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Quantitative Literacy
Geometry

1
Perimeter and Circumference

Problem 1

Find the perimeter of a rectangle with a width of \(5\) yards and a length of \(8\) yards.

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Stephanie cc
Stephanie
Winston cc
Winston
Gordon cc
Gordon
Anthony spanish language icon
Anthony
Problem 2

Find the perimeter of each stamp. Write your answer as a decimal, round to the nearest tenth.

  1. Each side is \(35.0\) millimeters

  2. Base \(=2\frac{5}{8}\) inches, other two sides\( =1\frac{7}{8}\)

  3. Length \(=1.56\) inches, width \(=0.99\) inches

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Julieta cc
Julieta
Aaron cc
Aaron
Anthony spanish language icon
Anthony
Problem 3
example image
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Julieta cc
Julieta
Logan cc
Logan
Julieta cc spanish language icon
Julieta
Problem 4

Find the circumference of each coin.

  1. Diameter \(=23.25\) millimeters

  2. Radius \(=0.52\) inches

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Aaron cc
Aaron
Betsy cc
Betsy
Anthony spanish language icon
Anthony
Problem 5

If the circumference of the Earth is about \(24,900\) miles at the equator, what is the diameter of the Earth to the nearest \(10\) miles?

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Julieta cc
Julieta
Aaron cc
Aaron
Anthony spanish language icon
Anthony

2
Area

Problem 1

A parallelogram has a base of \(5\) centimeters and a height of \(2\) centimeters. Find the area.

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Betsy cc
Betsy
Aaron cc
Aaron
Anthony spanish language icon
Anthony
Problem 2

A triangle has a base of \(6\) centimeters and a height of \(3\) centimeters. Find the area.

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Julieta cc
Julieta
Anthony spanish language icon
Anthony
Problem 3
example image
Choose instructor to watch:
Julieta cc
Julieta
Aaron cc
Aaron
Anthony spanish language icon
Anthony
Problem 4

A circular stamp has a radius of \(14.5\) millimeters. Find it’s area to the nearest whole number.

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Ana
Ana
Gordon cc
Gordon
Anthony spanish language icon
Anthony
Problem 5

Find the area.

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Julieta cc
Julieta
Gordon cc
Gordon
Problem 6

How much will it cost to plant a new lawn in an area of \(30\) feet by \(60\) feet if the price of sod is \(\$3.15\) per square yard

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Logan cc
Logan
Julieta cc spanish language icon
Julieta

3
Surface Area

Problem 1

For the polyhedra shown, list the number of faces, vertices, and edges.

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Mr. McKeague cc
Mr. McKeague
Logan cc
Logan
Julieta cc spanish language icon
Julieta
Problem 2

Find the surface area of a box with a width of \(3\) inches, a length of \(4\) inches, and a height of \(5\) inches.

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Aaron cc
Aaron
Anthony spanish language icon
Anthony
Problem 3

Find the surface area of the prism shown.

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Mr. McKeague cc
Mr. McKeague
Logan cc
Logan
Julieta cc spanish language icon
Julieta
Problem 4

A drinking straw has a radius of \(0.125\) inch and a length of \(6\) inches. How much material was used to make the straw?

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Mrs. Mooney cc
Mrs. Mooney
Gordon cc
Gordon
Anthony spanish language icon
Anthony
Problem 5

Find the slant height of the pyramid.

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Mr. McKeague cc
Mr. McKeague
Logan cc
Logan
Julieta cc spanish language icon
Julieta
Problem 6

Find the surface area of the pyramid.

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Mr. McKeague cc
Mr. McKeague
Logan cc
Logan
Julieta cc spanish language icon
Julieta
Problem 7

FInd the slant height and surface area of the cone.

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Mr. McKeague cc
Mr. McKeague
Logan cc
Logan
Julieta cc spanish language icon
Julieta
Problem 8

A figure is composed of a right circular cylinder with half a sphere on top. The cylinder has a radius of \(5\) inches and a height of \(10\) inches. Find the surface area of the figure assuming it is closed on the bottom.

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Julieta cc
Julieta
Aaron cc
Aaron
Anthony spanish language icon
Anthony

4
Volume

Problem 1

Find the volume of a rectangular solid with length \(15\) inches, width is \(3\) inches, and height \(5\) inches.

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Aaron cc
Aaron
Edwin spanish language icon
Edwin
Problem 2

A drinking straw has a radius of \(0.125\) inch and a length of \(6\) inches. To the nearest thousandth, find the volume of the liquid that it will hold.

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Julieta cc
Julieta
Gordon cc
Gordon
Problem 3

Find the volume of the pyramid.

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Logan cc
Logan
Problem 4

Find the volume of a cone with a radius \(3\) centimeters and height \(5\) centimeters.

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Lauren cc
Lauren
Aaron cc
Aaron
Edwin spanish language icon
Edwin
Problem 5

A figure is composed of a right circular cylinder with half a sphere on top. To the nearest tenth, find the total volume enclosed by the figure.

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Julieta cc
Julieta
Gordon cc
Gordon

5
Similar Figures

Problem 1

Two triangles are similar. Find side \(x\).

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Mr. McKeague cc
Mr. McKeague
Katrina cc
Katrina
Aaron cc
Aaron
David cc spanish language icon
David
Problem 2

The width and height of the two video clips are proportional. Find the height, \(h\), in pixels of the larger video window.

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Mr. McKeague cc
Mr. McKeague
Betsy cc
Betsy
David cc spanish language icon
David
Problem 3

Draw a triangle similar to triangle \(ABC\), if \(AC\) is proportional to \(DF\). Make \(E\) the third vertex of the new triangle.

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Mr. McKeague cc
Mr. McKeague
Arielle cc
Arielle
Aaron cc
Aaron
David cc spanish language icon
David
Problem 4

A building casts a shadow of \(105\) feet while a \(21\)-foot flagpole casts a shadow that is \(15\) feet. Find the height of the building.

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Mr. McKeague cc
Mr. McKeague
Arielle cc
Arielle
Winston cc
Winston
Julieta cc spanish language icon
Julieta
Problem 5

Use a proportion to determine the perimeter \(P\) of the new board.

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Joshua cc
Joshua
Lauren cc
Lauren
Cynthia spanish language icon
Cynthia

6
The Pythagorean Theorem

Problem 1

Solve for the \(x\) in the right triangle.

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Joshua cc
Joshua
Julieta cc spanish language icon
Julieta
Problem 2

The vertical rise of the Forest Double chair lift is \(1,170\) feet and the length of the chair lift is \(5,750\) feet. To the nearest foot, find the horizontal distance covered by a person riding in the lift.

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Stefanie cc
Stefanie
Aaron cc
Aaron
Edwin cc spanish language icon
Edwin
Problem 3

If the shortest side of a \(30^{\circ}-60^{\circ}-90^{\circ}\) triangle is \(5\), find the other two sides.

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Mr. McKeague cc
Mr. McKeague
Stefanie cc
Stefanie
Gordon cc
Gordon
Gordon cc spanish language icon
Gordon
Problem 4

Simplify \(\sqrt{\displaystyle\frac{1}{2}}\)

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Betsy cc
Betsy
Molly S. cc
Molly S.
Preston cc
Preston
Edwin spanish language icon
Edwin
Problem 5

Simplify \(\sqrt{\displaystyle\frac{2}{3}}\)

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Betsy cc
Betsy
Molly S. cc
Molly S.
Preston cc
Preston
Cynthia spanish language icon
Cynthia
Problem 6

A ladder is leaning against a wall. The top of the ladder is \(4\) feet above the ground and the bottom of the ladder makes an angle of \(60^{\circ}\) with the ground. How long is the ladder, and how far from the wall is the bottom of the ladder?

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Mr. Perez cc
Mr. Perez
Stefanie cc
Stefanie
Gordon cc
Gordon
Gordon cc spanish language icon
Gordon
Problem 7

A \(10\)-foot rope connects the top of a tent pole to the ground. If the rope makes an angle of \(45^{\circ}\) with the ground, find the length of the tent pole.

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Mr. Perez cc
Mr. Perez
Stefanie cc
Stefanie
Gordon cc
Gordon
Gordon cc spanish language icon
Gordon
Problem 8

Mini Lecture
Give the complement and supplement.

  1. \(10^{\circ}\)

  2. \(x\)

  3. Through how many degrees does the hour hand of a clock move in \(4\) hours?

  4. Fill in the missing sides of the triangle.

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Mr. McKeague cc
Mr. McKeague

7
Right Triangle Trigonometry

Problem 1

Triangle \(ABC\) is a right triangle with \(C=90^{\circ}\). If \(a=6\) and \(c=10\), find the six trigonometric functions of \(A\).

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Stefanie cc
Stefanie
CJ cc
CJ
Edwin cc spanish language icon
Edwin
Problem 2

Fill in the blanks so that each expression becomes a true statement.

  1. \(\sin\underline{\qquad}=\cos{30^{\circ}}\)

  2. \(\tan{y}=\cot\underline{\qquad}\)

  3. \(\sec{75^{\circ}}=\csc{\underline{\qquad}}\)

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Betsy cc
Betsy
Stefanie cc
Stefanie
CJ cc
CJ
Problem 3

Show that the following are true.

  1. \(\cos^2{30^{\circ}}+\sin^2{30^{\circ}}=1\)

  2. \(\cos^2{45^{\circ}}+\sin^2{45^{\circ}}=1\)

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Betsy cc
Betsy
Stefanie cc
Stefanie
CJ cc
CJ
Julieta spanish language icon
Julieta
Problem 4

Let \(x=30^{\circ}\) and \(y=45^{\circ}\) in each of the expressions that follow, and then simplify each expression as much as possible.

  1. \(2\sin x\)

  2. \(\sin{2x}\)

  3. \(4\sin{(3y-90^{\circ})}\)

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Stefanie cc
Stefanie
CJ cc
CJ
Problem 5

Mini Lecture

  1. \(\Delta ABC\) is a right triangle with \(C=90^{\circ}\). Find the six trigonometric functions of \(A\) if \(a=2\) and \(b=\sqrt{5}\).

  2. Find \(\sin A\), \(\cos A\), \(\tan A\), \(\sin B\), \(\cos B\), and \(\tan B\)

  3. \(\sin x=\cos{\underline{\qquad}}\)

  4. \(\left(\sin60^{\circ} +\cos60^{\circ}\right)^2\)

  5. \(\sec30^{\circ}\)

  6. \(\cot45^{\circ}\)

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Mr. McKeague cc
Mr. McKeague

8
Test & Summary

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