Algebra 2 Pre AP Chapters 2 & 12 Review Worksheet

Transcription

1 Algebra 2 Pre AP Chapters 2 & 12 Review Worksheet Directions: Complete the following problems on the packet. These packets will serve as a review of the entire year. For each equation given: (a) find the intercepts, (b) determine algebraically whether the equation s graph exhibits x axis, y axis, or origin symmetry, and (c) graph the equation Draw a sketch of a graph that exhibits the following types of symmetry. 4. x axis symmetry 5. y axis symmetry 6. no symmetry Identify the point described. 7. If the graph of an equation that is symmetric to the y axis contains the point ( ), then what other point is on the graph? 8. If the graph of an equation that is symmetric to the line y = 3 contains the point ( ), then what other point is on the graph?

2 Answer the following questions about slope and lines. 9. What is slope? What does it measure? 10. Find the slope of each of the lines, then write the equation that describes the line. (a) The line contains the point ( ) and ( ). (b) The line is perpendicular to the line and contains the point ( ). 11. Graph the following lines. (a) (b) 12. A Low Earth Orbit (LEO) satellite orbits the earth at 520 miles above the earth s surface. Suppose the satellite orbits the earth in a circular path and that the radius of the earth is 3959 miles. Write an equation that models the orbit of the satellite.

3 13. A cereal company finds that the number of people who will buy one of its products in the first month that it is introduced is linearly related to the money it spends on advertising. If it spends $40,000 on advertising, then 100,000 boxes of cereal will be sold, and if it spends $60,000, then 200,000 boxes will be sold. (a) Identify the dependent and independent variables. (b) Find the slope and interpret its meaning in context. (c) Write a linear equation that expresses number of boxes sold as a function of advertising expenditures. Write each circle in standard form and identify its center and radius The endpoints of the diameter of a circle are ( ) and ( ).

4 Write the variation model described. Unless its value can be determined, use k to represent the constant of variation. 17. M varies jointly with t and the square of d. 18. The period T of a pendulum (the time it takes for it to complete one oscillation) when the angle made to the vertical is less than is directly proportional to the square root of its length l (in feet). The constant of variation is. 19. The resistance (in ohms) of a circular conductor varies directly with the length of the conductor and inversely with the square of the radius of the conductor. If 50 feet of wire with a radius of inch has a resistance of 10 ohms, what would be the resistance of 100 feet of the same wire if the radius is increased to inch? 20. What remains constant in direct variation? inverse variation? And what is the graph of a basic inverse variation model? Solve the following systems of equations. 21. { 22. {

5 23. { 24. { 25. { 26. { Graph the following systems of inequalities. Identify each as bounded or unbounded. 27. { 28. {

6 Solve the following problems using a system of equations. 29. Frank went clothes shopping and bought 2 pairs of jeans, 2 specialty T shirts, and 4 plain T shirts for $ At the same store, Peter bought one pair of jeans and 3 plain T shirts for $42.50, while Kurt bought one pair of jeans, 3 specialty T shirts, and 2 plain T shirts for $ Determine the price of each clothing item. 30. A 1000 acre farm in Illinois is used to grow corn and soybeans. The cost per acre for raising corn is $65, and the cost per acre for soybeans is $45. If $54,325 has been budgeted for costs and all the acreage is to be used, how many acres should be allocated for each group? Solve the following linear programming problems. 31. Maximize subject to. 32. A factory produces gasoline engines and diesel engines. Each week the factory is obligated to deliver at least 20 gasoline engines and at least 15 diesel engines. Because of physical limitations, however, the factory cannot make more than 60 gasoline engines nor more than 40 diesel engines in any given week. Finally, to prevent layoffs, a total of at least 50 engines must be produced. If gasoline engines cost $450 each to produce and diesel engines cost $550 each to produce, how many of each should be produced per week to minimize the cost? What is the excess capacity of the factory; that is, how many of each kind of engine is being produced in excess of the number that the factory is obligated to deliver?