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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