Lesson 1

Moving in Circles

Problem 1

Here is a clock face. For each time given, name the number the second hand points at.

  1. 15 seconds after 1:00.
  2. 30 seconds after 1:00.
  3. 1 minute after 1:00.
  4. 5 minutes after 1:00.
A blank clock face with numbers 1 through 12.

Solution

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Problem 2

At 12:15, the end of the minute hand of a clock is 8 feet above the ground. At 12:30, it is 6.5 feet off the ground.

  1. How long is the minute hand of the clock? Explain how you know.
  2. How high is the clock above the ground?

Solution

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Problem 3

Here is a point on a circle centered at \((0,0)\).

Which equation defines the circle?

A circle on a coordinate plane, center at the origin. The point 6 comma 8 lies on the circle.
A:

\(x  + y = 10\)

B:

\(x^2 + y^2 = 10\)

C:

\(x^2 + y^2 = 100\)

D:

\((x-6)^2 + (y-8)^2 = 100\)

Solution

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Problem 4

The point \((3,4)\) is on a circle centered at \((0,0)\). Which of these points lie on the circle? Select all that apply.

A:

\((\text-3,\text-4)\)

B:

\((4,3)\)

C:

\((0,5)\)

D:

\((0,0)\)

E:

\((\text-5,0)\)

Solution

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Problem 5

Match each polynomial with its end behavior as \(x\) gets larger and larger in the positive and negative directions. (Note: some of the answer choices are not used and some answer choices may be used more than once.)

Solution

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(From Unit 2, Lesson 19.)

Problem 6

Find the solution(s) to each equation.

  1. \(x^2-6x+8=0\)
  2. \(x^2-6x+9=0\)
  3. \(x^2-6x+10=0\)

Solution

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(From Unit 3, Lesson 18.)