Free Printable Alg.2 Midterm Review

1.

Select all: Natural Numbers

a)

4.5

b)

5

c)

-2

d)

0

e)

7,652

2.

Select all: Integers

a)

4.2

b)

4

c)

-4.2

d)

4/3

e)

-2

3.

Which of the following is NOT an irrational number?

a)

$\sqrt[]{16}$

b)

5.58703...

c)

$\sqrt[]{96}$

d)

$\pi$

4.

Which of the following is NOT a natural number?

a)

12

b)

3,000

c)

5

d)

0

5.

Pi is an example of which type of number?

a)

Irrational number

b)

Natural number

c)

Unnatural number

d)

Fraction

6.

Classify the following number: 1.01276894...

a)

Rational

b)

Irrational

7.

Classify the Number: 120

a)

Counting, whole, integers rational, real

b)

Irrational, real

c)

whole

d)

Whole, counting

8.

What type of number is $3.\overline{5}$ ?

a)

Integer

b)

Rational Number

c)

Irrational Number

d)

Natural Number

9.

Solve the following: -8 + (15 - 3) ÷ 4

a)

-5

b)

1

c)

-11

d)

11

10.

Simplify: 8 + 5 ∙ 4 + (7 - 3)

a)

32

b)

23

c)

25

d)

12

11.

Simplify: 91 + 27 ÷ (72 ÷ 24)

a)

100

b)

96

c)

90

d)

127

12.

Solve the following: -2 x (3 + 8 ÷ 4)²

a)

-16

b)

1.375

c)

4

d)

-50

13.

Solve for x: 2x + 5 = 12

a)

7

b)

3

c)

3.5

d)

8.5

14.

Solve for x: 4x + 1 = 7x - 5

a)

-1

b)

2

c)

6/11

d)

8

15.

Solve for x: 6(2x + 1) = 18

a)

3

b)

17/12

c)

1

d)

2

16.

Solve for x: 2(3x + 4) + 2 = 4 + 3x

a)

2

b)

-2/3

c)

10

d)

-2

17.

Solve for x: 7 - 2(10x + 1) = 25

a)

2/5

b)

2

c)

1

d)

-1

18.

For the function f(x) = -3(x-1) find f(0).

a)

0

b)

-3

c)

3

d)

-1

19.

What is f(1)?

a)

1

b)

5

c)

0

d)

4

20.

If f(x) = 2x + 1, find f(1).

a)

f(1) = 1

b)

f(1) = 4

c)

f(1) = 0

d)

f(1) = 3

21.

Let w(x) = 3x - 7. If w(x) = 14, find x.

a)

7

b)

35

c)

2.33333

d)

-49

22.

Select THREE TRUE statements

a)

The y-intercept is at (0, -4).

b)

There are three zeros at x = -1, x = 2, x = 4.

c)

The function has one local maximum and an absolute maximum.

d)

The domain is [-1, 4].

e)

The function has four local maximum points.

23.

What is the RANGE of the function?

a)

(−∞, ∞)

b)

(−∞, 0]

c)

[0, ∞)

d)

[−∞, ∞]

24.

Where is the function increasing and decreasing?

a)

Decreasing: (0, ∞)

Increasing: (−∞,0)

b)

Decreasing: (0, −∞)

Increasing: (0, ∞)

c)

Decreasing: (−∞,0)

Increasing: (0, ∞)

d)

Decreasing: (−∞, ∞)

Increasing: none

25.

What are the increasing, decreasing and constant intervals of the function?

a)

Increasing: (-4, ∞)

Decreasing: (-4, 2)

Constant: (2, 2)

b)

increasing: (2, ∞)

Decreasing: (-4, 2)

Constant: (-∞, -4)

c)

Increasing: (2, -4)

Decreasing: (-4, ∞)

Constant: (-∞, -4)

d)

Increasing: (2, -4)

Decreasing: (-2, ∞)

Constant: (-6, -4)

26.

What is the slope-intercept form of a line?

a)

$Ax+By=C$

b)

$y=mx+b$

c)

$y-y_1=m\left(x-x_1\right)$

d)

$y=Ax+By$

27.

Write the equation of this line

a)

y = 2x + 2

b)

y = -2x - 3

c)

y = -x - 3

d)

y = x -3

28.

What is standard form of a line?

a)

y = mx + b

b)

Ax + By = C

c)

y - y1 = m(x - x1)

d)

y = Ax + By

29.

Which equation is written in STANDARD form?

a)

y = 1/2x + 2

b)

y - 3 = -5(x + 2)

c)

7x + 2y = 9

d)

3x + 2 = y

30.

Name the x- and y-intercepts for the equation: 5x - 3y = 15

a)

(3, 0) and (0, -5)

b)

(0, 3) and (-5, 0)

c)

(5, 15) and (15, 3)

d)

(0, -3) and (5, 0)

31.

Write this equation in Standard Form: 13 - 6x - y = 0

a)

-6x - y = -13

b)

13 - 6x = y

c)

6x + y = 13

d)

y = -6x + 13

32.

Write x + 5y = 10 in slope-intercept form.

a)

$y=-5x\ +\ 2$

b)

$y\ =\ -\frac{1}{5}x\ +\ 5$

c)

$y\ =\ 5x\ +\ 2$

d)

$y\ =\ -\frac{1}{5}x\ +\ 2$

33.

Write -2x - 3y = 12 in slope-intercept form.

a)

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

b)

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

c)

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

d)

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

34.

How would you write the equation with a slope of 2/3 and a y-intercept of -3

a)

y = 3/2x + 3

b)

y = 2/3 - 3

c)

y = 2/3x - 3

d)

y = 2/3x + 3

35.

In slope-intercept form, write the equation of the line passing through the points (-3, 4) and (-4, 2).

a)

y = -2x + 10

b)

y = -2x - 10

c)

y = 2x - 10

d)

y = 2x + 10

36.

Write the equation of the line passes through the point (2,1) and has a slope = 4.

a)

y = 3x - 2

b)

y = 4x - 7

c)

y = 4x + 7

d)

y = 3x + 3

37.

Given the equation, 3x - 2y = -10, identify the slope and the y-intercept.

a)

slope: -3, y-intercept: -10

b)

slope: -2/3, y-intercept: -5

c)

slope: 3/2, y-intercept: 5

d)

slope: -3/2, y-intercept: 5

38.

y = -2/3x + 2 and y = 3/2x + 9. These lines are...

a)

Parallel

b)

Perpendicular

c)

Neither

39.

Are the given lines parallel, perpendicular, or neither?

$y=\frac{1}{2}x+2$ and $y=\frac{1}{2}x-4$

a)

Parallel

b)

Perpendicular

c)

Neither

40.

Write an equation of a line that passes through the point (-9,2) and is perpendicular to the line y = 3x - 12

a)

y = (-1/3)x - 1

b)

y = (1/3)x - 2

c)

y = -3x + 12

d)

y = 3x - 1

41.

What is the solution to this system?

a)

(1, -1)

b)

(-1, 1)

c)

(0, -2)

d)

(2, 0)

42.

The solution (x, y) to a system of equations is the point where they...?

a)

Run off the graph

b)

Don't touch

c)

Intersect

d)

Exist

43.

If a system of linear equations has infinitely many solutions, what does this mean about the two lines?

a)

Intersecting lines

b)

Same line

c)

Parallel lines

44.

Solve the system of equations

a)

Infinite solutions

b)

(2, -2)

c)

(1, 0)

d)

(3, -4)

45.

Solve:

y = -1x - 5

4x - 8y = 4

a)

(-3, -2)

b)

(5, -7)

c)

(3, 9)

d)

(-5, 4)

46.

Solve:

y = 8x + 1

y = 6x + 3

a)

(1, 9)

b)

(4, 14)

c)

(0, 1)

d)

(2, 4)

47.

How many solutions does this system of equations have?

a)

One Solution

b)

No solution

c)

Infinitely Many Solutions

d)

Two Solutions

48.

Solve:

3x + 7y = 23

-3x - 7y = -17

a)

No solution

b)

ARN

c)

(-3, 3)

d)

(3, 3)

49.

Let's multiply the top equation by -2. What would be our new equation?

2x + 3y = 12

4x - 7y = - 54

a)

4x - 6y = -24

b)

-4x - 6y = 12

c)

-4x - 6y = 24

d)

-4x - 6y = -24

50.

Solve by elimination:
-2x + 6y = 16
-4x - 3y = 2

a)

(2, 2)

b)

(-2, -2)

c)

(-2, 2)

d)

(2, 1)

51.

Is (-2,4) a solution to the system?

a)

Solution

b)

Not a solution

52.

Which of the following is NOT a solution to this system of inequalities?

a)

(0, -1)

b)

(0, 3)

c)

(4, 0)

d)

(6, -2)

53.

Which system of inequalities matches the graph?

a)

y > 2x - 4
y < 2

b)

y < 2x - 4
y < 2

c)

y > 2x - 4
y < 2

d)

y < 2x - 4
y < -2

54.

Which system of linear inequalities is represented by the graph?

a)

y ≤ 2x - 1

y > -2x + 3

b)

y > 2x - 1

y ≤ -2x + 3

c)

y < 2x - 1

y ≥ -2x + 3

d)

y ≤ 2x - 1

y > 2x + 3

55.

Solve the system.

a)

(5, -6, 3)

b)

(2, 3, -1)

c)

(-4, 2, 5)

d)

No Solution

56.

Solve the system of equations to find the value of z.

a)

4

b)

-4

c)

2

d)

-2

57.

Given the equation for this parabola: $y=-(x-4)^2-3,$ does this parabola have a maximum or minimum value?

a)

Maximum

b)

Minimum

58.

Given the equation for this parabola: $y=-(x-4)^2-3,$

what are the coordinates of the vertex?

a)

(4, 3)

b)

(4, -3)

c)

(0, -3)

59.

What is the y-intercept of this quadratic equation? $y=2(x-2)^2-2$

a)

(0, 6)

b)

(6, 0)

c)

(2, -2)

d)

(-2, 2)

60.

What is the axis symmetry of this quadratic equation?

$y=2(x-2)^2-2$

a)

x = 2

b)

x = -2

c)

y = 2

d)

y = -2

61.

What is the axis of symmetry? $f(x)=x^2-8x+15.$

a)

x = -4

b)

x = 4

c)

y = 4

d)

y = -4

62.

What is the y-intercept? $f(x)=-x^2-4x+12.$

a)

(12, 0)

b)

(0, 12)

c)

(-2, 16)

d)

(2, 0)

63.

Name the x-intercept(s)?

a)

(0, 0)

b)

(2, 4)

c)

(0, 0) and (0, 4)

d)

(0, 0) and (4, 0)

64.

What is the vertex of the graph?

a)

(2, 4)

b)

(3, -1)

c)

(0, 8)

d)

(4, 2)

65.

What is the axis of symmetry? f(x) = x²- 8x + 15.

a)

x = -4

b)

x = 4

c)

y = 4

d)

y = -4

66.

What is the vertex? f(x) = -x²- 4x + 12.

a)

(-2, 16)

b)

(2, 0)

c)

(2, 4)

d)

(-2, 4)

67.

Which equation has a vertex of (-3, 4)?

a)

y = 2(x + 3)²+ 4

b)

y = (x + 3)² - 4

c)

y = (x - 3)² + 4

d)

y = 2(x - 3)² + 4

68.

Maximum or Minimum? $y=2\left(x-3\right)^2+6$

a)

Max = -3

b)

Min = 3

c)

Min = 6

d)

Max = 6

69.

What is the x-intercepts of the parabola? y = -3(x + 5)(x - 9)

a)

(-5, 0) and (9, 0)

b)

(5, 0) and (-9, 0)

c)

(5, 0) and (9, 0)

d)

(-3, 0) and (5, 0)and (-9, 0)

70.

What is the quadratic function for the graph in intercept form?

a)

y = (x - 2)(x - 6)

b)

y = - (x - 2)(x - 6)

c)

y = (x + 2)(x + 6)

d)

y = (x + 4)(x - 4)

71.

Determine the vertex of j(x) = (x - 8)(x + 3)

a)

(-8, 3)

b)

(8, -3)

c)

(2.5, -30.25)

d)

(5, -24)

72.

Convert to Vertex Form: f(x) = x² + 8x + 14

a)

f(x) = (x - 4)² + 2

b)

f(x) = (x - 4)² - 2

c)

f(x) = (x + 4)² + 2

d)

f(x) = (x + 4)² - 2

73.

Convert to standard form: $y=\left(x+5\right)^2-15$

a)

$y=x^2+10$

b)

$y=x^2+10x\ +10$

c)

$y=x^2+25$

d)

$y=x^2+10x+25$

74.

Convert to standard form: $y=-2\left(x-3\right)^2+6$

a)

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

b)

$y=-2x^2+6x+15$

c)

$y=-2x^2+12x-18$

d)

$y\ =\ -2x^2-12$

75.

Convert to vertex form: $y=x^2-12x+30$

a)

$y=\left(x-6\right)^2+6$

b)

$y=\left(x+6\right)^2-36$

c)

$y=\left(x-6\right)^2$

d)

$y=\left(x-6\right)^2-6$

Alg.2 Midterm Review

Total questions: 75

Worksheet time: 1hrs 15mins

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