9 March 2011
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Transcript of 9 March 2011
9 March 2011
Algebra 2
Algebraic Operations 3/9• Like Terms Terms are considered “like” if they
have the same variable AND the same powers on the variable.
Mathematics.XEI.303: (16-19) Combine like terms
Algebraic Operations 3/9• Like Terms Terms are considered “like” if they
have the same variable AND the same powers on the variable.
Example: x2, 2x, 5x3, 8x2
Only x2, 8x2 are like terms
Mathematics.XEI.303: (16-19) Combine like terms
Which of the following are like terms?
1 2 3 4 5
0% 0% 0%0%0%
1. 2x and2x2
2. 3x and 33. 4x2 and 4x3
4. 5x3 and 8x3
5. x and xy
0 of 30
60
Algebraic Operations 3/9• Like Terms When you are combining like terms,
add the coefficients.
Mathematics.XEI.303: (16-19) Combine like terms
Algebraic Operations 3/9• Like Terms When you are combining like terms,
add the coefficients.
Example: 2xy + xy + 5xy = ?
Mathematics.XEI.303: (16-19) Combine like terms
Algebraic Operations 3/9• Like Terms When you are combining like terms,
add the coefficients.
Example: 2xy + xy + 5xy = ?
2 + 1 + 5 = 8
Mathematics.XEI.303: (16-19) Combine like terms
Algebraic Operations 3/9• Like Terms When you are combining like terms,
add the coefficients.
Example: 2xy + xy + 5xy = ?
2 + 1 + 5 = 8, so
2xy + xy + 5xy = 8xy
Mathematics.XEI.303: (16-19) Combine like terms
2a3 + a2 + a + 3a – 4a3 = ?
1 2 3 4
0% 0%0%0%
1. a9
2. 2a7 - 4a3
3. 2a3 + a2 + 4a4. -2a3 + a2 + 4a
0 of 30
60
2a3 + a2 + a + 3a – 4a3 = ?
2a3 + a2 + a + 3a – 4a3 = ?Combine like
terms-2a3 + a2 + 4a
Like Terms:
• Choose any 10 questions from the first 15• Write the question #, show your work, and
write the letter answer choice on your sheet• You have 10 minutes.
09000 01 87654321590 04 98765432103 9876543210987654321021 987654321098765432100Hours Minutes Seconds
Time Left
Algebraic Operations 3/9• Exponent
RulesYou can multiply or divide the same variable, even if the powers are different.
Mathematics.NCP.604: (28-32) Apply rules of exponents
Algebraic Operations 3/9• Exponent
RulesYou can multiply or divide the same variable, even if the powers are different.
Multiplication: Add exponentsDivision: Subtract exponents
Example: (x2)(x3)(x5)(x7) = ?
Mathematics.NCP.604: (28-32) Apply rules of exponents
Algebraic Operations 3/9• Exponent
RulesExample: (x2)(x3)(x5)(x7) = ?
Mathematics.NCP.604: (28-32) Apply rules of exponents
Algebraic Operations 3/9• Exponent
RulesExample: (x2)(x3)(x5)(x7) = ?
Add all the exponents on ‘x’
2 + 3 + 5 + 7 = 17
Mathematics.NCP.604: (28-32) Apply rules of exponents
Algebraic Operations 3/9• Exponent
RulesExample: (x2)(x3)(x5)(x7) = ?
Add all the exponents on ‘x’
2 + 3 + 5 + 7 = 17
(x2)(x3)(x5)(x7) = x17
Mathematics.NCP.604: (28-32) Apply rules of exponents
Algebraic Operations 3/9• Exponent
RulesExample 2:
5
23
xyyx
Mathematics.NCP.604: (28-32) Apply rules of exponents
Algebraic Operations 3/9• Exponent
RulesExample 2:
Larger x is on top, subtract the bottom power from the top power:
5
23
xyyx
5
22
yyx
Mathematics.NCP.604: (28-32) Apply rules of exponents
Algebraic Operations 3/9• Exponent
RulesExample 2:
Larger x is on top, subtract the bottom power from the top power:
Larger y is on bottom, subtract the top power from the bottom power:
5
23
xyyx
5
22
yyx
3
2
yx
Mathematics.NCP.604: (28-32) Apply rules of exponents
(xy2)(x3y2) = ?
1 2 3 4 5
0% 0% 0%0%0%
1. x3y4
2. x2y3. x4y4
4. xy7
5. xy8
0 of 30
60
(xy2)(x3y2) = ?
• (xy2)(x3y2) = ?
x4
(xy2)(x3y2) = ?
• (xy2)(x3y2) = ?
x4y4
Algebraic Operations 3/9• Exponent
RulesIf you are raising a variable with an exponent, multiply the powers.
Example: (a3)4
Mathematics.NCP.604: (28-32) Apply rules of exponents
Algebraic Operations 3/9• Exponent
RulesIf you are raising a variable with an exponent, multiply the powers.
Example: (a3)4
3*4 = 12
Mathematics.NCP.604: (28-32) Apply rules of exponents
Algebraic Operations 3/9• Exponent
RulesIf you are raising a variable with an exponent, multiply the powers.
Example: (a3)4
3*4 = 12
(a3)4 = a12
Mathematics.NCP.604: (28-32) Apply rules of exponents
Exponent Rules:
• Complete ten questions out of # 16-30• Write the question #, show your work, and
write the letter answer choice on your sheet• You have 10 minutes.
09000 5 87654321541 04 98765432103 9876543210987654321021 987654321098765432100Hours Minutes Seconds
Time Left:
Algebraic Operations 3/9• Adding
FractionsIf you are adding two fractions with the SAME denominator:
?64xx
Mathematics.NCP.201: (13-15) Recognize equivalent fractions
Algebraic Operations 3/9• Adding
FractionsIf you are adding two fractions with the SAME denominator:
Add the numerators together.
?64xx
Mathematics.NCP.201: (13-15) Recognize equivalent fractions
Algebraic Operations 3/9• Adding
FractionsIf you are adding two fractions with the SAME denominator:
Add the numerators together.4 + 6 = 10
?64xx
Mathematics.NCP.201: (13-15) Recognize equivalent fractions
Algebraic Operations 3/9• Adding
FractionsIf you are adding two fractions with the SAME denominator:
Add the numerators together.4 + 6 = 10
?64xx
xxx1064
Mathematics.NCP.201: (13-15) Recognize equivalent fractions
.
1 2 3 4 5
0% 0% 0%0%0%
1. 7x/62. 7x/33. 10x/94. 10x/65. 10x/3
?35
32
xx
0 of 30
60
Algebraic Operations 3/9• Adding
FractionsIf you are adding two fractions with a different denominator:
?53
yx
Mathematics.NCP.501: (24-27) Find and use the least common multiple
Algebraic Operations 3/9• Adding
FractionsIf you are adding two fractions with a different denominator:
Multiply the denominators:
?53
yx
xyyx?53
Mathematics.NCP.501: (24-27) Find and use the least common multiple
Algebraic Operations 3/9• Adding
FractionsIf you are adding two fractions with a different denominator:
Cross Multiply
?53
yx
xyyx
yx3553
Mathematics.NCP.501: (24-27) Find and use the least common multiple
Adding Fractions:
• Complete # 31-40• Write the question #, show your work, and
write the letter answer choice on your sheet• You have 10 minutes.
09000 01 87654321590 04 98765432103 9876543210987654321021 987654321098765432100Hours Minutes Seconds
Time Left
Simplifying Expressions 3/8
Simplify 3(2q + r)
Mathematics.XEI.402: (20-23) Add and subtract simple algebraic expressions
Simplifying Expressions 3/8
Simplify 3(2q + r)
6q + 3r + 20q – 35r
Mathematics.XEI.402: (20-23) Add and subtract simple algebraic expressions
Simplifying Expressions 3/8
Simplify 3(2q + r)
6q + 3r + 20q – 35r
Mathematics.XEI.402: (20-23) Add and subtract simple algebraic expressions
Notes: Multiplying Binomials 3/8Box Method You can use the box method to
multiply two binomials:
Example 1: (x + 4)(x – 3)
Make a 2x2 square box
XEI.405:Multiply 2 Binomials
Notes: Multiplying Binomials 3/8Box Method You can use the box method to
multiply two binomials:
Example 1: (x + 4)(x – 3)
Write the first binomial across the top x +4
XEI.405:Multiply 2 Binomials
Notes: Multiplying Binomials 3/8Box Method You can use the box method to
multiply two binomials:
Example 1: (x + 4)(x – 3)
Write the second binomial going down x +4x
-3
XEI.405:Multiply 2 Binomials
Notes: Multiplying Binomials 3/8Box Method You can use the box method to
multiply two binomials:
Example 1: (x + 4)(x – 3)
Multiply x*x x +4x x2
-3
XEI.405:Multiply 2 Binomials
Notes: Multiplying Binomials 3/8Box Method You can use the box method to
multiply two binomials:
Example 1: (x + 4)(x – 3)
Multiply x*4 x +4x x2 +4x
-3
XEI.405:Multiply 2 Binomials
Notes: Multiplying Binomials 3/8Box Method You can use the box method to
multiply two binomials:
Example 1: (x + 4)(x – 3)
Multiply -3*x x +4x x2 +4x
-3 -3x
XEI.405:Multiply 2 Binomials
Notes: Multiplying Binomials 3/8Box Method You can use the box method to
multiply two binomials:
Example 1: (x + 4)(x – 3)
Multiply -3*4 x +4x x2 +4x
-3 -3x -12
XEI.405:Multiply 2 Binomials
Notes: Multiplying Binomials 3/8Box Method You can use the box method to
multiply two binomials:
Example 1: (x + 4)(x – 3)
List each term inside the box x +4x x2 +4x
-3 -3x -12
x2 + 4x – 3x - 12XEI.405:Multiply 2 Binomials
Notes: Multiplying Binomials 3/8Box Method You can use the box method to
multiply two binomials:
Example 1: (x + 4)(x – 3)
Simplify x +4x x2 +4x
-3 -3x -12
x2 + 4x – 3x – 12 = x2 + x - 12XEI.405:Multiply 2 Binomials
Multiplying Expressions:
• Complete # 41-50• Write the question #, show your work, and
write the letter answer choice on your sheet• You have 10 minutes.
09000 01 87654321590 04 98765432103 9876543210987654321021 987654321098765432100Hours Minutes Seconds
Time Left