ExponentsI. Write in exponential form.

4 » x • x • y y • y - 4x2 y3 The cube of c - 4 - (c - 4)3

1. a * a * a • b

2. mn • mn • mn * mn

3. 9 * x * x * x * x * x » y y z

4. 5 (c + 1) (c + 1) (c + 1)

5. (a + b) squared

li. Evaluate each expression if x ~ '1, y

6. The quotient of 3 and the cube of y + 2

7.

8. (-x)(-x)(-x)

9. 3 • ab * ab • ab * ab

10. The square of x2 y - 3

= 2, z = "3

5x2z2 = 5 • x • x • z • z = 5 • '1 * "1 • "3 • '3 = 45

1. x5

2. x2 yz

3. 4y3z

4 x5y*z3

5. -(xyz)

6. 10z5

7. x2yz2

8. ~2xy2

10. l l x 2

Solving Equations With Variables on Both Sides

1. 4x - 6 = X + 9

2. 4 - 7x = 1 - 6x

3. ~4x-3 = "6x+9

4. 41 -- 2n - 2 + n

5. 6 (2 + y) = 3 (3 - y)

6. 4y = 2 ( y - 5) - 2

7. 6 x - 9 x - 4 = ~2x- 2

8. -(x + 7) = '6x + 8

9. 3 - 6 a = 9 - 5 a

10. ‘9x + 6 = -x + 4

11. 5 x - 7 = "lOx + 8

12. 7y + 3 = A y - 18

13. '3 (y + 3) = 2y + 3

14. 2 ( 3a + 5) = ‘4 (a + 4)

15. 7x - 3 = 2 (x + 6)

16. '6x + 9 = 4 (5 - x)

17. 3 (x+ 2) = '5 - 2 ( x - 3)

18. 2 (x - 3) = (x - 1) + 7

19. — (6 y - 9) = “2y + 13

20. - ( 1 2 - 6 x ) = 5 (x + 4) 6

Equations: A Little M agicSet up and solve each equation, In a magic square, each row, column, and diagonal has the same sum.

3 x -5 = 2 (2x + 5) 10x+8 = 12x-18

o!XCMII1X, 3 ( / r 4) = b y + 30

3 (2 /+ 4) = 4 (y + 7) - 2 '6 /= 1 0 -4 / '27 - 6x = 3x 7y + 3 = ] 2 y - 2

2 y + 2 = 3 /+ 3 OO

X 1 s X 1 II O 6 y - 10 + 4 y 6 (x + 7) = 2 (x + 7)

Two consecutive whole numbers total 17. Find the larger,

Two consecutive odd numbers total «20. Find the smaller.

One number is 4 less than 3 times

another. Their sum is '16. Find the smaller.

Two consecutive odd numbers total 32, Find the smaller.

Magic Sum is

More Problem Solving Using EquationsSet up and solve each equation,

------- =------- — ■The sum of two numbers is 52. The difference of the same two numbers is 20. Find the numbers.

x - one number 52 - x = second numberx - (52 - x) = 20 52 - x = 52 -3 6 = 16

x - 52 + x = 20 :2x - 52 = 20

2x - 52 + 52 = 20 + 522x 722 ~ 2x = 36

The numbers are 36 and 16.

:. ......... J

1. One number is four times another. Their sum is 35. Find the numbers.

2. The sum of two numbers is 21, One number is three less than the other, Find the numbers.

3. The greater of two numbers is one less than 8 times the smaller.Their sum is 98. Find the numbers.

4. In a triangle, the second angle measures tw ice the first, and the third angle measures 5 more than the second. If the sum of the angles' measures is 180°, find the measure of each angle,

5. The length of a rectangle is 4 centimeters (cm) less than three times the width. The perimeter is 64 cm, Find the width and length,(Hint: Perimeter = 21 + 2w)

6. The sum of three numbers is 64, The second number is 3 more than the first. The third number is 11 less than tw ice the first. Find the numbers,

7. Bill can type 19 words per minute faster than Bob. Their com bined typing speed is 97 words per minute, Find Bob's typing speed.

Finding the Slope of a LineSlope = vertical change

horizontal change

Identify the slope of the line using the graph.

11Using points 1 & 2 vertical change = '3 horizontal change = ’1

slope = — = 3

Find the slope.

c change in /-values V2 change in x-values x2

Find the slope of the line passing through the given points.

- y ] 6. (0,0) (3, 5)

-*17. (5, “2) (7, 4)

8. ("6, 3) 02, 9)

(-1,5) (3, -2) 9. (6,-9) 04, 3)

"2 -5 "7S l0 p e = 3 - C l ) = 4 10. 03, 11) (2, 7 )

11. (7, 3) ('8, 3)

12. (0,0) (4,-3)

13. C2.-3) (2, 5)

14. C4, 8) C4, -3)

Basic Inequalities: Solve and Graph

1. x + 4 > 12 8. ' 15 x - 2 < 3 x - 11

-<4 I I I 11 I I I I I l--+--M-444444-*- —I—I—I—I—t—I-■ I I r44444444444-4--» -.10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

2. 32 > '4 (Ay) 9. 2 ( t+ 3) < 3 ( f+ 2)

+4-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

3. 3k + 1 < 1 3

4-1 i I I i I 1444 M il l- l 4444-

10. 15x - 2 (x - 4) > 3

hH-H-4-+4 I I I ! I ■ +4 44444444--»--10 -9 -8 .-7 -6 -5 -4 -3 -2 - I 0 1 2 3 4 5 6 7 8 9 10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

11. x - 1.5 < 0.5 (x + 4)4. 10 — < 2z + 18 —

4444444444-4444-44-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

5. 2 - f < - l 12. '3 (2m - 8) < 2 (m + 14)

+444444444 I I I H4444-+4-»- -*444444444444444444444-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

6. ‘2 x - 5 > 6 13. 2x + 3 < 6 x - 1

44-H444444444444444-*- -*444-4-H4444444444444-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -IQ -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 B 9 10

7- '3m + 6 (m - 2) > 9 14. 3 x - 2 > 7 x - 10

-H44444444444444444—► -<444444444444444-10 -9 -8 -7 -8 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Graphing EquationsGraph each equation by plotting points. Use your own graph paper.

2. y = ' 2x+4

3. x + y = 2

4. 3x + y - 9

6. y = '3x + 5

X y20'1

y = 5

X y730

8. 3x + 4y = 12

X y40'4

Pythagorean Magic

3. A 10-foot ladder is leaning against a house with its base 4 feet from the base of the house. How far up the house does the ladder touch the house? (Hint: Draw a picture.)

4. A 5-foot tall tree casts an 8-foot shadow on the ground. How far is it from the end of the shadow to the top of the tree?(Hint: Draw a picture.)

5. A guy wire is secured into the ground 15 feet from the base of a 36-foot pole. How long is the guy wire if it is attached at the top of the 36-foot pole? (Hint: Draw a picture.)

6. An airplane travels due east 65 miles, and then due north 72 miles. How far is the airplane from its starting point? (Hint: Draw a picture.)

Systems of Equations: Substitution Methodx - 5 = 10

'2x + y - 7 y - 2x + 7 Solution ('5, ~3)

x - 5 (2x + 7) = 10 x - I Ox - 35 = 10

~9x - 35 = 10 '9x = 45

x = ' 5

1«lI!i•

1. y = 5 - 4x 8. y = -x + 6

3 x - 2y = 12 x - 2y = '6

2. 3x + 2y = 8 9. 2 y - x = 6

x = 3y + 10 3 y - x = 4

3. 3 x - 4 y - "15 10. 5 x - 6 y - 16

5x + y = 2 5x + y - 2

4. x + y - 2 11. y - 3x

3x + 2y = 5 x + y = 8

5. x = 3 - 3 y 12. x - 3y = '5

4y = x + 11 2x + y = 11

6. X - y = ‘ 15 13. -x + y = 5

x + y = ' 5 y = '3x + 1

7. 2x + y = ' 6 14. 2x = 3y

3 x+ y = "10 x = 3 y - 3

Systems of Equations: Elimination Methodx + y = 6 x + y = 6

x - y = 4 + x - y = 43y = ' 7 x + 7 7x + 3 y = 7

2y ~ 7 x ~ 1 “ (7x ~ 2y = 7)2x = 10

x = 5

x + y ~ 5 + y = 6

K= 1Solution (5, 1)

5y - 0

y = 0

2y - 7x ~ 7 = ► 0 = 7x - 7

7 = 7x

1 = X

Solution (1 ,0 )

1. 2x + y = "6 8. 7y + 15 = 3x

3x + y = '10 15 = 3x + 2y

2. 8x - y = 20 9. 25x = 91 - 16y

*5x + y = "8 16y = 64 - 16x

3. 2x+ y = 0 10. 4 x - 2 y = ' 2

2 x - 3y = '8 4x+ 3y = '12

4. 5x+ 3y = 10 11. 2x + y = 7

2 x - 3y = 4 y = 3x + 3

5. 9 x - 3y = 9 12. 3 x = ' 2 y + 1 0

x + 3y = 11 x = 2y + 6

6. x + 3 y - - 9 13. x + 4y = 2

x - 2y = '6 x - 2 y = 8

7. 2x + y = 4 .14, x + 5y + 11 = 0

2x + 2y = 2 3 x - 5 y - 7 = 0