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6th Grade Accelerated Chapter 7
No Calculators
Name:_________________________
Date:
Core:
Vocabulary
Write the definition for the following terms. Then give an example of each.
Term
1) Variable
Expression:
2) Like Terms:
3) Constant:
4) Equation:
5) Coefficient:
6) Inverse
Operations:
7) Inequality:
8) Function:
Definition
Example
9) Linear
Function:
10) Equivalent
Expressions:
11) Domain:
12) Range:
Skills
Match the verbal phrase or sentence with the appropriate variable expression or
equation. Put the letter in the blank provided.
𝑤
7
____13) 14 decreased by a number
a)
____14) 4 times a number
b) 14 – p
____15) Twice the sum of a number and 4
c) 15 + r = 27
____16) A number divided by 7 is 6
d) 4m
____17) 15 increased by a number equals 27
e) 2(b + 4)
Simplify the expressions for questions 18-22. SHOW EACH STEP!
18) 7w + 25 + 19 – 28w
19) 4 – 8b + 9b – 3
=6
20) 10 + 7(d – 4)
21) –22g + 14g – 13 + 22
22) 6(5 – 3k) – 17 + 5k
Solve the equations. Check your solution. SHOW EACH STEP!
23) y + 6= 15
(solve)
(check)
24) n + 23= -14
(solve)
(check)
25) 7.4 + m = -19.2
(solve)
(check)
26) a – 15 = -8
(solve)
(check)
27) -11 = n – 7
(solve)
(check)
28) 6c = 84
(solve)
(check)
(solve)
(check)
30)
(solve)
(check)
2
29) y = -6
5
𝑑
−12
= -7
Solve the two-step equations. Check your solution. SHOW EACH STEP!
31) 2m + 6 = 64
33)
𝑛
6
- 8 = 10
(solve)
(check)
32) -3h + 4 = -1
(solve)
(check)
34) 3.4b – 1.7 = 15.3
(solve)
(solve)
(check)
(check)
Solve the inequalities. Check your solution. SHOW EACH STEP!
35) 14 + r > 43
(solve)
(check)
36) -63 + w ≥ 120
37) -5a < 20
(solve)
(check)
38) q ≤ -18
2
3
(solve)
(check)
(solve)
(check)
Write a function rule for the input/output table. SHOW EACH STEP!
39)
40)
Input x
-4 -3 -2 -1 0 1 2
Output y 2 3 4 5 6 7 8
Input x
0 2 4 6
8 10 12
Output y 0 4 8 12 16 20 24
41) Which function rule is the correct function rule for the input-output table?
Input x
-3 -2 -1 0 1 2 3
Output y 5 3 1 -1 -3 -5 -7
A)
B)
C)
D)
y = 2x + 1
y = 2x – 1
y = 1 – 2x
y = -1 – 2x
Applications
Answer the following questions. Be sure to label your answers. SHOW EACH STEP!
42) A plane climbs 20,000 feet to reach an elevation of 21,250 feet. Write and solve an equation to
find the elevation from which the plane took off.
43) A computer repair store charges you $28 per hour for labor, and you buy anti-virus software for
$36. If your total bill is $85 write and solve an equation to find how long they worked on your
computer.
44) a) Draw a rectangular picture that is two times longer than it is wide.
b) Write and simplify an expression for the perimeter of the rectangle in terms of the width (w).
c) Find the length and width if the perimeter is 24 inches.
45) Your suitcase weighs 3.6 pounds empty. The airport’s luggage weight limit is 40 pounds. Write an
inequality to represent how much the contents of your suitcase can weigh.
46) When you walk slowly, your body burns about 2 calories every minute. This situation can be
represented by the function y = 2x, where y is the number of calories burned and x is the number of
minutes you walk. Graph the function.
Input x
Output y
Writing
Answer the following questions in complete sentences. Be sure to use examples
and correct math vocabulary.
47)
A paperback version of “Freak the Mighty” costs $7.95. This cost is $5.45 less than the cost of
the hardcover version of the book. Write an equation to solve the problem. Justify your answer by
showing your work and explaining how to solve the equation.
48)
Mr. Wise runs 6 miles in one hour.
a) Make an input/output table that represents how many miles Mr. Wise runs in 5 hours.
Input x
Output y
b) Write a function rule using this data. ____________________________________________________
c) Graph the function.