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Ohio - OGT - Spring 2005 - Math

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  • Ms. Chen drew a diagram for a new patio in her backyard.

    45°
    67.5°
    120°
    135°


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  • Ted and Bob each must type a 1,500-word research paper. The graph represents their normal typing rates. Based on the information in the graph, which of these is a valid conclusion?

    Bob can type his research paper in half the time it takes Ted to type his paper.
    Ted can type his research paper in half the time it takes Bob to type his paper
    Ted will take 4 minutes longer than Bob to type his research paper.
    Bob will take 4 minutes longer than Ted to type his research paper.


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  • Joseph plans to tile his kitchen floor. All the tiles will be identical regular polygons. Joseph wants three tiles to meet at each vertex with no space left over. What shape of tile should he use?

    pentagon
    hexagon
    triangle
    square


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  • Neal is selecting a new health club. The one he likes has monthly dues of $24 and a start-up fee of $400. He has determined that the equation y = 400 + 24x can be used to find y, the total cost of being a member at the club based on the number of months, x. After how many months will Neal have spent exactly $1,000 at this health club?

    16
    25
    41
    58


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  • A diagram of the floor plan of a storage room is shown. If the ceiling is 12 feet above the floor, what is the capacity of the storage room, in cubic feet?

    118 ft3
    600 ft3
    1,416 ft3
    1,800 ft3


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  • Sheila collects the statistics about baseball games played by the local Youth League team. Which statistic shows a non-linear rate of increase over time?

    number of wins
    average number of spectators per game
    average number of sodas sold per game
    average number of hot dogs sold per game


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  • Which graph represents the equation y = -x2 + 3?


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  • Jane has determined that 169 < x < 196. What must be true about √(x) ?

    13 < √(x ) < 14
    84.5 < √(x ) < 98.0
    338 < √(x ) < 392
    28,561 < √(x ) < 38,416


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  • Lester keeps his frog in a glass container with the dimensions shown. He pours water into the container to a height of 1.5 inches. What is the volume of water in the container?

    135 cubic inches
    216 cubic inches
    1,440 cubic inches
    2,160 cubic inches


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  • A state game warden has been observing deer during a particularly severe winter. She recorded that 14 of the 96 deer she observed throughout the state appeared to be suffering from malnutrition. The state has an estimated deer population of 600,000. Based on her observations, approximately how many deer would she predict are suffering from malnutrition?

    14000
    72000
    88000
    96,000


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  • Ms. Patrick wrote the fractions 0.75/1, 1.5/2, 3/4 and 9/12 on the board. Then she asked Sabrina to describe the relationship among the numbers. Which statement describes the relationship among the numbers?

    The fractions are equivalent.
    The fractions are in ascending order.
    The fractions are in descending order.
    The fractions are doubling from left to right.


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  • Under ideal conditions, there is an inverse relationship between the pressure (P) and the volume (V) of a gas. The table shows the relationship of the experimental pressures recorded for four different volumes of the gas. Which equation shows the relationship between the pressure and the volume of this gas?


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  • Susan is flying a kite behind her house. She drops her string holder, and the kite gets caught in the top of a tree. If the string makes a 44º angle with the ground, and the holder is 90 feet from the base of the tree, how tall is the tree, rounded to the nearest whole foot?

    63 feet
    65 feet
    74 feet
    87 feet


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  • The area of a right triangle is 24 square feet. A second right triangle has a base that is 2 times as long as the first triangle’s base and a height that is 3 times as long as the first triangle’s height. What is the area of the second triangle?

    48 square feet
    72 square feet
    144 square feet
    864 square feet


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  • Mara packed a blue denim shirt, a red striped shirt, a red plaid shirt, and a black tank top to take on vacation. She also packed one pair of denim shorts, one pair of white shorts and one pair of beige shorts. Mara took two different pairs of shoes with her. How many different combinations of outfits with one shirt, one pair of shoes and one pair of shorts could Mara use on her vacation?

    12
    24
    84
    504


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  • Aaron wants the mean of his 5 geometry test scores to be at least 90%. His scores on the first four tests are 85%, 83%, 96%, and 91%. Which of the following is the minimum score Aaron can earn on the fifth test to meet his goal?

    0.89
    0.9
    0.95
    1


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  • Dominic cuts out the largest possible circle from his 2-foot by 2-foot piece of art paper Which is a reasonable estimate of the fraction of the art paper that is left over?

    less than 1/4
    between 1/4 and 1/2
    between 1/2 and 3/4
    more than 3/4


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  • Which expression is equivalent to

    19
    84
    89
    512


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  • The shadow cast by a one-foot ruler is 8 inches long. At the same time, the shadow cast by a pine tree is 24 feet long. What is the height, in feet, of the pine tree?

    3 feet
    16 feet
    36 feet
    192 feet


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  • Under what circumstances will the product of three numbers always be negative?

    when at least one number is less than zero
    when at least one number equals zero
    when one number is greater than zero and the other two are less than zero
    when one number is less than zero and the other two are greater than zero


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  • For every lawn that she mows, Jane charges $8 per hour for every hour that she works. For each lawn that he mows, Bob charges a fixed fee of $20 and an additional $5 for every hour that he works. What is the fewest number of hours that both could work so that Jane’s total pay for a lawn will be greater than Bob’s?

    1 hour
    5 hours
    6 hours
    7 hours


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  • The depth of a lake is measured at the same location and on the same day every year for a number of years. The table shows the measurements. If the pattern continued, what was the depth of the lake in 2002?

    30 feet
    29 feet
    28 feet
    25 feet


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  • Susan entered a highway at 1:00. On the highway, she had driven a total of 32 miles by 1:30, 61 miles by 2:00, and 125 miles by 3:00. Which kind of data display would be an appropriate way to show how Susan’s total driving distance varied with time?

    line graph
    circle graph
    stem-and-leaf plot
    box-and-whisker plot


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  • The vertices of a quadrilateral are (2, 2), (4, 6), (8, 2), and (10, 6). Which describes this quadrilateral?

    parallelogram
    rectangle
    rhombus
    square


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  • Marny wants to approximate the amount of wax needed to make a crayon. The dimensions of the crayon are shown below. About how many cubic centimeters of wax are needed to make this crayon?

    18 cm3
    22 cm3
    28 cm3
    88 cm3


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  • Sara ordered 2 slices of pizza and a 12-ounce cola and paid $3.00. Sydney ordered 3 slices of pizza and 2 12-ounce colas for $4.75. How much does a slice of pizza cost?

    0.5
    1
    1.25
    2.5


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  • Jeffrey wants to determine the favorite professional sport of the students in his high school. Which sample should Jeffrey use?

    a random sample of the students in the chess club
    a random sample of the students on the football team
    a random sample of the students on the official school roster
    a random sample of the students in the library during fifth period


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  • The diameter of the sun is 864,000 miles. How can this value be expressed in scientific notation?

    8.64 × 105
    0.864 × 105
    86.4 x 103
    8.64 × 10–5


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  • The approximate value of √(34) is labeled by a point on the number line. Which of the points correctly displays this value?

    P
    Q
    R
    S


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  • The anchoring wire of a telephone pole has snapped and needs to be replaced. The telephone pole is 30 feet tall. The anchor for the wire is 13.8 feet from the bottom of the pole. Which of these is approximately the minimum length necessary for the new wire?

    10 ft
    21 ft
    35 ft
    44 ft


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