Download Expressions Study Guide

Name __________________________________________ Period ____ Date _______________
Expressions STUDY GUIDE
Directions: Show ALL work. NO WORK, NO CREDIT.
Answer Column
1. Write the algebraic expression that best matches each verbal expression.
Not all expressions have a match.
2
n
(4n – 2)²
+4
+ 4 (7 – n)²
2n + 4
2(n – 4 )
n
2
Part A: Twice the difference of a number and 4.
Part B: Two less than the product of 4 and a number, squared.
Part C: Four more than the ratio of a number and 2.
1. A: ________________
4(n – 2)
B: ________________
C: ________________
2. ___________________
2. Which expression best represents the statement? “A number multiplied by 4 is
subtracted from the difference of the same number and 65.”
A. 4x – (x – 65)
B. 4x – x – 65
C. (x – 65) – 4x
D. x – 65 + 4x
3. ___________________
4. ___________________
5. A: ________________
6. ___________________
3. What is the expression (0.5)² - (0.4)² ● (0.3) simplified?
7. A: ________________
B: ________________
8. A: ________________
4. Kieran starts with $85 dollars in her savings account and adds $7 to the account
each week. After w weeks, the number of dollars in Kieran’s account can be
represented by 7w + 35. What conclusion can be supported by the expression?
A. Kieran deposited an extra $50 into her account.
B. Kieran withdrew $50 from her account
C. Kieran saved an extra $7 each week.
D. Kieran spent $7 from her account.
5. The area of a trapezoid can be calculated with the formula A =
ab
● h,
2
where a and b are the lengths of the bases, and h is the height.
B: ________________
9. A: ________________
B: ________________
10. __________________
11. __________________
12. __________________
Part A: What is the area of a trapezoid when a = 8, b = 4, and h = 7?
13. A: _______________
14. __________________
Part B: Jenny wrote the formula for the area of a trapezoid as A =
h
● (a + b). 15. B: _______________
2
ab
● h? _______
2
Explain your reasoning and give an example to support your claim.
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
_______________________________________________________________
Will her formula give the same area as the formula A =
C: ________________
6. Which expressions are equivalent to 4 + 8x? Mark all that apply.
A. (2x)(4x + 2)
B. 4x + 2(2 + 2x)
C. 8(x + 1) + 3
D. 4x + 2 + 2(x + 1)
E. 2(x + 1) + 2(3x + 1)
F. 4(1 + 2x)
7. Consider the expression 8y² + 12x + 5y + 7
Part A: What are the coefficients in the expression?
Part B: How many terms does the expression have?
8. A customer hired an artist to paint a rectangular mural 9 feet long and 3 feet high. The customer then
asked the artist to increase the height by y feet. The new size of the mural is show below.
(3 + y) feet
9 feet
Part A: Write an expression to represent the perimeter of the mural. Simplify the expression.
Part B: Write an expression to represent the area of the mural. Simplify the expression.
9. Ms. Geidel wrote the four expressions below on the board.
Expression 1: 12 + 7x – 4 + 8x
Expression 2: x + 14
Expression 3: 10x + 5
Expression 4: 5(1 + 2x)
Part A: Which two expressions are equivalent to each other?
Part B: Which expression is equivalent to 16x + 6 – x + 2?
Part C: One of Ms. Geidel’s students said that the expression 7x – 6 – 2x + 8 is equivalent to
Expression 2, because when she substituted 3 for x into both expressions, she got 17.
Is she correct? Explain your reasoning. _______
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
2
1
10. Which expression is equivalent to the expression   ?
3
2
1
1
1
1
1
A.
B.
●
C.
● ●
6
3
3
3
3
3
D.
2
3
x
+ y². Which statements are true? Mark all that apply.
2
A. When x = –4 and y = 6, the value of the expression is 34.
11. Consider the expression
B. When x = 12 and y = –8, the value of the expression is –58.
C. When x = –8 and y = 7, the value of the expression is 52.
D. When x = 10 and y = –5, the value of the expression is 30.
12. What is the result of adding -2.9a + 6.8 and 4.4a – 7.3?
13. The dimensions of a rectangle are given in terms of x as shown below.
Part A: Write an expression representing the perimeter of the
rectangle as the sum of the four side lengths.
Part B: Explain how the expression 2(2x +
4
) also represents the
5
x
x+
4
5
perimeter of the rectangle.
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
14. Simplify this expression: –
3
3
3
– (2 – ) +
2
8
2
15. Amit and Tiana simplified the expression –4[8 + (–6) + 3] in different ways. Amit’s first step was to add the
three numbers within the brackets. Tiana’s first step was to multiply each of the numbers within the brackets
by –4.
Part A: Write an expression to represent Tiana’s first step. In the expression, show which numbers are
being multiplied together, but don’t find each of the products.
Part B: What should Tiana have written as the product when she multiplied –6 by –4?
Part C: Whose first step was correct, Amit’s or Tiana’s? Explain.
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________
____________________________________________________________________