Work must be shown to support each answer and should be done neatly on separate paper. Be sure to CIRCLE final answers.

Transcription

1 Work must be shown to support each answer and should be done neatly on separate paper. Be sure to CIRCLE final answers. Solve the equation x 1 3 x x 6 x Solve the equation for y. 3. 3y 5x xy y 15 Solve the inequality. Then graph your solution on a number line. 5. 3x x x a 7 13 Determine whether the lines are parallel, perpendicular, or neither. 9. Line 1: 1,5 and 4, 5 6,7 and 3,6 1, 9 and 2, 3 1, 9 and 1, 3 Line 2: 10. Line 1: Line 2: 11. Write the equation of the line that passes through the points 5,3 and 5, 3. Determine whether the relation is a function and state the domain and the range. 12. {(3, 4), (6, 4), (5, 4), (7, 5)} Simplify the expressions: ( x 2 y 17 ) x 5 y ( ) ( x 8 y 3 ) ( 27) æ è ç -7a 3 b 4 c 0 5a 5 b 6 c 7 ö ø -2 2 x x x ( 9x 6 2 ) 1 Use graph paper to graph the equation using the most appropriate method. Be sure to include key points x 3y f x x 2 3

2 Factor the polynomial x 2 11x a 2 56a x 2 2x x x x 5x 45 x x x 2-11x x x x 2 + 6x x p 2 q 2 16c r 2 + r p 2 20p x w 2 29w + 40 Find the product of the polynomials x x 3x 5 x x (x + 5)(x + 6) 38. 5t(4t 2 3t) 40. (8 + 5y)(8 5y) Evaluate/Simplify the expressions. 41. Evaluate b 2 4ac given that a = 3, b = 5, and c = Evaluate b 2 4ac given that a = 2, b = 3, and c = Evaluate 2x 3 3x 2 + 5x 9 for x = Evaluate -x 2y for x = 2 and y = Evaluate x( y + z) for x = 3, y = 3, and z = Evaluate 47. Simplify: 8p 7m 2n for m = -4, n = 2, and p = 1.5. n g 48. Combine like terms: -3x 5 2x x 2 x 49. Combine like terms: : (3x 2 5x + 2) + ( x 2 + 7x 8)

3 50. Combine like terms: ( 2x 2 + 4x 7) (8x 10) 51. Evaluate the formula for Bh V for B=9 in 2 and h = 3 in Evaluate b 2a c for a = -7, b = 3, and c = -7. Find the correct answer. 53. Find the distance between the points (3, 17) and (-2, 5). 54. Find the midpoint of the line segment joint the points (-3, 1) and (5, -7). 55. Find the slope of the line passing through the points (-1, 16) and (4, 2). 56. What is the slope of the line 2x 3y = 12? 57. Find an equation of the vertical line containing the point 4,5 and state its slope. 58. Find an equation of the horizontal line containing the point 4,5 and state its slope. 59. For the linear equation y 3, state the slope and graph the line. 60. For the linear equation x 2, state the slope and graph the line. 61. For the linear equation 5x 3y 6: a. Find the x and y intercepts b. Find the slope c. Graph the line 62. Find the slope of the linear equation y 3x Find an equation of the line containing the point 1, 3 with slope m 4 (a) Find the slope of the line passing through the points 4,2 and 2, 7 (b)find an equation of the line described in part (a). 64. The graph of 4x y 12 = 0 crosses the x-axis at x =. 65. Identify the property illustrated by 4 + x = x Identify the property illustrated by (4 + x) + y = 4 + (x + y).

4 67. The difference of two numbers is 3; and three times the greater exceeds twice the less by 18. Find the numbers. 68. A retailer bought a portable CD player for $54. He added $5.78 for expenses and $8.92 for net profit. At what price (to the nearest WHOLE dollar) did he sell the radio? 69. In 1995, there was a total of 7.2 million acres of pine forests in Florida. All of the forests were either natural or planted by people. Given that people planted 4.4 million acres of these pine forests, how many millions of acres of these pine forests were natural? 70. An artist sells earrings from a booth at a fair. Rent for the booth is $250. The artist makes $6 from each pair of earrings sold. The profit in dollars, P, can be found using the following equation, where n is the number of pairs of earrings sold. P = 6n 250. How many pairs of earrings must the artist sell to earn a profit of $500? 71. A store advertised a ⅓ off ticket price sale of all its summer clothing. If you chose a suit with a ticket price of $ and a pair of shoes priced at $37.98, EXACTLY how much money would you need to buy both items? 72. Happy Toy Store s owner bought x dozen toy dolls at a cost of $4.00 per dozen, and sold each doll for $ Express the profit P(in dollars) as a function of x. 73. The dairy section of a supermarket occupies 2400 square feet of space in a store that has a total area of 36,000 square feet. What is the ratio of dairy space to all other space? 74. A budget includes an allowance of $55 a week for food and $15 a week for entertainment out of a total allowance of $250. What is the ratio of all other costs to the total? 75. Translate to an algebraic expression: seven less than twice a number 76. Translate to an algebraic expression: three-fifths of a number

5 77. Use the commutative law of multiplication to write an expression equivalent to: wd s 78. Use the associative law of addition to write an expression equivalent to: wd s Use the distributive law to write an expression equivalent to: 3 wd s 80. In a class of 40 students, 35% work full time. How many students in that class work full time? 81. On a test of 64 items, a student got 56 correct. What percent were correct? 82. A computer is on sale for a 15% reduction. If the sale price is $ , what was the original price? 83. Rent in Austin has increased by 55% since If monthly rent for a 2 bedroom apartment is now $850, what would rent have been for the same apartment in 1990? Round your answer to the nearest cent. 84. The sum of three consecutive odd integers is 87. What are the integers? 85. The second angle of a triangle is 4 times as large as the first. The third angle is 45 degrees less than the sum of the other two angles. Find the measure of each angle 86. The length of a rectangle is 3 feet less than 4 times its width. If the perimeter of the rectangle is 64 feet, what are the dimensions of the rectangle? 87. Two angles are complementary if the sum of their angles is 90 degrees. One of two complementary angles is 12 degrees more than twice the other. Find the measure of each angle. 88. There were 200 tickets sold for a volleyball game. Tickets for students were $2 each and for adults were $3 each. The total amount collected was $530. How many of each type of ticket were sold? 89. Emilio wishes to mix peanuts worth $2.52 per pound with almonds worth $3.80 per pound to make 480 pounds of a mixture worth $3.44 per pound. How much of each should he use?

6 90. The length of a rectangle is one foot less than three times the width. Find the length and width if the area is 30 square feet. 91. A water pipe runs diagonally under a rectangular garden that is 7 feet longer than it is wide. If the pipe is 13 feet long, what are the dimensions of the garden? 92. The length of one leg of a right triangle is 12 meters. The length of the hypotenuse is 8 meters longer than the other leg. Find the lengths of the hypotenuse and the other leg of the triangle. 93. Two angles are supplementary if the sum of their angles is 180 degrees. One of two supplementary angles is 8 degrees less than three times the other. Find the measure of each angle. 94. A sample of 125 light bulbs contained 3 defective bulbs. How many defective bulbs would you expect in a batch of 3000 light bulbs?

7 95. Without the aid of a calculator determine the exact values of the following 9 i ii iii. 8 3 iv v vi. vii. viii. Expression Convert to decimal notation: Convert to scientific notation: Multiply and write your answer in scientific notation: ANSWER ix... Divide and write your answer in scientific notation: A 1,500-gallon tank contains 200 gallons of water. Water begins to run into the tank at the rate of 75 gallons per hour. When will the tank be full but not overflowing? 97. Write the number 2.4 in the form b a, using integers, to show that it is a rational number.

8 98. Find the unit rate for number of parts manufactured per hour if 1630 parts are made in 6 hours. Round to the nearest integer. 99. A van travels 220 miles on 10 gallons of gas. Write and solve a proportion to find how many gallons the van needs to travel 550 miles The total cost and revenue (in million dollars) for the production and sale of x units are given respectively, by: C ( x ) = 32x R( x) = 300x x 2. Find the profit function P(x), if Profit = Revenue Cost. BONUS: Factor completely. x 3 2x 1 x 3 2x 1

9 GEOMETRY Vocabulary List The following words, formula & Properties should be in your vocabulary section when you finish. Please make sure they accompanied by a picture if possible. Definition Collinear Coplanar Line Segment Congruent Segments Midpoint Bisects Ray Coordinate midpoint Property Angle Vertex Sides Measure of an Angle Degrees Protractor Congruent Angles Angle Bisector Incoming Angle Outgoing Angle Counterexample Whole box of Beginning Steps to Creating a Good Definition Arrow Marks Parallel Lines Perpendicular Lines Skew Lines Right Angle Acute Angle Obtuse Angle Polygon-side-vertex Consecutive sides Consecutive angles Consecutive vertices Names of polygons from 3 sides to n-gon Diagonal Convex Concave Congruent Polygons Equilateral Polygon Equiangular Polygon Regular Polygon Circle Radius Diameter Congruent Circles Concentric Circles Arc of a Circle Endpoints Semicircle Minor Arc Major Arc Arc Measure Central Angle Space Probability Slope Whole box of Slope Formula