Algebra 2 Final Exam Review
Algebra 2 Final Exam Review
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Evaluate the logarithm.
____ 1. [pic]
|a. |7 |b. |3 |c. |2 |d. |–3 |
____ 2. [pic]
|a. |7 |b. |–1 |c. |2 |d. |–2 |
State the property or properties of logarithms used to rewrite the expression.
____ 3. [pic]
|a. |Difference Property |c. |Power Property |
|b. |Product Property |d. |Quotient Property |
____ 4. [pic]
|a. |Product Property |c. |Quotient Property |
|b. |Commutative Property |d. |Power Property |
Multiply or divide. State any restrictions on the variables.
____ 5. [pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic][pic] |
____ 6. [pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 7. Solve [pic]. Round to the nearest thousandth.
|a. |365.878 |b. |1,095.633 |c. |365.211 |d. |1,096.966 |
Write the expression as a single natural logarithm.
____ 8. [pic]
|a. |[pic] |b. |[pic] |c. |[pic] |d. |[pic] |
Simplify the rational expression. State any restrictions on the variable.
____ 9. [pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 10. [pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 11. Solve [pic].
|a. |[pic] |b. |[pic] |c. |[pic] |d. |[pic] |
Graph the exponential function.
____ 12. [pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
Expand the logarithmic expression.
____ 13. [pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 14. [pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
Write the equation in logarithmic form.
____ 15. [pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 16. [pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
Write the expression as a single logarithm.
____ 17. [pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
____ 18. Find the coordinates of the midpoint of the segment whose endpoints are H(2, 11) and K(4, 1).
|a. |(3, 6) |b. |(1, 5) |c. |(6, 12) |d. |(2, 10) |
Use natural logarithms to solve the equation. Round to the nearest thousandth.
____ 19. [pic]
|a. |0.742 |b. |0.236 |c. |0.482 |d. |–2.697 |
Simplify the complex fraction.
____ 20. [pic]
|a. |[pic] |b. |[pic] |c. |[pic] |d. |[pic] |
____ 21. Write the expression (x + 6)(x – 4) as a polynomial in standard form.
|a. |x2 – 10x + 2 |c. |x2 + 2x – 24 |
|b. |x2 + 10x – 24 |d. |x2 + 10x – 10 |
Write in standard form an equation of the line passing through the given point with the given slope.
____ 22. slope = –8; (–2, –2)
|a. |8x + y = –18 |b. |–8x + y = –18 |c. |8x – y = –18 |d. |8x + y = 18 |
____ 23. Graph the function [pic].
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
Solve the matrix equation.
____ 24. [pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
Find the product.
____ 25. [pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[12] |
Divide using synthetic division.
____ 26. [pic]
|a. |[pic] |c. |[pic] |
|b. |[pic] |d. |[pic] |
Algebra 2 Final Exam Review
Answer Section
MULTIPLE CHOICE
1. ANS: B PTS: 1 DIF: L3
REF: 8-3 Logarithmic Functions as Inverses
OBJ: 8-3.1 Writing and Evaluating Logarithmic Expressions STA: MS AII 6a | MS AII 6b
TOP: 8-3 Example 3 KEY: evaluating logarithms
2. ANS: D PTS: 1 DIF: L4
REF: 8-3 Logarithmic Functions as Inverses
OBJ: 8-3.1 Writing and Evaluating Logarithmic Expressions STA: MS AII 6a | MS AII 6b
TOP: 8-3 Example 3 KEY: evaluating logarithms
3. ANS: D PTS: 1 DIF: L3 REF: 8-4 Properties of Logarithms
OBJ: 8-4.1 Using the Properties of Logarithms STA: MS AII 6d
TOP: 8-4 Example 1 KEY: properties of logarithms | Quotient Property of Logarithms
4. ANS: D PTS: 1 DIF: L4 REF: 8-4 Properties of Logarithms
OBJ: 8-4.1 Using the Properties of Logarithms STA: MS AII 6d
TOP: 8-4 Example 1 KEY: properties of logarithms | Power Property of Logarithms
5. ANS: A PTS: 1 DIF: L2 REF: 9-4 Rational Expressions
OBJ: 9-4.2 Multiplying and Dividing Rational Expressions STA: MS AII 5a
TOP: 9-4 Example 3
KEY: simplifying a rational expression | restrictions on a variable | multiplying rational expressions
6. ANS: B PTS: 1 DIF: L2 REF: 9-4 Rational Expressions
OBJ: 9-4.2 Multiplying and Dividing Rational Expressions STA: MS AII 5a
TOP: 9-4 Example 4 KEY: restrictions on a variable | dividing rational expressions
7. ANS: A PTS: 1 DIF: L3 REF: 8-6 Natural Logarithms
OBJ: 8-6.2 Natural Logarithmic and Exponential Equations TOP: 8-6 Example 3
KEY: natural logarithmic equation | properties of logarithms
8. ANS: B PTS: 1 DIF: L3 REF: 8-6 Natural Logarithms
OBJ: 8-6.1 Natural Logarithms TOP: 8-6 Example 1
KEY: simplifying a natural logarithm | properties of logarithms
9. ANS: C PTS: 1 DIF: L2 REF: 9-4 Rational Expressions
OBJ: 9-4.1 Simplifying Rational Expressions STA: MS AII 5a
TOP: 9-4 Example 1
KEY: rational expression | simplifying a rational expression | restrictions on a variable
10. ANS: C PTS: 1 DIF: L2 REF: 9-4 Rational Expressions
OBJ: 9-4.1 Simplifying Rational Expressions STA: MS AII 5a
TOP: 9-4 Example 1
KEY: rational expression | simplifying a rational expression | restrictions on a variable
11. ANS: C PTS: 1 DIF: L3
REF: 8-5 Exponential and Logarithmic Equations OBJ: 8-5.2 Solving Logarithmic Equations
STA: MS AII 6c | MS AII 6d TOP: 8-5 Example 6
KEY: logarithmic equation | properties of logarithms
12. ANS: C PTS: 1 DIF: L3 REF: 8-1 Exploring Exponential Models
OBJ: 8-1.1 Exponential Growth STA: MS AII 6d TOP: 8-1 Example 1
KEY: exponential function | graphing
13. ANS: A PTS: 1 DIF: L3 REF: 8-4 Properties of Logarithms
OBJ: 8-4.1 Using the Properties of Logarithms STA: MS AII 6d
TOP: 8-4 Example 3
KEY: properties of logarithms | expanding logarithms | Product Property of Logarithms | Power Property of Logarithms
14. ANS: C PTS: 1 DIF: L3 REF: 8-4 Properties of Logarithms
OBJ: 8-4.1 Using the Properties of Logarithms STA: MS AII 6d
TOP: 8-4 Example 3
KEY: properties of logarithms | expanding logarithms | Quotient Property of Logarithms
15. ANS: C PTS: 1 DIF: L3
REF: 8-3 Logarithmic Functions as Inverses
OBJ: 8-3.1 Writing and Evaluating Logarithmic Expressions STA: MS AII 6a | MS AII 6b
TOP: 8-3 Example 2 KEY: logarithm | logarithmic form
16. ANS: B PTS: 1 DIF: L3
REF: 8-3 Logarithmic Functions as Inverses
OBJ: 8-3.1 Writing and Evaluating Logarithmic Expressions STA: MS AII 6a | MS AII 6b
TOP: 8-3 Example 2 KEY: logarithm | logarithmic form
17. ANS: A PTS: 1 DIF: L4 REF: 8-4 Properties of Logarithms
OBJ: 8-4.1 Using the Properties of Logarithms STA: MS AII 6d
TOP: 8-4 Example 2
KEY: properties of logarithms | logarithm | Product Property of Logarithms | Power Property of Logarithms
18. ANS: A PTS: 1 DIF: L2 REF: 1-8 The Coordinate Plane
OBJ: 1-8.2 Finding the Midpoint of a Segment
NAT: NAEP 2005 M1e | ADP J.1.6 | ADP K.10.3 TOP: 1-8 Example 3
KEY: coordinate plane | Midpoint Formula
19. ANS: C PTS: 1 DIF: L4 REF: 8-6 Natural Logarithms
OBJ: 8-6.2 Natural Logarithmic and Exponential Equations TOP: 8-6 Example 4
KEY: exponential equation | properties of logarithms
20. ANS: C PTS: 1 DIF: L2
REF: 9-5 Adding and Subtracting Rational Expressions OBJ: 9-5.2 Simplifying Complex Fractions
STA: MS AII 5a TOP: 9-5 Example 5
KEY: complex fraction | simplifying a rational expression | simplifying a complex fraction
21. ANS: C PTS: 1 DIF: L2 REF: 6-2 Polynomials and Linear Factors
OBJ: 6-2.1 The Factored Form of a Polynomial STA: MS AII 1d
TOP: 6-2 Example 1 KEY: polynomial | standard form of a polynomial
22. ANS: A PTS: 1 DIF: L2 REF: 2-2 Linear Equations
OBJ: 2-2.2 Writing Equations of Lines TOP: 2-2 Example 4
KEY: point-slope form | standard form of linear equation
23. ANS: A PTS: 1 DIF: L2 REF: 2-6 Families of Functions
OBJ: 2-6.2 Stretches | Shrinks | and Reflections TOP: 2-6 Example 5
KEY: stretch and shrink | reflection
24. ANS: B PTS: 1 DIF: L2 REF: 4-3 Matrix Multiplication
OBJ: 4-3.1 Multiplying a Matrix by a Scalar STA: MS AII 7d
TOP: 4-3 Example 3 KEY: scalar | scalar multiplication | matrix | matrix equation
25. ANS: D PTS: 1 DIF: L3 REF: 4-3 Matrix Multiplication
OBJ: 4-3.2 Multiplying Matrices STA: MS AII 7d TOP: 4-3 Example 4
KEY: matrix multiplication | matrix
26. ANS: D PTS: 1 DIF: L3 REF: 6-3 Dividing Polynomials
OBJ: 6-3.2 Using Synthetic Division TOP: 6-3 Example 3
KEY: division of polynomials | polynomial | synthetic division
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