Algebra 2 Final Review

NAME______

Algebra 2 Final Review

1. Which quadrant does the point (-2, 5) lie in?

2. A team of biologists tagged 130 fish and released them into a local lake. A few weeks

later they caught 80 fish, 17 of which were tagged. Use this information to estimate

the number of fish in the lake.

3. Solve the following equations for the missing variable. Use your calculator minimally

and as a check.

a. b. c.

d. e.

f. g.

h. i.

j. k.

l. m.

4. Solve the following inequalities.

a. b. c.

5. Write or look up the following equations.

a. slope-intercept form b. point-slope form

6. Write the equation of a line that has the given information.

a. the line has a slope of -4 and passes through (0, -6)

b. the line has a slope of and passes through (-7, -2)

c. the line passes through the points (6, -1) and (-4, -3)

d. the line passes through (4, 5) and is perpendicular to the line

7. The wind chill temperatures for a wind speed of 35 mph are given in the table.

a. Find the rate of change (slope).

b. Write an equation in slope-intercept form and in point-slope form.

c. If the temperature is 52, what is the wind chill?

8. Solve for y.

a. b. c.

d. e.

9. Graph the following functions and inequalities.

a. b. c. d.

e. f. g.

h. i. j.

10. Solve the system using substitution or elimination.

11. Use the properties of exponents to rewrite each expression (use only positive

exponents).

a. b. c.

d. e. f.

12. Phil’s friend Shawna buys an antique car for $22,000. She estimates that it will

increase in value by 3% each year.

a. Write an equation to calculate the value, y, of Shawna’s car after x years.

b. Show how you would use your equation (not your table or graph) to find the

value of the car in 10 years. Round the value to the nearest dollar.

13. You needed to borrow $8200 from a bank to purchase your first car. The annual interest rate is 5.25%, compounded monthly. Answer the following:

a. How much do you owe after one month, assuming you do not make any

payments yet.

b. What would you owe after one year if you didn’t make any payments?

14. Graph the following and describe the graph’s domain and range.

a. b.

15. Given and , find the following:

a. f(5) = b. g(-4) = c. find x if f(x) = 12

d. f(g(7)) = e.

16. Factor the following:

a. b. c.

d. e. f.

g. h.

17. Simplify the following:

a. b. c.

d. e.

f. g.

18. Use the zero-product property to find the roots.

a. b. c.

19. Convert to general form.

20. Write into vertex form.

21. Solve the equation by completing the square. Leave your answer in

radical form.

22. Solve the equation using the quadratic formula. Round to the nearest

tenth.

23. A baseball is hit straight up in the air. The ball’s height, h, in meters, t seconds after

it is hit is .

a. Find h(3) and give a real-world meaning for this value.

b. When is the ball 30 meters above the ground? Give your answer to the

nearest hundredth of a second.

c. The ball was caught 2 meters above ground? How long was it in the air? Give

your answer to the nearest hundredth of a second.

24. Simplify. No calculators.

a. b. c. d. e.

25. Find the inverse of the following functions:

a. b. c.

26. If possible, perform the following operations on the matrices. If you can’t do the

problem, explain why.

27. Lesson 6.1 p323 #10

28. Use finite differences and matrices to find the equation of the following polynomial.

29. Lesson 7.7 p426-427 #1-4, 7

30. Divide

31. Graph the following.

a. b.

32. Find the coordinates of the foci for both a and b above.

33. Find the equations of the asymptotes for #31b above.

34. Solve for the missing variables.