Lesson 1

Moving in Circles

Let’s think about 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.

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?

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:

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

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:

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

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.)

A:

\(f(x)=\dfrac{6}{x-6}\)

B:

\(g(x)=\dfrac{3x}{x-6}\)

C:

\(h(x)=\dfrac{3x-18}{x-6}\)

D:

\(k(x)=\dfrac{3x^2-16x+12}{x-6}\)

E:

\(m(x)=\dfrac{(x+5)(x-4)(x-6)}{x-6}\)

1:

The graph approaches \(y=6\).

2:

The graph approaches \(y=3\).

3:

The graph approaches \(y=0\).

4:

The graph approaches \(y=x^2+x-20\).

5:

The graph approaches \(y =3x^2+16x-12\).

6:

The graph approaches \(y=3x+2\).

7:

The graph approaches \(y=x-3\).

(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. \(x^2-6x+10=0\)
(From Unit 3, Lesson 18.)