algebra 2 unit 1.1
TRANSCRIPT
UNIT 1.1 PATTERNS AND EXPRESSIONS
1.1
Perform the indicated operation.
1. 12 1.5 2. 3.3 7
ANSWER 8 ANSWER 23.1
3. 11.6 – 5.9
ANSWER 5.7
4. Julia ran 10 2miles last week and 8 5
miles this week.
How many more miles did she run last week?3 6
ANSWER 1 5 mi6
1.1 Vocabulary
Variable – a letter that is used to replace a
number
Algebraic expression – an expression that
contains numbers, varailbes, and operations.
Evaluate and algabreic expression – to find the
value of an algabreic expression by substituting a
number for each variable.
Power – an expression that represents reapeated
multiplication of the same factor.
1.1 VocabularyExponent – the number or variable that represents
the number of times the base of a power is used as
a factor.
Base of a power – the number or expression that is
used as a factor in repeated multiplication.
Example
9³Base Exponent
1.1
Evaluate the expression when n = 3.
Substitute 3 for n.
Multiply.
Substitute 3 for n.
Subtract.
c. n – 1 = 3 – 1
= 2
Substitute 3 for n.
= 3 Divide.
93
b.9n
=
Substitute 3 for n.
Add.
d. n + 8 = 3 + 8
= 11
a. 13 n = 13 3
= 39
1.1
1. 12
3. 6
2. 4
Evaluate the expression when y = 2.
1. 6y
2.8y
3. y + 4
4. 94. 11 – y
ANSWERS
1.1
Movies
The total cost of seeing a movie at a theater can be
represented by the expression a + r where a is the
cost (in dollars) of admission and r is the cost (in
dollars) of refreshments. Suppose you pay $7.50 for
admission and $7.25 for refreshments. Find the total
cost.
1.1
Add.
The total cost is $14.75
ANSWER
Write expression.
Substitute 7.50 for a and
7.25 for r.= 7.50 + 7.25
= 14.75
Total cost =
SOLUTION
a + r
1.1
WHAT IF? In Example 2, suppose you go back to the theater with a friend to see an afternoon movie.You pay for both admissions. Your total cost (indollars) can be represented by the expression 2a. Ifeach admission costs $4.75, what is your total cost?
The total cost is $9.50.
ANSWER
1.1
Product
Write the power in words and as a product.
Power Words
seven to the first powera. 71 7
five to the second power,
or five squared
b. 52 5 5
c. 12
3one half to the third power,
or one half cubed
1 1 12 2 2
z to the fifth powerd. z5 z z z z z
1.1
Write the power in words and as a product.
Power Words Product
Nine to the fifth power6. 95
Two to the eighth power7. 28
n to the fourth power
9 9 9 9 9
2 2 2 2 2 2 2 2
8. n4 n n n n
1.1
a. x4 = 24
= 2 2 2 2
= 16
Evaluate the expression.
a. x4 when x = 2
b. n3 = 1.53
= (1.5)(1.5)(1.5)
= 3.375
b. n3 when n = 1.5
SOLUTION
1.1
Evaluate the expression.
9. x3 when x = 8 9. 512
10. 6.2510. k3 when k = 2.5
ANSWERS
11. d4 when d = 1
311.
1
81
1.1
SOLUTION
Storage cubes
Write formula for volume.
Substitute 14 for s.
Evaluate power.
V = s3
= 143
= 2744
Each edge of the medium-sized
pop-up storage cube shown is 14
inches long. The storage cube is
made so that it can be folded flat
when not in use. Find the
volume of the storage cube.
The volume of the storage cube is 2744 cubic inches.
1.1
WHAT IF? In Example 5, suppose
the storage cube is folded flat to
form a square. Find the area of the
square.
The area of square is 196 in2.
ANSWER
1.1
3. 54
ANSWER 0.9
ANSWER 625
Evaluate the expression or power.
1. 13g when g = 7 2. 1.65 – a when a = 0.75
ANSWER 9113
3
4.
ANSWER 127
5. Emily is saving for a $300 bicycle. She has saved
$128.25. The amount she still needs to save is given
by the expression c – s, where c is the cost of the
bicycle and s is the amount she has saved. How
much does she have left to save?
$171.75ANSWER
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