Winter Packet - AMC
6th Grade American Math
1) Carissa drew the figures below on a sheet of
paper.
Which of the following does not describe the
figures Carissa drew?
A. The ratio of circles to all figures is 3 to 9.
B. The ratio of triangles to squares is 4 to 5.
C. The ratio of squares to circles is 5 to 3.
D. The ratio of all figures to squares is 12 to 5.
2. Joaquin created the figures below using design
software on his computer.
What is the ratio of quadrilaterals to all figures in
simplest form?
Name: ___________________________
Date:_______________ Section: ______
4. A recipe for a mixed berry pie calls for 5
ounces of blackberries for every 9 ounces of
raspberries. Which of the following statements
is true?
A. The recipe calls for 5/14 ounce of blackberries
for every ounce of raspberries.
B. The recipe calls for 14/5 ounce of blackberries
for every ounce of raspberries.
C. The recipe calls for 5/9 ounce of blackberries
for every ounce of raspberries.
D. The recipe calls for 9/5 ounce of blackberries
for every ounce of raspberries.
5. Mariluz will be spending her vacation at her
uncle's house in the mountains. She drove 582
kilometers from her home to her uncle's house
in 6 hours. At what rate did Mariluz complete
her trip?
A. 0.01 km per hour
B. 79 km per hour
C. 97 km per hour
D. 100 km per hour
6. Jackson analyzes polling results for elections
across the country. Over the last 10 years,
Jackson has correctly predicted the winner of
an election 78% of the time. Which of the
following statements best describes Jackson's
results?
A. For every 100 elections, Jackson has predicted
the winner 78 times.
B. For every 1,000 elections, Jackson has
predicted the winner 78 times.
3. Tito went to a concert given by a jazz band. The C. Jackson has predicted the winner of 78 of the
band had 5 saxophone players and 4 trumpet
last 100 elections.
players. What was the ratio of trumpet players to D. Jackson has predicted the winner of the last 78
saxophone players in the band?
elections.
Answer: _____________________
Answer: _____________________
7. Yukiko plays on the soft ball team at her school.
The team won 9 of its first 12 games. At that
rate, how many games will Yukiko's team win if
it plays 64 games in all?
Answer: _____________________
8. John rode his mountain bike over some trails in
a state park. He biked a total of 5 ½ miles.
How many yards did John bike?
There are 1,760 yards in a mile.
Answer: _____________________
9. Jeffrey builds wooden decks for his clients'
houses. His standard deck uses a fixed amount
of lumber. The table below shows how much
lumber Jeffrey needs to buy for different
numbers of decks.
LUMBER NEEDED
NUMBER OF DECKS LUMBER (in ft²)
2
1,052
3
1,578
4
2,104
5
2,630
6
3,156
7
?
Based on the data in the table, how much lumber
would Jeffrey need to buy to build 7 standard
decks?
Answer: _____________________
10. At the local greenmarket, Debra bought 5
ounces of Chinese long beans for $13.55. At
that rate, how much would she pay for 8
ounces of Chinese long beans?
Answer: _____________________
11. A recipe for salad dressing calls for fresh lime
juice and honey. The ratio of tablespoons of
honey to tablespoons of lime juice is 8:16.
According to the recipe, how many
tablespoons of honey are needed for every
tablespoon of lime juice? Write your answer as
a fraction in simplest form.
Answer: _____________________
12. A carabiner is a key piece of equipment for a
mountain climber. Ken's Mountain Adventures
store is having a sale on carabiners. During the
sale, you can buy 4 carabiners for $29.60.
What is the unit price of the carabiners?
Answer: _____________________
13. Felipe makes salads at a restaurant. On
average, Felipe can make 12 salads in 20
minutes. At that rate, how many salads could
Felipe make in 45 minutes?
Answer: _____________________
14. What is 45% of 120?
Answer: _____________________
15. The students in Emily's school raised money
to help the victims of a natural disaster in Asia.
Emily's sixth grade class raised 40% of the
total amount by the school. If Emily's class
raised $580, how much money did the school
raise in all?
Answer: _____________________
16. An adult giraffe can have a mass of as much
as 1,360 kilograms. What is 1,360 kilograms
in grams? 1 kilogram = 1,000 grams.
Answer: _____________________
17. Which point is located at (-5, -6)?
20. Dora earns an annual salary of $85,608. How
much does she earn every month?
A. $6,144
B. $7,134
C. $7,144
D. $7,234
21. Which of the following statements is NOT
true?
A. -11 is the opposite of 11.
B. 0 is the opposite of 0.
C. 5.3 is the opposite of 3.5.
D. 21 is the opposite of -21.
22. Andie is taking a sewing class. Her first
assignment is to stitch together 49 identical
fabric rectangles from end to end to create a
long banner. If each rectangle measures 8.3
centimeters long, what will be the length of the
completed banner?
Answer: _____________________
Answer: _____________________
18. Naury has 4 cups of hot chocolate in her
thermos. She offers 5/8 cups servings of hot
chocolate to some close friends. What is the
greatest number of friends Naury can offer hot
chocolate to?
23. Nisha is following a recipe for tomato sauce
that calls for 1¾ teaspoons of oregano. She is
using a measuring spoon that holds ⅛ teaspoon.
How many times will she need to fill the
measuring spoon with oregano to make the
tomato sauce?
Answer: _____________________
Answer: _____________________
19. What is the absolute value of the number
represented by the point on this number line?
24. Sandy is putting 64 cookies and 40 chocolate
truffles into gift boxes. Each box will have the
same number of cookies and the same number
of chocolate truffles. What is the greatest
number of boxes Sandy can make with no
cookies or chocolate truffles left over?
Answer: _____________________
Answer: _____________________
25. Find the quotient: 1,203 ÷ 3
Answer: _____________________
29. Duke and Hilda went scuba diving to study
migrating fish 41 feet beneath the ocean's
surface. They returned to the surface after 15
minutes. Which integer best describes their
location when they surfaced?
26. Plot and label the following 10 points on the
graph provided.
A (-3, -1)
B (5, -3)
C (4, 2)
D (-2, 6)
E (6, 2)
F (-4, 2)
G (1, 5)
H (2, -1)
I (-1, -5)
J (-4, -4)
27. Mack is working on his science project. He
dropped a ball filled with sand from the
balcony of a building 42 feet from the ground.
Which of the following statements is true?
A. Mack's ball traveled a distance of 42
feet because |-42| is 42.
B. Mack's ball traveled a distance of -42
feet because |-42| is -42.
C. Mack's ball traveled a distance of 0
feet because |0| is 0 and the ball ended at
ground level.
D. Mack's ball traveled a distance of 24
feet because |-42| is 24.
28. Serena wants to buy reusable bamboo plates
and cups for a barbecue. Plates are sold in
packages of 8. Cups are sold in packages of
12. What is the least number of packages
Serena can buy to have an equal number of
plates and cups?
Answer: _________ packages of plates
_________ packages of cups
Answer: _____________________
30. What quadrant is (-3, 8) located in?
Answer: _____________________
31. Which of the following is equivalent to
48 + 18?
A.
B.
C.
D.
4(6 + 3)
6(6 + 3)
6(8 + 3)
8(6 + 3)
32. Paul, Raul, and Saul had a competition to see
who could pick the greatest amount of
strawberries in three minutes. Paul picked 1⅝
pounds of strawberries, Raul 1¾ pounds, and
Saul 111/16 pounds. Who came in second?
Show your work.
Answer: _____________________
33. Plot the points -3 and -8.1 on the number line
below.
Explain the position of -3 in relation to -8.1 on
the number line. What does this mean?
______________________________________
______________________________________
34. 34.Which verbal expression represents the
algebraic expression 3(5 + 3)?
A. 5 plus 3 times 3
B. 3 times 5 plus 3
C. 3 times the sum of 5 and 3
D. the product of 5 and 3
40. Which expression is equivalent to
b + b + b + b?
A. 4b
B. 4 + b
C. b4
D. 4(b + b)
35. Which is equivalent to 3 x 3 x 3 x 3 x 3?
A. 3 x 5
B. 3³
C. 53
D. 35
41. Reina scored twice as many goals at her last
field hockey game as she did during the first
game of the season. If f represents the number
of goals Reina scored during the first game,
which expression represents the number of
goals she scored during the last game?
A. 2f
B. 2 – f
C. 2 + f
D. 2 ÷ f
36. Catya had $70 saved. She received some
more money as a graduation gift. Now she has
$150. Which equation could be used to
determine how much money Catya received on
her graduation?
42. Evaluate 6 ÷ 3 • 2a for a = 2.
A. 70 + 150 = g
B. 70 + g = 150
C. 150 + g = 70
Answer: _____________________
D. g – 70 = 150
37. Which is equivalent to y5?
A. 5y
B. y + 5
C. y • y • y • y • y
D. y + y + y + y + y
43. The formula for the volume of a cube is V =
s3. What is the volume of a cube with a side
length, s, of 3 feet?
38. Which algebraic expression represents the
verbal expression “7 decreased by m”?
A. m – 7
B. 7m
C. 7 – m
D. 7 + m
44. Which expression is equivalent to 15x – 6?
A. 3(5x – 2)
B. 3(5x – 6)
C. 5(3x – 6)
D. 6(9x – 1)
39. Which verbal expression represents the
algebraic expression 3y?
A. 3 increased by y
B. the product of 3 and y
C. y to the third power
D. the quotient of 3 and y
Answer: _____________________
45. Which pair of expressions are equivalent?
A. 20p – 18 and 2(10p – 16)
B. g + g + g and g3
C. 3z + 26 and 3z and 62
D. 8(2r + 3) and 16r + 24
46. The table shows the relationship between the
number of smoothies, n, and the total cost in
dollars of the smoothies, c, at Juicy's
Smoothies.
JUICY'S SMOOTHIES
n
c
1
2
2
4
3
6
4
8
5
10
Write an equation to model the relationship
between the cost and the number of smoothies.
_________________________
48. Andrea spent twice as many hours studying as
Jonah this month. Jonah spent 7 fewer hours
studying this month than last month.
A. Let h represent the number of hours Jonah
spent studying last month. Write an algebraic
expression for the number of hours Andrea
spent studying this month.
Answer: _____________________
B. Andrea used “the difference of 2 times h and
7” to write the expression. Explain why she is
correct or incorrect.
Answer: ________________________
_____________________________________
Which variable is the independent variable? ____
_____________________________________
Which variable is the dependent variable? _____
_____________________________________
47. Carrie has 11 board games. This is 8 more
board games than Marisol has. The equation
11 = m + 8 can be used to find the number of
board games that Marisol has. How many
board games does Marisol have?
Answer: _____________________
49. Simplify the expression:
3x – 2y + 5x + 3y
Answer: _____________________
50. Simplify the expression:
2(s – 5) + 12 – s
Answer: _____________________
51. Simplify the expression:
12m + 8m • 3 – 2
Answer: _____________________
52. Solve for j: j – 9.2 = 22.5
Answer: _____________________