Download Friday, September 21: 3-1 Modeling and - annedavenport

Monday, August 24: 1-2 Modeling Relationships with
Variables
Def: A variable is an unknown quantity which is usually
represented with a letter.
Def: A variable expression is a mathematical phrase that uses
numbers, variables, and operation symbols. For example, in the
variable expression 3x + 2, x is the variable.
Def: A term is a number, a variable, or the product or quotient
of numbers and variables (not sum or difference).
How many terms are there in the following expressions?
1. 7 x2  3x 10
2. 2  b2
a
3. 139x7 y6 z
Note: The number of terms is simply the number of expressions
being added and subtracted.
Def: If two expressions are equal to each other, you can write
this as an equation. For example, if x + 3 and 2x – 7 have the
same value, then x + 3 = 2x – 7.
Note: Equations always have an equals sign, but expressions do
not.
4. Suppose you apply for a job at McDonalds and they pay
$6.25 an hour. Define 2 variables and write an equation for the
total amount of money you will earn during your first week.
5. Suppose you go to a local pizza place and the price for a
large pizza is $8 plus $1.50 per topping. Define 2 variables and
write an equation to represent the total amount it will cost for a
large pizza (ignore tax).
6. Suppose you were paying for your pizza with a $20 bill.
Define 2 variables and write an equation to represent the amount
of change you will receive (ignore tax).
Use an equation to model the relationship in each table:
7.
Hours 1
2 3
4
Pay
7.50 15 22.50 30
8.
Distance 10 20 30 40
Time
15 30 45 60
9.
Miles in Taxi 1 2 3 4
Cost
5 8 11 14
00000000000
Wednesday, August 26: 3-1 Modeling and Solving
Equations
Review: An equation shows that two expressions are equal
(remember, equations always have an = sign!)
Def: The solutions of an equation are the values of the variable
that make the equation true.
Ex: x = 5 is a solution of x + 7 = 12 since 5 + 7 = 12 is a
true statement.
Ex: x = 10 is not a solution of x + 7 = 12 since 10 + 7 = 12
is not a true statement.
One way to solve an equation is to get the variable alone on one
side of the equals sign. To do this, you must use inverse
operations, which are operations that undo each other.
For example, addition and subtraction are inverse operations.
Ex: 3 + 5 – 5 = 3
(subtracting 5 undoes the addition of 5)
For example, multiplication and division are inverse operations.
Ex: 3 x 5 ÷ 5 = 3
(dividing by 5 undoes the multiplication by 5)
Properties of equality:
Addition: if a = b, then a + c = b + c
Subtraction: if a = b, then a – c = b – c
Multiplication: if a = b, then ac = bc
Division: if a = b, then a  b (c  0)
c
c
Solve the following equations:
1. x + 7 = -2
2. – 3 + x = 8
3. 4x = 20
4. x = 1
Solve and check:
5. 42 = 31 + f
6. -12k = 3
7. 2  y  1
8.  t  2
3
2
3
5 3
9. The weight of a father and his daughter together is 202.1
pounds. If the father weighs 175.4 pounds by himself, write an
equation to model and then solve the equation.
Friday, August 28: 3-2 Modeling and Solving Two-Step
Equations
When you are solving two-step equations, go through the order
of operations in reverse.
 Addition and Subtraction
 Multiplication and Division
 Exponents
 Parentheses
Solve and check:
1. 3x + 2 = 20
2. y  5  12
3. 1 m  1
4. 1.3n – 4 = 2.5
5. 2  1 k
6. 34 = 14 – 4p
4
12
2
Define a variable and use an equation to model and solve each
problem.
7. A taxi charges $5 plus $4 per mile. If a ride costs $20, how
many miles was the trip?
8. A teacher takes a class of students to a museum. Tickets for
adults are $8 and student tickets are $5. If the total cost for
everyone is $113, how many students were on the trip?
Monday, August 31: 3-3 Combining Like Terms to Solve
Equations
Review: A term is a number or variable or product or quotient
of numbers and variables.
Def: If a term has a variable, the numerical factor is called the
coefficient.
Ex: Name the coefficient:
2x
3x
-2y
-y
3
Def: Terms are like terms if they have exactly the same variable
factors.
Ex: 3x and 2 x are like terms
3
Ex: 3x2 and 2 x are not like terms since the variable has
3
different exponents
To simplify expressions, combine like terms by adding their
coefficients.
Simplify:
1. -2 + 6k + m – 5k + 7 + 4m2
2. 4 – 2x + 3y + 4 + 2x – 7y + 4y2
Solve and check. Combine like terms first!
3. 7x – 3x – 6 = 6
4. -13 = 2b – b – 10
5. 1 – 6t – 4t = 1
6. 72 + 4 – 14r = 36
Define a variable, write an equation, and solve.
7. The sum of 3 consecutive integers is 42. What are they?
8. A rectangle has a perimeter of 40 cm. The length is 2 cm
longer than the width. Find the dimensions.
Wednesday, September 2: 3-4 Using the Distributive
Property
For all real numbers a, b, c:
a(b + c) = ab + ac
a(b – c) = ab – ac
ex: 8(2 + 3) = 8(2) + 8(3)
8(5) = 16 + 24
40 = 40
ex: 4(5 – 2) = 4(5) – 4(2)
4(3) = 20 = 8
12 = 12
Simplify each expression:
1. 7(t – 4)
2. –(x – 3)
3. (5 + 2x)3
4. 3 12g  8
Solve each equation:
4
5. m + 5(m – 1) = 11
7.. 1  m 16  7
4
6. 0.5(x – 12) = 4
8. (8n  4) 3  2
4
9. 6(x + 4) – 2x = -8
Define a variable, write an equation, and solve.
10. The height of a computer screen is 3 inches less than its
width. If the perimeter is 50 inches, find the dimensions.
11. At a video store, new releases are $4 and older movies are
$2.50. In one month, a family rented 10 movies and paid $31.
How many of each type did they rent?
Friday, Sept 4: 3-5 Rational Numbers and Equations
When solving an equation in which a variable is being
multiplied by a fraction, multiply both sides by the reciprocal of
the fraction.
Review: The reciprocal of a is b
b
Solve and check:
1.  2 x  6
3
a
2. 7 a  14
3. 2  4c
8
9
To simplify equations with fractions in more than one term,
multiply each side of the equation by the least common
denominator.
4. x  3  5
5. x  3x  17
2 2
6. 2 x  x  7
3
2
4
5
Define a variable, write and equation and solve.
7. Suppose you can buy 11 pounds of meat for $8. How much
3
does the meat cost per pound?
8. Suppose you drive 210 miles in 3 1 hours. How fast were
2
you going? Hint: d = rt.
Wednesday, Sept 9: 3-7 Percent Equations/Quiz 3-4 to 3-5
Quiz 3-4 to 3-5
Converting percents to decimals: Move the decimal 2 places to
the left (divide by 100):
Ex: 35% =
7% =
125% =
8.25% =
Converting decimals to percents: Move the decimal 2 places to
the right (multiply by 100):
Ex: .28 =
.03 =
.0025 =
3.8 =
When you are translating a verbal sentence into a mathematical
equation,
 “is” means equals
 “of” means multiply
 “what” is an unknown value (use a variable for this, such as
x or n)
1. What is 40% of 8?
2. 16 is 25% of what?
3. What percent of 40 is 5?
4. 32 is what percent of 40?
5. What is 250% of 10?
6. 32 is 40% of what?
7. In a survey, 32 students had a graphing calculator. If this
represents 25% of the total, how many were surveyed?
8. On a 18 question test, a student gets 13 correct. What
percent did he get correct?
Simple interest formula: I = PRT, where I = interest earned, P =
principle (amount invested), R = interest rate (as a decimal) and
T = time in years.
9. Suppose you invested $400 for 2 years at 6%. How much
interest will you earn?
10. Suppose you earned $15 in interest over 6 years at 5%.
How much was your initial investment?
Friday, Sept 11: 3-8 Percent of Change (calc ok)
In the news you often hear statements like:
“home sales are down 8%”
“gas prices are up 15%”
To find these percents of change:
percent of change = new amount - original amount
original amount
Find the percent of change (round to the nearest percent):
1. 18 inches to 21 inches
2. 16 ounces to 12 ounces
3. $6.25 to $7.00
4. If the price of a gallon of gas was 1.50 last year and is 2.50
now, find the percent of change.
5. If the median price of a home was 210,000 last year and is
200,000 this year, find the percent of change.
6. If the price of milk has increased 12% from $2.13/gallon,
find the new price.
Monday, September 14: Review chapter 3
Solve:
1. -34 = 14 – 6p
3. 12 + 4 –
r
2 = 36
2. 2 = -3 –
k
4
4. 1 – 6t – 4t = 71
7
5. 6(x + 4) – 2x = 36
6. 8 a  5  16
x  3x  34
7. 4 5
8. 32 is 40% of what
number?
9. A group of adults and children went to the movies. If adult
tickets cost $8 and student tickets cost $6 and the total for 12
people was $78, how many adults were there?
10. Suppose that there are 504 freshmen at CDO and they
represent 30% of the student body. How many students are
there at CDO?
Wednesday, September 16: Chapter 3 Test