Name: ______________________
Class: _________________
Date: _________
ID: A
ALGEBRA 2 FINAL EXAM REVIEW
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
____
1. Classify –6x5 + 4x3 + 3x2 + 11 by degree.
a. quintic
b. cubic
c.
d.
quartic
quadratic
2. Classify 8x4 + 7x3 + 5x2 + 8 by number of terms.
a. trinomial
c. polynomial of 5 terms
b. binomial
d. polynomial of 4 terms
Consider the leading term of each polynomial function. What is the end behavior of the
graph?
____
____
8
7
6
3. 5x ! 2x ! 8x + 1
a. The leading term
down and up.
b. The leading term
down.
c. The leading term
up and up.
d. The leading term
and down.
5
4
8
is 5x . Since n is even and a is positive, the end behavior is
8
is 5x . Since n is even and a is positive, the end behavior is up and
8
is 5x . Since n is even and a is positive, the end behavior is
8
is 5x . Since n is even and a is positive, the end behavior is down
3
4. !3x + 9x + 5x + 3
a. The leading term
up.
b. The leading term
down and down.
c. The leading term
up and down.
d. The leading term
and up.
5
is !3x . Since n is odd and a is negative, the end behavior is up and
5
is !3x . Since n is odd and a is negative, the end behavior is
5
is !3x . Since n is odd and a is negative, the end behavior is
5
is !3x . Since n is odd and a is negative, the end behavior is down
Write the polynomial in factored form.
____
5. x3 + 9x2 + 18x
a. 6x(x + 1)(x + 3)
b. 3x(x + 6)(x + 1)
c.
d.
1
x(x + 6)(x – 3)
x(x + 3)(x + 6)
Name: ______________________
ID: A
What are the zeros of the function? Graph the function.
____
6. y = x(x ! 2)(x + 5)
a. 2, –5
b.
____
0, –2, 5
7. Divide 4x 3 + 2x 2 + 3x + 4 by x + 4.
a. 4x 2 ! 14x + 59
b. 4x 2 + 18x ! 53, R 240
c.
0, 2, –5
d.
2, –5, –2
c.
d.
4x 2 ! 14x + 59, R –232
4x 2 + 18x ! 53
c.
d.
!6x + 30x ! 19, R –20
2
6x ! 30x + 19, R 20
Divide using synthetic division.
____
3
2
8. Divide !6x + 18x ! 7x ! 10 by (x ! 2).
a.
b.
2
!6x + 6x + 5
2
6x ! 6x ! 5
2
2
Name: ______________________
____
ID: A
9. Use the Rational Root Theorem to list all possible rational roots of the polynomial equation
x 3 ! 6x 2 + 4x + 9 = 0. Do not find the actual roots.
a. –9, –1, 1, 9
c. –9, –3, –1, 1, 3, 9
b. 1, 3, 9
d. no roots
Use Pascal’s Triangle to expand the binomial.
____ 10. (d ! 2) 6
a. d 6 + 12d 5 + 60d 4 + 160d 3
b. d 6 ! 6d 5 + 15d 4 ! 20d 3 +
c. d 6 ! 12d 5 + 60d 4 ! 160d 3
d. d 6 + 6d 5 + 15d 4 + 20d 3 +
+ 240d 2 + 192d + + 64
15d 2 ! 6d + 1
+ 240d 2 ! 192d + 64
15d 2 + 6d + 1
____ 11. Find all the real square roots of 0.0004.
a. 0.00632 and –0.00632
b. 0.06325 and –0.06325
c.
d.
0.0002 and –0.0002
0.02 and –0.02
c.
!
c.
11
c.
x
7 !x
d.
!
42x
Find the real-number root.
____ 12.
3
a.
!
125
343
25
49
b.
!
125
343
125
1029
d.
!
5
7
Multiply and simplify if possible.
____ 13.
4
a.
____ 14.
a.
b.
11 "
4
3
3
b.
Ê
7x ÁÁÁÁ
Ë
x !7
7
x
7 ! 49
x
7x ! 49x
11
4
3
d.
˜ˆ˜
˜˜
¯
49
What is the simplest form of the expression?
____ 15.
3
a.
b.
108a 16 b 9
3a 5 b 3
4a 5 b 3
3
3
3
4a
c.
3a 5 b
3a
d.
none of these
3
a
4
33
Name: ______________________
ID: A
What is the simplest form of the product?
7
____ 16.
7
50x y "
4
6
a.
2x y
b.
10x y
4
6xy
4
4
6
75y
c.
5x y
3y
d.
30x y
5
4
12
5
y
What is the simplest form of the quotient?
3
____ 17.
162
3
a.
2
3
3
3
b.
3
162
c.
3
3
3
d.
3
What is the simplest form of the radical expression?
____ 18. 3
2a ! 6
a.
!6
b.
9
2a
2a
2a
c.
!3
2a
d.
not possible to simplify
What is the simplest form of the expression?
____ 19.
20 +
45 !
5
a.
4
5
c.
13
b.
6
5
d.
5
5
5
What is the product of the radical expression?
Ê
____ 20. ÁÁÁÁ 7 !
Ë
____ 21.
2
˜ˆ˜ ÁÊÁ 8 +
˜˜ ÁÁ
¯Ë
a.
54 + 56
b.
54 !
2
˜ˆ˜
˜˜
¯
2
2
ÊÁ
ˆÊ
ÁÁ 5 ! 2 ˜˜˜ ÁÁÁ 5 +
ÁË
˜¯ ÁË
a. 23
b. 20
c.
13 + 15
2
d.
58 + 56
2
c.
d.
27
18
ˆ
2 ˜˜˜˜
¯
4
3
Name: ______________________
ID: A
How can you write the expression with rationalized denominator?
____ 22.
3 !
6
3 +
6
!1 ! 2
a.
18
3
!3 ! 2
b.
18
9
c.
!3 + 2
2
d.
9 !2
18
____ 23.
2 +
3
3
3
6
2
a.
3
6 +9
3
18
c.
6
2
b.
3
36 + 3
3
2
d.
6
2
3
6 +9
3
4
6
2
3
36 + 3
3
4
6
Simplify.
1
____ 24. 3
1
3
"9
a.
____ 25. 16
a.
b.
3
9
b.
3
3
c.
3
d.
3
1
2
16
4
2
c.
d.
16
2
16
3
____ 26. Write the exponential expression 3x 8 in radical form.
a.
3
8
x3
b.
8
3x 3
c.
3
3
3
x8
d.
3
8
What is the solution of the equation?
____ 27.
2x + 8 ! 6 = !4
a. 4
b.
–2
c.
12
d.
–3
b.
2
c.
26
d.
38
3
____ 28. ( x + 6 )
a. 14
5
= 8
5
8
x3
Name: ______________________
ID: A
____ 29. Let f(x) = 4x ! 5 and g(x) = 6x ! 3. Find f(x) ! g(x).
a. 10x – 8
b. 10x – 2
c. –2x – 8
d.
–2x – 2
d.
–10
____ 30. Let f(x) = 3x + 2 and g(x) = 7x + 6. Find f " g and its domain.
2
a. 6x 2 + 4x + 42; all real numbers except x = !
3
b. 6x 2 + 4x + 42; all real numbers
c. 21x 2 + 32x + 12; all real numbers
6
d. 21x 2 + 32x + 12; all real numbers except x = !
7
____ 31. Let f(x) = x 2 ! 16 and g(x) = x + 4. Find
a.
b.
c.
d.
x + 4;
x + 4;
x ! 4;
x ! 4;
all
all
all
all
real
real
real
real
numbers
numbers
numbers
numbers
except
except
except
except
f
g
and its domain.
x#4
x # !4
x#4
x # !4
____ 32. Let f(x) = x + 2 and g(x) = x 2 . Find ÊÁË g û f ˆ˜¯ ( !5 ) .
a. 9
b. –3
c. 49
What is the inverse of the given relation?
____ 33. y = 7x 2 ! 3.
a.
y = ±
b.
x =
x+3
7
y+3
7
____ 34. y = 3x + 9
1
a. y = x + 3
3
b.
y = 3x ! 3
x!3
7
c.
y2 =
d.
y = ±
c.
y = 3x + 3
d.
y=
6
x!3
7
1
x!3
3
Name: ______________________
ID: A
Graph the exponential function.
____ 35. y = 4 x
a.
b.
c.
d.
____ 36. Suppose you invest $1600 at an annual interest rate of 4.6% compounded continuously. How much will
you have in the account after 4 years?
a. $800.26
b. $6,701.28
c. $10,138.07
d. $1,923.23
____ 37. How much money invested at 5% compounded continuously for 3 years will yield $820?
a. $952.70
b. $818.84
c. $780.01
d. $705.78
Write the equation in logarithmic form.
____ 38. 2 5 = 32
a. log 32 = 5 " 2
b. log 2 32 = 5
c.
d.
7
log 32 = 5
log 5 32 = 2
Name: ______________________
ID: A
Evaluate the logarithm.
____ 39. log 5
a.
1
625
–3
b.
5
c.
–4
d.
4
b.
–5
c.
4
d.
3
b.
–2
c.
2
d.
10
____ 40. log 3 243
a.
5
____ 41. log 0.01
a. –10
Write the expression as a single logarithm.
____ 42. 3 log b q + 6 log b v
a.
b.
log b (q 3 v 6 )
Ê 3 + 6 ˆ˜
˜˜
log b ÁÁÁÁ qv
˜¯
Ë
c.
d.
( 3 + 6 ) log b ÊÁË q + v ˆ˜¯
Ê 3
6ˆ
log b ÁÁÁÁ q + v ˜˜˜˜
Ë
¯
____ 43. log 3 4 ! log 3 2
a.
log 3 2
b.
log 3 2
c.
log 2
d.
Expand the logarithmic expression.
____ 44. log 3
d
12
log 3 d
a.
log 3 d ! log 3 12
c.
b.
!d log 3 12
d.
log 3 12 ! log 3 d
log 3 12
____ 45. log 3 11 p 3
a.
log 3 11 " 3 log 3 p
c.
log 3 11 + 3 log 3 p
b.
log 3 11 ! 3 log 3 p
d.
11 log 3 p
____ 46. Use the Change of Base Formula to evaluate log 7 28.
a.
b.
1.712
3.332
c.
d.
8
1.712
1.447
3
log 2
Name: ______________________
ID: A
Solve the exponential equation.
____ 47.
1
= 64 4x ! 3
16
1
a.
12
____ 48. 4
b.
1
4
c.
7
12
d.
11
12
b.
8
3
c.
3
8
d.
2
4x
=8
3
a.
4
Solve the logarithmic equation.
____ 49. 3 log 2x = 4
a. 10.7722
b.
5
Round to the nearest ten-thousandth if necessary.
c.
2.7826
d.
0.6309
6
____ 50. Find the horizontal asymptote of the graph of y =
!4x + 6x + 3
6
.
a.
y=1
c.
8x + 9x + 3
y=0
b.
1
y=!
2
d.
no horizontal asymptote
Simplify the rational expression. State any restrictions on the variable.
2
____ 51.
p ! 4p ! 32
p +4
!p + 8; p # !4
p ! 8; p # !4
a.
b.
c.
d.
!p ! 8; p # 4
p + 8; p # 4
2
____ 52.
q + 11q + 24
2
q ! 5q ! 24
q +8
a.
; q # !3, q # !8
q !8
!(q + 8)
b.
;q # 8
q !8
c.
d.
9
q +8
; q # !3, q # 8
q !8
!(q + 8)
; q # !3, q # 8
q !8
Name: ______________________
ID: A
What is the product in simplest form? State any restrictions on the variable.
____ 53.
4a
5
7b
4
a.
"
2b
2
2a
4
4a
9
7b
6
4a
b.
7b
2
, a # 0, b # 0
c.
, a # 0, b # 0
d.
7b
4a
2
, a # 0, b # 0
4 9 6
a b , a # 0, b # 0
7
What is the quotient in simplified form? State any restrictions on the variable.
____ 54.
x+2
÷
x+4
2
x!1
x + 4x ! 5
(x + 2)(x + 5)
a.
, x # ! 5, ! 4
x+4
(x + 2)(x + 4)
b.
, x # 1, ! 5
2
(x ! 1) (x + 5)
c.
d.
(x + 2)(x + 4)
, x # 1, ! 5, ! 4
2
(x ! 1) (x + 5)
(x + 2)(x + 5)
, x # 1, ! 4
x+4
Simplify the sum.
____ 55.
7
+
a +8
a.
7
2
a ! 64
7a ! 49
(a ! 8)(a + 8)
14
b.
2
a + a ! 56
c.
14
(a ! 8)(a + 8)
d.
7a + 63
(a ! 8)(a + 8)
Simplify the difference.
2
____ 56.
b ! 2b ! 8
2
b +b !2
a.
!
6
b !1
b ! 10
c.
2
b.
b ! 2b ! 14
2
b +b !2
d.
10
b !4
b !1
b ! 10
b !1
Name: ______________________
ID: A
Simplify the complex fraction.
2
____ 57.
5t
1
2t
!
+
a.
3
3t
1
2t
3
!
5
b.
!4
c.
!
5
3
d.
!
1
4
d.
!
11
3
d.
6
4
____ 58.
x+3
1
+3
x
12x + 4
a.
2
x + 3x
4x
b.
3x + 9
c.
4x
2
3x + 10x + 3
d.
not here
c.
!
c.
–9 and –6
Solve the equation. Check the solution.
____ 59.
!2
x+4
4
x+3
13
!
6
a.
____ 60.
=
a
2
a ! 36
a. –9
b.
+
2
a !6
=
!11
8
3
1
a +6
b. –6
11
ID: A
ALGEBRA 2 FINAL EXAM REVIEW
Answer Section
MULTIPLE CHOICE
1. ANS:
OBJ:
TOP:
KEY:
DOK:
2. ANS:
OBJ:
TOP:
KEY:
DOK:
3. ANS:
OBJ:
STA:
TOP:
KEY:
4. ANS:
OBJ:
STA:
TOP:
KEY:
5. ANS:
REF:
OBJ:
STA:
TOP:
KEY:
6. ANS:
REF:
OBJ:
STA:
TOP:
DOK:
7. ANS:
OBJ:
STA:
TOP:
DOK:
8. ANS:
OBJ:
STA:
TOP:
DOK:
A
PTS: 1
DIF: L2
REF: 5-1 Polynomial Functions
5-1.1 To classify polynomials
STA: MA.912.A.2.5| MA.912.A.4.5
5-1 Problem 1 Classifying Polynomials
degree of a polynomial | polynomial function | standard form of a polynomial function
DOK 1
D
PTS: 1
DIF: L2
REF: 5-1 Polynomial Functions
5-1.1 To classify polynomials
STA: MA.912.A.2.5| MA.912.A.4.5
5-1 Problem 1 Classifying Polynomials
degree of a polynomial | polynomial function | standard form of a polynomial function
DOK 1
C
PTS: 1
DIF: L2
REF: 5-1 Polynomial Functions
5-1.2 To graph polynomial functions and describe end behavior
MA.912.A.2.5| MA.912.A.4.5
5-1 Problem 2 Describing End Behavior of Polynomial Functions
polynomial | end behavior
DOK: DOK 1
C
PTS: 1
DIF: L3
REF: 5-1 Polynomial Functions
5-1.2 To graph polynomial functions and describe end behavior
MA.912.A.2.5| MA.912.A.4.5
5-1 Problem 2 Describing End Behavior of Polynomial Functions
polynomial | end behavior
DOK: DOK 1
D
PTS: 1
DIF: L2
5-2 Polynomials, Linear Factors, and Zeros
5-2.1 To analyze the factored form of a polynomial
MA.912.A.4.3| MA.912.A.4.5| MA.912.A.4.7| MA.912.A.4.8
5-2 Problem 1 Writing a Polynomial in Factored Form
DOK: DOK 2
C
PTS: 1
DIF: L3
5-2 Polynomials, Linear Factors, and Zeros
5-2.1 To analyze the factored form of a polynomial
MA.912.A.4.3| MA.912.A.4.5| MA.912.A.4.7| MA.912.A.4.8
5-2 Problem 2 Finding Zeros of a Polynomial Function
DOK 2
C
PTS: 1
DIF: L2
REF: 5-4 Dividing Polynomials
5-4.1 To divide polynomials using long division
MA.912.A.4.3| MA.912.A.4.4| MA.912.A.4.6
5-4 Problem 1 Using Polynomial Long Division
KEY:
DOK 2
A
PTS: 1
DIF: L3
REF: 5-4 Dividing Polynomials
5-4.2 To divide polynomials using synthetic division
MA.912.A.4.3| MA.912.A.4.4| MA.912.A.4.6
5-4 Problem 3 Using Synthetic Division
KEY: synthetic division
DOK 2
1
ID: A
9. ANS:
REF:
OBJ:
STA:
KEY:
10. ANS:
OBJ:
TOP:
DOK:
11. ANS:
OBJ:
TOP:
DOK:
12. ANS:
OBJ:
TOP:
DOK:
13. ANS:
REF:
OBJ:
TOP:
DOK:
14. ANS:
REF:
OBJ:
TOP:
DOK:
15. ANS:
REF:
OBJ:
TOP:
DOK:
16. ANS:
REF:
OBJ:
TOP:
DOK:
17. ANS:
REF:
OBJ:
TOP:
DOK:
18. ANS:
OBJ:
TOP:
KEY:
C
PTS: 1
DIF: L2
5-5 Theorems About Roots of Polynomial Equations
5-5.1 To solve equations using the Rational Root Theorem
MA.912.A.4.6| MA.912.A.4.7
TOP: 5-5 Problem 1 Finding a Rational Root
Rational Root Theorem
DOK: DOK 1
C
PTS: 1
DIF: L2
REF: 5-7 The Binomial Theorem
5-7.1 To expand a binomial using Pascal's Triangle
STA: MA.912.A.4.12
5-7 Problem 1 Using Pascal's Triangle
KEY: Pascal's Triangle | expand
DOK 2
D
PTS: 1
DIF: L4
REF: 6-1 Roots and Radical Expressions
6-1.1 To find nth roots
STA: MA.912.A.10.3
6-1 Problem 1 Finding All Real Roots
KEY: nth root
DOK 1
D
PTS: 1
DIF: L3
REF: 6-1 Roots and Radical Expressions
6-1.1 To find nth roots
STA: MA.912.A.10.3
6-1 Problem 2 Finding Roots
KEY: radicand | index | nth root
DOK 1
D
PTS: 1
DIF: L2
6-2 Multiplying and Dividing Radical Expressions
6-2.1 To multiply and divide radical expressions
STA: MA.912.A.6.2| MA.912.A.10.3
6-2 Problem 1 Multiplying Radical Expressions
KEY:
DOK 1
A
PTS: 1
DIF: L4
6-2 Multiplying and Dividing Radical Expressions
6-2.1 To multiply and divide radical expressions
STA: MA.912.A.6.2| MA.912.A.10.3
6-2 Problem 1 Multiplying Radical Expressions
KEY:
DOK 2
A
PTS: 1
DIF: L3
6-2 Multiplying and Dividing Radical Expressions
6-2.1 To multiply and divide radical expressions
STA: MA.912.A.6.2| MA.912.A.10.3
6-2 Problem 2 Simplifying a Radical Expression
KEY: simplest form of a radical
DOK 1
B
PTS: 1
DIF: L3
6-2 Multiplying and Dividing Radical Expressions
6-2.1 To multiply and divide radical expressions
STA: MA.912.A.6.2| MA.912.A.10.3
6-2 Problem 3 Simplifying a Product
KEY: simplest form of a radical
DOK 2
A
PTS: 1
DIF: L2
6-2 Multiplying and Dividing Radical Expressions
6-2.1 To multiply and divide radical expressions
STA: MA.912.A.6.2| MA.912.A.10.3
6-2 Problem 4 Dividing Radical Expressions
KEY: simplest form of a radical
DOK 1
C
PTS: 1
DIF: L2
REF: 6-3 Binomial Radical Expressions
6-3.1 To add and subtract radical expressions
STA: MA.912.A.6.2
6-3 Problem 1 Adding and Subtracting Radical Expressions
like radicals DOK: DOK 1
2
ID: A
19. ANS:
OBJ:
TOP:
DOK:
20. ANS:
OBJ:
TOP:
DOK:
21. ANS:
OBJ:
TOP:
22. ANS:
OBJ:
TOP:
23. ANS:
OBJ:
TOP:
24. ANS:
OBJ:
TOP:
KEY:
25. ANS:
OBJ:
TOP:
KEY:
26. ANS:
OBJ:
TOP:
KEY:
27. ANS:
REF:
OBJ:
STA:
TOP:
DOK:
28. ANS:
REF:
OBJ:
STA:
TOP:
DOK:
29. ANS:
OBJ:
TOP:
30. ANS:
OBJ:
TOP:
A
PTS: 1
DIF: L3
REF: 6-3 Binomial Radical Expressions
6-3.1 To add and subtract radical expressions
STA: MA.912.A.6.2
6-3 Problem 3 Simplifying Before Adding or Subtracting
DOK 2
B
PTS: 1
DIF: L2
REF: 6-3 Binomial Radical Expressions
6-3.1 To add and subtract radical expressions
STA: MA.912.A.6.2
6-3 Problem 4 Multiplying Binomial Radical Expressions
DOK 1
A
PTS: 1
DIF: L3
REF: 6-3 Binomial Radical Expressions
6-3.1 To add and subtract radical expressions
STA: MA.912.A.6.2
6-3 Problem 5 Multiplying Conjugates
DOK: DOK 1
C
PTS: 1
DIF: L3
REF: 6-3 Binomial Radical Expressions
6-3.1 To add and subtract radical expressions
STA: MA.912.A.6.2
6-3 Problem 6 Rationalizing the Denominator
DOK: DOK 1
D
PTS: 1
DIF: L2
REF: 6-3 Binomial Radical Expressions
6-3.1 To add and subtract radical expressions
STA: MA.912.A.6.2
6-3 Problem 6 Rationalizing the Denominator
DOK: DOK 1
C
PTS: 1
DIF: L3
REF: 6-4 Rational Exponents
6-4.1 To simplify expressions with rational exponents STA: MA.912.A.6.3| MA.912.A.6.4
6-4 Problem 1 Simplifying Expressions with Rational Exponents
rational exponents
DOK: DOK 1
B
PTS: 1
DIF: L2
REF: 6-4 Rational Exponents
6-4.1 To simplify expressions with rational exponents STA: MA.912.A.6.3| MA.912.A.6.4
6-4 Problem 1 Simplifying Expressions with Rational Exponents
rational exponents
DOK: DOK 1
A
PTS: 1
DIF: L2
REF: 6-4 Rational Exponents
6-4.1 To simplify expressions with rational exponents STA: MA.912.A.6.3| MA.912.A.6.4
6-4 Problem 2 Converting Between Exponential and Radical Form
rational exponents
DOK: DOK 1
B
PTS: 1
DIF: L2
6-5 Solving Square Root and Other Radical Equations
6-5.1 To solve square root and other radical equations
MA.912.A.6.4| MA.912.A.6.5| MA.912.A.10.3
6-5 Problem 1 Solving a Square Root Equation
KEY: square root equation
DOK 2
C
PTS: 1
DIF: L3
6-5 Solving Square Root and Other Radical Equations
6-5.1 To solve square root and other radical equations
MA.912.A.6.4| MA.912.A.6.5| MA.912.A.10.3
6-5 Problem 2 Solving Other Radical Equations
KEY: radical equation
DOK 2
D
PTS: 1
DIF: L3
REF: 6-6 Function Operations
6-6.1 To add, subtract, multiply, and divide functions
STA: MA.912.A.2.7| MA.912.A.2.8
6-6 Problem 1 Adding and Subtracting Functions
DOK: DOK 2
C
PTS: 1
DIF: L3
REF: 6-6 Function Operations
6-6.1 To add, subtract, multiply, and divide functions
STA: MA.912.A.2.7| MA.912.A.2.8
6-6 Problem 2 Multiplying and Dividing Functions
DOK: DOK 2
3
ID: A
31. ANS:
OBJ:
TOP:
32. ANS:
OBJ:
TOP:
DOK:
33. ANS:
REF:
OBJ:
TOP:
DOK:
34. ANS:
REF:
OBJ:
TOP:
DOK:
35. ANS:
REF:
OBJ:
STA:
TOP:
DOK:
36. ANS:
REF:
OBJ:
STA:
TOP:
DOK:
37. ANS:
REF:
OBJ:
STA:
TOP:
DOK:
38. ANS:
REF:
OBJ:
STA:
TOP:
KEY:
39. ANS:
REF:
OBJ:
STA:
TOP:
DOK:
D
PTS: 1
DIF: L3
REF: 6-6 Function Operations
6-6.1 To add, subtract, multiply, and divide functions
STA: MA.912.A.2.7| MA.912.A.2.8
6-6 Problem 2 Multiplying and Dividing Functions
DOK: DOK 2
A
PTS: 1
DIF: L3
REF: 6-6 Function Operations
6-6.2 To find the composite of two functions
STA: MA.912.A.2.7| MA.912.A.2.8
6-6 Problem 3 Composing Functions
KEY: composite function
DOK 2
A
PTS: 1
DIF: L3
6-7 Inverse Relations and Functions
6-7.1 To find the inverse of a relation or function
STA: MA.912.A.2.11
6-7 Problem 2 Finding an Equation for the Inverse
KEY: inverse relation
DOK 2
D
PTS: 1
DIF: L3
6-7 Inverse Relations and Functions
6-7.1 To find the inverse of a relation or function
STA: MA.912.A.2.11
6-7 Problem 2 Finding an Equation for the Inverse
KEY: inverse relation
DOK 2
D
PTS: 1
DIF: L2
7-1 Exploring Exponential Models
7-1.1 To model exponential growth and decay
MA.912.A.8.1| MA.912.A.8.3| MA.912.A.8.7
7-1 Problem 1 Graphing an Exponential Function
KEY: exponential function
DOK 2
D
PTS: 1
DIF: L2
7-2 Properties of Exponential Functions
7-2.2 To graph exponential functions that have base e
MA.912.A.2.5| MA.912.A.2.10| MA.912.A.8.1| MA.912.A.8.3| MA.912.A.8.7
7-2 Problem 5 Continuously Compounded Interest
KEY: continuously compounded interest
DOK 2
D
PTS: 1
DIF: L3
7-2 Properties of Exponential Functions
7-2.2 To graph exponential functions that have base e
MA.912.A.2.5| MA.912.A.2.10| MA.912.A.8.1| MA.912.A.8.3| MA.912.A.8.7
7-2 Problem 5 Continuously Compounded Interest
KEY: continuously compounded interest
DOK 2
B
PTS: 1
DIF: L2
7-3 Logarithmic Functions as Inverses
7-3.1 To write and evaluate logarithmic expressions
MA.912.A.2.5| MA.912.A.2.11| MA.912.A.8.1| MA.912.A.8.3
7-3 Problem 1 Writing Exponential Equations in Logarithmic Form
logarithm
DOK: DOK 2
C
PTS: 1
DIF: L3
7-3 Logarithmic Functions as Inverses
7-3.1 To write and evaluate logarithmic expressions
MA.912.A.2.5| MA.912.A.2.11| MA.912.A.8.1| MA.912.A.8.3
7-3 Problem 2 Evaluating a Logarithm
KEY: logarithm
DOK 2
4
ID: A
40. ANS:
REF:
OBJ:
STA:
TOP:
DOK:
41. ANS:
REF:
OBJ:
STA:
TOP:
DOK:
42. ANS:
OBJ:
TOP:
43. ANS:
OBJ:
TOP:
44. ANS:
OBJ:
TOP:
45. ANS:
OBJ:
TOP:
46. ANS:
OBJ:
TOP:
DOK:
47. ANS:
REF:
OBJ:
TOP:
KEY:
48. ANS:
REF:
OBJ:
TOP:
KEY:
49. ANS:
REF:
OBJ:
TOP:
DOK:
50. ANS:
REF:
OBJ:
TOP:
DOK:
A
PTS: 1
DIF: L2
7-3 Logarithmic Functions as Inverses
7-3.1 To write and evaluate logarithmic expressions
MA.912.A.2.5| MA.912.A.2.11| MA.912.A.8.1| MA.912.A.8.3
7-3 Problem 2 Evaluating a Logarithm
KEY: logarithm
DOK 2
B
PTS: 1
DIF: L4
7-3 Logarithmic Functions as Inverses
7-3.1 To write and evaluate logarithmic expressions
MA.912.A.2.5| MA.912.A.2.11| MA.912.A.8.1| MA.912.A.8.3
7-3 Problem 2 Evaluating a Logarithm
KEY: logarithm
DOK 2
A
PTS: 1
DIF: L3
REF: 7-4 Properties of Logarithms
7-4.1 To use the properties of logarithms
STA: MA.912.A.8.2| MA.912.A.8.6
7-4 Problem 1 Simplifying Logarithms
DOK: DOK 2
A
PTS: 1
DIF: L2
REF: 7-4 Properties of Logarithms
7-4.1 To use the properties of logarithms
STA: MA.912.A.8.2| MA.912.A.8.6
7-4 Problem 1 Simplifying Logarithms
DOK: DOK 2
A
PTS: 1
DIF: L2
REF: 7-4 Properties of Logarithms
7-4.1 To use the properties of logarithms
STA: MA.912.A.8.2| MA.912.A.8.6
7-4 Problem 2 Expanding Logarithms
DOK: DOK 2
C
PTS: 1
DIF: L3
REF: 7-4 Properties of Logarithms
7-4.1 To use the properties of logarithms
STA: MA.912.A.8.2| MA.912.A.8.6
7-4 Problem 2 Expanding Logarithms
DOK: DOK 2
A
PTS: 1
DIF: L3
REF: 7-4 Properties of Logarithms
7-4.1 To use the properties of logarithms
STA: MA.912.A.8.2| MA.912.A.8.6
7-4 Problem 3 Using the Change of Base Formula
KEY: Change of Base Formula
DOK 2
C
PTS: 1
DIF: L4
7-5 Exponential and Logarithmic Equations
7-5.1 To solve exponential and logarithmic equations STA: MA.912.A.8.5
7-5 Problem 1 Solving an Exponential Equation – Common Base
exponential equation
DOK: DOK 2
C
PTS: 1
DIF: L2
7-5 Exponential and Logarithmic Equations
7-5.1 To solve exponential and logarithmic equations STA: MA.912.A.8.5
7-5 Problem 1 Solving an Exponential Equation – Common Base
exponential equation
DOK: DOK 2
A
PTS: 1
DIF: L2
7-5 Exponential and Logarithmic Equations
7-5.1 To solve exponential and logarithmic equations STA: MA.912.A.8.5
7-5 Problem 5 Solving a Logarithmic Equation
KEY: logarithmic equation
DOK 2
B
PTS: 1
DIF: L3
8-3 Rational Functions and Their Graphs
8-3.1 To identify properties of rational functions
STA: MA.912.A.5.6
8-3 Problem 3 Finding Horizontal Asymptotes
KEY: rational function
DOK 2
5
ID: A
51. ANS:
OBJ:
TOP:
DOK:
52. ANS:
OBJ:
TOP:
DOK:
53. ANS:
OBJ:
TOP:
DOK:
54. ANS:
OBJ:
TOP:
DOK:
55. ANS:
REF:
OBJ:
TOP:
56. ANS:
REF:
OBJ:
TOP:
57. ANS:
REF:
OBJ:
TOP:
DOK:
58. ANS:
REF:
OBJ:
TOP:
DOK:
59. ANS:
OBJ:
KEY:
60. ANS:
OBJ:
KEY:
B
PTS: 1
DIF: L2
8-4.1 To simplify rational expressions
8-4 Problem 1 Simplifying a Rational Expression
DOK 2
C
PTS: 1
DIF: L3
8-4.1 To simplify rational expressions
8-4 Problem 1 Simplifying a Rational Expression
DOK 2
B
PTS: 1
DIF: L2
8-4.2 To multiply and divide rational expressions
8-4 Problem 2 Multiplying Rational Expressions
DOK 2
D
PTS: 1
DIF: L3
8-4.2 To multiply and divide rational expressions
8-4 Problem 3 Dividing Rational Expressions
DOK 2
A
PTS: 1
DIF: L2
8-5 Adding and Subtracting Rational Expressions
8-5.1 To add and subtract rational expressions
8-5 Problem 2 Adding Rational Expressions
D
PTS: 1
DIF: L3
8-5 Adding and Subtracting Rational Expressions
8-5.1 To add and subtract rational expressions
8-5 Problem 3 Subtracting Rational Expressions
A
PTS: 1
DIF: L2
8-5 Adding and Subtracting Rational Expressions
8-5.1 To add and subtract rational expressions
8-5 Problem 4 Simplifying a Complex Fraction
DOK 2
C
PTS: 1
DIF: L3
8-5 Adding and Subtracting Rational Expressions
8-5.1 To add and subtract rational expressions
8-5 Problem 4 Simplifying a Complex Fraction
DOK 2
D
PTS: 1
DIF: L2
8-6.1 To solve rational equations TOP: 8-6 Problem
rational equation
DOK: DOK 2
A
PTS: 1
DIF: L4
8-6.1 To solve rational equations TOP: 8-6 Problem
rational equation
DOK: DOK 2
6
REF: 8-4 Rational Expressions
STA: MA.912.A.10.3
KEY: rational expression | simplest form
REF: 8-4 Rational Expressions
STA: MA.912.A.10.3
KEY: rational expression | simplest form
REF: 8-4 Rational Expressions
STA: MA.912.A.10.3
KEY: rational expression | simplest form
REF: 8-4 Rational Expressions
STA: MA.912.A.10.3
KEY: rational expression | simplest form
DOK: DOK 2
DOK: DOK 2
KEY: complex fraction
KEY: complex fraction
REF: 8-6 Solving Rational Equations
1 Solving a Rational Equation
REF: 8-6 Solving Rational Equations
1 Solving a Rational Equation