 4:
Example 5:
Example 6:
Example 7:
Example 8:
y = 2x + 3 and y = -2x – 5
(-2,-1)
y = 2x + 1 and y = 2x – 3
No Solution
y = 5x + 1 and y = -4x + 10
(1,6)
y = -2/3x + 16/3 and y = 1/2x – ½ (5,2)
p = 5m – 7 and p = 7m – 11
(2,3)
y = -5/6x – 4/3 and y = -2/3x – 5/3 (2,-3)
y = x + 3 and y = x + 4/3
No Solution
y = -1/4x + ¾ and y = -1/4x + ¾ Inf. Many Sol.
Slope-Intercept Form
y=mx+b
• Putting equations in slope intercept form given:
• Slope and a Point
• Example 1: (-2,5) Slope 3
• Example 2: (4,-7) Slope -1
• Two Points
• Example 3: (3,1) (2,4)
• Example 4: (-1,12) (4,-8)
Slope-Intercept Form
y=mx+b
• Putting equations in slope intercept form given:
• Real World Data
• Example 1: In 1904, a dictionary cost $0.30. Since then the
cost of a dictionary has risen an average of $0.06 per year.
• Write a linear equation to find the cost C of a dictionary y
years after 1904.
• If the trend continues, what will the cost of a dictionary be in
2020.
Years after
1904
Cost
Slope-Intercept Form
y=mx+b
• Putting equations in slope intercept form given:
• Real World Data
• Example 2: Jackson is ordering tickets for a concert online.
There is a processing fee for each order, and the tickets are
$52 each. Jackson ordered 5 tickets and the cost was $275.
• Determine the processing fee. Write a linear equation to
represent the total cost C for t tickets.
• Make a table of values for at least three other numbers of
tickets.
• Predict the cost of 8 tickets.
Slope Intercept Form
• Tool: Graphing Calculator
• Example 1: C=0.30 + 0.06y
• Example 2: C = 15t + 15
Scatter Plots
• Scatter Plots show the relationship between a set of data with
two variables
• Graphic Organizer
Scatter Plots
• Scatter Plots- shows the relationship between a
set of data with two variables, graphed as
ordered pairs on a coordinate plane.
• Tool: Graphing Calculator
• Graph scatter plots and find line of best fit to
predict data.
Scatter Plots
• Example 1: The table shows the largest vertical drops of
nine roller coasters in the United Sates and the number
of years after 1988 that they were opened.
• Identify the independent and dependent variables.
• Is there a relationship between the data? If so, predict
the vertical drop in a roller coaster built 30 years after
1988.
Years
since
1988
1
Vertical
Drop
(ft.)
151 155
3
5
8
12
12
12
13
15
225 230 306 300 255 255 400
Scatter Plots
• Example 2: The Body Mass Index (BMI) is a measure of body
fat using height and weight. The heights and weights of
twelve men with normal BMI are given in the table.
• Make Scatter Plot and Draw Line of Best Fit
• Predict the normal weight for a man who is 84 inches tall.
• A man’s weight is 188 pounds. Use the equation of the line
of fit to predict the height of the man.
Height
(in)
62
63
65
67
67
68
68
68
68
72
73
73
Weight
(Lb.)
115
124
120
134
140
138
144
152
147
155
168
166
Projects and Resources
• Stained Glass Window
• Wheel of Theodorus
• Kuta Software (worksheets)
• Math-Drills (worksheets)
• Khan Academy (Videos)
• Teachers pay Teachers
Thank you!