ANSWER THE FOLLOWING
Math 6B-Expressions Unit Test
Connections Academy
1.3 raised to what power is equal to 81?
2.Which expression has the greater value, 26 or 92 ? For your answer, type 1 for 26 or type 2 for 92 .
3.What are the variables in the equation y=3x−4 ?(1 point)
A.3 and 4
B.x only
C.y only
D.x and y
4.A sign is being painted that includes 3 small squares with a side length of s and 2 large ones with a side length of S . Write an expression to find the total area of the sign that needs to be painted.(1 point)
Responses
2S2−3s2
2 upper S squared minus 3 s squared
3S2+2s2
3 upper S squared plus 2 s squared
3S2−2s2
3 upper S squared minus 2 s squared
2S2+3s2
5.Evaluate the expression at specific values of their variables.(1 point)
Evaluate a5 − bc + 4a ÷ c when a = 2, b = 3, and c = 8_________
6.The expression 25c+48a represents the total cost for a group of children and adults to attend the amusement park. The variable c represents the number of children attending. The variable a represents the number of adults attending. What is the total cost for 12 children and 4 adults?(1 point)
The total cost is $____
7.A truck rental costs $2 per miles, m , driven plus a $24 rental fee. Translate the words into an algebraic expression.(1 point)
The expression is____
8.The expression 5p is given. What is this expression translated into words?(1 point)
Responses
the sum of 5 and a
number p
the quotient of 5 and a number p
the product of 5 and a number p
the difference of 5 and a number p
9.In the equation 9c=18 , the 9 is called a(1 point)
Responses
term.
term.
variable.
variable.
coefficient.
coefficient.
product.
10.What is the coefficient in the expression 9+8b−56 ?
11.Simplify: 12−4÷43+1
12.Which of the following shows the correct pairing of a property of operations and its example?(1 point)
2(a+3) = 2a+6; Commutative Property
2 times open paren A plus 3 close paren is equal to 2 A plus 6 ; Commutative Property
2a +3b = 3b + 2a; Distributive Property
2 A plus 3 b is equal to 3 b plus 2 A ; Distributive Property
2(a+3) = 2a+6; Associative Property
2 times open paren A plus 3 close paren is equal to 2 A plus 6 ; Associative Property
2a + 3b = 3b + 2a; Commutative Property
13.Which expression is equivalent to 2(x+3)+4(x+1) ?(1 point)
Responses
6x+10
6 x plus 10
2x+10
2 x plus 10
6x+7
6 x plus 7
3x+10
14.Apply the Associative and Commutative Properties to generate an expression equivalent to 2(a+5)+4(2a+3)−10 .(1 point)
Responses
12a+10
12 A plus 10
10a +22
10 A plus 22
10a +12
10 A plus 12
9a +12
1. 3 raised to what power is equal to 81?
The answer is 4 because 3^4 = 81.
2. Which expression has the greater value, 26 or 92?
The answer is 2 for 92 because 92 is greater than 26.
3. What are the variables in the equation y=3x−4?
The variables in the equation are x and y, so the answer is D. x and y.
4. A sign is being painted that includes 3 small squares with a side length of s and 2 large ones with a side length of S. Write an expression to find the total area of the sign that needs to be painted.
The expression is 3S^2 + 2s^2.
5. Evaluate the expression a^5 − bc + 4a ÷ c when a = 2, b = 3, and c = 8.
Substituting the values of a, b, and c into the expression gives (2^5) - (3*8) + 4(2) ÷ 8.
Simplifying this expression, we get 32 - 24 + 8 ÷ 8 = 32 - 24 + 1 = 9.
6. The expression 25c + 48a represents the total cost for a group of children and adults to attend the amusement park. The variable c represents the number of children attending, and a represents the number of adults attending. What is the total cost for 12 children and 4 adults?
Substituting c = 12 and a = 4 into the expression gives 25(12) + 48(4).
Evaluating this expression, we get 300 + 192 = 492.
The total cost for 12 children and 4 adults is $492.
7. A truck rental costs $2 per mile driven, plus a $24 rental fee. Translate the words into an algebraic expression.
The expression is 2m + 24, where m represents the number of miles driven.
8. The expression 5p is given. What is this expression translated into words?
The expression is "the product of 5 and the number p."
9. In the equation 9c = 18, the 9 is called a coefficient.
10. What is the coefficient in the expression 9+8b−56?
The coefficient is 8.
11. Simplify: 12 − (4 ÷ 4) + 1
First, perform the division inside the parentheses: 4 ÷ 4 = 1.
Next, subtract 1 from 12: 12 - 1 = 11.
Finally, add 11 and 1: 11 + 1 = 12.
The simplified expression is 12.
12. Which of the following shows the correct pairing of a property of operations and its example?
The correct pairing is: 2(a+3) = 2a+6; Distributive Property.
13. Which expression is equivalent to 2(x+3)+4(x+1)?
The expression equivalent to 2(x+3)+4(x+1) is 6x+10.
14. Apply the Associative and Commutative Properties to generate an expression equivalent to 2(a+5)+4(2a+3)−10.
Using the Associative Property, we can rearrange the terms in the expression:
2(a+5)+4(2a+3)−10 = 2a + 10 + 8a + 12 - 10
Using the Commutative Property, we can group like terms:
(2a + 8a) + (10 + 12 - 10) = 10a + 22
The equivalent expression is 10a + 22.