Free Printable Practice exam Alg 2

Worksheets

Practice exam Alg 2

Total questions: 40

Worksheet time: 4hrs 46mins

Name

Class

Date

| x + 3 | ≤ 2

No Solution

All Real Numbers

-5 ≤ x ≤ -1

1 ≤ x ≤ 5

3 | 2t - 3 | - 5 > 16

No Solution

All Real Numbers

t < -2 or t > 5

-2 < t < 5

3 | d + 1 | - 7 ≥ -1

No Solution

All Real Numbers

d ≤ -3 or d ≥ 1

-1 < d < 3

What is the equation of the graph below?

f(x) = I x I + 1

f(x) = I x I - 1

f(x) = -I x I + 1

f(x) = -I x I - 1

What is the domain of the absolute value function?

(4, 0)

(0, 4)

(-infinity, infinity)

[4, infinity)

| 2x + 12 | < 8
Which is the correct first step?

2x + 12 < 8 and 2x+12 >-8

2x + 12 < 8 or 2x+12 >-8

2x + 12 < 8 and 2x+12 <-8

2x + 12 < 8 or 2x+12 >-8

|2a - 10| = 6

a = 8, a = 5

a = 2

a = 8

a = 8, a = 2

−2|−2r − 4| = -12

{5,1}

{-5, -1}

{-5, 1}

No Solution

Find the equation of the axis of symmetry and the coordinates of the vertex of the graph y = -x² + 10x - 17.

( x = -5 ); ( -5, -8 )

( x = -5 ); ( -5, 42 )

( x = 5 ); ( 5, 92 )

( x = 5 ); ( 5, 32 )

10.

Find the coordinates of the vertex of the graph y = -2x² - 8. Identify the vertex as a maximum or a minimum.

( -2, -16 ); minimum

( -2, 8 ); maximum

( 2, -16 ); maximum

( 0, -8 ); maximum

11.

Which equation corresponds to the graph shown?

y = x² + 1

y = -x² - 1

y = x²- 1

y = x²

12.

Describe how the graph of the function g(x) = -3x² - 2 is related to the graph of the function f(x) = -3x².

translation of f(x) = -3x² reflected over the x-axis and down 2 units

translation of f(x) = -3x² down 2 units

translation of f(x) = -3x² reflected over the x-axis and up 2 units

translation of f(x) = -3x² up 2 units

13.

Find the value of c that makes x² + 10x + c a perfect square trinomial.

a. -25

b. -5

c. 10

d. 25

14.

Which equation is equivalent to 3x² + 24x + 15 = 0?

a. (x + 7)² = 11

b. (x + 4)² = 1

c. (x + 2)² = -1

d. (x + 2)² = -11

15.

Which is not performed when solving x² + 12x - 6 = 0 by completing the square?

a. Add 6 to each side

b. Factor x² + 12x - 6

c. Add 36 to each side

d. Take the square root of each side

16.

Solve the equation ½x² + 2x + ³/₂ = 0 using the Quadratic Formula. Round to the nearest tenth if necessary.

-3, -1

3, -1

3, 1

17.

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

(3,4)

(-3,4)

(3, -4)

(-3,-4)

18.

What is the range of this function?

All real numbers.

All real numbers greater than or equal to 0.

All real numbers greater than or equal to -2.

All real numbers greater than or equal to 2.

19.

If the graph of a quadratic does not intercept the x-axis at any point, then it has:

1 Real Solution

2 Real Solutions

Half a Solution

No Real Solution

20.

What direction is the following equation opening?
y=-3x²-7x+8

Down

Left

Right

21.

How do you find the vertex?

y = ax² + bx + c

x = -b/(2a) and plug back in for y

x = b/(2a) and plug back in for y

x = -b/a and plug back in for y

x = b/a and plug back in for y

22.

Given the revenue function R(x) = -500x²+8000x+100. How can you find the max revenue?

Find the Vertex, then the max revenue will be the x value of the vertex.

Find the Vertex, then the max revenue will be the y value of the vertex.

The max revenue is the same as the y-intercept

Find the zeros and the larger value is the max revenue.

23.

Add

11 8
-4 2

3 2
-6 -6

-3 2
-4 -6

10 8
-6 2

24.

Find A+B

8 10
8 1

12 25
7 1

10 30
0 1

can't add two together because the rows dont match columns

25.

What are the dimensions of this matrix?

2 x 3

3 x 2

6 x 1

1 x 6

26.

find: B*A

47 30
9 5

17 15
42 35

10 25
7 1

not possible because rows do not match columns

27.

In Matrix R (pictured) what element is in the second row, third column?

9.01

28.

What is the name of each entry in a matrix?

Row

Column

Order

Element

29.

Multiply

20 15 -10
30 -5 0

-20 15 -10
30 -5 0

1 8 3
11 4 5

20 -15 10
-30 5 0

30.

What is the inverse of this matrix?

_{(1/25) (-4/25)}
_{(3/25) (13/25)}

_{(1/5) (-4/5)}
_{(3/5) (13/5)}

_{(6/25) (-2/25)}
_{(2/25) (9/25)}

_{(1/150) (-4/150)}
_{(3/150) (13/150)}

31.

Solve for the determinant of the following matrix:
⌈12 −3⌉
⌊−6 15⌋
*detA= ad-bc

198

162

-333

-9

32.

Are A and B inverses?
A = ⌈3 -10⌉
⌊1 4⌋
B = ⌈2/11 5/11⌉
⌊-1/22 3/22⌋
*AB=I

Yes

33.

Solve for x:

(hint: this notation is determinant)

x = 27

x = 3

x = -3

x = 6

34.

Find the product.

undefined

-3 16 17 12 8 -10

3 12 -15 -8 -1 -3

35.

Solve the system of equations using Cramer's Rule.

$\left(-3,-1\right)$

$\left(-6,6\right)$

$\left(5,-3\right)$

$\left(2,-6\right)$

36.

What are the two linear inequalities graphed here?

y ≤ - x + 4
y < x - 2

y ≤ - x + 4
y > x - 2

y ≤ - 2x + 4
y > 2x - 2

y ≤ - x + 2
y > x - 4

37.

Which points are solutions to the system shown?

(5, 3) (6, -3)

(3, 3) (5, -3)

(-2, 2) (-4, 4)

(1, 2) (1, 5)

38.

There are 15 animals in a barn. These animals are horses and chickens. There are 44 legs in all. Which system of equations represents the situation?

x + y = 15
4x + 2y = 44

4x + 2y = 15
x + y = 44

x = 2y + 44
4x = y + 15

2x - 4y = 44
x - y = 15

39.

Amy sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56. Adam sold 9 packages of sugar cookies and 3 packages of oatmeal cookies for $60. What is the price of 1 pack of sugar cookies and 1 pack of oatmeal cookies?

Sugar Cookies $5
Oatmeal Cookies $3

Sugar Cookies $4
Oatmeal Cookies $8

Sugar Cookies $2
Oatmeal Cookies $6

Sugar Cookies $3
Oatmeal Cookies $6

40.

When you graph the system:
y > -2x + 1
y≤ x + 3
Which of the following is a solution?

(2, 0)

(-1, 2)

(0, 4)

(0, -4)

100 %

Practice exam Alg 2

Total questions: 40

Worksheet time: 4hrs 46mins

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