Calculus - Santowski 11/10/2015 Calculus - Santowski 1 B.1.1b – Derivatives As Functions.
ALGEBRA 1 ~ UNIT 1: SOLVING EQUATIONS & INEQUALITIES...
Transcript of ALGEBRA 1 ~ UNIT 1: SOLVING EQUATIONS & INEQUALITIES...
ALGEBRA 1 ~ UNIT 1: SOLVING EQUATIONS & INEQUALITIES
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1.1A Verbal & Algebraic Sentences
I can:
Rewrite verbal sentences as equations.
Rewrite equations as verbal sentences.
Term Definition Picture/Example
Algebraic Sentence
Verbal Sentence
Equation
Formula
Twice
Squared
Cubed
Example #1: The sum of w and v equals the square of y.
Example #2: Three times a number t increased by three is sixty-six.
Example #3: Twice a number x is less than the difference of a and b.
ARE YOU A MASTER??
1. What is the difference between an algebraic expression and a verbal expression?
2. What does an equation have to have?
ALGEBRA 1 ~ UNIT 1: SOLVING EQUATIONS & INEQUALITIES
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1.1B Verbal & Algebraic Inequalities
I can:
Rewrite verbal sentences as inequalities.
Rewrite inequalities as verbal sentences.
Term Definition Example(s) Picture
>
<
≥
≤
Example #1: Five times a number is as much as forty-five. Example #2: Twice a number c is less than the sum of a and b.
Example #3: Twice a number x is greater than the difference of a and b.
ARE YOU A MASTER??
1. The difference of x and y are identical to 5 times a number z.
2. The difference of x and y is no more than 5 times a number z.
ALGEBRA 1 ~ UNIT 1: SOLVING EQUATIONS & INEQUALITIES
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1.2 Solving One-Step Equations & Inequalities
I can:
Solve equations & inequalities by adding.
Solve equations & inequalities by subtracting.
“MOVE” BY SUBTRACTING
Example #1: 5224 x Example #2: 117 x
Example #3: 2.412 x Example #4: 1423 q
Example #5: 9
7
9
4 x Example #6: nn 13412
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“MOVE” BY ADDING
Example #7: 712 x Example #8: 138.6 x
Example #9: 4
1
8
3 x Example #10:
2
1
8
3 x
Example #11: pp 463 Example #12: 821 x
ARE YOU A MASTER??
1. 2.97.2 x 2. 1410 k 3. 4
1)
8
1( x
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1.3 Solving One-Step Equations & Inequalities
I can:
Solve equations & inequalities by multiplying.
Solve equations & inequalities by dividing.
“CANCEL” STEP W/DIVISION
Example #1: 968 x Example #2: 243 x
Example #3: 8.98.2 x Example #4: x5.335.42
Example #5: 1368 x Example #6: 122 x
“CANCEL” STEP W/MULTIPLICATION
Example #7: 39
x
Example #8: 63
2x
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“CANCEL” STEP W/MULTIPLICATION
Example #9: 23
4 x
Example #10: 39
x
Example #11: 63
2 m Example #12:
4
3
8
1 x
ARE YOU A MASTER??
Which inequality does not have the solution 6x ?
A. 122 x B. 366 x C. 56
5x D.
4
3
8
1 x
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1.4 Solving Two-Step Equations & Inequalities
I can:
Solve two-step equations.
Solve two-step inequalities.
Example #1: 14173 x Example #2: 791113 d
Example #3: 7114
x
Example #4: 38152 x
Example #5: 21122
x
Example #6: 212325
9C
ARE YOU A MASTER??
1) 03
212 x 2) 2723 x
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1.5 Solving Multi-Step Equations & Inequalities
I can:
Solve multi-step equations.
Solve multi-step inequalities.
Example #1: 53
7
x Example #2: 5.13
2
14
x
Example #3: 10225 xx Example #4: 51915 xx
Example #5: 17132 x Example #6: 13273 xxx
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Example #7: xx 4884 Example #8: 123
153
x
Example #9: 89211534 nn Example #10: 22932 x
ARE YOU A MASTER??
a) kk 1812 b) 2313 xx
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1.6 Solving for a Given Variable
I can:
Solve for a given variable.
Term Definition Picture/Example Equivalent Equations
Solve for _____
TRUE or FALSE 3 + 2 = 5 is equivalent to 3 = 2 + 5?
TRUE or FALSE 3 + 2 = 5 is equivalent to 3 = 2 – 5?
TRUE or FALSE 3 + 2 = 5 is equivalent to 3 = 5 – 2?
Multiple Choice
Given: 3 + x = 5, which choice is equivalent?
A) 3 = x – 5 B) 3 = 5 – x C) 3 = x + 5 D) 3 = x
Example #1: 5 yx ; for x Example #2: 1274 yx ; for x
Example #3: cbyax ; for y Example #4: cbyax ; for a
ARE YOU A MASTER?? Solve for t:
2
t
rs
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1.7 Percents in the Real-World
I can:
Find percents.
Solve real-world problems using percents.
A Percentage is a Special Fraction
The % = “Per ______________________”
47% is simply another way of writing the fraction _____________________.
Example #1: Complete the chart:
PERCENT TO A DECIMAL
35% = 35/100
35% ÷ 100 .35
DECIMAL TO A PERCENT
2/100 = 23%
.23 100 23%
Percentage Fraction
7% 7/100
19% 19/100
83%
3%
15/100
47%
36/100
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Example #2: Complete the chart below:
Example #3: Jill obtained a score of 23 out of 32 in a science test. She wants to know what this will be as a
percentage?
Step 1: Write the result as a fraction:
Step 2: Change the fraction into a decimal:
Step 3: Change the decimal into a % by multiplying by 100:
Percentage Decimal Decimal Percentage
27% 0.87
2% 0.08
55% 0.42
5% 0.04
17% 0.71
98% 0.07
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Example #4: What percentage of the cars are green?
Step 1: Write the result as a fraction:
Step 2: Change the fraction into a decimal:
Step 3: Change the decimal into a % by multiplying by 100:
Your Turn:
1) What is your quiz percentage if you got 12 out of 25 problems correct?
2) What is your quiz percentage if you got 17.5 out of 31 problems correct?
3) A player scores 4 times out of 9 shots. What is their scoring percentage?
4) A player scores 44 times out of 69 shots. What is their scoring percentage?
5) 12 out of 30 students in this class have blue eyes. What percent of students have blue eyes?
Percent
Red
Green
Black
White
18
41 22
19
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How to find Percentage of a Number
Step 1: Change the percentage into a ______________ by dividing by 100 (or moving the decimal 2 left).
Step 2: Change the word ‘of ’ into a sign and multiply.
Example #5: In a survey of 120 students it was found that 20% had an iPhone 5. How many students had the
iPhone 5? (hint: find 20% of 120)
Step 1: Change the percentage to a decimal.
Step 2: Change the word ‘of ’ into a sign and multiply.
Your Turn:
1) 25% of 32
2) 75% of 36
3) 80% of 48
4) 10% of 142
5) 20% of 60
Example #6: You found a pair of jeans you absolutely love. The only issue is they are $90 and that’s over your
budget. The kind lady next to you gave you a 30% off coupon. How much will your pair of jeans be with the
coupon?
Step 1: What is 30% of $90?
Step 2: Let’s take off (subtract) that 30%.
Can anyone think of another way to solve this problem?
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ARE YOU A MASTER??
Which is the better deal? Show all work to find the total price for EACH item.
Reminder: Show all work.
Final Price: _______________________ Final Price: _______________________
Dicks Sporting Goods
Price: $39.99
Take 20% off today
only!
MC Sports
Price: $44.95
Take 25% off today only!