WorksheetsComplex Numbers
Total questions: 57
Worksheet time: 29mins
What is the imaginary unit in complex numbers?
i
j
x
e
What is a complex number composed of?
A real part and an imaginary part
Two real parts
Two imaginary parts
A rational and an irrational part
In a complex number a + bi, what does 'a' represent?
real part
imaginary part
modulus
argument
In a complex number a + bi, what does 'bi' represent?
imaginary part
real part
modulus
argument
In the complex plane, what does the horizontal axis represent?
Imaginary
Real
Both
None
In the complex plane, what does the vertical axis represent?
Real
Imaginary
Both
None
Fill in the blank: The horizontal axis in the complex plane is the ______ axis.
Real
Imaginary
Vertical
Polar
Fill in the blank: The vertical axis in the complex plane is the ______ axis.
Imaginary
Real
Principal
Polar
What are the basic operations you can perform with complex numbers?
Add/Subtract
Multiply/Divide
Integrate/Differentiate
When working with complex numbers, you should ______ like terms.
combine
subtract
divide
ignore
In complex numbers, multiplication of imaginary unit i by itself becomes _____
-1
0
1
i
What are complex conjugates?
Complex conjugates are pairs of complex numbers of the form a + bi and a - bi.
Complex conjugates are real numbers that are equal in value.
Complex conjugates are imaginary numbers with the same sign.
Complex conjugates are numbers that have no imaginary part.
When complex conjugates are multiplied, the product is ________.
real
imaginary
undefined
negative
When complex conjugates are multiplied, the product is real.
True
False
When dividing complex numbers, what should you multiply by?
The numerator
The conjugate of the denominator
The denominator
The reciprocal of the numerator
Simplify the following expression: (5 - i)^2 = (5−i)2 _______
24 - 10i
25 - 2i
26 - 5i
23 - 8i
Simplify the following expression and write your answer in terms of complex numbers: √-14
√14 i
-√14 i
14 i
-14
Simplify the following expression and write your answer in terms of complex numbers: √-2 = _______
√2 i
2i
-√2 i
i√-2
Simplify the following expression and write your answer in terms of complex numbers: √-27
3√3 i
-3√3 i
3i
√27
Simplify the following expression and write your answer in terms of complex numbers: √-12
2√3 i
2√6 i
3√2 i
4√3 i
Fill in the blank: In this section, you will recognize characteristics of _________
parabolas.
circles.
rectangles.
triangles.
Fill in the blank: In this section, you will understand how the graph of a _________ is related to its quadratic function.
parabola.
circle.
triangle.
rectangle.
Fill in the blank: In this section, you will determine a quadratic function’s _________ or _________ value.
minimum, maximum.
sum, product.
domain, range.
slope, intercept.
Fill in the blank: In this section, you will solve problems involving a quadratic function’s _________ or _________ value.
minimum, maximum.
sum, product.
average, median.
root, vertex.
What is the term used when a parabola becomes thinner?
thinner
wider
shifted
rotated
What is the term used when a parabola becomes wider?
wider
narrower
vertex
focus
What happens to a parabola when it is reflected over the x-axis?
opens down
opens up
shifts right
becomes a line
What is the term used when a parabola opens up?
opens up
opens down
vertex form
axis of symmetry
In the diagram, what is the name of the point where the parabola changes direction?
Vertex
Focus
Axis
Directrix
In the diagram, what is the vertical dashed line called?
Axis of Symmetry
Line of Best Fit
Tangent Line
Median
What are the two forms of quadratic equations mentioned in the notes?
Standard Form and General Form
Vertex Form and Slope Form
Factored Form and Linear Form
Exponential Form and Standard Form
In the Standard Form of a quadratic equation, what does the vertex represent?
The vertex represents the point (h, k).
The vertex represents the axis of symmetry.
The vertex represents the y-intercept.
The vertex represents the leading coefficient.
What is the axis of symmetry in the context of quadratic equations?
The axis of symmetry is a vertical line that passes through the vertex of the parabola.
The axis of symmetry is a horizontal line that passes through the focus of the parabola.
The axis of symmetry is the line where the parabola intersects the x-axis.
The axis of symmetry is the line that passes through the directrix of the parabola.
Which of the following is NOT a step to graph a quadratic equation?
A) Find vertex
B) Make table around vertex
C) Draw parabola
D) Find the area of the parabola
List the three steps to graph a quadratic equation as mentioned in the notes.
1. Find vertex 2. Make table around vertex 3. Draw parabola
1. Find x-intercepts 2. Draw a straight line 3. Shade the area above the line
1. Find the y-intercept 2. Draw a circle 3. Connect the points
1. Find the slope 2. Draw a tangent 3. Mark the inflection point
In the General Form of a quadratic equation, what are the two key features to identify?
Vertex and Axis
Roots and Discriminant
Focus and Directrix
Coefficient and Constant
Identify the vertex and axis of symmetry of the graphed function.
The vertex is (2, -3) and the axis of symmetry is x = 2.
The vertex is (-2, 3) and the axis of symmetry is x = -2.
The vertex is (3, 2) and the axis of symmetry is x = 3.
The vertex is (0, 0) and the axis of symmetry is x = 0.
Write the standard form of the equation of parabola with vertex ___ and passes through ___.
The answer cannot be provided as the vertex and the point are not specified in the question.
y = a(x - h)^2 + k, where (h, k) is the focus and a is any real number.
y = mx + c, where m is the slope and c is the y-intercept.
x2+y2=r2 , where r is the radius.
What are the maximum and minimum values of a quadratic equation called?
Maximum and minimum
Roots and zeros
Intercepts and slopes
Coefficients and constants
The maximum or minimum value of a quadratic equation occurs at the ________.
vertex
axis of symmetry
focus
origin
What is the formula used to solve quadratic equations called?
Quadratic formula
Pythagorean theorem
Binomial theorem
Cubic formula
To find the solutions of a quadratic equation, you need to ________ it.
solve
draw
multiply
subtract
What is the term for the function described in the section '2-03 POLYNOMIAL EQUATIONS'?
Polynomial Function
Exponential Function
Logarithmic Function
Trigonometric Function
In a polynomial equation, what are coefficients?
Coefficients are the numerical factors of the terms in a polynomial.
Coefficients are the exponents of the variables in a polynomial.
Coefficients are the variables themselves in a polynomial.
Coefficients are the solutions to the polynomial equation.
In a polynomial equation, what are terms?
Terms are the individual parts of a polynomial separated by plus or minus signs.
Terms are only the variables in a polynomial.
Terms are the exponents in a polynomial equation.
Terms are the coefficients of the highest degree in a polynomial.
In a polynomial equation, what is the constant term?
The constant term is the term without a variable.
The constant term is the term with the highest exponent.
The constant term is the coefficient of the variable.
The constant term is the sum of all coefficients.
What is the degree of a polynomial?
The degree is the highest exponent.
The degree is the sum of all coefficients.
The degree is the number of terms.
The degree is the constant term.
What is the leading coefficient in a polynomial?
The leading coefficient is the coefficient of the term with the highest exponent.
The leading coefficient is the constant term in the polynomial.
The leading coefficient is the sum of all coefficients in the polynomial.
The leading coefficient is the coefficient of the term with the lowest exponent.
How are the graphs of polynomial functions described?
Graphs are continuous, smooth, rounded turns.
Graphs are always straight lines.
Graphs have sharp corners and breaks.
Graphs are made up of disconnected points.
Polynomial functions always go towards ∞ or -∞ at either end of the graph. What does this statement describe?
End behavior
Vertex
Axis of symmetry
Roots
According to the table, what is the end behavior of a polynomial with an even degree and a positive leading coefficient?
Both ends go towards ∞ (upwards).
Both ends go towards -∞ (downwards).
Left end goes up, right end goes down.
Left end goes down, right end goes up.
According to the table, what is the end behavior of a polynomial with an odd degree and a negative leading coefficient?
Left end goes to ∞, right end goes to -∞ (downwards).
Left end goes to -∞, right end goes to ∞ (upwards).
Both ends go to ∞ (upwards).
Both ends go to -∞ (downwards).
What is a zero of a polynomial?
A zero of a polynomial is a value for which the polynomial equals zero.
A zero of a polynomial is the highest degree of the polynomial.
A zero of a polynomial is the sum of all coefficients.
A zero of a polynomial is the constant term of the polynomial.
If x = a is a zero of a polynomial, then which of the following is true?
a is a solution to the polynomial equation
a is an x-intercept
a is a factor of the polynomial
All of the above
For a polynomial of degree n, what is the maximum number of zeros it can have (counting multiplicity)?
n
n+1
n-1
2n
For a polynomial of degree n, what is the maximum number of turning points it can have?
n - 1
n
n + 1
n - 2
True or False: The number of zeros of a polynomial of degree n can be more than n.
True
False
