alg 2 midterm review revised march 7 2007 3

8/3/2019 Alg 2 Midterm Review Revised March 7 2007 3

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Midterm Review Algebra 2

1. Solve and graph the following inequality -4 < 2 – x < 6 ?

2. Solve and graph the following absolute inequality. 214

3≥+ x

3. What is the y-intercept and the x-intercept of the line y = 4x + 12?

4. What is the equation of the line that passes through the point (7, 8) and (2, 18)?

5. Which of the ordered pairs is a solution of 2x – 3y < 2?

(0, -1) (3, 2) (-3, -6)

6. Find the vertex and the y-intercept of the function 743 −−−= x y ?

7. Solve the following system of linear equations.

4x + 3y = 3

2x + y = -3

8. Solve the following system of linear equations.

2x + 3y = 123x – 4y = 1

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9. Determine if each ordered pair is a solution of the following system of linear

inequalities.

2

12

≥+

<−

y x

y x(0, 0) (1, 1) (1, 2)

10. Does the following function open up or down and is it wider or narrower than2 x y = ?

22 x y −=

11. Solve the following linear system.

x + 2y – z = 3

x – 3y + z = -1

-x + y – 3z = 5

12. Divide. Use synthetic division when possible.

( ) ( )5 4 2

5 6 28 10 5 x x x x x+ − − + ÷ +

13. Divide. Use synthetic division when possible.

( ) ( )26 8 2 3 x x x+ − ÷ −

14. Factor the polynomial given that ( ) 0 f k = .

( ) ( )3 210 11 70; 5 0 f x x x x f = + + − − =

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15. Given one zero of the polynomial function, find the other zeros.

( ) 3 22 7 33 18; (6) 0= − − + = f x x x x f

16. What is the vertex of the graph of y x x= − − +2 4 72?

17. What is a complete factorization of 6 33 152 x x− + ?

18. What are the solutions of ( ) 21544

1 2

=+− x ?

19. Find the product. )62)(4( ii +−−

20. Solve. 010422

=−− x x

21. Solve. 01352

=−+ x x ?

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22. Write the quadratic equation in vertex form for a graph whose vertex is (4, 1)

which passes through the point (2, -3)?

23. Find the product. (2x+1)(x² – x – 3)

24. Factor. .25812

− x

25. Expand.3)3( − x

26. Simplify.4 5 2(3 ) x y

27. Simplify.4 1 0 7

4 2 3 3

4 15

15 2

x y x y

x y x y

−

− −•

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Imaginary

Real



28. Sketch the graph of 5 2i− .

29. Simplify. (7 2 ) (4 6 )i i− − + .

30. Simplify.3 2 3

(8 7 5 ) (3 7 8) x x x x x+ − + − − +

31. Describe the end behavior of the following graph symbolically (i.e. using limits.)

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32. What is the standard form of the quadratic function 4)1(32−−−= x y ?

33. What is the standard form of the quadratic function 4( 5)( 3) y x x= − + − ?

34. What is the complete solution to the equation 1152 =− x ?

35. Determine if the lines going through the given points are parallel, perpendicular

or neither.

L1: (-3, 5) and (4, -3) L2: (-5, 1) and (2, -7)

36. Graph 52

1−≥− y x

37. Two linear functions have infinite solutions if _______________________:

38. List the possible zeros of the function.

( ) 3 22 5 6 f x x x x= + − +

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39. Simplify.i

i

+

+

4

32

40. Solve. 17102

2

−=+ x x

41. Write the point-slope form equation of the line that has a slope of –⅔ and passes

through the point (-6,11). Then rewrite the equation in slope-intercept form.

42. Simplify. All exponents need to be positive.

( )3

3 5

2 8

2

6

x y

x y

−

−

43. Find all the zeros of the polynomial function.

( ) 4 23 4 f x x x= + −

44. Find all the zeros of the polynomial function.

( ) 3 22 25 50 f x x x x= − + −

45. Factor. 22122

−+ x x

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Answer questions #41-50 without using your calculator! Show all your work.



46. Solve using completing the square. 1382

++ x x =0

Solve the inequality and graph the solution on a number line.

47. 753 <− x

48. Write the equation the quadratic function that has x-intercepts of (-5, 0) and (3, 0)and passes through the point (1, 12).

49. Graph the following quadratic function:

422

−+−= x x y

50. Use synthetic substitution to evaluate 534)(3

−+−= x x x f when 2= x .

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alg 2 midterm review revised march 7 2007 3

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