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CTJan27 Online Year 8 Mathematics Reasoning 29052024

Multiple Choice
Identify the choice that best completes the statement or answers the question.
 

 1. 

An ice cream cone manufacturer wants to increase the capacity of its sugar cones by 60%. Which change in dimensions will achieve this goal?
mc001-1.jpg
a.
Multiply the height of the cone by 1.6.
b.
Multiply both the radius and the height of the cone by 1.6.
c.
Multiply the radius of the cone by 60.
d.
Multiply the diameter of the cone by 0.6.
 

 2. 

Which graph best represents the inequality mc002-1.jpg?
a.
mc002-3.jpg
c.
mc002-5.jpg
b.
mc002-4.jpg
d.
mc002-6.jpg
 

 3. 

The product of mc003-1.jpg and mc003-2.jpg is
a.
mc003-4.jpg
c.
14
b.
mc003-5.jpg
d.
4
 

 4. 

Karen works part time assembling computer desks for an office supplies store. The store purchases the desks for $54, and Karen is paid $7.25 per hour to assemble them. Each computer desk is then sold to customers for a cost of $100. The profit earned by the store can be found using the equation P = (100 – 54)d – 7.25h. In the equation, d is the number of computer desks built and h is the number of hours Karen spent assembling them. If Karen gets a raise of $0.35 per hour, how will this equation change?
a.
P = (100 – 54)d – 7.60h
c.
P = (100 – 54)d – 7.60(h +0.35)
b.
P = (100 – 54)d – 7.60– 0.35
d.
P = (100 – 54)d – 7.65h
 

 5. 

A producer has fixed expenses of $860 to put on a 3-day production of a play. Each ticket to the play will be sold for $5.25. The line shows the net profit or loss of the producer based on selling x tickets. What is the minimum number of tickets the producer must sell over the 3-day period in order to earn a profit?
Net Profit or Loss
mc005-1.jpgmc005-2.jpg
          Tickets Sold
a.
211 tickets
c.
186 tickets
b.
163 tickets
d.
164 tickets
 

 6. 

Written in simplest form, the expression mc006-1.jpg is equivalent to
a.
mc006-3.jpg
c.
mc006-5.jpg
b.
mc006-4.jpg
d.
mc006-6.jpg
 
 
The students in a theatrical design class are designing a set for an upcoming show. The structure is shown in the picture below.
nar001-1.jpg
Layer one has one triangle nar001-2.jpg and layer two contains three triangles nar001-3.jpg.
 

 7. 

Refer to the information above. How many top down mc007-1.jpg triangles will be required to make a 12-layer set if the pattern is continued?
a.
14
c.
12
b.
120
d.
66
 
 
Several of the German students at a high school went to Germany over their school’s winter break. The students converted their money to Euros (€). One Euro was worth $1.25.
 

 8. 

Refer to the information above. If one student converted $281.25, how many Euros did the student receive at the money exchange?
a.
351.56 €
c.
281.25 €
b.
22.5 €
d.
225 €
 
 
Find the roots of the quadratic equation. Solve by factoring.
 

 9. 

mc009-1.jpg
a.
–3, –1
c.
3, 1
b.
–7, –9
d.
9, 8
 
 
The linear function nar004-1.jpg shown below gives the height of a hang glider after it begins its descent to the ground.
Hang Glider Height
 
nar004-2.jpgnar004-3.jpgnar004-4.jpg
 

 10. 

According to the linear function shown above, what was the height of the hang glider when it began its descent?
a.
13 feet
c.
600 feet
b.
575 feet
d.
10 feet
 

 11. 

The parabola shown in the accompanying diagram undergoes a reflection in the y-axis.

mc011-1.jpg

What will be the coordinates of the turning point after the reflection?
a.
mc011-2.jpg
c.
mc011-4.jpg
b.
mc011-3.jpg
d.
mc011-5.jpg
 

 12. 

A piggy bank contains 6 quarters, 3 dimes, 9 nickels, and 7 pennies. Suppose you randomly select a coin from the bank without looking. What is the probability of selecting any coin but a penny?
a.
mc012-3.jpg
c.
mc012-5.jpg
b.
mc012-4.jpg
d.
mc012-6.jpg
 
 
The table shows the number of students in each grade who participate in foreign language clubs at Meadowlark High School. Each student participates in only one club.
Foreign Language Clubs
Language
9th Grade
10th Grade
11th Grade
12th Grade
Spanish
7
5
5
12
German
7
15
8
15
French
5
10
8
10
 

 13. 

According to the data above, how many students at Meadowlark High School participate in a foreign language club?
a.
70
c.
102
b.
37
d.
107
 

 14. 

Refer to the data above. What percent of the 10th graders who participate in a foreign language club speak German? Round your answer to the nearest tenth if necessary.
a.
78.9%
c.
50%
b.
55.7%
d.
45.8%
 

 15. 

Which expression is equivalent to mc015-1.jpg?
a.
mc015-3.jpg
c.
mc015-5.jpg
b.
mc015-4.jpg
d.
mc015-6.jpg
 
 
The Department of Motor Vehicles is investigating different license plate designs. They have come up with five designs:
Design 1:Two letters (A-Z) followed by four numbers (0-9).
Design 2:Three letters (A-Z) followed by three numbers (0-9).
Design 3:Three numbers (0-9) followed by three letters (A-Z).
Design 4:Four numbers (0-9) followed by two letters (A-Z).
Design 5:Three letters (A-Z) followed by three numbers (0-9), with an image of the state bird on the plate.
All designs allow for the repetition of letters and numbers. The plates are assigned randomly to drivers.
 

 16. 

Refer to the information above. If a driver is assigned a plate of Design 1, what is the probability it will begin with the letter S?
a.
mc016-2.jpg
c.
mc016-4.jpg
b.
mc016-3.jpg
d.
mc016-5.jpg
 
 
The bar graph below shows several students’ responses to a survey that asked what kinds of pets they have in their homes. Some students may have more than one kind of pet.
Kinds of Pets
nar007-1.jpgnar007-2.jpg
 

 17. 

According to the graph above, which of the following could be the number of students surveyed?
a.
7
c.
6
b.
13
d.
5
 

 18. 

Hal plans to collect data and plot them in a scatterplot to look for a relationship. He will compare the amount of time spent studying for a test and the grade earned. What type of relationship would you expect Hal to see in his scatterplot?
a.
positive relationship
c.
no relationship
b.
skew relationship
d.
negative relationship
 

 19. 

The box-and-whisker plot shows the recorded high temperatures in Jim’s city last month. Which of the following would be the most accurate measures of central tendency for the data?
High Temperatures (°F)
mc019-1.jpg
a.
the median or mode
c.
the mean or median
b.
the mean or range
d.
the mode or range
 

 20. 

The number of students in second period music class who play certain instruments is shown in the Venn diagram below. How many students play only the piano?
Number of Students
Who Play Instruments
mc020-1.jpg
a.
21
c.
9
b.
6
d.
7
 

 21. 

Angelina is drawing a map of the recess area at her school on a coordinate grid. If the scale of the map is 1 grid = 4 feet, what is the distance from the jungle gym to the four-square courts? Round your answer to the nearest tenth if necessary.
mc021-1.jpg
a.
8.5 feet
c.
34.2 feet
b.
45.3 feet
d.
59.5 feet
 

 22. 

Figure ABCD is a rhombus. If x = 6, what is the length of mc022-1.jpg?
mc022-2.jpg
a.
8 units
c.
16 units
b.
4 units
d.
11.2 units
 

 23. 

What transformation would describe the relationship between Triangle A and Triangle B?
mc023-1.jpg
a.
slide
c.
reflection
b.
rotation
d.
dilation
 

 24. 

If the figure below is rotated 360 degrees about the given line, which of the following three-dimensional shapes will be formed?
mc024-1.jpg
a.
mc024-2.jpg
c.
mc024-4.jpg
b.
mc024-3.jpg
d.
mc024-5.jpg
 

 25. 

Marina needs to build a frame for her painting. What are the dimensions of the painting? Round to the nearest tenth if necessary.
mc025-1.jpg
a.
26.5 inches × 20 inches
c.
20 inches × 20 inches
b.
16 inches × 20 inches
d.
33.2 inches × 20 inches
 

 26. 

Which of the following expressions could be used to determine the shaded area of the figure?
mc026-1.jpg
a.
mc026-5.jpg square feet
c.
mc026-7.jpg square feet
b.
mc026-6.jpg square feet
d.
mc026-8.jpg square feet
 

 27. 

A metalworker welded a cylinder to a rectangular prism as shown in the figure. The cylinder has a height of 5 centimeters and radius 3 centimeters. Which expression could be used to find the volume of the finished product?
mc027-1.jpg
a.
mc027-5.jpg cubic centimeters
c.
mc027-7.jpg cubic centimeters
b.
mc027-6.jpg cubic centimeters
d.
mc027-8.jpg cubic centimeters
 

 28. 

A team at the Junior Physicists competition designed a rocket with the dimensions shown in the figure below. What is the volume of the rocket? Use 3.14 for pi and round your answer to the nearest tenth.
mc028-1.jpg
a.
167.5 cubic inches
c.
201 cubic inches
b.
105.5 cubic inches
d.
249.5 cubic inches
 

 29. 

The graph below shows the function mc029-1.jpg.

mc029-2.jpg

Which graph represents the function mc029-3.jpg?
a.
mc029-4.jpg
c.
mc029-6.jpg
b.
mc029-5.jpg
d.
mc029-7.jpg
 

 30. 

Julia is designing a decal in art class to put on her math folder. She will cut the decal from a 5-inch by 7-inch sheet of decal paper using the design below and then decorate it. In the upper two corners of the decal, she wants to cut out two quarter circles both with radius 1.5 inches. What is the perimeter of the final product? Use 3.14 for pi and round your answer to the nearest tenth.
mc030-1.jpg
a.
22.7 inches
c.
27.4 inches
b.
33.6 inches
d.
13.9 inches
 

 31. 

An architect made the rough sketch of the master bedroom in a new house shown below. If the scale used to create the sketch is 0.25 inches = 1 foot, what is the actual length of the room?
mc031-1.jpg
a.
16 feet
c.
1 foot
b.
8 feet
d.
21 feet
 

 32. 

Mr. Matthews built a tree house for his son. The ladder going up to the tree house has 11 rungs that are each spaced 11 inches apart. If the top rung is actually built into the floor of the tree house, how high is the floor above the ground? Round your answer to the nearest tenth of a foot.
a.
16.6 feet
c.
10.1 feet
b.
121 feet
d.
7.8 feet
 

 33. 

Justi filled a large basin with pond water using a 5-gallon bucket so that he could store his fish in it while cleaning out the water garden. If it took 117 buckets of pond water to fill the basin, what is the volume of the basin in cubic feet? (There are approximately 7.5 gallons in each cubic foot of water.) Round your answer to the nearest tenth.
a.
92.8 cubic feet
c.
3,290.6 cubic feet
b.
78 cubic feet
d.
4,387.5 cubic feet
 

 34. 

A bathtub was filled with 45 gallons of water when the drain was pulled to empty the tub. The table shows how much water was left in the tub at certain times since the plug was pulled. Assuming the tub drains at a constant rate, about how many minutes will it take until it is empty? Round your answer to the nearest tenth of a minute if necessary.
Bath Tub Drain
Time
(seconds)
Amount
(gallons)
0
45
30
42.6
a.
6.1 minutes
c.
18.8 minutes
b.
11.9 minutes
d.
9.4 minutes
 
 
A peanut butter cookie recipe is shown below.
Peanut Butter Cookies
1 cupsugar
1 cuppeanut butter
1egg
1 tspvanilla
Mix above ingredients well. Drop by half-teaspoonfuls onto cookie sheet. Bake at 325° for 10 minutes. Makes 3 dozen cookies.
 

 35. 

Refer to the recipe above. The serving size is 4 cookies. If each cup of peanut butter contains 136 grams of fat and the recipe makes 3 dozen cookies, how many grams of fat are in each serving?
a.
1,224
c.
15.1
b.
3.8
d.
1.1
 

 36. 

The solution set of mc036-1.jpg is
a.
mc036-4.jpg
c.
mc036-6.jpg
b.
mc036-5.jpg
d.
mc036-7.jpg
 

 37. 

A student in cooking class needs to measure out 32 fluid ounces of water for a recipe, but she only has a measuring cup labeled in pints, not in ounces. How many pints of water should she add to the recipe?
a.
mc037-2.jpg
c.
mc037-4.jpg
b.
mc037-3.jpg
d.
mc037-5.jpg
 

 38. 

A student in cooking class needs to measure out 80 fluid ounces of water for a recipe, but he only has a measuring cup labeled in quarts, not in ounces. How many quarts of water should he add to the recipe?
a.
mc038-2.jpg
c.
mc038-4.jpg
b.
mc038-3.jpg
d.
mc038-5.jpg
 

 39. 

Which of the following symbols will make a true sentence when inserted in the blank?
mc039-1.jpg ____ 1
a.
mc039-7.jpg
c.
mc039-9.jpg
b.
mc039-8.jpg
d.
mc039-10.jpg
 

 40. 

The formula mc040-1.jpg can be used to approximate the distance, in miles, that you can see across the ocean on a clear day if you are positioned at a height of h feet above the water. Simplify the expression mc040-2.jpg to approximate how far a helicopter pilot can see on a clear day if the helicopter is 1,250 feet above the surface of the ocean. Round your answer to the nearest tenth of a mile, if necessary.
a.
35.4 miles
c.
66.8 miles
b.
49.5 miles
d.
41.8 miles
 

 41. 

Last summer the cost of a bushel of corn rose from $3.29 to $3.59. What was the percent of increase in cost? Round your answer to the nearest tenth of a percent, if necessary.
a.
4.4%
c.
8.4%
b.
0.1%
d.
9.1%
 

 42. 

The expression mc042-1.jpg is equivalent to
a.
mc042-3.jpg
c.
mc042-5.jpg
b.
mc042-4.jpg
d.
mc042-6.jpg
 

 43. 

Malcom needs a laser printer for his home business and is considering lease and purchase options. He can lease the printer for a one time processing fee of $50 plus $32.25 per month. He could also buy the laser printer outright for $745. If Malcom decides to purchase the printer, for how many months will he need to use it in order to save money over the lease option?
a.
22 months
c.
24 months
b.
21 months
d.
20 months
 

 44. 

If mc044-1.jpg and mc044-2.jpg, what is the value of the expression mc044-3.jpg?
a.
mc044-5.jpg
c.
mc044-7.jpg
b.
mc044-6.jpg
d.
mc044-8.jpg
 

 45. 

What is a number that would appear between –2.5 and mc045-1.jpg on the number line?
a.
–0.1
c.
–4.9
b.
–2.5
d.
0
 

 46. 

What is a number that would appear to the right of both 1.3 and mc046-1.jpg on the number line?
a.
0
c.
3.8
b.
–0.9
d.
1.8
 
 
Five points are plotted on the number line as shown below.
nar009-1.jpg
 

 47. 

Refer to the number line above. Which of the five points would have the smallest value when squared?
a.
D
c.
A
b.
C
d.
E
 

 48. 

Light travels at a speed of approximately 300 million meters per second. How far does light travel in 15 seconds, expressed in scientific notation?
a.
mc048-1.jpg meters
c.
mc048-3.jpg meters
b.
mc048-2.jpg meters
d.
mc048-4.jpg meters
 

 49. 

The solution set of the equation mc049-1.jpg is
a.
mc049-2.jpg
c.
mc049-4.jpg
b.
mc049-3.jpg
d.
mc049-5.jpg
 

 50. 

What is the best estimate of the area of the figure below? Each square represents one square unit.
mc050-1.jpg
a.
23 square units
c.
7 square units
b.
38 square units
d.
31 square units
 

 51. 

The expression mc051-1.jpg is equivalent to
a.
mc051-3.jpg
c.
mc051-5.jpg
b.
mc051-4.jpg
d.
mc051-6.jpg
 

 52. 

The expression mc052-1.jpg is equivalent to
a.
mc052-2.jpg
c.
mc052-4.jpg
b.
mc052-3.jpg
d.
mc052-5.jpg
 

 53. 

Factored completely, the expression mc053-1.jpg is equivalent to
a.
mc053-3.jpg
c.
mc053-5.jpg
b.
mc053-4.jpg
d.
mc053-6.jpg
 



 
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