Geometry, Measurement, Data Flashcards
(30 cards)
A two-dimensional net of a certain three-dimensional figure includes five faces, nine edges, and six vertices. Which of the following three-dimensional figures is represented by the net?
A. Triangular pyramid
B. Triangular prism
C. Rectangular pyramid
D. Rectangular prism
B. Triangular prism
Option (B) is correct. The question requires an understanding of three-dimensional geometry. Triangular pyramids and rectangular prisms have four and six faces, respectively. Triangular prisms have five faces: two are triangles, and three are quadrilaterals. Rectangular pyramids also have five faces: one is a rectangle, and four are triangles. Triangular prisms have nine edges, while rectangular pyramids only have eight edges.
Week Customers 1 52 2 79 3 44 4 110 5 90 6 68 7 125 8 96 9 88 Bobby runs a small store. The total number of customers who shopped at the store during each of nine consecutive weeks is recorded in the chart shown. If the number of customers who shopped at the store during the tenth week were included in the data, the mean and median of the data would change but the range would not change. Which of the following could be the number of customers who shopped at the store during the tenth week?
A. 39
B. 41
C. 73
D. 132
C. 73
Option (C) is correct. The question requires an understanding of basic statistical concepts. The range is obtained by subtracting the smallest value, 44, from the largest value, 125. In order to modify the mean and median but not the range, the number of customers that shopped at the store during the tenth week must be greater or equal to 44 and less than or equal to 125.
chicken chicken spaghetti chicken pizza pizza tacos chicken pizza pizza pizza tacos spaghetti tacos spaghetti tacos tacos spaghetti tacos tacos A teacher asked 20 students to name their favorite school lunch. The students’ responses are shown in the table.
The teacher then asked the students to organize and display the data in a bar graph. Which bar graph correctly displays the data?
A.
B.
C.
D.
C.
This on I just counted the chicken and spaghetti and each had four. So the answer was C because that is the only one that both chicken and spaghetti had 4 each.
Question:
question
In the figure shown, quadrilateral ABFG is a square and quadrilateral FCDE is a rectangle. Which of the following statements must be true about the figure?
Select all that apply.
A. G lies on the x-axis.
B. C lies on the y-axis.
C. A is in the first quadrant.
D. D is in the fourth quadrant.
E. The area of the polygon ABCDEFG is 27 square units.
F. The perimeter of the polygon ABCDEFG is 25 units.
Correct Answer: A,D,E
Options (A), (D), and (E) are correct. The question requires an understanding of the coordinate plane and area of polygons. Since the x-axis is the horizontal axis, point G lies on the x-axis and has coordinates (–3, 0). The points in the fourth quadrant have a positive x-coordinate and a negative y-coordinate. Since point D has coordinates (4, –3), point D is in the fourth quadrant. The polygon is made of a square, a right triangle, and a rectangle. The length of the side of the square is 3 units; therefore, the area of the square is 9 square units. The lengths of the sides of the right triangle are 3 and 4 units, respectively; therefore, the area of the right triangle is 6 square units. The lengths of the sides of the rectangle are also 3 and 4 units, respectively; therefore, the area of the rectangle is 12 square units. Finally, the area of the polygon is the sum of the areas of its parts; that is, 9 + 6 + 12, or 27 square units.
A pencil is 18 centimeters in length. How long is the pencil in millimeters?
A. 0.18
B. 1.8
C. 180
D. 1,800
C. 180
Option (C) is correct. The question requires an understanding of the metric system. Since 1 centimeter equals 10 millimeters, 18 centimeters equal 180 millimeters.
In which quadrant is the point (−8,2) located?
A. Quadrant I
B. Quadrant II
C. Quadrant III
D. Quadrant IV
B. Quadrant II
Option (B) is correct. The question requires an understanding of the coordinate plane. Since points in the second quadrant have a negative x-coordinate and a positive y-coordinate, the point with coordinates (−8,2) is located in quadrant II.
Which of the following could be used to describe the polygon shown? A. Regular and convex B. Regular and concave C. Irregular and convex D. Irregular and concave
D. Irregular and concave
The figure shows a ruler with inches marked and two line segments drawn. To the nearest eighth of an inch, how much longer, in inches, is the length of AB¯¯¯¯ than the length of CD¯¯¯¯ ? A. 3 3/4 B. 1 3/4 C. 1 5/8 D. 1 3/8
D. 1 3/8
Option (D) is correct. The question requires an understanding of measuring and comparing lengths of objects using standard tools. Line segment AB¯¯¯¯ measures 3 6/8 inches, and line segment CD¯¯¯¯ measures 2 3/8 inches. When subtracting the two lengths, line segment AB¯¯¯¯ is 1 3/8 inches longer than line segment CD¯¯¯¯ .
Which of the following statements can be inferred from the graph shown?
Select all that apply.
A. For each country shown, exports to the United States increased each year from the previous year.
B. The country that had the greatest yearly exports to the United States for each of the years shown had a three-year export total between $11 billion and $12 billion.
C. The exports from Country A to the United States more than doubled from 1995 to 1997.
B, C
Options (B) and (C) are correct. The question requires an understanding of bar graphs and the ability to read and interpret them. The scale is in billions of dollars and rises in increments of $0.5 billion. The exports from Country C decreased a small amount from 1995 to 1996, so the statement in (A) cannot be inferred from the graph. The statements in (B) and (C) can be inferred, since Country B had the greatest yearly exports, for a three-year total of about $11.5 billion. Also, the exports from Country A more than doubled, going from $2 billion to just over $4 billion.
Wai tossed a fair coin 9 times with an outcome of H H T T T T H H H, where H means heads and T means tails. What is the probability that the next toss will be T ?
A. 0.2
B. 0.4
C. 0.5
D. 1.0
C. 0.5
Option (C) is correct. This question requires an understanding of basic probability. If a coin is fair, the probability of tossing heads is the same as the probability of tossing tails. There are only two possible outcomes, so the probability of tossing tails is 1/2. The number 1/2 can also be written as 0.5. Please note that since each toss of the coin is an independent event, which means that the previous results do not affect the current toss of the coin, each time the coin is tossed, the probabilities of H or T would always be the same, 0.5.
If the perimeter of each of the seven regular hexagons in the figure shown is 18, what is the perimeter of the figure?
A. 54
B. 63
C. 108
D. 126
A. 54
Option (A) is correct. The question requires an understanding of geometric reasoning. Since each of the small hexagons in the figure is regular, each hexagon’s sides are equal in length. Therefore, the length of any one hexagon’s side is 18÷6, or 3. The perimeter of the large figure shown is found by multiplying the number of exposed hexagon’s sides by the length of one hexagon side. There are 18 exposed sides, and each one is 3 units long. Therefore, the perimeter of the figure is 18×3, or 54.
The Clearbrook Wildcats basketball team scored an average of 77 points in four games. In the first three games, the team scored 70, 76, and 82 points. How many points did they score in their last game?
A.70
B.76
C.77
D.80
D.80
Option (D) is correct. The question requires an understanding of average (or arithmetic mean) and the ability to set up and solve several computations. An average of 77 points in four games means that they scored a total of 77 times 4, or 308 points. Since the scores for the first three games are given as 70, 76, and 82 points, it is necessary to add these up (228 points) and subtract from the four-game total of 308 points. This leaves 80 points for the last game’s score.
On Greg’s map, 1 inch represents 30 miles, and on Lori’s map, 1 inch represents 20 miles. The area of a 1-inch by 1-inch square represents how many more square miles on Greg’s map than on Lori’s map?
A.100
B.250
C.400
D.500
D.500
Option (D) is correct. The question requires an understanding of calculating areas using standard, real-world miles on a map. Area is a two-dimensional representation of a surface (length times width, base times height, etc.). A 1-inch by 1-inch square on Greg’s map represents a square 30 miles on each side. The area of this square is 30 miles multiplied by 30 miles, or 900 square miles. On Lori’s map, the 1-inch by 1-inch square represents a square 20 miles on each side. The area of this square is 20 miles multiplied by 20 miles, or 400 square miles. The difference between these is 500 square miles.
Bill went to sleep at 9:57 P.M. and awoke the next morning at 6:28 A.M. For how many hours and minutes did he sleep?
A. 9 hours and 31 minutes
B. 9 hours and 25 minutes
C. 8 hours and 31 minutes
D. 8 hours and 25 minutes
C. 8 hours and 31 minutes
Option (C) is correct. The question requires an understanding of calculating with standard units of time. Bill slept for 3 minutes from 9:57 P.M. until 10:00 P.M. and for 2 hours from 10:00 P.M. until 12:00 A.M. (midnight). Then he slept another 6 hours and 28 minutes until 6:28 A.M. This adds up to 8 hours and 31 minutes.
The rectangular region shown in Figure 1 is cut along the dotted line and reassembled as shown in Figure 2. Which of the following statements about the area and perimeter of Figure 1 and Figure 2 is true?
A. The area of Figure 1 is equal to the area of Figure 2, and the perimeter of Figure 1 is equal to the perimeter of Figure 2.
B. The area of Figure 1 is equal to the area of Figure 2, and the perimeter of Figure 2 is greater than the perimeter of Figure 1.
C. The area of Figure 1 is greater than the area of Figure 2, and the perimeter of Figure 1 is greater than the perimeter of Figure 2.
D. The area of Figure 1 is greater than the area of Figure 2, and the perimeter of Figure 1 is equal to the perimeter of Figure 2.
B. The area of Figure 1 is equal to the area of Figure 2, and the perimeter of Figure 2 is greater than the perimeter of Figure 1.
Option (B) is correct. The question requires an understanding of area and perimeter. Since the two figures are composed of exactly the same subparts, their areas are equal. Figure 2 features the hypotenuses of the two triangles, each of which contributes additional length to the perimeter of Figure 2.
Mary has a rectangular garden in her backyard. The garden measures 5 3/4 feet wide by 7 1/2 feet long. What is the area of the garden?
Answer the question by selecting the correct response.
A. 26 1/2 square feet
B. 35 3/8 square feet
C. 36 1/8 square feet
D. 43 1/8 square feet
D. 43 1/8 square feet
7 1/2×5 3/4=15/2×23/4=345/8 square feet, that is, 43 1/8 square feet.
Change the mixed fractions to improper fractions. Then divide 345 by 8 and it gives me 43.12 which is 43 1/8. D. is the only choice for 43.
Which of the following is a statistical question?
Select ALL that apply.
Answer the question by selecting the correct response or responses.
A. What is the daily high temperature for an August day in Cheyenne, Wyoming?
B. How many speeches did George Washington make during his life?
C. How many minutes did Hannah spend talking on her phone on August 28, 2016 ?
D. What was the average number of miles a week run by the members of the Hereford High School cross-country team last month?
A and D
Options (A) and (D) are correct. The question requires an understanding of how to identify statistical questions. A statistical question is one that can be answered by collecting data and one where there will be variability in the data collected. To answer the question in option (A), one must collect the daily high temperature for each day in August. Such values will vary. To answer the question in option (D), one must collect the number of miles a week run by each of the members of the team during the past month. Such values will vary.
Which word describes each angle in an equilateral triangle?
Answer the question by selecting the correct response.
A. Acute
B. Obtuse
C. Right
D. Straight
A. Acute
Option (A) is correct. The question requires an understanding of how to classify angles based on their measure. An equilateral triangle is also equiangular; that is, all its angles have the same measure. Therefore, each angle has a measure of 180 divided by 3180÷3, or 60 degrees. An acute angle is an angle that measures less than 90 degrees. Therefore, the angles of an equilateral triangle are all acute.
Lily, Matthew, Natalie, and Owen each walked from their houses to the mall. Lily walked 1/4 mile, Matthew walked 3/8 mile, Natalie walked 5/6 mile, and Owen walked 7/12 mile.
Which list shows these distances in order from least to greatest?
Answer the question by selecting the correct response.
A. 1/4 mile, 3/8 mile, 5/6 mile, 7/12 mile
B. 1/4 mile, 3/8 mile, 7/12 mile, 5/6 mile
C. 1/4 mile, 5/6 mile, 3/8 mile, 7/12 mile
D. 7/12 mile, 3/8 mile, 5/6 mile, 1/4 mile
B. 1/4 mile, 3/8 mile, 7/12 mile, 5/6 mile
First find the common denominator in this case it was 24. 1/4 divide both numerator and denominator by 6 to get 6/24.
The following boxplots compare the incomes of two professions.
Boxplots. (detailed description follows)
The figure shows two boxplots over the same horizontal axis. The horizontal axis is labeled “Annual Income, in thousands of dollars,” and the numbers 0 through 140, in increments of 20, are indicated. The boxplots represent the following two professions: Nuclear Engineer and Police Officer. The data represented by the boxplots are as follows. Note that all values are approximate.
Nuclear Engineer.
The boxplot extends from 50 to 119. A box extends from 60 to 95. A vertical line segment at 70 divides the box into two parts.
Police Officer.
The boxplot extends from 12 to 60. A box extends from 21 to 44. A vertical line segment at 30 divides the box into two parts.
End figure description.
Based on the boxplots, which of the following statements is true?
Answer the question by selecting the correct response.
A. All nuclear engineers earn more than all police officers.
B. Exactly 50% of nuclear engineers earn more than all police officers.
C. The range of incomes for nuclear engineers is the same as that for police officers.
D. The median income for nuclear engineers is greater than the maximum income for police officers.
D. The median income for nuclear engineers is greater than the maximum income for police officers.
Graph. (detailed description follows)
The figure shows the graph of 4 points labeled J, K, L, and M, in the x y coordinate plane. The number 1 is indicated on both axes. The coordinates of each data point are as follows.
Point J. negative 4 comma 2. Point K. 4 comma 5. Point L. 2 comma negative 3. Point M. negative 3 comma negative 3. End figure description.
In the preceding coordinate plane, which point is located in Quadrant 1I?
Answer the question by selecting the correct response.
A. J
B. K
C. L
D. M
B. K
Option (B) is correct. The question requires an understanding of how to identify the x-axis, the y-axis, the origin, and the four quadrants in the coordinate plane. The x-axis and the y-axis intersect at the origin and divide the coordinate plane into four quadrants. Quadrant 1I is the quadrant above the x-axis and to the right of the y-axis. Point K lies within this quadrant.
The surface area of a cube is 54 square inches. What is the volume of the cube?
Answer the question by selecting the correct response.
A. 27 cubic inches
B. 54 cubic inches
C. 81 cubic inches
D. 108 cubic inches
A. 27 cubic inches
Option (A) is correct. The question requires an understanding of how to solve problems involving elapsed time, money, length, volume, and mass. If the length of the side of the cube is s inches, then its surface area is 6, s squared6s2 square inches. Since the surface area is 54 square inches, the length of the side of the cube, in inches, can be found by solving the equation 6, s squared, equals 546s2=54, which yields s equals 3s=3. The volume of the cube can then be found by solving the equation V equals s cubedV=s3; thus V equals 3 cubedV=33. Therefore, the volume is 27 cubic inches.
A certain polygon has the following attributes.
- There are 2 pairs of parallel sides.
- It is a quadrilateral.
- One pair of parallel sides has length 2, and the other pair of parallel sides has length 4.
Which of the following types of polygons has all of the attributes listed?
Answer the question by selecting the correct response.
A. Parallelogram
B. Rhombus
C. Triangle
D. Square
A. Parallelogram
The following list shows Caleb’s scores for the first 6 quizzes in his algebra class.
90, 90, 95, 90, 85, 90
If he receives a score of 95 on the 7th quiz, which of the following statements will be true?
Answer the question by selecting the correct response.
A. The average (arithmetic mean) of the 7 quiz scores is less than the average of the first 6 quiz scores.
B. The mode of the 7 quiz scores is greater than the mode of the first 6 quiz scores.
C. The median of the 7 quiz scores is equal to the median of the first 6 quiz scores.
D. The range of the 7 quiz scores is greater than the range of the first 6 quiz scores.
C. The median of the 7 quiz scores is equal to the median of the first 6 quiz scores.
