Name ___________________________________________ Period ________________ Unit 1: Laws of Exponents and Scientific Notation Answer the following.

Date ________ Final Review

1) Write the standard numeral for each of the following exponential expressions: a) 25 ______ e) (.4)2 ______ b) (-3)4 ______ f) (-5)3 ______ x= 3, y= -2, and z = 4 d) (xy)2 e) 3x4 – 4z c) 21 ______ d) 23______

2) Evaluate each of the following expressions if: a) y2 b) 2xy2 c) y3 + 2x

3) Simplify each of the following. Write your answers in exponential form, with no negative exponents! a) x4 • x6 ______ d) (72)(74) ______ b) a5 • a ______ e) (33)(3-2) ______ c) 58 • 5 • 5-4 ______ f) (8-3)(83) ______

4) Express each of the following with positive exponents: a) 3-6 ______ b) x-2 ______ c) 3-4 ______ d) 5-2 ______

e) (42)3 _______

f) (55)3 ______

g) (9-4)2 ______

h) (33)3 _______

i) 36÷32 ______

j) 7-2÷7-4 ______

k)

_______

l)

_______

5) Write the following in scientific notation a) 56,000,000,000 b) 0.000434 _____________ _____________

c) 32.7 x 105 ______________

d) 231 x 10-3 ____________

6) Write the following in standard form a) 5.16 x 10-4 __________ b) 2.13 x 107 ____________

7) Perform each operation. Make sure your answer is in scientific notation! a) (8 x 10-2)(2 x 108) b) ( 2.5 x 109)(4.8 x 10-3) c) (5.2 x 10-9)(2.3 x 10-2)

d) 6 x 105 2 x 102

e) (1.5 x 105) ÷ (5 x 102)

f) 9 x 106 3 x 103

8) Mars is approximately 6 x 107 km away from Earth. If the moon is approximately 3 x 105, how much greater is the distance to Mars than the distance to the moon?

Unit 2: Equations Review Solve the following equations algebraically. 1) 4x – 7 = 2x + 15 2) 11(2c + 8) = -22 3) 4(-5x + 4) – 2x = -7(2x + 4)

4)

3 x - 12 = -27 7

5)

2x − 5 =5 3

6)

1 1 (-16x + 32) = (4x – 32) 4 2

7) 3.2x – 7.1 = 6.8 – 1.8x

8) 0.4(y – 9) = 0.3(y + 4)

9)

3 x −2 = x +2 7

Solve each equation algebraically for the given variable. 10) Solve for w: v = l • w • h 11) Solve for s: r+s =y 9

12) Solve for x: y + xb = 12

Solve each equation for x in terms of the other variables 13) a + x = bc 14) bx – a = 5a + c

15) 3(2x – h) = v

Solve each equation if possible. State whether the equation is an Identity or a Contradiction and explain what that means in terms of the solution. 16) 3x + 7 = 3(x + 2) 17) 2x + 9 = 2(x + 4) + 1

Define a variable(s), write an equation and solve each word problem. Final answer is a sentence.

18) When four times a number is decreased by 12, the result is -36. Find the number.

19) Together two items cost $130. One item costs $8 more than the other. Find the cost of each item.

Unit 3: Geometry Review Important Vocabulary: Point, line, plane, line segment, ray, angle, obtuse, acute, straight angle, vertical angles, congruent, perpendicular, adjacent angles, complementary, supplementary, parallel, transversal, alternate interior angles, alternate exterior angles, corresponding angles, Triangles (acute, obtuse, right, scalene, isosceles, equilateral), quadrilaterals (square, rhombus, rectangle, parallelogram, trapezoid, kite), Pythagorean Theorem, sum of interior angles (n-2)x 180º

Use the diagram to the left: 1. Name a pair of vertical angles 2. Name 4 pairs of corresponding angles 3. Name a pair of supplementary angles 4. If m 0 D) The equation has no solution

11) This relationship represented in this table names a function where x is the independent variable and y is the dependent variable: x 0 1 2 3 y 5 5 6 6 Is this relation a function? Explain? ____________________

________________________________________________

12) Tyler and Jason were discussing the relation shown by the table below. The boys decided that that if x is the input and y is the output that the relation would not be a function, however, if they were allowed to reverse the input and output, the relation would be a function. Do you agree or disagree with the boys