1.
Which word best describes the 2 in the expression 3x^{2} + 4x + 7.
Correct Answer
C. Exponent
Explanation
The number 2 in the expression 3x2 + 4x + 7 is best described as an exponent. In this expression, the 2 is the exponent of the variable x, indicating that x is being raised to the power of 2. The exponent determines the degree of the term and represents how many times the base (in this case, x) is multiplied by itself.
2.
Which word best describes the 3 in the expression 3x^{2} + 4x + 7.
Correct Answer
A. Coefficient
Explanation
The word "coefficient" best describes the 3 in the expression 3x2 + 4x + 7. In algebraic expressions, a coefficient is a numerical or constant factor that multiplies a variable. In this case, the coefficient of the term 3x2 is 3, indicating that the variable x is multiplied by 3.
3.
Which word best describes the x in the expression 3x^{2} + 4x + 7.
Correct Answer
E. Variable
Explanation
The expression 3x^2 + 4x + 7 represents a quadratic equation with x as the variable. In algebraic equations, a variable is a symbol that represents an unknown value or quantity. In this case, x can take on different values, and its power (exponent) in the equation indicates its degree. Therefore, the word "Variable" best describes x in the given expression.
4.
Which word best describes the 7 in the expression 3x^{2} + 4x + 7.
Correct Answer
B. Constant
Explanation
In the expression 3x2 + 4x + 7, the term "7" does not have any variable attached to it and does not change. It remains the same regardless of the value of x. Therefore, it can be described as a constant.
5.
Which word best describes the 4x in the expression 3x^{2} + 4x + 7.
Correct Answer
D. Term
Explanation
In the expression 3x^2 + 4x + 7, the term "4x" represents a single entity that includes both a coefficient (4) and a variable (x). A term is a combination of a coefficient and one or more variables, and it can be added or subtracted within an expression. Therefore, the word "Term" best describes the 4x in the given expression.
6.
Simplify [ a^{2} – 2a + 7a^{2} + 9a + a – 4a^{2} ] by collecting like terms.
Correct Answer
D. 4a^{2} + 8a
Explanation
The given expression is simplified by combining like terms. In this case, the terms with the same variable (a) are combined. The terms 4a^2 and -4a^2 cancel each other out, leaving only the term 8a. Therefore, the simplified expression is 4a^2 + 8a.
7.
Simplify [ –6p^{2} – 20p – 4p – 10p^{2} – 3 + 2p + 5 ] by collecting like terms.
Correct Answer
B. –16p^{2} – 22p + 2
Explanation
The given expression can be simplified by combining like terms. The terms with the same variable and exponent can be added or subtracted together. In this case, the terms -6p^2 and -10p^2 can be combined to give -16p^2. The terms -20p, -4p, and 2p can be combined to give -22p. The constant terms -3 and 5 can be combined to give 2. Therefore, the simplified expression is -16p^2 - 22p + 2.
8.
Simplify [ 2n^{2} + 2n + 1 – 10n^{2} – n – 15n + 9 – n ] by collecting like terms.
Correct Answer
D. –8n^{2} – 15n + 10
Explanation
The given expression is simplified by combining like terms. By combining the like terms, we get -8n^2 - 15n + 10.
9.
Simplify [ –11x + 2y + 5 + 3y + 7 + 1 – 6x ] by collecting like terms.
Correct Answer
B. –17x + 5y + 13
Explanation
The given expression involves collecting like terms, which means combining the terms that have the same variables and exponents. By collecting like terms, we can simplify the expression. In this case, we have -11x and -6x, which can be combined to give -17x. We also have 2y and 3y, which can be combined to give 5y. Finally, we have 5, 7, and 1, which can be combined to give 13. Therefore, the simplified expression is -17x + 5y + 13.
10.
Simplify [ 5a^{2} + 4a + 17 – 2a + 3a^{2} – 4 ] by collecting like terms.
Correct Answer
C. 8a^{2} + 2a + 13
Explanation
The given expression is simplified by combining like terms. The terms with the same variable and exponent are grouped together and their coefficients are added or subtracted. In this case, the terms 5a2 and 3a2 are combined to give 8a2. The terms 4a, -2a, and 2a are combined to give 4a. The constant terms 17 and -4 are combined to give 13. Therefore, the simplified expression is 8a2 + 2a + 13.
11.
Which of the following is equivalent to the expression 3(x + 2) – 7?
Correct Answer
B. 3x + 6 – 7
Explanation
The expression 3(x + 2) - 7 can be simplified by distributing the 3 to both terms inside the parentheses. This gives us 3x + 6 - 7. Simplifying further, we combine like terms to get 3x - 1. Therefore, the expression 3x + 6 - 7 is equivalent to 3(x + 2) - 7.
12.
Which of the following expressions mean the same thing? [Select two options]
Correct Answer(s)
A. 2(4 + 5)
C. (4 + 5)(2)
Explanation
The expressions 2(4 + 5) and (4 + 5)(2) mean the same thing because both of them represent the multiplication of the sum of 4 and 5 by 2.
13.
Which of the following expressions mean the same thing? [Select two options]
Correct Answer(s)
A. 5(2x + 7)
D. (2x + 7)(5)
Explanation
The expressions 5(2x + 7) and (2x + 7)(5) mean the same thing because they both represent the product of 5 and the sum of 2x and 7. In both expressions, the 2x and 7 are being multiplied by 5. The order in which the terms are written does not affect the result of the multiplication, so both expressions are equivalent.
14.
Which of the following expressions mean the same thing? [Select two options]
Correct Answer(s)
A. –8(6x – 4)
C. –48x + 32
Explanation
The two expressions that mean the same thing are -8(6x - 4) and -48x + 32. Both expressions simplify to the same result when expanded and simplified.
15.
Which expression shows –3(x + 5) in expanded form?
Correct Answer
D. –3x – 15
Explanation
The given expression, -3(x + 5), can be expanded by distributing the -3 to both terms inside the parentheses. This means multiplying -3 with both x and 5. The result is -3x - 15, which matches the answer given.
16.
Which of the following expressions mean the same thing? [Select all the correct options]
Correct Answer(s)
A. –9(6y – 4y)
C. –54y + 36y
D. –18y
Explanation
The expressions -9(6y - 4y), -54y - 36y, and -18y all mean the same thing.
17.
Which of the following is equivalent to the expression 8(2x + 2) – 3(4x + 6)?
Correct Answer
C. 4x – 2
Explanation
The given expression can be simplified using the distributive property. Multiplying 8 by each term inside the parentheses, we get 16x + 16. Similarly, multiplying 3 by each term inside the other parentheses, we get 12x + 18. Subtracting these two expressions, we get 16x + 16 - (12x + 18). Simplifying further, we get 16x + 16 - 12x - 18. Combining like terms, we get 4x - 2, which is equivalent to the given expression.
18.
Simplify the expression:
( - 8v^{4 }+ 4v^{3} + 3v) + (- 8v^{4 }+ 4v - 7)
Correct Answer
B. -16v^{4} + 4v^{3} + 7v - 7
19.
Simplify the expression:
(–6p^{4} + p^{3} + 1) – ( 8p^{4}–8p^{3 }+ 7)
Correct Answer
A. –14p^{4} + 9p^{3} – 6
Explanation
The given expression is simplified by distributing the negative sign to each term inside the parentheses. This results in the expression -6p4 - p3 - 1 - 8p4 + 8p3 - 7. Combining like terms, we get -14p4 + 9p3 - 6. Therefore, the correct answer is -14p4 + 9p3 - 6.
20.
Simplify the following expression
(r^{2} + s^{2}) – (5r^{2} + 4s^{2})
Correct Answer
B. –4r^{2} – 3s^{2}
Explanation
The given expression is (r^2 + s^2) - (5r^2 + 4s^2). To simplify this expression, we need to distribute the negative sign to both terms inside the parentheses. This gives us -5r^2 - 4s^2. Combining like terms, we get -4r^2 - 3s^2. Therefore, the correct answer is -4r^2 - 3s^2.
21.
The measure of two side of a triangle is x^{2}+ 2x. If the perimeter is 4x^{2}+ x, what is the measure of the third side?
Correct Answer
A. 3x^{2}– x
Explanation
The perimeter of a triangle is the sum of the lengths of all three sides. In this case, the given perimeter is 4x^2 + x. We are also given that two sides of the triangle have a combined length of x^2 + 2x. To find the measure of the third side, we need to subtract the sum of the lengths of the two given sides from the perimeter. Therefore, the measure of the third side is 4x^2 + x - (x^2 + 2x) = 3x^2 - x.
22.
Simplify the expression:
(5b - 3b^{3} - 8b^{2}) - (2b^{3} - 4b^{2} + 6b - 3b^{4})
Correct Answer
D. 3b^{4} - 5b^{3} - 4b^{2} - b
Explanation
By simplifying the expression, we can combine like terms by adding or subtracting their coefficients. In this case, we have the terms with b raised to different powers: b, b^2, b^3, and b^4. By combining the coefficients of these terms, we get 3b^4 - 5b^3 - 4b^2 - b as the simplified expression.
23.
Simplify the expression:
(7k + 2k^{3} - 8k^{4}) - (4k^{3} - 5k + 4k^{2} - 7k^{4)}
Correct Answer
A. -k^{4} - 2k^{3} - 4k^{2} + 12k
Explanation
The given expression involves subtracting two sets of terms. To simplify the expression, we combine like terms by adding or subtracting coefficients with the same variable and exponent. In this case, we have terms with the variable k raised to different powers. By rearranging the terms and combining like terms, we obtain the answer: -k^4 - 2k^3 - 4k^2 + 12k.
24.
Expand and Simplify:
(5x + 2) (x^{2 }– 3x + 6)
Correct Answer
C. 5x^{3} – 13x^{2} + 24x + 12
Explanation
The correct answer is 5x3 – 13x2 + 24x + 12. This is the correct answer because when we expand and simplify the given expression, we multiply each term in the first polynomial (5x + 2) by each term in the second polynomial (x2 – 3x + 6). After combining like terms, we get the expression 5x3 – 13x2 + 24x + 12.
25.
Is the polynomial expression in standard form?
7x^{3} – 8x^{2} + 9
Correct Answer
A. True
Explanation
The polynomial expression is in standard form because the terms are arranged in descending order of their exponents. The highest exponent is 3, followed by 2, and then there is a constant term.
26.
Choose all the polynomial expressions that are in standard form (Multiple options might be correct)
Correct Answer(s)
B. 7x^{3} – 3x^{2}
D. 3x^{9} + 4x^{2} – 6x + 10
Explanation
The polynomial expressions 7x^3 - 3x^2 and 3x^9 + 4x^2 - 6x + 10 are in standard form because they are written in descending order of the exponents of the variables, with the coefficients of each term included.
27.
Simplify:
5(3x+2) + (2x - 3)
Correct Answer
B. 17x + 7
Explanation
The given expression is 5(3x+2) + (2x - 3). To simplify this expression, we can distribute the 5 to both terms inside the parentheses, which gives us 15x + 10. Then, we can combine like terms by adding the 15x and 2x, which gives us 17x. Finally, we add the constant terms 10 and -3 to get 7. Therefore, the simplified expression is 17x + 7.
28.
Which expression is equivalent to
2(3g - 4) - (8g + 3)?
Correct Answer
D. -2g - 11
Explanation
To simplify the expression, we distribute the 2 to both terms inside the parentheses: 2(3g - 4) becomes 6g - 8. Then, we distribute the negative sign to both terms inside the parentheses: -(8g + 3) becomes -8g - 3. Now we can combine like terms: 6g - 8 - 8g - 3 = -2g - 11. Therefore, the expression is equivalent to -2g - 11.
29.
If C = 2a^{2}−5 and D = 3 – a , then C – 2D equals to:
Correct Answer
C. 2a^{2 }+ 2a – 11
Explanation
The given expression is C - 2D. Substituting the values of C and D, we get (2a^2 - 5) - 2(3 - a). Simplifying further, we have 2a^2 + a - 8. Therefore, the correct answer is 2a^2 + a - 8.
30.
Simplify:
(2x + 8) – 3(x - 2)
Correct Answer
B. –x + 14
Explanation
The given expression is (2x + 8) - 3(x - 2). To simplify the expression, we distribute the -3 to both terms inside the parentheses: 2x + 8 - 3x + 6. Combining like terms, we get -x + 14.
31.
Jim is twice as old as John.
If x represents John's age, which expression represents
how old Jim is in six years?
Correct Answer
D. 2n + 6
Explanation
Jim is twice as old as John, so if x represents John's age, then Jim's age can be represented as 2x. In six years, both John and Jim will be six years older. Therefore, Jim's age in six years can be represented as 2x + 6.
32.
Expand and Simplify
(2x + 1)(x - 5)
Correct Answer
C. 2x^{2} - 9x - 5
Explanation
The given expression is a product of two binomials: (2x + 1) and (x - 5). To expand and simplify this expression, we can use the distributive property. By multiplying each term in the first binomial by each term in the second binomial, we get: 2x * x + 2x * (-5) + 1 * x + 1 * (-5). Simplifying this further, we have: 2x^2 - 10x + x - 5. Combining like terms, we get the final simplified expression: 2x^2 - 9x - 5.
33.
The length of a rectangle is four more than the width. The width is equal to x.
Find the area of the rectangle. [ Hint: A = LW ]
Correct Answer
B. X^{2} + 4x
Explanation
The area of a rectangle is calculated by multiplying its length and width. In this case, the length of the rectangle is given as "four more than the width". Since the width is equal to x, the length can be expressed as (x + 4). Therefore, the area of the rectangle is (x * (x + 4)), which simplifies to x^2 + 4x.
34.
Which of the following expressions has 3 unlike terms?
Correct Answer
B. 6x^{2} + 6x + 8
Explanation
The expression 6x2 + 6x + 8 has 3 unlike terms because each term has a different variable or exponent. The term 6x2 has a different exponent than the term 6x, and both of these terms have different variables than the constant term 8. Therefore, this expression has 3 unlike terms.
35.
Expand and Simplify:
-4x (3x^{2} - 2x + 1)
Correct Answer
D. -12x^{3 }+ 8x^{2 }- 4x
Explanation
The given expression is a multiplication of -4x with the expression (3x^2 - 2x + 1). To expand and simplify, we distribute -4x to each term inside the parentheses. This gives us -12x^3 + 8x^2 - 4x. Therefore, the answer is -12x^3 + 8x^2 - 4x.
36.
Find the perimeter of the rectangle { Hint: P = 2L + 2W)
Correct Answer
C. 12x + 22
Explanation
The given answer, 12x + 22, is the correct expression for finding the perimeter of a rectangle. The formula for the perimeter of a rectangle is P = 2L + 2W, where L represents the length and W represents the width. In this case, the length is represented by 6x and the width is represented by 11. Therefore, substituting these values into the formula, we get P = 2(6x) + 2(11) = 12x + 22.
37.
Simplify the algebraic expression:
(3x^{2} + 2x - 4) - (5x^{2} + 6x + 2) + (4x^{2} - x + 1)
Correct Answer
A. 2x^{2} - 5x - 5
Explanation
The given algebraic expression involves adding and subtracting terms with the same variable, x, and different exponents. By combining like terms, we can simplify the expression. In this case, we combine the terms with x^2, the terms with x, and the constant terms separately. After simplifying, the resulting expression is 2x^2 - 5x - 5.
38.
Simplify the expression: 4(5y - 2y^{2} + 11) - 2y^{2}
Correct Answer
B. -10y^{2} + 20y + 44
Explanation
The expression is simplified by distributing the 4 to each term inside the parentheses, resulting in 20y - 8y^2 + 44. Then, subtracting 2y^2 from this expression gives -10y^2 + 20y + 44.
39.
Expand and Simplify the expression:
4 (6y^{2 }- 2y) - 3y (4y - 3)
Correct Answer
D. 12y^{2 }+y
Explanation
The given expression is a combination of terms that can be simplified by applying the distributive property and combining like terms. By multiplying 4 with each term inside the parentheses and then multiplying -3y with each term inside the second set of parentheses, we can expand the expression. This results in 24y^2 - 8y - 12y^2 + 9y. Combining like terms, we get 12y^2 + y.
40.
Simplify the expression.
-4(9 + 3x) - 4(x - 2)
Correct Answer
A. -16x-28
Explanation
To simplify the expression, we need to distribute the -4 to both terms inside the parentheses. This gives us -36 - 12x - 4x + 8. Combining like terms, we get -16x - 28.
41.
Simplify the expression
-6x - 5(10x + 3)
Correct Answer
A. -56x - 15
Explanation
The expression is simplified by distributing the -5 to both terms inside the parentheses. This gives us -6x - 50x - 15. Combining like terms, we get -56x - 15.
42.
Simplify the expression.
-6(10n + 7) + 9n
Correct Answer
B. -51n - 42
Explanation
The expression -6(10n + 7) + 9n can be simplified by distributing the -6 to both terms inside the parentheses, resulting in -60n - 42. Then, adding 9n to this expression gives -51n - 42.
43.
Simplify
x^{2}(2x+3)
Correct Answer
D. 2x^{3}+3x^{2}
Explanation
The given expression is x^2(2x+3). To simplify this expression, we need to distribute the x^2 to both terms inside the parentheses. This gives us 2x^3 + 3x^2. Therefore, the correct answer is 2x^3 + 3x^2.
44.
Correct Answer
A. 8x^{4}
Explanation
The correct answer is 8x4 because when you multiply 8 by 4, you get the product of 32.
45.
Correct Answer
B. 5w^{ 2} − 4w + 3
46.
Correct Answer
D. 4x^{4 }- 9x^{2}
Explanation
In the given expression, we have a combination of multiplication and addition/subtraction operations. The expression can be simplified by performing the multiplication first and then the addition/subtraction.
-5x10 = -50
4x4 = 16
18x6 = 108
-6x4 = -24
16x2 = 32
Now, substituting these values back into the expression, we get:
-50 + 16 + 108 - 24 + 32
Simplifying further, we get:
-50 + 16 + 108 - 24 + 32 = 82
Therefore, the correct answer is 82.
47.
4k^{2}(6k^{2} + 9kq - 5q^{2})
Correct Answer
C. 24k^{4 } + 36k^{3}q - 20k^{2}q^{2}
Explanation
The given expression is a product of two terms: 4k^2 and (6k^2 + 9kq - 5q^2). To simplify the expression, we need to distribute 4k^2 to each term inside the parentheses. This results in 24k^4 + 36k^3q - 20k^2q^2. Therefore, the correct answer is 24k^4 + 36k^3q - 20k^2q^2.
48.
Simplify
7x^{2}y^{3} (2x^{4}y^{5}+6xy^{3})
Correct Answer
C. 14x^{6}y^{8}+42x^{3}y^{6}
Explanation
The given expression is the product of 7x^2y^3 and the sum of (2x^4y^5 + 6xy^3). To simplify, we need to distribute the 7x^2y^3 to each term inside the parentheses. This gives us 14x^6y^8 + 42x^3y^6. Therefore, the correct answer is 14x^6y^8 + 42x^3y^6.
49.
The perimeter of the garden in the diagram is 170 m. Determine the value of w and the length of each side.
Correct Answer
C. 34 m (w = 15)
Explanation
Based on the given information, the perimeter of the garden is 170 m. The perimeter of a rectangle is calculated by adding the lengths of all four sides. Let's assume the length of the garden is L and the width is W. The formula for the perimeter is P = 2L + 2W. Since we are given that the perimeter is 170 m, we can set up the equation as 170 = 2L + 2W. We are also told that the width is equal to 15, so we can substitute W with 15. Solving the equation, we get 170 = 2L + 2(15), which simplifies to 170 = 2L + 30. By subtracting 30 from both sides, we have 140 = 2L. Dividing both sides by 2, we get L = 70. Therefore, the length of each side is 70 m and the width is 15 m, giving us the answer 34 m (w = 15).
50.
Solve for x:
–2x + 3 = –5
Correct Answer
B. 4
Explanation
To solve for x, we need to isolate the variable on one side of the equation. By adding 2x to both sides of the equation, we can eliminate the -2x term on the left side. This leaves us with 3 = -5 + 2x. Next, we can simplify the equation by adding 5 to both sides, resulting in 8 = 2x. Finally, by dividing both sides of the equation by 2, we find that x = 4.