Download Keystone Algebra I EOC Exam and more Exams Technology in PDF only on Docsity!
Question 1. What is the result when you simplify the expression 3x + 4x – 2x? A) 5x B) 7x C) x D) 6x Answer: A Explanation: Combine like terms: 3x + 4x = 7x, then 7x – 2x = 5x. Question 2. Which is the greatest common factor (GCF) of 12x³ and 18x²? A) 6x B) 3x² C) 6x² D) 12x² Answer: C Explanation: The GCF of 12 and 18 is 6, and the lowest power of x is x², so 6x². Question 3. Simplify: (2x² + 3x) – (x² – 5x) A) x² + 8x B) 3x² – 2x C) x² + 2x D) x² + 7x Answer: C Explanation: (2x² – x²) + (3x + 5x) = x² + 8x. Question 4. Which property justifies the equation 7 + (4 + x) = (7 + 4) + x? A) Distributive Property B) Associative Property of Addition C) Commutative Property of Addition D) Identity Property Answer: B Explanation: The associative property allows grouping to change in addition. Question 5. Simplify: 4(x – 2) + 3x A) 7x – 8 B) 4x – 8 + 3x C) 4x – 2 + 3x D) 7x – 2 Answer: A Explanation: Distribute: 4x – 8 + 3x = 7x – 8. Question 6. Factor the expression: 9x³ – 6x² A) 3x²(3x – 2)
B) 3x(3x² – 2x) C) x²(9x – 6) D) 3x²(3 – 2x) Answer: A Explanation: The GCF is 3x², so 3x²(3x – 2). Question 7. Which of the following illustrates the distributive property? A) 2 + 3 = 3 + 2 B) 2(x + 4) = 2x + 8 C) (2 + 3) + 4 = 2 + (3 + 4) D) 5 × 1 = 5 Answer: B Explanation: The distributive property is a(b + c) = ab + ac. Question 8. What is the simplified form of (-2x³y²)(3x²y)? A) – 6x⁵y³ B) – 5x⁵y³ C) 6x⁵y³ D) – 6x⁶y³ Answer: A Explanation: Multiply coefficients: – 2 × 3 = – 6, add exponents: x³ × x² = x⁵, y² × y = y³. Question 9. Evaluate: (√50) A) 5 B) 7. C) 5√ D) 5√ Answer: C Explanation: 50 = 25 × 2, so √50 = √25 × √2 = 5√2. Question 10. Simplify: (x²y³) × (xy²) A) x³y⁵ B) x²y⁶ C) x³y⁶ D) x²y⁵ Answer: A Explanation: Add exponents: x² × x = x³, y³ × y² = y⁵. Question 11. Which is equivalent to x⁰, where x ≠ 0? A) 0 B) 1 C) x
Answer: A Explanation: Divide each term by 3x: (6x²/3x) – (9x/3x) = 2x – 3. Question 17. What is the sum of (4x² + 5x – 2) and (–3x² + 2x + 7)? A) x² + 7x + 5 B) x² + 3x + 9 C) 7x² + 7x + 5 D) x² + 3x + 5 Answer: D Explanation: 4x² – 3x² = x², 5x + 2x = 7x, – 2 + 7 = 5. Question 18. Which property is illustrated by: x + 0 = x? A) Identity Property of Addition B) Inverse Property C) Commutative Property D) Distributive Property Answer: A Explanation: Adding zero leaves the number unchanged; identity property. Question 19. Which of the following is the product of (x + 2)(x – 3)? A) x² – x – 6 B) x² – x + 6 C) x² + 5x – 6 D) x² – 6 Answer: A Explanation: FOIL: x² – 3x + 2x – 6 = x² – x – 6. Question 20. Simplify: (3x²y³) ÷ (x y) A) 3x y² B) 3x²y² C) 3x y³ D) 3x²y³ Answer: A Explanation: Subtract exponents: x²/x¹ = x¹, y³/y¹ = y². Question 21. Which is the GCF of 14a²b³ and 21a³b²? A) 7a²b² B) 7ab² C) 14a²b³ D) 21a³b² Answer: A Explanation: GCF of 14 and 21 is 7; lowest powers: a² and b².
Question 22. Simplify: (x² – 4) ÷ (x – 2) A) x – 2 B) x + 2 C) x² – 2 D) x – 4 Answer: B Explanation: x² – 4 factors to (x – 2)(x + 2); divide by (x – 2): answer is x + 2. Question 23. What is the simplified form of 2(x + 3) – 4x? A) 2x + 6 – 4x B) – 2x + 6 C) 2x – 4x + 3 D) – 2x + 3 Answer: B Explanation: Distribute: 2x + 6 – 4x = – 2x + 6. Question 24. Which of the following is equivalent to (3x²)⁰? A) 0 B) 1 C) 3x² D) x² Answer: B Explanation: Any nonzero quantity to the power of zero is 1. Question 25. Simplify: x³ × x⁴ × x² A) x⁹ B) x⁷ C) x⁶ D) x⁸ Answer: B Explanation: Add exponents: 3 + 4 + 2 = 9. Question 26. Subtract: (7x² – 4x + 9) – (3x² + 2x – 5) A) 10x² – 6x + 14 B) 4x² – 6x + 14 C) 4x² – 6x + 4 D) 10x² – 2x – 4 Answer: B Explanation: 7x² – 3x² = 4x², – 4x – 2x = – 6x, 9 – (–5) = 14.
B) 2x² + 8x – 3x – 12 C) 2x² + 5x + 12 D) 2x² + 8x – 3 Answer: A Explanation: Multiply: 2x² + 8x – 3x – 12 = 2x² + 5x – 12. Question 33. What is the reciprocal of 7/3? A) 3/ B) – 7/ C) 7/ D) – 3/ Answer: A Explanation: The reciprocal of a/b is b/a. Question 34. Simplify: (x²y)/(xy²) A) x/y B) y/x C) x²/y² D) x/y² Answer: A Explanation: x²/x = x, y/y² = 1/y. Question 35. Which is equivalent to (2x³y²)²? A) 4x⁶y⁴ B) 2x⁶y⁴ C) 4x⁶y² D) 4x³y⁴ Answer: A Explanation: (2)² = 4, (x³)² = x⁶, (y²)² = y⁴. Question 36. Simplify: 5√ A) 5√ B) 15√ C) 5√ D) 5 × 9 Answer: B Explanation: √27 = √9 × √3 = 3√3, 5 × 3√3 = 15√3. Question 37. Factor: 18x²y – 27xy² A) 9xy(2x – 3y) B) 9x²y(2 – 3y) C) 9xy(2y – 3x)
D) 9xy²(2x – 3) Answer: A Explanation: GCF is 9xy: 18x²y/9xy = 2x, 27xy²/9xy = 3y. Question 38. Simplify: (x⁴) ÷ (x²) A) x² B) x⁶ C) x³ D) x Answer: A Explanation: Subtract exponents: x⁴/x² = x². Question 39. What is the result of (3x⁵y⁴) ÷ (x²y)? A) 3x³y³ B) 3x²y³ C) 3x³y⁴ D) 3x⁵y³ Answer: A Explanation: Subtract exponents: x⁵/x² = x³, y⁴/y = y³. Question 40. Which property is shown: 6 + x = x + 6? A) Commutative Property of Addition B) Associative Property C) Distributive Property D) Inverse Property Answer: A Explanation: The order of addition can be switched; commutative property. Question 41. Simplify: (4x²y³)³ A) 64x⁶y⁹ B) 12x⁶y⁹ C) 64x⁶y⁶ D) 12x⁵y⁶ Answer: A Explanation: (4)³ = 64, (x²)³ = x⁶, (y³)³ = y⁹. Question 42. What is the product of (x – 1)(x + 1)? A) x² + 1 B) x² – 1 C) x² – x + 1 D) x²
Question 48. What is the simplified form of √18 + √8? A) 5√ B) 7√ C) 7√ D) 4√ Answer: A Explanation: √18 = 3√2, √8 = 2√2, 3√2 + 2√2 = 5√2. Question 49. Simplify: (x² – 9)/(x – 3) A) x + 3 B) x – 3 C) x² – 3 D) x – 9 Answer: A Explanation: x² – 9 = (x – 3)(x + 3); divide by x – 3: answer is x + 3. Question 50. Which is the simplified form of (5x³y²z⁴)⁰? A) 0 B) x³y²z⁴ C) 1 D) 5 Answer: C Explanation: Any nonzero expression to the 0 power is 1. Question 51. Which property justifies x × 1 = x? A) Identity Property of Multiplication B) Inverse Property C) Commutative Property D) Distributive Property Answer: A Explanation: The identity for multiplication is 1. Question 52. Simplify: 6x²y – 4x²y A) 2x²y B) 10x²y C) 2xy D) 6x² – 4xy Answer: A Explanation: 6x²y – 4x²y = (6 – 4)x²y = 2x²y.
Question 53. What is the result of (–2x²y³) × (3xy²)? A) – 6x³y⁵ B) – 5x³y⁵ C) – 6x²y⁵ D) 6x³y⁵ Answer: A Explanation: – 2 × 3 = – 6; x² × x = x³; y³ × y² = y⁵. Question 54. Simplify: (x + 4)² A) x² + 4 B) x² + 8x + 16 C) x² + 4x + 16 D) x² + 16 Answer: B Explanation: (x + 4)² = x² + 2 × 4x + 16 = x² + 8x + 16. Question 55. What is the simplified form of (x²/y³) × (y/x)? A) 1/y² B) x/y² C) x/y³ D) x²/y² Answer: B Explanation: x²/x = x, y/y³ = 1/y². Question 56. Which is equivalent to x³ × x⁴? A) x¹² B) x⁷ C) x¹ D) x⁴ Answer: B Explanation: Add exponents: 3 + 4 = 7. Question 57. Simplify: √ A) 8√ B) 4√ C) 16√ D) 2√ Answer: B Explanation: 32 = 16 × 2, so √32 = 4√2. Question 58. What is the greatest common factor of 30a³b and 45a²b²? A) 15a²b
D) 5/
Answer: B Explanation: Flip the fraction and keep the sign: – 5/4. Question 64. Simplify: (x⁴y³)/(x²y) A) x²y² B) x⁶y² C) x²y³ D) x³y² Answer: A Explanation: x⁴/x² = x², y³/y = y². Question 65. Which property is shown: (ab)c = a(bc)? A) Distributive B) Commutative C) Associative Property of Multiplication D) Identity Answer: C Explanation: Grouping changes in multiplication; associative property. Question 66. Simplify: (3x – 2)² A) 9x² + 4 B) 9x² – 12x + 4 C) 3x² – 4x + 2 D) 9x² – 4 Answer: B Explanation: (3x – 2)(3x – 2) = 9x² – 6x – 6x + 4 = 9x² – 12x + 4. Question 67. Which is the simplified form of √45? A) 3√ B) 5√ C) 9√ D) 15 Answer: A Explanation: √45 = √9 × √5 = 3√5. Question 68. What is the simplified form of (2x²y)/(4xy²)? A) x/(2y) B) 2x²/(y) C) x/y D) (1/2)x/y
Answer: A Explanation: 2/4 = 1/2, x²/x = x, y/y² = 1/y. Question 69. Simplify: (a²b)³ A) a⁶b³ B) a³b³ C) a⁶b⁶ D) a⁵b³ Answer: A Explanation: (a²)³ = a⁶, (b)³ = b³. Question 70. Which property is illustrated by: x + (–x) = 0? A) Identity B) Inverse C) Associative D) Distributive Answer: B Explanation: Adding a number and its opposite equals zero; inverse property. Question 71. What is the value of x in the equation 2x + 3 = 11? A) 3 B) 5 C) 4 D) 7 Answer: B Explanation: 2x = 8, x = 4. Question 72. Solve: 5(x – 2) = 15 A) x = 1 B) x = 2 C) x = 5 D) x = 7 Answer: D Explanation: 5(x – 2) = 15, x – 2 = 3, x = 5. Question 73. What is the solution to the equation 3x – 7 = 2x + 5? A) x = 12 B) x = – 12 C) x = 2 D) x = 7 Answer: A Explanation: 3x – 2x = 5 + 7 ⇒ x = 12.
Question 79. What is the solution to the equation 2(x + 7) = 18? A) x = 2 B) x = 9 C) x = 1 D) x = 7 Answer: D Explanation: 2(x + 7) = 18 ⇒ x + 7 = 9 ⇒ x = 2. Question 80. Solve: 3x – 7 = 2x + 8 A) x = – 1 B) x = 15 C) x = 1 D) x = – 15 Answer: B Explanation: 3x – 2x = 8 + 7 ⇒ x = 15. Question 81. Solve for p: 2p + 1 = 11 A) p = 5 B) p = 6 C) p = 4 D) p = 10 Answer: A Explanation: 2p = 10, p = 5. Question 82. What is the solution for x: 4x – 8 = 0? A) x = 0 B) x = 2 C) x = – 2 D) x = 8 Answer: B Explanation: 4x = 8, x = 2. Question 83. Solve: 2(x – 4) + 3x = 7 A) x = 3 B) x = 5 C) x = 2 D) x = 7 Answer: B Explanation: 2x – 8 + 3x = 7 ⇒ 5x = 15 ⇒ x = 3. Question 84. Solve the equation: 6x + 5 = 3x – 4 A) x = – 3
B) x = 3 C) x = – 9 D) x = 9 Answer: A Explanation: 6x – 3x = – 4 – 5 ⇒ 3x = – 9 ⇒ x = – 3. Question 85. Solve for t: t/5 + 2 = 6 A) t = 30 B) t = 20 C) t = 10 D) t = 40 Answer: B Explanation: t/5 = 4, t = 20. Question 86. If 3x = 27, what is x? A) 24 B) 9 C) 3 D) 6 Answer: D Explanation: x = 27/3 = 9. Question 87. Solve for x: x/2 – 7 = 3 A) x = 10 B) x = 20 C) x = – 20 D) x = 14 Answer: D Explanation: x/2 = 10, x = 20. Question 88. What is the solution to – 5x = 25? A) x = – 5 B) x = 5 C) x = – 25 D) x = 25 Answer: A Explanation: x = 25/–5 = – 5. Question 89. Solve for y: y – 8 = – 3y + 4 A) y = 3 B) y = – 1 C) y = – 3
Answer: B Explanation: x/3 = 3, x = 9. Question 95. Solve: 4x – 9 = 3x – 2 A) x = 7 B) x = – 7 C) x = – 9 D) x = 9 Answer: A Explanation: 4x – 3x = – 2 + 9 ⇒ x = 7. Question 96. What is the value of x in 2x – 5 = 7x + 10? A) x = – 3 B) x = 3 C) x = – 15/ D) x = 15/ Answer: A Explanation: 2x – 7x = 10 + 5 ⇒ – 5x = 15 ⇒ x = – 3. Question 97. Solve for y: 3y + 2 = 5y – 4 A) y = 3 B) y = – 3 C) y = 2 D) y = – 2 Answer: D Explanation: 3y – 5y = – 4 – 2 ⇒ – 2y = – 6 ⇒ y = 3. Question 98. What is the solution for x: 7x + 9 = 2x + 19? A) x = 2 B) x = – 2 C) x = – 7 D) x = 7 Answer: A Explanation: 7x – 2x = 19 – 9 ⇒ 5x = 10 ⇒ x = 2. Question 99. Solve for x: 10x – 2 = 3x + 12 A) x = 2 B) x = – 2 C) x = 14/ D) x = – 14/ Answer: A Explanation: 10x – 3x = 12 + 2 ⇒ 7x = 14 ⇒ x = 2.
Question 100. Solve: 5x + 7 = 2x – 8 A) x = – 5 B) x = 5 C) x = – 15/ D) x = 15/ Answer: A Explanation: 5x – 2x = – 8 – 7 ⇒ 3x = – 15 ⇒ x = – 5. Question 101. Solve the literal equation for y: x = 3y + 2 A) y = (x – 2)/ B) y = x/3 + 2 C) y = 3x – 2 D) y = x – 2 Answer: A Explanation: Subtract 2: x – 2 = 3y ⇒ y = (x – 2)/3. Question 102. Solve for x: ax + b = c A) x = (c – b)/a B) x = (c + b)/a C) x = (a – b)/c D) x = (b – c)/a Answer: A Explanation: ax = c – b ⇒ x = (c – b)/a. Question 103. Solve for y: 2x – 3y = 6 A) y = (2x – 6)/ B) y = (6 – 2x)/ C) y = (2x + 6)/ D) y = (6 + 2x)/ Answer: B Explanation: – 3y = 6 – 2x ⇒ y = (6 – 2x)/– 3 ⇒ y = (2x – 6)/3. Question 104. Solve for b: A = bh A) b = A/h B) b = h/A C) b = A × h D) b = h – A Answer: A Explanation: b = A/h.
