Algebra I Semester Exam
- 1.
Solve the following equation 3x + 9 = 24
- A.
X =-5
- B.
X = 15
- C.
X = 3
- D.
X = 5
Correct Answer
D. X = 5Explanation
To solve the equation 3x + 9 = 24, we need to isolate the variable x. First, we subtract 9 from both sides of the equation to get 3x = 15. Then, we divide both sides by 3 to solve for x, which gives us x = 5. Therefore, the correct answer is x = 5.Rate this question:
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- 2.
Solve the following equation 8( x - 5) = -40
- A.
X = 0
- B.
X = 10
- C.
X = -10
- D.
X = 5
Correct Answer
A. X = 0Explanation
By distributing the 8 to both terms inside the parentheses, the equation becomes 8x - 40 = -40. Adding 40 to both sides of the equation, we get 8x = 0. Finally, dividing both sides by 8, we find that x = 0.Rate this question:
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- 3.
Identify the property that is illustrated in the following expression. 6( 12 - 3) = 6(12) - 6(3)
- A.
Associative Property
- B.
Distributive Property
- C.
Commutative Property
- D.
Multiplicative Property of Zero
Correct Answer
B. Distributive PropertyExplanation
The expression 6(12 - 3) = 6(12) - 6(3) demonstrates the Distributive Property. This property states that when multiplying a number by the sum or difference of two other numbers, we can distribute the multiplication to each term inside the parentheses. In this case, the 6 is being multiplied by the difference (12 - 3), and we can distribute the multiplication to both terms inside the parentheses, resulting in 6(12) - 6(3).Rate this question:
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- 4.
Simplify the following expression.
- A.
5/4
- B.
-5/4
- C.
4/5
- D.
-4/5
Correct Answer
C. 4/5Explanation
The given expression can be simplified by combining like terms. The fractions -5/4 and 5/4 are like terms because they have the same denominator. When we subtract -5/4 from 5/4, we get 10/4. Similarly, the fractions -4/5 and 4/5 are like terms. When we subtract -4/5 from 4/5, we get 8/5. Therefore, the simplified expression is 10/4 - 8/5.Rate this question:
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- 5.
Write an algebraic expression for the phrase the quotient of n and 6.
- A.
N + 6
- B.
6n
- C.
N/6
- D.
N - 6
Correct Answer
C. N/6Explanation
The phrase "the quotient of n and 6" means dividing n by 6. Therefore, the algebraic expression for this phrase would be n/6.Rate this question:
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- 6.
Simplify -
- A.
-3
- B.
3
- C.
0
- D.
1
Correct Answer
A. -3 -
- 7.
Simplify the following expression: -20 - (-5)()
- A.
40
- B.
-60
- C.
-40
- D.
60
Correct Answer
C. -40Explanation
The expression -20 - (-5) can be simplified by removing the parentheses and applying the rule of subtracting a negative number, which is equivalent to adding the positive number. So, -20 - (-5) becomes -20 + 5, which equals -15. However, none of the given answer options match the correct answer of -15, so the correct answer is not available.Rate this question:
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- 8.
Which expression is equivalent to 2b - 3a +b + a?
- A.
B - 2a
- B.
B - 4a
- C.
3b - 4a
- D.
3b - 2a
Correct Answer
D. 3b - 2aExplanation
The given expression can be simplified by combining like terms. 2b and b can be combined to give 3b, and -3a and a can be combined to give -2a. Therefore, the equivalent expression is 3b - 2a.Rate this question:
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- 9.
What is the reciprocal of -40?
- A.
40
- B.
1/40
- C.
-1/40
- D.
-1
Correct Answer
C. -1/40Explanation
The reciprocal of a number is obtained by dividing 1 by that number. In this case, the reciprocal of -40 would be -1/40, since -40 divided by 1 is -1/40.Rate this question:
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- 10.
What is the opposite of 3/2?
- A.
2/3
- B.
-2/3
- C.
-3/2
- D.
1
Correct Answer
C. -3/2Explanation
The opposite of a fraction is obtained by changing the sign of the numerator while keeping the denominator the same. In this case, the opposite of 3/2 would be -3/2, as the numerator is changed to its opposite sign while the denominator remains unchanged.Rate this question:
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- 11.
Simplify 4 + 10( 5 -3)^2
- A.
28
- B.
44
- C.
56
- D.
404
Correct Answer
B. 44Explanation
The expression follows the order of operations, which states that we should first simplify within parentheses, then perform any exponents, and finally perform any multiplication or division from left to right. In this case, within the parentheses, 5 - 3 equals 2. Then, we have 10 multiplied by 2 squared, which equals 40. Finally, we add 4 to 40, resulting in 44.Rate this question:
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- 12.
Which of these sets of numbers is ordered from least to greatest?
- A.
-3.4, 0, -3 5.3
- B.
-3.4, -3, 0, 5.3
- C.
-3, -3.4, 0, 5.3
- D.
0, -3, -3.4, 5.3
Correct Answer
B. -3.4, -3, 0, 5.3Explanation
The numbers in the set are arranged in ascending order, from least to greatest. The first number, -3.4, is the smallest, followed by -3, then 0, and finally 5.3, which is the largest.Rate this question:
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- 13.
What is the value of 5x + 2y when x = -1 and y = 4
- A.
-3
- B.
3
- C.
13
- D.
18
Correct Answer
B. 3Explanation
To find the value of 5x + 2y when x = -1 and y = 4, we substitute the given values into the expression. Plugging in x = -1 and y = 4, we get 5(-1) + 2(4) = -5 + 8 = 3. Therefore, the value of 5x + 2y when x = -1 and y = 4 is 3.Rate this question:
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- 14.
Solve 5( x - 1) = 2x + 4(2x + 1)
- A.
-9/5
- B.
-5/9
- C.
-1/5
- D.
5/9
Correct Answer
A. -9/5Explanation
To solve the equation, we first distribute the 4 to the terms inside the parentheses on the right side of the equation, resulting in 5(x - 1) = 2x + 8x + 4. Then, we distribute the 5 to the term inside the parentheses on the left side of the equation, giving us 5x - 5 = 2x + 8x + 4. Next, we combine like terms on both sides of the equation, resulting in 5x - 5 = 10x + 4. To isolate the variable, we subtract 10x from both sides, giving us -5x - 5 = 4. Finally, we add 5 to both sides and divide by -5 to solve for x, which gives us x = -9/5.Rate this question:
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- 15.
Simplify (
- A.
2x^2 - 7x + 1
- B.
2x^2 - 7x + 15
- C.
2x^2 + 3x + 1
- D.
2x^2 + 3x + 15
Correct Answer
D. 2x^2 + 3x + 15Explanation
The given expression cannot be simplified any further because there are no common factors or like terms that can be combined. Therefore, the expression 2x^2 + 3x + 15 is already in its simplest form.Rate this question:
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- 16.
Solve 3( x + 2) - 5 = 16
- A.
3
- B.
5
- C.
7
- D.
9
Correct Answer
B. 5Explanation
To solve the equation 3(x + 2) - 5 = 16, we first distribute the 3 to the terms inside the parentheses: 3x + 6 - 5 = 16. Then, we combine like terms by subtracting 5 from both sides of the equation: 3x + 1 = 16. Next, we isolate the variable by subtracting 1 from both sides: 3x = 15. Finally, we solve for x by dividing both sides by 3: x = 5.Rate this question:
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- 17.
Which of these lists the correct order of operation to simplify the expression 5( 3 +7) - 9 3
- A.
Add,multiply, divide, subtract
- B.
Add,multiply, subtract, divide
- C.
Add, subtract, multiply, divide
- D.
Multiply,add, subtract, divide
Correct Answer
A. Add,multiply, divide, subtractExplanation
The expression can be simplified by following the order of operations. First, we need to perform the addition inside the parentheses: 3 + 7 = 10. Then, we multiply 5 by 10: 5 * 10 = 50. Next, we need to divide 9 by 3: 9 / 3 = 3. Finally, we subtract 3 from 50: 50 - 3 = 47. Therefore, the correct order of operations to simplify the expression is add, multiply, divide, subtract.Rate this question:
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- 18.
Solve: 2(n -3) = -14
- A.
N = -7
- B.
N=-4
- C.
N = 6
- D.
N = 5
Correct Answer
B. N=-4Explanation
To solve the equation 2(n - 3) = -14, we first distribute the 2 to both terms inside the parentheses, giving us 2n - 6 = -14. Then, we isolate the variable by adding 6 to both sides of the equation, resulting in 2n = -8. Finally, we divide both sides by 2 to solve for n, giving us n = -4. Therefore, the correct answer is n = -4.Rate this question:
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- 19.
Multiply ( x + 6)(x + 3)
- A.
X^2 + 9x + 9
- B.
X^2 + 9x + 18
- C.
2x^2 + 9x + 18
- D.
2x^2 + 6x + 9
Correct Answer
B. X^2 + 9x + 18Explanation
The given expression is a multiplication of two binomials, (x + 6) and (x + 3). To multiply these binomials, we use the distributive property. We multiply the first terms of each binomial, which gives us x * x = x^2. Then, we multiply the outer terms, which gives us x * 3 = 3x. Next, we multiply the inner terms, which gives us 6 * x = 6x. Finally, we multiply the last terms, which gives us 6 * 3 = 18. Combining all these terms, we get x^2 + 9x + 18, which is the correct answer.Rate this question:
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- 20.
Simplify (2n^4)^3
- A.
8n^7
- B.
8n^12
- C.
6n^7
- D.
2n^12
Correct Answer
B. 8n^12Explanation
To simplify (2n^4)^3, we need to raise both the coefficient and the exponent inside the parentheses to the power of 3. The coefficient 2 raised to the power of 3 is 8. The exponent n^4 raised to the power of 3 is 12, since we multiply the exponents. Therefore, the simplified expression is 8n^12.Rate this question:
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Mar 20, 2023Quiz Edited by
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Dec 18, 2013Quiz Created by
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