1.
4^{2 = }
Correct Answer
B. 16
Explanation
The expression 4^2 represents 4 raised to the power of 2. In mathematical terms, this is referred to as "four squared." When you square a number, you multiply the number by itself.
So, 4^2 is calculated as follows:
4×4=16
Thus, 4^2 equals 16.
2.
What will be the value of x in this equation: 2x - 4 = 0
Correct Answer
C. 2
Explanation
To find the value of
𝑥 in the equation 2x−4=0, you can follow these steps:
Add 4 to both sides of the equation to isolate the term with
x on one side:
2x−4+4=0+4
2x=4
Divide both sides by 2 to solve for 𝑥
2x / 2 = 4/2
x=2
Thus, the value of
x is 2.
3.
Use the formula above, when x = -1 to find the value for y.
Correct Answer
A. 6
Explanation
To find the value of ( y ) when ( x = -1 ) using the given formula, we can substitute ( x ) into the equation shown on the graph:
[ y = (x-1)^2 + 2 ]
Substituting ( x = -1 ):
[ y = (-1-1)^2 + 2 = (-2)^2 + 2 = 4 + 2 = 6 ]
Therefore, when ( x = -1 ), the value of ( y ) is ( 6 ).
4.
What is the slope of a line containing the points (3,2) and (-1,0).
Correct Answer
D. 1/2
5.
Solve: 4/2 + 7/2 =
Correct Answer
B. 5 1/2
Explanation
The given expression involves adding two fractions with a common denominator of 2. When we add 4/2 and 7/2, we get a sum of 11/2. However, 11/2 can be simplified to the mixed number 5 1/2. Therefore, the correct answer is 5 1/2.
6.
Which term describes a polynomial with two terms?
Correct Answer
B. Binomial
Explanation
In algebra, a polynomial with two terms is called a binomial. Each term is referred to as a monomial, and a binomial consists of two such monomials. Common examples include expressions like x+y and 3x2−2x. The prefix "bi-" indicates two, aligning with the number of terms.
7.
Use the formula above to find a when b = 4, c = 5.
Correct Answer
E. 3
Explanation
To find the value of ( a ) using the Pythagorean theorem when ( b = 4 ) and ( c = 5 ), the formula used is:
[ a^2 + b^2 = c^2 ]
Given ( b = 4 ) and ( c = 5 ), substitute these values into the formula:
[ a^2 + 4^2 = 5^2 ]
[ a^2 + 16 = 25 ]
Now, solve for ( a^2 ):
[ a^2 = 25 - 16 ]
[ a^2 = 9 ]
Taking the square root of both sides gives:
[ a = √{9} ]
[ a = 3 ]
Thus, when ( b = 4 ) and ( c = 5 ), the value of ( a ) is ( 3 ).
8.
Find the value of x in this equation: x + 2(x + 7) = 14x– 7.
Correct Answer
B. 21/11
Explanation
To find the value of x in the equation, we first distribute the 2 to the terms inside the parentheses: x + 2x + 14 = 14x - 7. Then, we combine like terms: 3x + 14 = 14x - 7. Next, we isolate the variable terms on one side and the constant terms on the other side: 14 + 7 = 14x - 3x. Simplifying further, we have 21 = 11x. Finally, we divide both sides by 11 to solve for x, resulting in x = 21/11.
9.
What will be the value of z in this equation- 5(z + 1) = 3(z + 2) + 11.
Correct Answer
A. 6
10.
(x – 2) / 4 – (3x + 5) / 7 = – 3, x = ?
Correct Answer
C. 10
11.
12q – 10 = 14q + 2. Find q.
Correct Answer
C. -6
Explanation
Start by isolating the variable q on one side of the equation. To do this, you need to move all terms with q to one side and constants to the other side.
12q - 14q = 2 + 10
-2q = 12
Now, divide both sides by -2 to solve for q:
(-2q) / (-2) = 12 / (-2)
q = -6
So, the value of q is q = -6.
12.
What is the value of 𝑥 in the equation 2𝑥+3=11?
Correct Answer
B. 4
Explanation
To solve for x, you need to isolate x on one side of the equation. Start by subtracting 3 from both sides to eliminate the constant term on the left side:
2x+3−3=11−3
This simplifies to:
2x=8
Next, divide both sides by 2 to solve for
2x= 8/2
Resulting in:
x=4
13.
Which expression represents the distributive property?
Correct Answer
A. [a(b+c)=ab+ac]
Explanation
The distributive property states that multiplying a number by a sum is the same as multiplying the number by each addend separately and then adding the results. In this case, a(b+c) = ab + ac demonstrates the distributive property, where "a" is distributed to both "b" and "c." The other expressions represent different mathematical properties: B) is the commutative property of addition, C) is the associative property of multiplication, and D) is another form of the distributive property but with subtraction.
14.
Simplify: (x^{2}−3x+2)−(2x^{2}−5x+4)
Correct Answer
A. -x^{2}+2x−2
Explanation
To simplify this expression, distribute the negative sign across the terms in the second polynomial:
x2−3x+2−2x2+5x-4
Combine like terms (terms with the same variable raised to the same power):
(x2−2x2)+(−3x+5x)+(2−4)
This results in:
-x2+2x−2
15.
Solve for y in the equation: 3y−6=9.
Correct Answer
B. 5
Explanation
Begin by adding 6 to both sides to remove the constant term from the left side:
3y−6+6=9+6
Simplifying gives:
3y=15
y=15/3
y=5