Algebra Maureen Steddin
table of contents To the Student......................... v Part 1: Introduction.................................... 1 General Approach to Math Questions................... 1 Specific Strategies for Algebra......................... 1 Part 2: Reference Information........................ 7 Test-Taking Glossary................................. 7 Content-Specific Definitions and Formulas.............. 8 Part 3: Exponents and Radicals..................... 11 Set 1 (Scientific Notation)........................... 11 Set 2 (Working with Exponents)...................... 13 Set 3 (Perfect Squares and Their Roots)................. 15 Part 4: Algebraic Expressions........................ 17 Set 4 (Combining Like Terms)......................... 17 Set 5 (Evaluating Expressions)........................ 19 Part 5: Linear Equations and Inequalities.......... 21 Set 6 (Linear Equations)............................ 21 Set 7 (Linear Equations)............................. 23 Set 8 (Linear Inequalities)............................ 25 Part 6: Word Problems and Translations............ 27 Set 9 (Straight Translation)........................... 27 Set 10 (Straight Translation).......................... 29 iii
Set 11 (Translation in Context)........................ 31 Set 12 (Translation in Context)........................ 33 Part 7: Graphing Points and Lines.................. 35 Set 13 (Points)..................................... 35 Set 14 (Points)..................................... 38 Set 15 (Lines)...................................... 41 Part 8: Functions and Patterns...................... 45 Set 16 (Functions).................................. 45 Set 17 (Functions).................................. 48 Set 18 (Numerical Patterns).......................... 51 Set 19 (Numerical Patterns).......................... 53 Set 20 (Visual Patterns).............................. 55 iv
PART 3 exponents and radicals Set 1 1. Which of the following is equal to 5.29 10 3? 4. Write 0.000456 in scientific notation. A. 0.000529 B. 0.00529 C. 529 D. 5,290 E. 529,000 2. Which of the following expresses 99,900,000,000 in scientific notation? A. 999 10 8 B. 99.9 10 9 C. 9.99 10 8 D. 9.99 10 9 E. 9.99 10 10 3. Which of the following is equal to 1.23 10 4? 5. Ella reads that the Moon is approximately 2.39 10 5 miles from Earth. How is this number of miles written in standard form? A. 0.00000239 B. 0.0000239 C. 239,000 D. 2,390,000 E. 23,900,000 A. 0.0000123 B. 0.000123 C. 12,300 D. 1,230,000 2004 Walch Publishing 11 Test Time! Algebra, 5 6
Set 1 (continued) 6. A millimeter is one thousandth, or 1 --------------, of a meter. How is this number 1,000 written in scientific notation? 9. Which is greater, 9.99 10 5 or 1.2 10 10? Explain your answer. A. 1 10 1 B. 1 10 2 C. 1 10 3 D. 1 10 4 7. How is 5.03 10 5 written in standard form? A. 0.00000503 B. 0.0000503 C. 0.000503 D. 0.00503 10. How is 30,400,000 written in scientific notation? A. 304 10 5 B. 30.4 10 6 C. 3.04 10 5 D. 3.04 10 6 E. 3.04 10 7 8. 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. 71 10 7 B. 71 10 8 C. 7.1 10 7 D. 7.1 10 8 STOP 2004 Walch Publishing 12 Test Time! Algebra, 5 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. 25 2. Which of the following is equal to 4 7? A. 4 7 B. 7(4) C. 4 4 4 4 4 4 4 D. 7 7 7 7 5. How is 6 4 represented in expanded form? A. 6 6 6 6 B. 4 4 4 4 4 4 C. 6 4 D. 4(6) 3. Which of the following shows 2 2 2 written in exponential form? A. 2 2 B. 2 3 C. 3 2 D. 3 3 2004 Walch Publishing 13 Test Time! Algebra, 5 6
Set 2 (continued) 6. What is the value of 8 2? A. 6 B. 10 C. 16 D. 64 9. Which of the following is equal to 4 2 + 5 3? A. 4 2 + 5 3 B. 4 3 + 5 2 C. 4 4 + 5 5 5 D. 4 4 4 + 5 5 7. Write 10 10 10 10 10 10 10 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
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. 20 2. Which of the following is NOT a perfect square? A. 16 B. 25 C. 34 D. 49 5. What is the square root of 100? A. 5 B. 10 C. 15 D. 20 E. 50 3. What is the value of 4 2? A. 2 B. 4 C. 8 D. 16 E. 32 2004 Walch Publishing 15 Test Time! Algebra, 5 6
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. 49 9. The square root of a number is 9. Which of the following is the number? A. 3 B. 9 C. 27 D. 81 7. Name a perfect square that is greater than 50 and less than 100. 10. 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. 36 8. 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
PART 4 algebraic expressions Set 4 1. 3x + 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. 18 + 2z C. 11z D. 9 + 2z 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
Set 4 (continued) 6. 10m 2 =? A. 8m B. 5 + m C. 12m D. 5 E. 5m 9. Evaluate the following expression: 2(12x) 4 7. 5(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 5 8. 3(2s + s) =? A. 6s B. 7s C. 9s D. 6 + s STOP 2004 Walch Publishing 18 Test Time! Algebra, 5 6
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. 5 + 2x A. 4 B. 7 C. 9 D. 14 2. If n = 5, evaluate: 3 2n A. 7 B. 2 C. 8 D. 13 5. Which of the following is equal to g 2 + g when g = 4? A. 8 B. 12 C. 16 D. 20 E. 64 3. If a = 2 and b = 3, evaluate: 5a + 2b. A. 4 B. 11 C. 16 D. 19 2004 Walch Publishing 19 Test Time! Algebra, 5 6
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. 60 7. 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. 20 8. 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