Honors Algebra II Midterm Review - TypePadleagueland.typepad.com/files/midterm-review-3.pdf ·...

Honors Algebra II Midterm Review Name___________________________________

_____1. A quadratic function with a negative discriminant will have

(a) Two real roots

(b) One real double root

(c) No x-intercepts

(d) One real root and one complex root

_____2. What value of b will make the following equation true?

22 3 3 24 14 24bx x b x x

(a) 3 (b) 4 (c) 5 (d) None of these

_____3. What value of c will make the following equation true?

2216 9 4 3x cx x

(a) 4 (b) 3 (c) 12 (d) 24

_____4. If one of the factors of a quadratic function is 3 2x i , what must the other factor

be?

(a) 3 2x i (b) 3 2x i (c) 3 2x i (d) None of these

_____5. Which of the following graphs represents a quadratic function with a discriminant of

zero?

(a) (b) (c) (d)

Honors Algebra II Midterm Review

_____6. If the x-intercepts of a quadratic equation are 5,0 and 2,0 , what is a possible

vertex of the corresponding parabola?

(a) 3

,02

(b) 3

, 42

(c)

3,4

2

(d) 3

, 42

_____7. What is the discriminant of 23 5 2 0x x ?

(a) 49 (b) 1 (c) 1 (d) 49

_____8. Which statement is correct for the quadratic function graphed below?

(a) The function of the graph is 3 1y a x x with a maximum value of 8.

(b) The function of the graph is 3 1y a x x with a maximum value of 8.

(c) The function of the graph is 3 1y a x x with a minimum value of 8.

(d) The function of the graph is 3 1y a x x with a minimum value of 8.

_____9. Which quadratic function opens up and has a vertex at 0,3 ?

(a) 2 6 9f x x x (b) 2 6 9f x x x

(c) 2 3f x x (d) 2 3f x x


_____10. Which quadratic function has an axis of symmetry of 2x and a minimum value of

4 ?

(a) 2

3 2 4y x (b) 2

3 2 4y x

(c) 2

3 2 4y x (d) 2

3 2 4y x

_____11. An even function contains the point 3, 5 . What other point must the function

contain?

(a) 3, 5 (b) 3,5 (c) 3,5 (d) 5, 3

_____12. Factor 2(3 1) (3 1) 20p p

(a) 3 5 3 4p p (b) 9 2 1p p (c) 9 2 1p p

(d) not factorable

_____13. What is the degree for the polynomial 15 17 13 2 3 7 172 2 ( ) ( ) 9 ( )x x x x x x x when it

is properly simplified?

(a) 17 (b) 26 (c) 21 (d) 18

_____14. What is the remainder if 3( ) 3 2 4f x x x is divided by 2x ?

(a) 12 (b) 24 (c) 20 (d) 16


_____15. The graph of a polynomial function is shown. Which statement about the function

is true?

(a) The degree of the function is odd.

(b) The degree of the function is even.

(c) The leading coefficient of the function is positive.

(d) ( )f x as x .

_____16. What is the degree of the function 4 28 5 3h t t t ?

(a) 1 (b) 2 (c) 3 (d) 4 (e) None of these

_____17. If 3x is a factor of 3 2 17 15x x x , what is another factor?

(a) 1x (b) 1x (c) 5x (d) 3x

_____18. Which are not possible rational zeros of 3 2( ) 3 11 5 6f x x x x ?

(a) 1

2 (b)

2

3 (c) 2 (d) 6

_____19. What is the leading coefficient of the polynomial function 2 3( ) 3 4 5 6f x x x x ?

(a) 3 (b) 4 (c) 5 (d) 6

_____20. What is the solution of 3 26 14 2x x x x ?

(a) , 2 and 0,8 (b) , 2 and 0,8

(c) 2,0 and 8, (d) 2,0 and 8,


_____21. What is the complete factorization of 3 2 25 25x x x ?

(a) 1 5 5x x x (b) 1 5 5x x x (c) 21 25x x

(d) 21 25x x (e) 1 25x x

_____22. What is the quotient when 4 3 29 45 37 2x x x x is divided by 29 1x ?

(a) 6 2x (b) 2 5 4x x (c) 2

2

6 25 4

9 1

xx x

x

(d) 2

2

5 46 2

9 1

x xx

x

(e)

2

2

2

9 1

x x

x

_____23. Factor 38 27x

(a) 3

2 3x (b) 22 3 4 12 9x x x

(c) 22 3 4 6 9x x x (d) 22 3 4 6 9x x x

(e) None of these

_____24. If 2x is a factor of a polynomial f x , which of the following statements does not

have to be true?

(a) 2 0f (b) 2 0f

(c) 2 is a root of f x (d) 2 is a zero of f x

_____25. Between what two consecutive whole numbers does 31 lie?

(a) 4 and 5 (b) 6 and 7 (c) 5 and 6 (d) 7 and 8


_____26. Simplify the expression: 45 4 20 2 125b b b

(a) 5b (b) 12 5b (c) 5b (d) 45 4 20 2 125 b

_____27. Multiply and write the product in simplest form: 9 3 8

(a) 9 3 18 2 (b) 3 11 (c) 27 72 (d) 3 3 6 2

_____28. Simplify the expression: 2 516r s

(a) 24rs s (b) 2 44r s s (c) 24 s (d) 2 24rs s

_____29. Simplify the expression: 9

5

147x

x

(a) 27 3x (b) 47 3x (c) 449 3x (d) 2 147x

_____30. Perform the indicated operation: 2

4 8x y

(a) 4 8x y (b) 4 2 8x xy y (c) 4 8 2 8x xy y (d) 4 8x y

_____31. Rationalize the denominator and simplify: 5

5 2 5

(a) 110 1)

9 (b) 1

2 19

(c) 110 1

9 (d) 1

10 111


_____32. Perform the indicated operation: 7

21

n

m n

(a) 7 21

21

mn

m n

(b)

7 7 3

7

mn n

m n

(c)

7 7 3

21

mn n

m n

(d)

7 7 3

21

mn n

m n

_____33. Solve the equation: 3 2 3 2 2x x

(a) 4

15x (b)

8

15x (c)

4

3x (d)

8

3x

_____34. Solve: 3 12 1x x

(a) 4x (b) 2x (c) 2x or 4x (d) 4x or 2x

_____35. Solve: 2 5 9x

(a) 2, 18 (b) 0, 6 (c) 6, (d) no solution

_____36. Write 4

3 38a

in simplest form.

(a) 4

16

a (b) 416a (c)

4

1

16a (d) none of these


_____37. Find the function f whose graph is given below.

(a)

2

1 3

2

x xf x

x

(b)

2 1 3

2

x xf x

x

(c)

3

2 1 3

2

x xf x

x

(d)

2

2 1 3

2

x xf x

x

_____38. If function f is defined by 2

2

4 12

9

x xf x

x

, then at 3x

(a) the graph of f has a vertical asymptote.

(b) the graph of f has a hole on the x -axis.

(c) 0f x

(d) the graph of f has a hole at 3,2

_____39. Which of the following has a slant asymptote?

(a) 5

4 2

1

3 2

xf x

x x

(b)

2

3 2

1

1

xf x

x x

(c) 2

2

4 1x xf x

x

(d)

5

2 1

xf x

x


_____40. Multiply: 2 2

2

3 2

1 3

z z z

z z z

(a) 2 2

3

z z

z

(b)

2

3

z

z

(c)

2 1

3 1

z z

z z

(d)

3

2

z

z z

_____41. If a rational function is defined as the quotient of two polynomial functions, which

of the following is not a rational function?

(a) 1

f xx

(b) 4

8

xf x

x

(c)

3

5

xf x

x

(d)

2

2

1

2 1

xf x

x x

_____42. Find any points of discontinuity for the rational function:

6 2 8

9 7

x x xf x

x x

(a) 6, 2, 8x x x (b) 9. 7x x

(c) 9, 7x x (d) 6, 2, 8x x x

_____43. What are the vertical and horizontal asymptotes of 1

32

f xx

?

(a) VA: 2x ; HA: 3y (b) VA: 2x ; HA: 3y

(c) VA: 2x ; HA: 3y (d) VA: 2x ; HA: 3y


_____44. Simplify: 2 2

2 4

2 3 2

x x

x x x x

(a)

22 6

2 1 1

x x

x x x

(b)

22 2

2 1 1

x x

x x x

(c)

26 2

2 1 1

x x

x x x

(d)

26 6

2 1 1

x x

x x x

_____45. Find the function f whose graph is given below.

(a) 2

2

3 4

xf x

x x

(b) 2

2

3 4

xf x

x x

(c) 2

2

3 4

xf x

x x

(d) 2

2

3 4

xf x

x x

_____46. Which of the following functions has a hole at 1,4 ?

(a)

1

1 5

xf x

x x

(b)

2

1

1

xf x

x

(c) 4

1f x

x

(d)

1 11 1

1 2

x xf x

x x


_____47. Simplify: 3 2 2

2 2

5 6 3 2

4 2 3

x x x x x

x x x

(a) 1 (b) x (c) 2

2

x x

x

(d)

2

x

x

_____48. Which of the following functions has a zero, a vertical asymptote, and a horizontal

asymptote?

(a)

4

4 5

xf x

x x

(b)

2

2

2 1

4 7

x xf x

x x

(c)

2 5

4 5

xf x

x x

(d)

25 8

4

x xf x

x

_____49. Simplify:

2

3

2

2

5 6

3 10

4

x x

xx x

x

(a)

8 3

3 5

x

x

(b)

2 2

5

5 6 3 10

4

x x x x

x

(c)

4 3 2

5 2

x x

x x x

(d)

4 3

5

x

x x

_____50. Write the equation of the parent function 1

f xx

after a translation 3 units to the

left and 5 units down.

(a) 1

53

f xx

(b) 1

53

f xx

(c) 1

53

f xx

(d) 1

53

f xx


_____51. Which of the following functions has a hole, one zero, a slant asymptote, and no

vertical asymptote?

(a)

27 1

7 5

x xf x

x x

(b)

27 1

7 2

x xf x

x x

(c)

3

2

7 4

7 5

x xf x

x x

(d)

7

7 5

xf x

x x

_____52. Use the graph of 4

3

xf x

x

below to solve the inequality

40

3

x

x

.

(a) 4x

(b) 4 3x

(c) 4 3x

(d) no solution

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