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CC7 Mastery Check Name:______________________________ Date:___________ Per:_____

Concept Category 7: Circles Teacher Score: NY 1 2 3 4 Directions: As you solve each problem, show a solution pathway that illustrates your reasoning, include correct mathematical notation in order to receive full credit. DOK 1: Recall & Reproduction 1. Find x in the given diagrams. a. Find x b. Find x

c. Find length of d. Find x

DOK 2: Routine Problems – Skill/Concept 2. Given: with tangent , secant , diameter , , and, Find the following a. = ___________

b. c. = ___________

JKH!

⊙T BZ VZVU m∠VTW = 144° m∠TWV = 18°

m∠AUV = 37°

m∠TWZ

mAU! = ________

m∠VZB

A: 15-16 B: 11-14 C: 7-10 D: 3-6

Should we continue to do Alpha? (circle) YES or NO

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3. Error Analysis: You are Terry’s Peer Tutor. The problem has a circle with radius = 7.5 and KN = 9, MN= 12 and the circle has diameter . He is given the task to see if = . He said it didn’t because the three numbers didn’t work when he used them in the Pythagorean theorem formula. His teacher said he was wrong.

a. Explain his error and show him that the Pythagorean theorem does work. b. Can you explain why = another way without using the Pythagorean theorem? DOK 3: Non-Routine Problems – Strategic Reasoning 4. Tony and Susan invited friends and their kids over to

their house to have pizza. In total there were 9 adults (7 adults plus Tony and Susan) and 5 kids. Susan ordered one large 16-inch diameter pizza that was cut into 8 equal pieces and one medium uncut 12-inch diameter pizza.

a. To ensure that each adult got the same amount (area) of pizza, Tony wants to cut one more slice from the medium pizza. What (central) angle should Tony cut at to ensure his slice is the same area as the other adults? Be sure to explain your process/work for full credit.

b. The left-over medium pizza will be divided equally among the 5 kids. What is the area of each kid slice?

KMm∠KNM 90o

m∠KNM 90o