Free Printable Finals: STUDY GUIDE

1.

What is a function?

a)

Has inputs and outputs

b)

Every input has only ONE output

c)

Inputs have different outputs every time

d)

x-values and y-values

2.

What are all the y values or outputs called?

a)

Domain

b)

Range

c)

Relation

d)

Function

3.

What are all the x values or inputs called?

a)

Domain

b)

Range

c)

Relation

d)

Function

4.

Which is NOT the same

a)

Range

b)

Input

c)

Dependent Value

d)

Y-Value

5.

What is the domain of the graph?

a)

1≤ x ≤ 4

b)

1 < x < 4

c)

1≤ y ≤ 4

d)

1 < y < 4

6.

What is the domain? An open circle means it DOES NOT equal that number - use < and >. Only use ≤ and ≥ with a closed circle.

a)

-4 < x ≤ 5

b)

-4 ≤ x < 5

c)

-3 < y < 3

d)

-3 ≤ y ≤ 3

7.

Arcadia Inc. manufactures videogames. This is a graph showing the profit, in thousands of dollars, made by the company over the first six months of the year. Which statement about the company's profits is incorrect?

a)

The profits increased from January to February.

b)

The largest profit for the six-month period was $275,000.

c)

The profit decreased from April to June.

d)

The smallest profit for the six-month period was $150,000.

8.

Match the story that best describes the graph.

a)

It snowed heavily at first then slowed down.

b)

It snowed lightly at first, then heavily, and then it stopped.

c)

It snowed lightly for a while, stopped for a while, snowed heavily, and then stopped.

9.

8. Compare the quantity in Column A with the quantity in Column B.

a)

The quantity in Column A is greater.

b)

The quantity in Column B is greater.

c)

The two quantities are equal.

d)

The relationship cannot be determined on the basis of the information supplied.

10.

Compare the quantity in Column A with the quantity in Column B.

a)

The quantity in Column A is greater.

b)

The quantity in Column B is greater.

c)

The two quantities are equal.

d)

The relationship cannot be determined on the basis of the information supplied.

11.

Apply function notation in problem-solving: If f(x) = 4x - 1 and g(x) = 2x + 3, find f(3) + g(2).

a)

15

b)

10

c)

7

d)

20

12.

Using the pictured graph, what is f(-3)?

a)

-3

b)

-1

c)

1

d)

3

13.

Determine f(3)

a)

Undefined

b)

1

c)

2

d)

3

14.

Given f(x) = 3x + 10
and g(x) = x - 2
Find f(g(5))

a)

19

b)

23

c)

-10

d)

None of these.

15.

f(x) = 3x + 10
g(x) = x - 2
Find (f∘g)(0)

a)

16

b)

4

c)

-4

d)

None of these.

16.

Determine the slope and y-intercept from the following equation: y = 3/2x + 3

a)

slope: 5 y-intercept: (0,3)

b)

slope: 3/2 y-intercept: (0,3)

c)

slope: 4 y-intercept: (0,3/2)

d)

slope: 1/5 y-intercept: (0,5)

17.

Bob has $150 in his savings account and saves $40 per month. Which function models his savings?

a)

y = 150 + 40

b)

y = 40x + 150

c)

y = 150x + 40

18.

Which statement is TRUE?

a)

A vertical line has a slope of zero.

b)

A line that contains points in Quadrant I and Quadrant III must have a negative slope.

c)

A line that rises as you move to the right along the line has a positive slope.

d)

A horizontal line has no slope.

19.

Which of the following is NOT a function?

a)

y = 4

b)

x = 3

c)

y=2x

d)

y=x

20.

Which of the following is the Point-Slope Form given the point (c, d) and the slope m?

a)

$y-d=m\left(x-c\right)$

b)

$y=mx+b$

c)

$y=mx-b$

d)

$Ax+By=C$

21.

What has the GREATER rate of change.

a)

y = 7x + 10

b)

Someone who starts with $6 and gets $8 each day.

c)

y = 5x + 20

d)

Someone who starts with $8 and gets $6 each day.

22.

Emma, Olivia, and Ava are trying to solve a system of equations. They found that the lines representing the equations are parallel. What does this mean for their solution?

a)

They have one common solution

b)

They have no common solution

c)

They have an infinite number of solutions

d)

They have two common solutions

23.

Susan is solving the system of equations by using elimination.

$5x-3y=-7$

$3x+15y=-1$

Which of the following could NOT be equivalent to her system after she performs the first step?

a)

b)

c)

d)

24.

Which of the following statements is/are true?

i. A system of linear equations cannot have more than one solution.

ii. In a system of two linear equations, if the coefficients are equal, the system has no solution.

iii. If the graphs of the system of two linear equations coincide, it means the system has infinitely many solutions.

a)

iii only

b)

i and ii

c)

all of them

d)

i and iii

25.

Which of the ff. statements is/are FALSE?

i. In a system of linear equations, it's possible for the lines represented by the equations to not intersect at any point.

ii. In a system of linear equations, every system with more equations than unknowns is inconsistent.

iii. A solution to a system of two linear equations can be found at the point of intersection of their graphical representation.

a)

ii only

b)

i only

c)

iii only

d)

none of the them

26.

The solution of a system of linear equations is the point where the lines cross each other.

a)

true

b)

false

27.

An inconsistent system of linear equations is when all the equations in the system intersect at one point.

a)

true

b)

false

28.

An electronics store makes a profit of $90 for every television sold and $72 for every computer sold. The manager’s target is to make at least $360 a day on sales from televisions and computers. Write a linear inequality and graph the solutions. What are three possible solutions to the problem?

a)

b)

c)

d)

29.

Which inequality represents the graph?

a)

b)

c)

d)

30.

Fill in the formula

$x^2-6x-40=0$

BLUE= (a) RED= (b)

GREEN= (c)

Choose from the below words

-6

1

-40

-1

6

40

31.

Which of the following statements is FALSE

a)

The complex number system is an extension of the real number system, where an imaginary unit i is defined by $i^2=-1$

b)

The addition of two complex numbers results in another complex number.

c)

A complex number is made up of two parts, a real part and an imaginary part which is multiplied by i (the square root of 1).

32.

Why are quadratic equations set equal to zero?

a)

Because zero is an easy number to work with.

b)

Because we are trying to find the x-intercepts and that happens when y=0.

c)

Because setting it equal to zero helps us find the y-intercepts.

d)

None of the above

33.

Match the type of number with its definition

a)

Complex Number

1.

$a+bi,\ a\ne0,\ b\ne0$

b)

Imaginary number

2.

$a+bi,\ a=0,\ b\ne0$

c)

Real Number

3.

$a+bi,\ \ b=0$

34.

John is trying to solve a complex number problem and he needs to find the value of i⁵². What is the correct value?

a)

i

b)

-i

c)

1

d)

-1

35.

The axis of symmetry for a vertical parabola always matches...

a)

the y-intercept

b)

the y-value of the vertex

c)

the x-value of the vertex

d)

the x-intercepts

36.

Which of these is NOT another term for "solution" when we're talking about quadratics?

a)

y-intercept

b)

zero

c)

root

d)

x-intercept

37.

Rewrite the quadratic functions in standard form. $f\left(x\right)=-\left(x+2\right)^2+17$

a)

$f\left(x\right)=2x^2+x-17$

b)

$f\left(x\right)=x^2+2x+17$

c)

$f\left(x\right)=-x^2-4x+13$

d)

$f\left(x\right)=x^2+4x-13$

38.

Determine how many solutions:

a)

One Solution

b)

Two Solutions

c)

No Solutions

d)

Infinitely Many Solutions

39.

What is the minimum value?

a)

(-1,0)

b)

-4

c)

(0,-3)

d)

(3,0)

e)

(1,-4)

40.

What do you know about the discriminant?

a)

It equals zero

b)

It is greater than zero

c)

It is less than zero

d)

It has no discriminant

41.

If the discriminant is positive, then the solution will be

a)

one real solution

b)

two real solutions

c)

no real solutions

d)

two imaginary solutions

42.

Which is FALSE about the graph pictured?

a)

The discriminant is negative.

b)

The y-intercept is (0, -1).

c)

The discriminant is 0.

d)

The A value is negative.

43.

Find the Axis of Symmetry of y = x² - 12x + 46

a)

x = 12

b)

x = 6

c)

x = -12

d)

x = -6

44.

Which polynomial has a degree of 5?

a)

$f\left(x\right)=\left(x^2-4\right)\left(x^2+9x+14\right)$

b)

$f\left(x\right)=x\left(x^2-1\right)\left(x^3+27\right)$

c)

$f\left(x\right)=\left(x^5+x^4+3x^3\right)\left(x^2-25\right)$

d)

$f\left(x\right)=\left(x^3+2x^2-x\right)\left(x^2-16\right)$

45.

How many zeros does the polynomial contain? $p\left(x\right)=\left(x^2-4\right)\left(x^2+4x+3\right)$

a)

2

b)

3

c)

4

d)

none

46.

Determine the factored form of the polynomial.
$p\left(x\right)=\left(x^2-1\right)\left(x^2-5x+6\right)$

a)

$p\left(x\right)=\left(x+1\right)\left(x-1\right)\left(x-3\right)\left(x-2\right)$

b)

$p\left(x\right)=\left(x-1\right)\left(x+3\right)\left(x+2\right)$

c)

$p\left(x\right)=\left(x+1\right)\left(x-1\right)\left(x+1\right)\left(x+6\right)$

d)

$p\left(x\right)=x\left(x-1\right)\left(x+6\right)$

47.

Determine a correct first step in factoring the given polynomial.
$p\left(x\right)=6x^3+24x^2+18x$

a)

$p\left(x\right)=6\left(x^3+24x^2+3x\right)$

b)

$p\left(x\right)=\left(6x^2+3x\right)\left(6x^2+24x\right)$

c)

$p\left(x\right)=6x\left(x^2+4x+3\right)$

d)

$p\left(x\right)=6x\left(4x+3\right)+3x\left(8x+3\right)$

48.

Rohan's savings = 2x² + 3x + 5
Arjun's savings = 3x² - 7x + 12
If Rohan's savings + Charlotte's savings = Arjun's savings,
what must Charlotte's savings equal?

a)

x² - 10x + 7

b)

5x² - 4x + 17

c)

x² - 4x + 7

d)

5x² - 10x + 17

49.

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient

a)

Leading Coefficient Positive
Degree - Even

b)

Leading Coefficient Positive
Degree - Odd

c)

Leading Coefficient Negative
Degree - Even

d)

Leading Coefficient Negative
Degree - Odd

50.

Determine end behavior of function with the given function:

$f\left(x\right)\ =1\ +x^7-x^5-2x^8$

a)

$x\rightarrow-\infty;\ f\left(x\right)\ \rightarrow\ -\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow+\infty$

b)

$x\rightarrow-\infty;\ f\left(x\right)\rightarrow+\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow-\infty$

c)

$x\rightarrow-\infty;\ f\left(x\right)\rightarrow-\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow\ -\infty$

d)

$x\rightarrow-\infty;\ f\left(x\right)\rightarrow+\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow+\infty$

51.

Determine end behavior of function with the given function:

$f\left(x\right)\ =1\ +x^7-x^5$

a)

$x\rightarrow-\infty;\ f\left(x\right)\ \rightarrow\ -\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow+\infty$

b)

$x\rightarrow-\infty;\ f\left(x\right)\rightarrow+\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow-\infty$

c)

$x\rightarrow-\infty;\ f\left(x\right)\rightarrow-\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow\ -\infty$

d)

$x\rightarrow-\infty;\ f\left(x\right)\rightarrow+\infty$ $x\rightarrow+\infty;\ f\left(x\right)\rightarrow+\infty$

52.

Based on the end behavior which option best describes the leading term?

a)

negative coefficient, even degree

b)

negative coefficient, odd degree

c)

negative degree, odd coefficient

d)

negative degree, even coefficient

53.

Kai, Henry, and Liam are trying to write a polynomial in standard form for their math homework. Which of the following polynomials have they written correctly in standard form?

a)

-3x + 8x² + 9x³ - 11

b)

9x³ + 8x²- 3x - 11

c)

8x²+ 9x³ -11 - 3x

d)

-11 - 3x + 8x² + 9x³

54.

What is the CONSTANT TERM of this polynomial?

2x³- 8x²+ 3x - 7

55.

What should be the order of the polynomial coefficients if
(3x - 4x³ + 6x⁴ + 1) / (x + 3)

a)

3 0 -4 6 1

b)

6 -4 3 1 0

c)

6 -4 0 3 1

d)

-6 4 0 -3 -1

56.

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.

57.

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

58.

What is the formula for the difference of squares?

a)

a² - b² = (a+b)(a+b)

b)

a² - b² = (a+b)(a-b)

c)

a² - b² = (a-b)(a+b)

d)

a² - b² = (a-b)(a-b)

59.

Which of the following are identities used in the expressions a³ + b³ and a³ - b³? (a) (b)

Choose from the below words

Square of a trinomial

Cubes of binomial

Sum of cubes

Difference of squares

Difference of cubes

Square of binomial

60.

Factor:

27x³ - 8

a)

(3x -2)(3x² + 6x + 4)

b)

(3x - 2)(9x² + 6x - 4)

c)

(3x -2)(9x² + 6x + 4)

d)

(27x - 8)(729x² + 216x + 64)

61.

Select all the factors for:

8x³ + y³

a)

(8x + y)

b)

Can't Factor

c)

(8x² - 2xy + y²)

d)

(2x + y)

e)

(4x² - 2xy + y²)

62.

Which of the following is a perfect square trinomial?

a)

x² – 4x – 4

b)

x² – 6x – 9

c)

x² + 6x – 9

d)

x² – 4x + 4

63.

Which of the following is a perfect square trinomial?

a)

x² + 14x – 49

b)

x² + 20x + 100

c)

x² – 8x + 4

d)

x² – 5x + 6

64.

Which of the following is NOT a perfect square trinomial?

a)

x² – 16x + 64

b)

x² – 10x + 20

c)

x² – 28x + 196

d)

x² – 24x + 144

65.

$\frac{\left(x-3\right)\left(x+4\right)}{x\left(x-3\right)}$
State the values of x that must be excluded to prevent division by zero.

a)

0 and 3

b)

0 and -3

c)

3 and -4

d)

0, 3, and -4

66.

$Simplify:\ \frac{5a^3c^{10}}{20a^5c^4}$

a)

$\frac{4c^6}{a^2}$

b)

$\frac{1a^2c^6}{4}$

c)

$\frac{1c^6}{4a^2}$

d)

$\frac{1a^2}{4c^6}$

67.

a)

$\frac{2\left(n-1\right)}{3n-10}$

b)

$\frac{4\left(n-1\right)}{3n-10}$

c)

$\frac{2\left(n-2\right)}{3n-10}$

d)

$\frac{4\left(n-1\right)}{3n-10}$

68.

Simplify the following rational function:

$\frac{\left(x+1\right)\left(x-2\right)\left(x+3\right)\left(x-4\right)}{\left(x+4\right)\left(x+3\right)\left(x+1\right)\left(x+2\right)\left(x-2\right)}$

a)

$\frac{1}{x+2}$

b)

$\frac{\left(x+3\right)}{\left(x-2\right)\left(x-4\right)}$

c)

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

d)

$\frac{x-4}{\left(x+4\right)\left(x+2\right)}$

69.

How do you find the x-intercept?

a)

replace all x-values with 0

b)

replace the y-value with 0 or make the numerator equal 0

c)

set denominator equal to 0

d)

compare the degrees of the numerator and denominator

70.

A discontinuity is found by setting the _________= to zero and solving for x

a)

Numerator

b)

Denominator

c)

Right side

d)

Left side

71.

The end behavior of a rational function equals zero when:

a)

the degree of the numerator and denominator are equal

b)

the degree of the numerator is less than the degree of the denominator

c)

the degree of the numerator is greater than the degree of the denominator

d)

the numerator equals zero

72.

What is an asymptote?

a)

an imaginary line that your function never touches

b)

a part of your function

c)

a point on your graph

d)

a type of fruit

73.

What discontinuities are present?

a)

A hole when x = 2

b)

A vertical asymptote at x = 2

c)

there is no hole or vertical asymptote

d)

A vertical asymptote a x = 2 and hole at x = 1

74.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

75.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

76.

Identify the point(s) of discontinuity.

$f\left(x\right)=\frac{x+2}{\left(x-3\right)\left(x+2\right)}$

a)

Only x = 2

b)

Only x = -2

c)

Only x = 3

d)

x = 2 and x = 3

e)

x = -2 and x = 3

77.

Determine all removable points of discontinuity (holes), vertical asympotes, and horizontal asympotes for the following function.

$f\left(x\right)=\frac{2x-1}{2x^2+5x-3}$

a)

Holes: x = -3
Vertical: x = 1/2
Horizontal: y = 0

b)

Holes: x = 1/2
Vertical: x = -3
Horizontal: y = 0

c)

Holes: Do Not Exist
Vertical: x = 1/2 and x = -4
Horizontal: y = 1

d)

Holes: x = 1/2
Vertical: x = -3
Horizontal: y = 1

e)

Holes: x = -3
Vertical: x = 1/2
Horizontal: Does Not Exist

78.

Find f(g(0)).

a)

-2

b)

3

c)

4

d)

1

79.

Which of the following best describes the continuity at x = -4?

a)

Continuous

b)

Removable Discontinuity

c)

Infinite Discontinuity

d)

Jump Discontinuity

80.

What is the domain?

a)

$\left(-\infty,\ -3\right]$

b)

$\left[3,\ -\infty\right)$

c)

$\left(-\infty,3\right]$

d)

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

e)

None of the answer choices

81.

What is the SUM of the roots of quadratic equation x² + 13x + 42 = 0?

a)

-42

b)

-13

c)

13

d)

42

82.

Determine the SUM of the roots of the given quadratic equation below:

3x^2+11x-4=0

a)

$-\frac{11}{3}$

b)

$\frac{11}{3}$

c)

$-\frac{4}{3}$

83.

Determine the PRODUCT of the roots of the given quadratic equation below:

3x^2+11x-4=0

a)

$-\frac{11}{3}$

b)

$-\frac{4}{3}$

c)

$\frac{4}{3}$

84.

Determine the SUM of the roots of the given quadratic equation below:

4x^2+6x-1=0

a)

$-\frac{3}{2}$

b)

$\frac{3}{2}$

c)

$-\frac{1}{4}$

85.

Determine the PRODUCT of the roots of the given quadratic equation below:

14x^2+3x-5=0

a)

$-\frac{5}{14}$

b)

$\frac{5}{14}$

c)

$\frac{3}{14}$

Finals: STUDY GUIDE

Total questions: 85

Worksheet time: 6hrs 58mins

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