Free Printable Alg2 Hon Fall Exam Review

1.

Evaluate for g=-3 and h=2 for: $g^2-3\left|-2g-h^3\right|$

a)

3

b)

12

c)

24

d)

5

2.

Find the slope of the line that goes through the points (-8,6) and (7,-3).

a)

1/3

b)

-1/3

c)

-3/5

d)

-5/3

3.

Find the slope of the line and write the equation for this line.

a)

Undefined, y=-1

b)

0, y=-1

c)

1, x=-1

d)

-1, x=-1

4.

What is the equation of a line that is perpendicular to the given line and goes through (3, -4)?

y = 3x + 2

a)

y = 3x - 2

b)

y = -1/3x - 5

c)

y = 3x - 4

d)

y = -1/3x - 3

5.

What is the vertex equation for this parabola?

a)

y = 2(x - 2)² + 5

b)

y = -(x + 2)² + 4

c)

y = -(x - 2)² + 4

d)

y = (x + 2)² + 4

6.

What is the maximum/minimum of a parabola called?

a)

vertex

b)

point

c)

top

d)

bottom

7.

What is the vertex of the parabola: y=2(x-3)²+4

a)

(3,4)

b)

(-3,4)

c)

(3, -4)

d)

(-3,-4)

8.

What is the vertex form equation of this graph?

a)

f(x) = 8(x -5)² + 1

b)

f(x) = (x - 1)² - 5

c)

f(x) =1/8 (x + 1)² - 5

d)

f(x) = (x + 5)² +1

9.

Identify the vertex, whether the graph opens up or down, and is wide or narrow.

a)

(5, 2); opens up; wide

b)

(5, 2); opens down; narrow

c)

(-5, 2); opens up; wide

d)

(-5, 2); opens down; narrow

10.

Which of the following is a difference of squares?

a)

x² - 18

b)

4x² + 36

c)

9x² - 100

d)

x² + 4

11.

What are the factors of
25x² - 81?

a)

(5x - 9)(5x + 9)

b)

(5x - 9)(5x - 9)

c)

(5x + 9)(5x + 9)

d)

Cannot be factored

12.

Factor completely.
k² -2k - 24

a)

(k+4)(k-6)

b)

(k+4)(k+6)

c)

(k+6)(k-1)

d)

(k-4)(k+6)

13.

Solve for x:

6x²- 9x = -2x+3

There may be more than one solution.

a)

x= 3/2

b)

x = -1

c)

x= 1/6

d)

x = -1/3

14.

What should you do first to solve this equation using quadratic formula?

x² + 6x - 13 = 3

a)

Get factored form

b)

Write down: a=1, b=6, c=-13

c)

Make it equal 0 by subtracting 3 on each side

d)

Type it all in a calculator.

15.

Find the value of the discriminant and describe the number and nature of the zeros for

$y=-x^2-5x+12$

a)

23, 2 Real Zeros

b)

-23, 2 Complex Zeros

c)

73, 2 Real Zeros

d)

-73, 2 Complex Zeros

16.

Use the quadratic formula to find the solutions for
$y=-x^2-5x+12$

a)

No Real Solution

b)

$\frac{-5\pm\sqrt{73}}{2}$

c)

$\frac{5\pm\sqrt{73}}{2}$

d)

$\frac{-5\pm i\sqrt{23}}{2}$

17.

Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = 3x³ + 2x² - 6x + 7

a)

±1, ±7, ±1/3, ±7/3

b)

±1, 7

c)

±1, ±3, ±7, ±7/3

d)

±1, ±3, ±7, ±1/3, ±7/3

18.

Is this division problem worked correctly?

a)

This is correct!

b)

This is incorrect!

c)

Just the remainder is incorrect

19.

a)

y = ^_(x + 2)(x - 1)²

b)

y = -(x - 2)(x + 1)²

c)

y = (x - 2)(x + 1)²

d)

y = -x³

20.

Does this graph have an absolute max or relative max? If so, find it.

a)

Absolute max = ∞

b)

Relative Max = 4

c)

Absolute Max = 4

d)

Relative Max @ 1

21.

3 | d + 1 | - 7 ≥ -1

a)

No Solution

b)

All Real Numbers

c)

d ≤ -3 or d ≥ 1

d)

-1 < d < 3

22.

Solve | 2x - 1 | = -4

a)

x = ¹/₂ and x = -4

b)

No Solution

c)

x = ^-3/₂ and x = ⁵/₂

d)

x = ³/₂ and x = ^-5/₂

23.

Which function defines the graph?

a)

f(x) = |x - 4| + 3

b)

f(x) = |x - 3| + 4

c)

f(x) = |-x + 4| + 3

d)

f(x) = |x + 4| + 3

24.

Simplify
3(xy⁴)³

a)

3xy⁷

b)

3x³y⁷

c)

3x³y¹²

d)

27x³y¹²

25.

a)

2xy²z

b)

-2y²z

c)

(2xy²)/z

d)

(2y²)/(3z)

26.

Which of the following lines is PARALLEL to the graph of y = -6x + 3 and goes through the point (-1,4)?

a)

y=1/6x +25/6

b)

y = 1/6x + 4

c)

y = -6x - 2

d)

y = -6x + 4

27.

Solve the system.

a)

(-2, -3)

b)

(-2, 3)

c)

(2, -3)

d)

(2, 3)

28.

Solve the system using your calculator.

a)

(2, -2, 3)

b)

(2, 1, 4)

c)

(-2, 2, -3)

d)

No Solution

29.

Simplify:
(10+ 15i) - (48 - 30i)

a)

58 - 45i

b)

58 - 15i

c)

-38 - 15i

d)

-38 + 45i

30.

-1(2x + 4) ≥ 6

a)

x ≤ -5

b)

x ≥ -5

c)

x ≤ -1

d)

x ≥ -1

31.

From the equation y = 3x + 18, what is the value of the x-intercept?

a)

-6

b)

6

c)

18

d)

3

32.

Find the slope.

a)

-1/7

b)

1/7

c)

-7

d)

7

33.

What is the range of the graph?

a)

(-∞,∞)

b)

[0,∞)

c)

(0,5)

d)

[-1,∞)

34.

What is the domain for this graph?

a)

(-3 , 3)

b)

[-4, 5]

c)

(-4, 5)

d)

(-3, 3]

35.

What is the equation in factored form of this graph?

a)

f(x) = (x-4)(x-1)²(x+2)(x+4)

b)

f(x) = (x-4)(x+1)²(x+2)(x+4)

c)

f(x) = (x-4)(x-1)²(x-2)(x+4)

d)

f(x) = (x+4)(x+1)²(x-2)(x-4)

36.

Factor 8x³-27

a)

(2x-3)(4x²+6x+9)

b)

(2x+3)(4x²-6x+9)

c)

(x-3)(2x²+3x-9)

d)

(x+3)(2x²-6x+9)

37.

Find all zeros. You may use your calculator.

y = x⁴ - 3x³+ 4x²- 8

a)

$1,-2,\ 1\pm\sqrt{3}$

b)

$-1,\ 2,\ 1\pm i\sqrt{3}$

c)

$1,-2,\ \frac{2\pm i\sqrt{5}}{2}$

d)

$-1,\ 2,\ \frac{2\pm\sqrt{5}}{2}$

38.

Solve by quadratic formula 8x²- 6x -1= 0

a)

$\frac{3\pm i}{8}$

b)

$\frac{6\pm\sqrt{68}}{16}$

c)

$\frac{-3\pm i}{8}$

d)

$\frac{3\pm\sqrt{17}}{8}$

39.

Is the leading coefficient positive or negative

a)

positive

b)

negative

40.

What is the domain of this function?

a)

(-∞,-1]U(1, 3)

b)

(-∞, 5)

c)

(-∞, ∞)

d)

(-∞,-1]U(1,∞)

41.

What is the range of this function?

a)

(-∞,∞)

b)

(-∞, 5)

c)

(-∞, 1] U (3, ∞)

d)

(-∞, 0] U (3, 5)

42.

Is this a graph of a function?

(a)

43.

Is this function even or odd degree?

a)

even

b)

odd

44.

Describe the end behavior for this graph?

As x→-∞, _.

a)

f(x)→+∞

b)

f(x)→-∞

45.

Simplify:
(7 + 2i)(9 - 6i)

a)

75-24i

b)

63 - 24i - 12i²

c)

51 - 24i

d)

58 + 60i

46.

If f(x)=x⁵-2x³-33x-5,
find f(-3).

a)

x⁴-3x³+7x²-21x+30

b)

49

c)

0

d)

-95

47.

You have a total of 17 coins. All of your coins are nickels and dimes. The total value of the coins is $1.35. Which system of equations represents this situation?

a)

n+d=17
.05n+.10d=1.35

b)

.05n+.10d=17
n+d=1.35

c)

.25n+.10d=1.35
n+d=17

48.

Determine which of the following is the set up for solving the given problem:

While exploring a haunted mansion, Shaggy and Scooby saw a ghost and bolted down the road at 15 mph. Fred hopped in his van to catch up to them but had some car trouble, so he started driving down the road 20 minutes after Shaggy and Scooby left. If Fred drives after them at an average of 35 mph, how long will it take for him to catch up?

a)

$15t=35\left(t-\frac{1}{3}\right)$

b)

$15\left(t+\frac{1}{4}\right)=35t$

c)

$15t=35\left(t+\frac{1}{3}\right)$

d)

$15t=35t$

49.

What amount of 20% salt solution should be mixed with a 8% salt solution to make 500 ml of a 15% salt solution?

a)

291.7 ml

b)

208.3 ml

c)

216.9 ml

d)

242.8 ml

50.

Rachel owns a car and a moped. She has at most 12 gallons of gas to be used between the car and the moped. The car's tank holds at most 10 gallons and the moped's 3 gallons. The mileage for the car is 20 mpg and for the moped is 100 mpg.
What are the constraints?

a)

x≤10, y≤3, x+y≤12

b)

0≤x≤10, 0≤y≤3, x+y≤12

c)

x≥0, y≥0, 10x+3y≤12

d)

x≤10, y≤3, 10x+3y≤12

51.

Tom Sawyer is paddling up the mighty Mississippi. He can travel 3mi in 6 hours upstream and 4 miles in 4 hours downstream. What is his paddling speed in still water?

a)

1/2 mph

b)

3/4 mph

c)

1 mph

d)

1.5 mph

52.

A goalie kicks a soccer ball upward. The quadratic function h(t) = -16t²+ 65t + 1 represents the height of the ball h in feet after t seconds. What is the maximum height of the ball?

a)

y-intercept

b)

x-value of the vertex

c)

y-value of the vertex

d)

Zeros/roots/solutions/x-intercepts of the function.

53.

A goalie kicks a soccer ball upward. The quadratic function h(t) = -16t²+ 65t + 1 represents the height of the ball h in feet after t seconds. How high off the ground did the goalie contact the ball to kick it?

a)

y-intercept

b)

x-value of the vertex

c)

y-value of the vertex

d)

Zeros/roots/solutions/x-intercepts of the function.

54.

The height of a golf ball in the air can be modeled by the equation h(t) = -16t²+ 76t, where h(t) represents the height in feet after t seconds. When will the ball hit the ground?

a)

y-intercept

b)

x-value of the vertex

c)

y-value of the vertex

d)

Zeros/roots/solutions/x-intercepts of the function.

55.

Which is the graph of y= -x + 2?

a)

A

b)

B

c)

C

d)

D

56.

Solve:

2x² + 5x ≥ 12

a)

[-4, 1.5]

b)

(−∞, -4) U (1.5, ∞)

c)

(−∞, -4] U [1.5, ∞)

d)

All real numbers

57.

What is the Binomial expansion of (x + 1)⁵ ?

a)

x⁵ + 5x⁴ + 10x³ + 10x² + 5x + 1

b)

x⁵ + 5x⁴ + 15x³ + 15x² + 5x + 1

c)

x⁵ + 6x⁴ + 15x³ + 15x² + 6x + 1

d)

x⁵ + 1

58.

What is row 5 of Pascal's Triangle?

a)

1, 2, 1

b)

1, 3, 3, 1

c)

1, 5, 10, 5, 1

d)

1, 5, 10, 10, 5, 1

59.

Find the 2nd term in the expansion of
(2b + 1)³

a)

12b²

b)

6b

c)

8b³

d)

4b²

60.

Solve:

- x²+ 3x> 0 , then find the interval notation of the inequality.

a)

(−∞, 0) U (3, ∞)

b)

(−∞, - 3) U (0, ∞)

c)

(-3, 0)

d)

(0, 3)

61.

Given the following rational roots, write the standard form equation for the polynomial.

-2 and 3i

a)

y=x³+2x²+9x+18

b)

y=x³-2x²+9x-18

c)

y=(x+2)(x-3i)(x+3i)

d)

y=(x-2)(x+3i)

62.

Which of following is a linear equation?

a)

$y=3x^2-4$

b)

$\sqrt[]{x}=5y+1$

c)

$\frac{4}{y}=2x-3$

d)

$2x-3y=0$

Alg2 Hon Fall Exam Review

Total questions: 62

Worksheet time: 5hrs 45mins

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