# 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.

- 15 seconds after 1:00.
- 30 seconds after 1:00.
- 1 minute after 1:00.
- 5 minutes after 1:00.

### 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.

- How long is the minute hand of the clock? Explain how you know.
- 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?

\(x + y = 10\)

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

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

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

### 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.

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

\((4,3)\)

\((0,5)\)

\((0,0)\)

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

### 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.)

### Problem 6

Find the solution(s) to each equation.

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