Free Printable Semester 1 Practice Final

1.

For the graph shown, the domain is

a)

$\left(-\infty,\ +\infty\right)$

b)

$x>0$

c)

$y\ge1$

d)

$\left(0,+\infty\right)$

2.

The interval $4\le x<10$ can be written in interval notation as

a)

$\left[4,\ 10\right]$

b)

$\left[4,\ 10\right)$

c)

$\left(4,\ 10\right)$

d)

$\left(4,\ 10\right]$

3.

How is the graph of $g\left(x\right)=x^2-5\$ transformed as compared to $f\left(x\right)=x^2$ ?

a)

$g\left(x\right)$ is moved

right 5 units

b)

$g\left(x\right)$ is moved

down 5 units

c)

$g\left(x\right)$ is moved

left 5 units

d)

$g\left(x\right)$ is moved

up 5 units

4.

Which equation shows a transformation to $f\left(x\right)=x^3$ of 2 units right, 4 units down, and a reflection over the x-axis?

a)

$g\left(x\right)=\left(x+2\right)^3+4$

b)

$g\left(x\right)=-\left(x+2\right)^3-4$

c)

$g\left(x\right)=-\left(x-2\right)^3-4$

d)

$g\left(x\right)=-\left(x-2\right)^3+4$

5.

Which table is the inverse of the function in the given table

a)

b)

c)

d)

6.

What is the inverse of the function
$f\left(x\right)=2x+4$ ?

a)

$f^{-1}\left(x\right)=4\left(x-2\right)$

b)

$f^{-1}\left(x\right)=\frac{x-4}{2}$

c)

$f^{-1}\left(x\right)=\frac{x}{2}-4$

d)

$f^{-1}\left(x\right)=\frac{x}{4}+2$

7.

What is the vertex of the graph of

g\left(x\right)=-2\left|x+3\right|-4

a)

$\left(-4,\ -3\right)$

b)

$\left(-2,\ -4\right)$

c)

$\left(3,\ -4\right)$

d)

$\left(-3,\ -4\right)$

8.

Consider the graph of: $g\left(x\right)=5\left|x-6\right|+4$ Which is NOT a transformation as compared to the graph of $f\left(x\right)=\left|x\right|$ ?

a)

reflected over the x-axis

b)

translated 6 units to the right

c)

translated 4 units up

d)

vertically stretched by a factor of 5

9.

solve the quadratic equation.

2x^{2\ }-7=81

a)

$\pm\sqrt{2}$

b)

$\pm\sqrt{88}$

c)

$\pm2\sqrt{11}$

d)

$\pm11\sqrt{2}$

10.

Solve the quadratic equation.

5x^2-2=-6

a)

$\pm\frac{2}{5}i$

b)

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

c)

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

d)

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

11.

Which of the following answer choices is an imaginary number?

a)

$i^2$

b)

$\left(i\sqrt{2}\right)^2$

c)

$\left(\sqrt{-3}\right)\left(\sqrt{-3}\right)$

d)

$\left(i\right)\left(i\right)\left(i\right)$

12.

Subtract complex numbers.

\left(-1-i\right)-\left(-3+6i\right)

a)

$2-7i$

b)

$-4+5i$

c)

$2+5i$

d)

$-4-7i$

13.

What is the equation of the graph shown here, written in $f\left(x\right)=a\left(x-h\right)^3+k$ form?

a)

$f\left(x\right)=1.2\left(x+3\right)^3+2$

b)

$f\left(x\right)=-0.8\left(x-3\right)^3+2$

c)

$f\left(x\right)=0.8\left(x-3\right)^3+2$

d)

$f\left(x\right)=0.8\left(x+3\right)^3+2$

14.

Find the sum.

(2x² + 5x - 7) + ( 3 - 4x² + 6x)

a)

2x²+ 3x +1

b)

-2x²- 11x - 4

c)

2x²+ 5x - 7

d)

-2x² + 11x - 4

15.

Find the difference.

(3 - 2x + 2x²) - (4x - 5 +3x²)

a)

x² + 6x + 8

b)

2x²+ 5x - 7

c)

-x²-6x + 8

d)

-2x² + 11x - 4

16.

Multiply and simplify:
$\left(3x^2-4x+2\right)\left(2x^2+3x-5\right)$

a)

$6x^4+17x^3+31x^2+26x-10$

b)

$6x^4+x^3-23x^2+26x-10$

c)

$6x^2-x-10$

d)

none of these

17.

What is the proper way to write the answer for the following problem?

a)

2x³-x²-25x+12

b)

2x⁴-x³-25x²-12x+0

c)

2x³-x²-25x-12

d)

2x⁴-x³-25x²-12x-0

18.

Cam divided (x⁴ + 3x² - 4x - 2) by factor of (x-2) using synthetic division. His work is shown above. Which best describes his mistake?

a)

Cam wrote the remainder incorrectly.

b)

Cam did not use a zero place holder for the x³ term.

c)

Cam added instead of subtracting the rows.

d)

Cam should have used -2 as his division since the factor was x-2.

19.

For synthetic division, what would be the number in the left hand box?

a)

0

b)

1

c)

2

d)

3

20.

Is this division problem worked correctly?

a)

This is correct!

b)

This is incorrect!

21.

Is (x-2) a factor of f(x)= x³-8x²+14x-4?

a)

Yes, (x-2) is a factor. There is a remainder.

b)

No, (x-2) is not a factor. The remainder is zero.

c)

Yes, (x-2) is a factor. The remainder is zero.

d)

No, (x-2) is not a factor. There is a remainder.

22.

Solve
x² + 2x - 24 = 0

a)

x = -6, x = 4

b)

x = 6, x = -4

c)

x = 12, x = -2

d)

x = 8, x = -3

23.

Solve
x² + 9x + 20 = 0

a)

x = -2, x = -10

b)

x = -3, x = -4

c)

x = -4, x = -5

d)

x = -4, x = -6

24.

What are the zeros to the equation

x² - 2x = 8?

a)

x = 2 or x = -4

b)

x = 1 or x = -8

c)

x = 4 or x = -2

d)

x = 8 or x = -1

25.

What is the equation of the graph shown here?

a)

$f\left(x\right)=\left|x+3\right|-2$

b)

$f\left(x\right)=2\left|x+3\right|-2$

c)

$f\left(x\right)=2\left|x-3\right|-2$

d)

$f\left(x\right)=\left|x-3\right|+2$

26.

Solve: $2\left|x+1\right|-5=3$

a)

$x=4,\ 8$

b)

$x=4,\ -4$

c)

$x=5,\ -3$

d)

$x=3,\ -5$

27.

If the graph of f(x) goes through (1, 4) and (4, 6), what points does f^-1(x) go through?

a)

(1, 4) and (4, 6)

b)

(-4, -1) and (-6, -4)

c)

(-1, -4) and (-4, -6)

d)

(4, 1) and (6, 4)

28.

What is the inverse of the function
$g\left(x\right)=\frac{7x+18}{2}$ ?

a)

$g^{-1}\left(x\right)=\frac{2}{7}x-18$

b)

$g^{-1}\left(x\right)=\frac{2}{7}x+18$

c)

$g^{-1}\left(x\right)=\frac{2}{7}x-\frac{18}{7}$

d)

$g^{-1}\left(x\right)=\frac{7}{2}x-9$

29.

Find the vertex y = x² - 2x - 5

a)

V(-2, 10)

b)

V(-1, 15)

c)

V(1, -6)

d)

V(1, -12)

30.

Does this graph have a maximum or minimum?

a)

Minimum

b)

Maximum

31.

What is the green dashed line called?

a)

roots or x-intercepts

b)

parabola

c)

axis of symmetry

d)

line of dashes

32.

What is the axis of symmetry for this graph?

a)

y=2

b)

x=2

c)

x=0

d)

y=0

33.

Which of these are like terms in the following expression:
3x + 7 - 9x + 24y + 2x²

a)

7, 24y

b)

3x, 9x

c)

3x, -9x

d)

3x, -9x, 2x²

34.

3+√-4

a)

1

b)

3-2i

c)

5

d)

3+2i

35.

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

a)

58 - 45i

b)

58 - 15i

c)

-38 - 15i

d)

-38 + 45i

36.

(1-3i)(2+5i)

a)

22-i

b)

16-i

c)

17-i

37.

(2i)(3i)

a)

5i

b)

-5

c)

6i

d)

-6

38.

The following quadratic has how many zeros?

a)

0

b)

1

c)

2

d)

3

39.

What is the value of the discriminant for the following function?

f\left(x\right)=3x^2-5x-6

a)

72

b)

-47

c)

25

d)

6.86

40.

What are the zeros?

a)

x= 0 and x= -4

b)

x= 0 and x= 4

c)

y= 0

d)

x= 2

41.

Which is a zero of the graph?

a)

0

b)

-1

c)

1.5

d)

-3

42.

The x-intercepts of a quadratic equation are known as the _____.

a)

vertices

b)

squares

c)

zeros

d)

formulas

43.

Factor x² - 9

a)

(x + 3)(x - 3)

b)

(x + 4)(x - 4)

44.

Factor x² - 25

a)

(x - 4)(x + 4)

b)

(x - 5)(x + 5)

45.

If you were dividing x⁶ + 4x³ + 2, how many 0's would you need when setting up the top row of your synthetic division?

a)

0

b)

2

c)

4

d)

6

46.

What is the quotient?

a)

x - 7

b)

x²- 7

c)

x + 7

d)

x²+ 3x - 54

47.

What is the proper way to write the answer for the following problem?

a)

2x³-x²-25x+12

b)

2x⁴-x³-25x²-12x+0

c)

2x³-x²-25x-12

d)

2x⁴-x³-25x²-12x-0

48.

Divide using synthetic division
(2x³ + 4x² - 5) by (x + 3).

a)

2x² + 2x - 4 R(-12)

b)

2x² - 2x + 6 R(-23)

c)

2x² - 2x + 8 R(-20)

d)

2x² - 4x + 1 R0

49.

What is the remainder when x⁴ - 5 is divided by x + 3?

a)

76

b)

81

c)

7

50.

What is the remainder of (x³ - 5x² - 8x +1) ÷ (x + 1)?

a)

-13

b)

1

c)

3

51.

a)

F

b)

G

c)

H

d)

J

52.

What is the Range of this linear function?

a)

-6 ≤ y ≤ 6

b)

0 ≤ y ≤ 6

c)

No Solution

d)

4 ≤ y ≤ 3

53.

What is the Domain of this linear function?

a)

-6 ≤ x ≤ 6

b)

0 ≤ x ≤ 7

c)

2 ≤ x ≤ 7

d)

No Solution

54.

What is the DOMAIN?

a)

x ≤ 2

b)

x ≥ 2

c)

All Real Numbers

d)

-2 ≤ x ≤ 2

55.

What is the RANGE?

a)

y ≤ 2

b)

y ≥ 2

c)

All Real Numbers

d)

-2 ≤ y ≤ 2

56.

A student worked out at a gym continuously for 50 minutes. The graph shows the remaining percentage of the workout as a linear function of x, the time in minutes.

Which answer choice best describes the domain and range of the function for this situation?

a)

Domain: all real numbers greater than or equal to 0 and less than or equal to 100.

Range: all real numbers greater than or equal to 0 and less than or equal to 50.

b)

Domain: {-2}

Range: {100}

c)

Domain: all real numbers greater than or equal to 0 and less than or equal to 50.

Range: all real numbers greater than or equal to 0 and less than or equal to 100.

d)

Domain: {100}

Range: {-2}

57.

The total cost in dollars, c, to purchase video games online can be found using the function c = 16.95x + 4.75, where x is the number of video games purchased. If at least 4 games but no more than 7 games are purchased online, what is the range of the function for this situation?

a)

{4, 5, 6, 7}

b)

4 ≤ x ≤ 7

c)

72.55 ≤ c ≤ 123.50

d)

{72.55, 89.50, 106.45, 123.40}

58.

What is the domain?

a)

(-3 , 3)

b)

[-4, 5]

c)

(-4, 5)

d)

(-3, 3]

Semester 1 Practice Final

Total questions: 58

Worksheet time: 3hrs 44mins

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