High School HS Geometry 1819 GSE Geometry Unit 5 Full Touchstone
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1 High School HS Geometry 1819 GSE Geometry Unit 5 Full Touchstone ID: Standard: GSE G-MG.1 1. A fish tank is in the shape of a rectangular prism. The dimensions of the tank are 18 inches by 17 inches by 38 inches. If 1 liquid gallon = 231 cubic inches, what is the amount of water the tank can hold to the nearest gallon? A. 7 gallons B. 50 gallons C. 1,558 gallons D. 7,231 gallons ID: Standard: GSE G-MG.1 2. A human s eyeball is shaped like a sphere with a diameter of 2.5 cm. A dog s eyeball is shaped like a sphere with a diameter of 1.75 cm. About how many times greater is the volume of a human s eyeball than the volume of a dog s eyeball? A. About 1.5 times greater B. About 3 times greater C. About 8 times greater D. About 23 times greater ID: Standard: GSE G-MG.1 3. A cylindrical soda can is made of aluminum. It is approximately 5 inches high and the top and bottom have a radius of approximately 1.25 inches. If SA = 2πr 2 + 2πrh, what is the approximate surface area of the soda can? A. The approximate surface area of the soda can is 41 square inches. B. The approximate surface area of the soda can is 47 square inches. C. The approximate surface area of the soda can is 49 square inches. D. The approximate surface area of the soda can is 55 square inches.
2 ID: Standard: GSE G-MG.2 4. The earth can be modeled as a sphere with diameter 12,700 km with about 30% percent potentially habitable by humans. There are approximately 7.1 billion people in the world. If the surface area of the earth is approximately 506,707,500 square km, what is the approximate population density of potentially habitable earth? A. About 4.6 people per sq. km B. About 46 people per sq. km C. About 460 people per sq. km D. About 4600 people per sq. km ID: Standard: GSE G-MG.2 5. The volume of a solid gold statue can be approximated as 1000 cm 3. If the density of gold is about 20 g/cm 3, what is the mass of the statue? A. 50 g B. 500 g C. 2,000 g D. 20,000 g 6. ID: Standard: GSE G-MG.2 Given the table above, which island has the greatest population density? A. Bermuda B. Cyprus C. Puerto Rico D. Samoa
3 ID: Standard: GSE G-MG.2 7. Demographers calculate the population density of a city as the number of people per square mile. In 2013, San Francisco had a population of 837,000 people living in 47 square miles. What was San Francisco s population density in 2013? A. 56 people per square mile B. 17,809 people per square mile C. 837,047 people per square mile D. 39,339,000 people per square mile ID: Standard: GSE G-MG.3 8. You want to design a cylindrical container for oatmeal that has a volume of 90 cubic inches. You also want the height of the container to be 3.5 times the radius. To the nearest tenth, what should the radius of the container be? A. 2.0 in B. 2.9 in C. 3.0 in D. 5.1 in 9. ID: Standard: GSE G-MG.3 A wire frame in the shape of the cube is used to support a pyramid-shaped basket, as shown. The vertex of the pyramid lies in the same plane as a face of the cube. To the nearest tenth, what is the volume of the pyramid-shaped basket? A. 0.7 cubic ft. B. 1.1 cubic ft. C. 1.7 cubic ft. D. 2.2 cubic ft.
4 ID: Standard: GSE G-MG A room measures 15 ft by 20 ft by 10 ft. If a basketball has a diameter of 9.6 inches, approximately how many basketballs will be needed to fill the room? A. Approximately 1,000 B. Approximately 4,000 C. Approximately 8,000 D. Approximately 11,000 ID: Standard: GSE G-GPE What is the equation of a circle with center (-3, 5) that passes through the point (1, 5)? A. (x - 3) 2 + (y + 5) 2 = 16 B. (x + 3) 2 + (y - 5) 2 = 16 C. (x - 3) 2 + (y + 5) 2 = 4 D. (x + 3) 2 + (y - 5) 2 = 4 ID: Standard: GSE G-GPE A circle has the equation x 2 + y x - 22y = What is the length of the diameter of the circle? A. 7 B. 14 C. 49 D. 98
5 ID: Standard: GSE G-GPE The center of a circle with radius 3 is (-1, 2) and a point on the circle is (x, y). Using the Pythagorean theorem, which of the statements correctly shows how to derive the equation of this circle? A. B. C. D. ID: Standard: GSE G-GPE Find the center and radius of the circle with equation (x 3) 2 + (y + 2) 2 = 25. A. center: (3, -2); radius: 25 B. center: (-2, 3); radius: 5 C. center: (3, -2); radius: 5 D. center: (-3, 2); radius: 25 ID: Standard: GSE G-GPE On a map of a park, statues are located at (4, -2), (-1, 3), and (-5, -5). A circular path connects the three statues, and the circle has a fountain at its center. What are the coordinates of the fountain? A. (-2, 1) B. (2, 1) C. (-1, -2) D. (1, -2)
6 ID: Standard: GSE G-GPE Which statement proves that A(1, 1), B(4, 4), C(6, 2) are the vertices of a right triangle? A. Δ ABC is not a right triangle because the slopes of AB and BC are not opposite reciprocals. B. Δ ABC is not a right triangle because the slopes of AB and AC are not opposite reciprocals. C. Δ ABC is a right triangle because the slopes of AB and BC are opposite reciprocals. D. Δ ABC is a right triangle because the slopes of AB and AC are opposite reciprocals. ID: Standard: GSE G-GPE Points A(-8, 12) and B(-10, 18) are endpoints of directed line segment AB. What are the coordinates of point P that partitions AB in the ratio 3:2? A. (-8.8, 0) B. (-8.8, -6) C. (-9.2, 0) D. (-9.2, 15.6) ID: Standard: GSE G-GPE Three of the four vertices of a quadrilateral located in the coordinate plane are (1, 4), (6, 6), and (3, 1). Which coordinates of a fourth point would make this quadrilateral a parallelogram? A. (-2, -1) B. (-2, -4) C. (-2, -5) D. (-4, 2)
7 ID: Standard: GSE G-GPE Which statement proves that A(-2, 3), B(4, 3), C(2, -2), and D(-4, -2) are the vertices of a parallelogram? A. ABCD is a parallelogram because the slopes of AB and CD equal 0 and the slopes of BC and DA equal 5/2. B. ABCD is a parallelogram because the slopes of AB and CD are undefined and the slopes of BC and DA equal 2/5. C. ABCD is not a parallelogram because opposite sides do not have perpendicular slopes. D. ABCD is not a parallelogram because opposite sides do not have parallel slopes. 20. ID: Standard: GSE G-GPE.4 When graphed on a coordinate plane, the coordinates of a new kind of triangular slice of bread are (-3, 0), (1, 2), and (5, 2). Where should the baker place her hand while spinning the dough so that the triangle is balanced? A. (2, 1) B. (1, 0) C. (0, 1.5) D. (1, 1.5) ID: Standard: GSE G-GPE Two vertices of a parallelogram are A(2, 3) and B(8, 11), and the intersection of the diagonals is X(7, 6). Find the coordinates of the other two vertices. A. (12, 9), (6, 1) B. (9/2, 9/2), (15/2, 17/2) C. (11, 8), (5, 0) D. (11/2, 11/2), (17/2, 19/2)
8 22. ID: Standard: GSE G-GPE.5 A. B. C. D. ID: Standard: GSE G-GPE Identify the equation of the line that is perpendicular to x - 4y = 16 and passes through the point (3,1). A. y= -4x - 2 B. y = 1/4 x + 13 C. y= -4x +13 D. y = 1/4x - 4
9 ID: Standard: GSE G-GPE Points A(-8, 12) and B(-10, 18) are endpoints of directed line segment AB. What are the coordinates of point P that partitions AB in the ratio 3:2? A. (-8.8, 0) B. (-8.8, -6) C. (-9.2, 0) D. (-9.2, 15.6) 25. ID: Standard: GSE G-GPE.7 A B C. 11 D ID: Standard: GSE G-GPE.7 A. 9 B. 8 C. 18 D. 64
10 27. ID: Standard: GSE G-MG.2 (NOTE: Your teacher will score your response to this problem using a 2 point rubric.)
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