Algebra. Maureen Steddin

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1 Algebra Maureen Steddin

2 table of contents To the Student v Part 1: Introduction General Approach to Math Questions Specific Strategies for Algebra Part 2: Reference Information Test-Taking Glossary Content-Specific Definitions and Formulas Part 3: Exponents and Radicals Set 1 (Scientific Notation) Set 2 (Working with Exponents) Set 3 (Perfect Squares and Their Roots) Part 4: Algebraic Expressions Set 4 (Combining Like Terms) Set 5 (Evaluating Expressions) Part 5: Linear Equations and Inequalities Set 6 (Linear Equations) Set 7 (Linear Equations) Set 8 (Linear Inequalities) Part 6: Word Problems and Translations Set 9 (Straight Translation) Set 10 (Straight Translation) iii

3 Set 11 (Translation in Context) Set 12 (Translation in Context) Part 7: Graphing Points and Lines Set 13 (Points) Set 14 (Points) Set 15 (Lines) Part 8: Functions and Patterns Set 16 (Functions) Set 17 (Functions) Set 18 (Numerical Patterns) Set 19 (Numerical Patterns) Set 20 (Visual Patterns) iv

4 PART 3 exponents and radicals Set 1 1. Which of the following is equal to ? 4. Write in scientific notation. A B C. 529 D. 5,290 E. 529, Which of the following expresses 99,900,000,000 in scientific notation? A B C D E Which of the following is equal to ? 5. Ella reads that the Moon is approximately miles from Earth. How is this number of miles written in standard form? A B C. 239,000 D. 2,390,000 E. 23,900,000 A B C. 12,300 D. 1,230, Walch Publishing 11 Test Time! Algebra, 5 6

5 Set 1 (continued) 6. A millimeter is one thousandth, or , of a meter. How is this number 1,000 written in scientific notation? 9. Which is greater, or ? Explain your answer. A B C D How is written in standard form? A B C D How is 30,400,000 written in scientific notation? A B C D E Greg s teacher tells his class that they must use scientific notation to represent numbers in their reports. How should Greg represent the number 710,000,000 in his report? A B C D STOP 2004 Walch Publishing 12 Test Time! Algebra, 5 6

6 Set 2 1. What is the value of 5 2? 4. Write 9 5 in expanded form. A. 3 B. 7 C. 10 D Which of the following is equal to 4 7? A. 4 7 B. 7(4) C D How is 6 4 represented in expanded form? A B C. 6 4 D. 4(6) 3. Which of the following shows written in exponential form? A. 2 2 B. 2 3 C. 3 2 D Walch Publishing 13 Test Time! Algebra, 5 6

7 Set 2 (continued) 6. What is the value of 8 2? A. 6 B. 10 C. 16 D Which of the following is equal to ? A B C D Write in exponential form. 10. Which is greater, 9 3 or 3 9? Justify your answer. 8. Meg calculates the value of 3 2. Then she finds the square of this result. What number does Meg end up with? A. 9 B. 12 C. 18 D. 36 E. 81 STOP 2004 Walch Publishing 14 Test Time! Algebra, 5 6

8 Set 3 1. Which of the following is a perfect square? 4. Is 81 a perfect square? Explain your answer. A. 9 B. 12 C. 15 D Which of the following is NOT a perfect square? A. 16 B. 25 C. 34 D What is the square root of 100? A. 5 B. 10 C. 15 D. 20 E What is the value of 4 2? A. 2 B. 4 C. 8 D. 16 E Walch Publishing 15 Test Time! Algebra, 5 6

9 Set 3 (continued) 6. The area of a square is equal to its side length squared. If the side of a certain square is an integer, which of the following could be the area of this square, in square units? A. 10 B. 24 C. 32 D The square root of a number is 9. Which of the following is the number? A. 3 B. 9 C. 27 D Name a perfect square that is greater than 50 and less than Jose is thinking of a number. The number is a perfect square that is odd and greater than 20. Which of the following could be the number? A. 16 B. 21 C. 25 D What is the value of 12 2? A. 6 B. 10 C. 14 D. 24 E. 144 STOP 2004 Walch Publishing 16 Test Time! Algebra, 5 6

10 PART 4 algebraic expressions Set x + 5x =? A. 2x B. 8x C. 8 + x D. 15x 4. Combine like terms in the following expression: 5a + 2b a + b 2. 11a 4a =? A. 7a B. 15a C. 7 a D. 44a 5. 9z 2 =? A. 18z B z C. 11z D z 3. Which of the following is equal to 9b? A. 9 + b B. 5b + 4a C. 10b b D. 9 b 2004 Walch Publishing 17 Test Time! Algebra, 5 6

11 Set 4 (continued) 6. 10m 2 =? A. 8m B. 5 + m C. 12m D. 5 E. 5m 9. Evaluate the following expression: 2(12x) (a + 2) =? A. 5a + 2 B. a + 10 C. 6a + 7 D. 5a + 10 E. 15a 10. All of the following are equal to 5y EXCEPT: A. 2y + 3y B. 11y 6y C. 5 y D. 30y (2s + s) =? A. 6s B. 7s C. 9s D. 6 + s STOP 2004 Walch Publishing 18 Test Time! Algebra, 5 6

12 Set 5 1. What is the value of the expression below when x = 2? 4. For p = 4, evaluate 3(p + 1). Show each step x A. 4 B. 7 C. 9 D If n = 5, evaluate: 3 2n A. 7 B. 2 C. 8 D Which of the following is equal to g 2 + g when g = 4? A. 8 B. 12 C. 16 D. 20 E If a = 2 and b = 3, evaluate: 5a + 2b. A. 4 B. 11 C. 16 D Walch Publishing 19 Test Time! Algebra, 5 6

13 Set 5 (continued) 6. What is the value of the expression below when n = 8? A. 16 B. 29 C. 37 D. 45 5n 3 + n 9. If c = 6, evaluate c(4 + c). A. 12 B. 24 C. 30 D. 36 E For x = 5, evaluate ( 2)x + x 2. Show each step. 10. In the equation below, if n = 2, what is the value of m? m = 5n + 8 n A. 8 B. 16 C. 18 D If x = 4, y = 3, and z = 2, evaluate: x 2 + 2y 4z A. 6 B. 8 C. 14 D. 30 STOP 2004 Walch Publishing 20 Test Time! Algebra, 5 6

Radical Expressions and Graph (7.1) EXAMPLE #1: EXAMPLE #2: EXAMPLE #3: Find roots of numbers (Objective #1) Figure #1:

Radical Expressions and Graph (7.1) Find roots of numbers EXAMPLE #1: Figure #1: Find principal (positive) roots EXAMPLE #2: Find n th roots of n th powers (Objective #3) EXAMPLE #3: Figure #2: 7.1 Radical