Dr. Fowler CCM1A

EXAM REVIEW 01

Pythagorean Theorem

leg

leg

hypotenuse

The hypotenuse is always the longest side of a right triangle and is always opposite the right angle.

Using aUsing a22 + b + b22 = c = c22

Looking for length ofLooking for length of

the hypotenusethe hypotenuse aa22 + b + b22 = c = c22

151522 + 20 + 2022 = c = c22

225 + 400 = c225 + 400 = c22

625 = c625 = c22

625 c2

25 c

Using aUsing a22 + b + b22 = c = c22

Find the LegFind the Leg aa22 + b + b22 = c = c22

6622 + b + b22 = 10 = 1022

36 + b36 + b22 = 100 = 100 -36 -36-36 -36 bb22 = 64 = 64 b = 8b = 8

Ex 1Find the distance between the points P(-3, 2) and Q (-2, 4).

1, 1( )x y 2, 2( )x y

2 22 1 2 1( ) ( )d x x y y

2 2( ) ( )d 2 3 24

2 2( ) ( )d 1 2

d 1 4

5 d

Work inside parentheses

Do powers before doing the addition!!!!!!

+ 4 + 4

3 · · 3

x = 36

12 – 4 = 8

123

x

2) Solve 4 83

x

1. Draw “the river”2. Add 4 to both

sides3. Simplify4. Clear the fraction -

Multiply both sides by 3

5. Simplify6. Check your

answer

D U

÷ 3- 4

+ 4· 3

364 8

3

3) Solve d 4

23

d – 4 = 6

+ 4 + 4

d = 10

1. Draw “the river”2. Clear the fraction -

Multiply both sides by 2

3. Simplify4. Add 4 to both sides5. Simplify6. Check your answer

D U

- 4÷ 2

· 2+ 4

42 3 2

2

d

10 43

2

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Solve With x’s on Both Sides 7x 5 3x 23

3x 3x 4x 5 23

5 5 4x 284 4

x 7

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13 = 4(3x – 7) + 5

13 = 12x - 28 + 5

13 = 12x - 23 +23 +23

36 = 12x__ ___ 12 12

3 = x

13 = 4(3 3 – 7) +5

13 = 4(9 - 7) + 5

13 = 8 + 5

13 = 13

13 = 4(2) + 5

Solve With The Distributive Property

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3y 6(y 2) 24 3y 6y 12 24

9y 12 24 12 12 9y 369 9

y 4

Solve With The Distributive Property

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2(3x 1) 4(10 2x)

8x 8x 14x 2 40

2 2 14x 4214 14

x 3

6x 2 40 8x

Solve With The Distributive PropertyChallenging One!

Excellent Job !!!Well Done

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