OAR Math Skills: Algebraic Expressions Questions and Answers — Questions and Answers
Question 1: Simplify the following algebraic expression: 5(2x - 3y) - (4x - 7y)
- 6x - 22y
- 6x + 8y
- 10x - 8y
- 6x - 8y (Correct answer)
Correct answer: 6x - 8y
First, distribute the 5 into the first parenthesis: 5 * 2x = 10x and 5 * -3y = -15y. This gives 10x - 15y. Next, distribute the negative sign into the second parenthesis: -1 * 4x = -4x and -1 * -7y = +7y. This gives -4x + 7y. Now, combine the like terms: (10x - 4x) + (-15y + 7y) = 6x - 8y.
Question 2: Evaluate the expression 3a² - 4ab + b² when a = -2 and b = 5.
- 77 (Correct answer)
- -3
- 27
- 47
Correct answer: 77
Substitute the given values for a and b into the expression: 3(-2)² - 4(-2)(5) + (5)². Follow the order of operations (PEMDAS). First, calculate the exponents: (-2)² = 4 and (5)² = 25. The expression becomes 3(4) - 4(-2)(5) + 25. Next, perform multiplication: 3(4) = 12 and -4(-2)(5) = 40. The expression is now 12 + 40 + 25. Finally, perform addition: 12 + 40 + 25 = 77.
Question 3: A small company's monthly profit is given by the expression P = 150x - (85x + 2500), where x is the number of units sold. Which of the following is a simplified expression for the monthly profit?
- P = 235x + 2500
- P = 65x - 2500 (Correct answer)
- P = 65x + 2500
- P = 235x - 2500
Correct answer: P = 65x - 2500
To simplify the expression P = 150x - (85x + 2500), you must first distribute the negative sign to both terms within the parentheses. This changes the expression to P = 150x - 85x - 2500. Then, combine the like terms (the terms with x): 150x - 85x = 65x. The constant term remains -2500. Therefore, the simplified expression is P = 65x - 2500.
Question 4: Which algebraic expression correctly represents the phrase 'five less than the product of a number and three'?
- 5 - 3x
- 3(x - 5)
- 3x - 5 (Correct answer)
- 5x - 3
Correct answer: 3x - 5
Break down the phrase. 'The product of a number and three' translates to 3x. 'Five less than' indicates that you subtract 5 from the previous part. Therefore, 'five less than the product of a number and three' is written as 3x - 5.
Question 5: Simplify the polynomial expression: (4a² + 3ab - 6b²) - (a² - 2ab + 3b²)
- 3a² + ab - 3b²
- 5a² + ab - 3b²
- 3a² + 5ab - 9b² (Correct answer)
- 3a² + ab - 9b²
Correct answer: 3a² + 5ab - 9b²
To simplify, distribute the negative sign to the second polynomial: - (a² - 2ab + 3b²) becomes -a² + 2ab - 3b². Now, rewrite the entire expression and combine like terms: (4a² - a²) + (3ab + 2ab) + (-6b² - 3b²). This simplifies to 3a² + 5ab - 9b².
Question 6: The formula for the area of a trapezoid is A = ½h(b₁ + b₂). What is the area of a trapezoid where the height (h) is 8 cm, base one (b₁) is 10 cm, and base two (b₂) is 15 cm?
- 120 cm²
- 100 cm² (Correct answer)
- 200 cm²
- 50 cm²
Correct answer: 100 cm²
Substitute the given values into the formula: A = ½(8)(10 + 15). Following the order of operations, first solve the part in the parentheses: 10 + 15 = 25. The equation becomes A = ½(8)(25). Now, multiply the numbers: ½ * 8 = 4. Then, 4 * 25 = 100. The area is 100 cm².
OAR Math Skills: Algebraic Expressions Questions and Answers
Simplify the following algebraic expression: 5(2x - 3y) - (4x - 7y)