Download ExamView - Algebra 2a Final Review.tst

Name: ________________________ Class: ___________________ Date: __________
Algebra 2 Final Review Fall Semester
Simplify. Write the answer in standard form.
1. (c − 9) (c + 7)
Factor the expression.
2. z 2 − 9z + 20
3. 15x 2 − 16xy + 4y 2
To which set of numbers does the number belong?
4.
55
5. –63
Evaluate the expression for the given value of the variable(s).
6.
3(3h + )
−6 + h
; h = −4
7. −x 2 − 3x + 2; x = –3
Combine like terms. What is a simpler form of each expression?
8. −2(−y + 8) + 6y
Solve the equation.
9. −5y − 13 = 3(y + 9)
10. x 2 + 4x + 4 = 81
11. x 2 − 8x + 16 = 16
Is the following always, sometimes, or never true?
12. 15 + 2x − 11 = 8x + 4 − 6x
Solve the inequality. Graph the solution set.
13. 2 + 3k ≤ –4
14. Make a mapping diagram for the relation.
{(–3, –3), (–2, 1), (0, –5), (5, 6)}
1
ID: A
Name: ________________________
ID: A
15. Find the domain and range of the relation.
Is the relation a function?
____ 16. {(13, 10), (8, 6), (10, 9), (14, 11), (8, 12)}
a.
b.
yes
no
2
Name: ________________________
ID: A
____ 17. Use the vertical-line test to determine which graph represents a function.
a.
c.
b.
d.
For each function, what is the output of the given input?
18. For f (x ) = −4x − 7 , find f (−3) .
Write the equation in slope-intercept form. What are the slope and y-intercept?
____ 19. −1x + 11y = −12
1
12
a. y = − x +
11 11
1
12
slope:
; y-intercept:
11
11
1
12
b. y = x − ;
11 11
1
12
slope:
; y-intercept: −
11
11
c.
d.
3
1
12
x+ ;
11 11
12
slope:
; y-intercept:
11
1
12
y=− x− ;
11 11
1
slope:
; y-intercept:
11
y=
1
11
12
11
Name: ________________________
ID: A
What is the graph of the equation?
____ 20. −3x + y = −3
a.
c.
b.
d.
Write an equation of the line, in point-slope form, that passes through the two given points.
____ 21. points: (−10,18), (4,−10)
a.
y − 10 = −2(x − 18)
c.
b.
y − 18 = −2(x + 10)
d.
4
1
y − 18 = − (x + 10)
2
1
y − 10 = − (x + 18)
2
Name: ________________________
ID: A
What is an equation of the line, in point-slope form, that passes through the given point and has the
given slope?
____ 22. point: (2,−3); slope: 7
a.
b.
y − 3 = 7(x + 2)
y + 3 = 7(x − 2)
c.
d.
y − 3 = 7(x − 2)
y + 3 = 7(x + 2)
What are the intercepts of the equation? Graph the equation.
____ 23. −2x + 3y = −6
a.
x-intercept: (–2, 0)
y-intercept: (0, 3)
c.
x-intercept: (3, 0)
y-intercept: (0, –2)
b.
x-intercept: (3, 0)
y-intercept: (0, –2)
d.
x-intercept: (–2, 0)
y-intercept: (0, 3)
5
Name: ________________________
ID: A
What is the equation of the line in slope-intercept form?
____ 24. the line parallel to y = 3x − 8 through (6, –6)
1
a. y = − x − 24
3
b. y = 3x − 24
c.
y = 3x − 12
d.
y = −3x − 24
1
____ 25. the line perpendicular to y = x + 8 through (–6, 3)
2
a.
y = − 2x − 9
c.
1
y = x−9
2
b.
1
y = − x−9
2
d.
y =2x − 9
What is the graph of each inequality?
26. –x + 4y > 5
Solve the system by graphing.
ÏÔÔ
ÔÔ −2x − y = 5
27. ÌÔ
ÔÔ x − 2y = −5
Ó
Solve the system of inequalities by graphing.
ÏÔÔ
ÔÔ y ≤ −2x − 1
28. ÌÔ
ÔÔ y > 2x − 4
Ó
Solve the system by elimination.
ÔÏÔÔ x − y − 2z = 7
ÔÔ
ÔÔ
29. ÔÔÌ −x − 2y + 2z = −1
ÔÔÔ
ÔÔ x − y − 2z = 7
ÔÓ
Solve the system by substitution.
ÏÔÔ
ÔÔ −2x + 3y + 2z = −3
ÔÔÔ
z = −1
30. ÔÔÌ
ÔÔÔ
ÔÔ 2x + y + 3z = −14
ÔÓ
Graph each function. How is each graph a translation of f(x) = x 2 ?
31. y = (x − 1) 2 − 2
6
Name: ________________________
____ 32. Which is the graph of y = (x + 2) 2 − 4 ?
a.
b.
ID: A
c.
d.
What are the vertex and the axis of symmetry of the equation?
33. y = 2x 2 + 12x − 10
What is the maximum or minimum value of the function? What is the range?
34. y = 2x 2 + 20x − 12
What is the graph of the equation?
35. y = x 2 − 2x + 1
What is the vertex form of the equation?
36. y = x 2 − 12x + 12
37. Sketch a parabola with an axis of symmetry x = −1, y-intercept 1, and point (1, –5).
7
Name: ________________________
ID: A
What is the expression in factored form?
38. x 2 + 17x + 70
What is the expression in factored form?
39. −12x 2 − 20x
40. 49x 2 − 9
What are the solutions of the quadratic equation?
41. x 2 + 9x = −18
Solve by graphing.
42. x 2 + 5x + 6 = 0
43. The function y = −16t 2 + 428 models the height y in feet of a stone t seconds after it is dropped from the
edge of a vertical cliff. How long will it take the stone to hit the ground? Round to the nearest hundredth of a
second.
What is the solution of each equation?
44. 4x 2 = 12
Solve the quadratic equation by completing the square.
45. −5x 2 + 3x = −3
Rewrite the equation in vertex form. Name the vertex and y-intercept.
46.
y = x 2 − 4x + 2
Use the Quadratic Formula to solve the equation.
47. 2x 2 − 5x − 6 = 0
Simplify the number using the imaginary unit i.
48.
−9
Simplify the expression.
49. (3 − 5i)(2 + 6i)
8
Name: ________________________
50.
ID: A
6 − 3i
−3 + 5i
9
ID: A
Algebra 2 Final Review Fall Semester
Answer Section
1. ANS:
c 2 − 2c − 63
PTS: 1
DIF: L2
REF: 0-8 Factoring Operations With Polynomials
OBJ: Factoring and Operations With Polynomials
TOP: Skills Handbook: Factoring and Operations With Polynomials
KEY: polynomials | operations with polynomials | multiply polynomials
2. ANS:
(z – 4)(z – 5)
PTS: 1
DIF: L1
REF: 0-8 Factoring Operations With Polynomials
OBJ: Factoring and Operations With Polynomials
TOP: Skills Handbook: Factoring and Operations With Polynomials
KEY: factoring
3. ANS:
(3x − 2y)(5x − 2y)
PTS: 1
DIF: L1
REF: 0-8 Factoring Operations With Polynomials
OBJ: Factoring and Operations With Polynomials
TOP: Skills Handbook: Factoring and Operations With Polynomials
KEY: factoring
4. ANS:
irrational numbers
PTS: 1
DIF: L2
REF: 1-2 Properties of Real Numbers
OBJ: 1-2.1 To graph and order real numbers
NAT: CC N.RN.3| N.1.i| N.5.f
TOP: 1-2 Problem 1 Classifying a Variable
5. ANS:
integers
PTS: 1
DIF: L2
REF: 1-2 Properties of Real Numbers
OBJ: 1-2.1 To graph and order real numbers
NAT: CC N.RN.3| N.1.i| N.5.f
TOP: 1-2 Problem 1 Classifying a Variable
6. ANS:
3
3
10
PTS:
OBJ:
NAT:
TOP:
1
DIF: L4
REF: 1-3 Algebraic Expressions
1-3.1 To evaluate algebraic expressions
CC A.SSE.1.a| N.1.d| N.3.a| N.3.b| A.3.b| A.3.d
1-3 Problem 3 Evaluating Algebraic Expressions
KEY: evaluate
1
ID: A
7. ANS:
2
PTS: 1
DIF: L3
REF: 1-3 Algebraic Expressions
OBJ: 1-3.1 To evaluate algebraic expressions
NAT: CC A.SSE.1.a| N.1.d| N.3.a| N.3.b| A.3.b| A.3.d
TOP: 1-3 Problem 3 Evaluating Algebraic Expressions
KEY: evaluate
8. ANS:
8y − 16
PTS: 1
DIF: L3
REF: 1-3 Algebraic Expressions
OBJ: 1-3.2 To simplify algebraic expressions
NAT: CC A.SSE.1.a| N.1.d| N.3.a| N.3.b| A.3.b| A.3.d
TOP: 1-3 Problem 5 Simplifying Algebraic Expressions
KEY: like terms
9. ANS:
= −5
PTS:
OBJ:
TOP:
KEY:
10. ANS:
7, –11
1
DIF: L2
REF: 1-4 Solving Equations
1-4.1 To solve equations
NAT: CC A.CED.1| CC A.CED.4| A.2.a| A.4.c
1-4 Problem 2 Solving a Multi-Step Equation
equation | solution of an equation | inverse operations
PTS: 1
DIF: L3
REF: 4-6 Completing the Square
OBJ: 4-6.1 To solve equations by completing the square
NAT: CC A.REI.4.b| A.2.a| A.4.c| A.4.g
TOP: 4-6 Problem 3 Solving a Perfect Square Trinomial Equation
11. ANS:
0, 8
PTS: 1
DIF: L2
REF: 4-6 Completing the Square
OBJ: 4-6.1 To solve equations by completing the square
NAT: CC A.REI.4.b| A.2.a| A.4.c| A.4.g
TOP: 4-6 Problem 3 Solving a Perfect Square Trinomial Equation
12. ANS:
always
PTS:
OBJ:
TOP:
KEY:
1
DIF: L3
REF: 1-4 Solving Equations
1-4.1 To solve equations
NAT: CC A.CED.1| CC A.CED.4| A.2.a| A.4.c
1-4 Problem 4 Equations with No Solutions and Identities
equation | identity
2
ID: A
13. ANS:
k ≤ –2
PTS:
OBJ:
NAT:
TOP:
14. ANS:
1
DIF: L2
REF: 1-5 Solving Inequalities
1-5.1 To solve and graph inequalities
CC A.CED.1| A.2.a| A.3.b| A.3.d| A.4.c
1-5 Problem 2 Solving and Graphing an Inequality
PTS: 1
DIF: L2
REF: 2-1 Relations and Functions
OBJ: 2-1.1 To graph relations
NAT: CC F.IF.1| CC F.IF.2| A.1.g| A.1.i| A.2.b| A.3.f
TOP: 2-1 Problem 1 Representing a Relation
KEY: relation
15. ANS:
domain: {–3.5, –1.5, 0, 1.5, 3.5}; range: {4, 2.5, –1.5}
PTS:
OBJ:
TOP:
16. ANS:
OBJ:
TOP:
17. ANS:
OBJ:
TOP:
18. ANS:
5
1
DIF: L2
REF: 2-1 Relations and Functions
2-1.1 To graph relations
NAT: CC F.IF.1| CC F.IF.2| A.1.g| A.1.i| A.2.b| A.3.f
2-1 Problem 2 Finding Domain and Range
KEY: domain | range | relation
B
PTS: 1
DIF: L2
REF: 2-1 Relations and Functions
2-1.2 To identify functions
NAT: CC F.IF.1| CC F.IF.2| A.1.g| A.1.i| A.2.b| A.3.f
2-1 Problem 3 Identifying Functions
KEY: function | relation
C
PTS: 1
DIF: L2
REF: 2-1 Relations and Functions
2-1.2 To identify functions
NAT: CC F.IF.1| CC F.IF.2| A.1.g| A.1.i| A.2.b| A.3.f
2-1 Problem 4 Using the Vertical-Line Test
KEY: vertical-line test | function
PTS:
OBJ:
TOP:
19. ANS:
REF:
NAT:
TOP:
KEY:
20. ANS:
REF:
NAT:
TOP:
KEY:
1
DIF: L2
REF: 2-1 Relations and Functions
2-1.2 To identify functions
NAT: CC F.IF.1| CC F.IF.2| A.1.g| A.1.i| A.2.b| A.3.f
2-1 Problem 5 Using Function Notation
KEY: function notation
B
PTS: 1
DIF: L3
2-3 Linear Functions and Slope-Intercept Form
OBJ: 2-3.2 To write equations of lines
CC A.CED.2| CC F.IF.4| CC F.IF.7| G.4.d| A.1.b| A.2.b
2-3 Problem 3 Writing Equations in Slope-Intercept Form
linear equation | slope-intercept form | slope | y-intercept
B
PTS: 1
DIF: L2
2-3 Linear Functions and Slope-Intercept Form
OBJ: 2-3.1 To graph linear equations
CC A.CED.2| CC F.IF.4| CC F.IF.7| G.4.d| A.1.b| A.2.b
2-3 Problem 4 Graphing a Linear Equation
linear equation | slope-intercept form
3
ID: A
21. ANS:
OBJ:
NAT:
TOP:
22. ANS:
OBJ:
NAT:
TOP:
KEY:
23. ANS:
OBJ:
NAT:
TOP:
24. ANS:
OBJ:
NAT:
TOP:
KEY:
25. ANS:
OBJ:
NAT:
TOP:
KEY:
26. ANS:
PTS:
OBJ:
TOP:
KEY:
B
PTS: 1
DIF: L2
REF: 2-4 More About Linear Equations
2-4.1 To write an equation of a line given its slope and a point on the line
CC A.CED.2| CC F.IF.7| CC F.IF.8| CC F.IF.9| G.4.d| A.2.a| A.2.b
2-4 Problem 2 Writing an Equation Given Two Points
KEY: point-slope form
B
PTS: 1
DIF: L2
REF: 2-4 More About Linear Equations
2-4.1 To write an equation of a line given its slope and a point on the line
CC A.CED.2| CC F.IF.7| CC F.IF.8| CC F.IF.9| G.4.d| A.2.a| A.2.b
2-4 Problem 1 Writing an Equation Given a Point and a Slope
point-slope form
C
PTS: 1
DIF: L3
REF: 2-4 More About Linear Equations
2-4.1 To write an equation of a line given its slope and a point on the line
CC A.CED.2| CC F.IF.7| CC F.IF.8| CC F.IF.9| G.4.d| A.2.a| A.2.b
2-4 Problem 4 Graphing an Equation Using Intercepts
B
PTS: 1
DIF: L3
REF: 2-4 More About Linear Equations
2-4.1 To write an equation of a line given its slope and a point on the line
CC A.CED.2| CC F.IF.7| CC F.IF.8| CC F.IF.9| G.4.d| A.2.a| A.2.b
2-4 Problem 6 Writing Equations of Parallel and Perpendicular Lines
parallel lines
A
PTS: 1
DIF: L3
REF: 2-4 More About Linear Equations
2-4.1 To write an equation of a line given its slope and a point on the line
CC A.CED.2| CC F.IF.7| CC F.IF.8| CC F.IF.9| G.4.d| A.2.a| A.2.b
2-4 Problem 6 Writing Equations of Parallel and Perpendicular Lines
perpendicular lines
1
DIF: L2
REF: 2-8 Two-Variable Inequalities
2-8.1 To graph two-variable inequalities
NAT: CC A.CED.2| CC F.IF.7.b
2-8 Problem 1 Graphing Linear Inequalities
linear inequality | boundary | half-plane | test point
4
ID: A
27. ANS:
(–3, 1)
PTS:
OBJ:
NAT:
TOP:
KEY:
28. ANS:
1
DIF: L2
REF: 3-1 Solving Systems Using Tables and Graphs
3-1.1 To solve a linear system using a graph or a table
CC A.CED.2| CC A.CED.3| CC A.REI.6| CC A.REI.11| A.4.d
3-1 Problem 1 Using a Graph or Table to Solve a System
system of linear equations | graphing | solution of a system
PTS: 1
DIF: L3
REF: 3-3 Systems of Inequalities
OBJ: 3-3.1 To solve systems of linear inequalities
NAT: CC A.CED.3| CC A.REI.6| CC A.REI.12| A.4.d
TOP: 3-3 Problem 2 Solving a System by Graphing
KEY: system of inequalities | graphing
29. ANS:
(–9, –2, –7)
PTS:
OBJ:
NAT:
KEY:
1
DIF: L2
REF: 3-5 Systems With Three Variables
3-5.1 To solve systems in three variables using elimination
CC A.REI.6| A.4.d
TOP: 3-5 Problem 1 Solving a System Using Elimination
system with three variables | solve by elimination
5
ID: A
30. ANS:
(–4, –3, –1)
PTS:
OBJ:
NAT:
KEY:
31. ANS:
1
DIF: L2
REF: 3-5 Systems With Three Variables
3-5.2 To solve systems in three variables using substitution
CC A.REI.6| A.4.d
TOP: 3-5 Problem 3 Solving a System Using Substitution
system with three variables | substitution method
f(x) translated down 2 unit(s) and translated to the right 1 unit(s).
PTS: 1
DIF: L3
REF: 4-1 Quadratic Functions and Transformations
OBJ: 4-1.1 To identify and graph quadratic functions
NAT: CC A.CED.1| CC F.IF.4| CC F.IF.6| CC F.IF.7| CC F.BF.3| G.2.c| A.2.d
TOP: 4-1 Problem 2 Graphing Translations of f(x)=x^2
KEY: graphing | quadratic functions | translations
32. ANS: A
PTS: 1
DIF: L3
REF: 4-1 Quadratic Functions and Transformations
OBJ: 4-1.1 To identify and graph quadratic functions
NAT: CC A.CED.1| CC F.IF.4| CC F.IF.6| CC F.IF.7| CC F.BF.3| G.2.c| A.2.d
TOP: 4-1 Problem 4 Using Vertex Form KEY: parabola | vertex form | graphing | translation
33. ANS:
vertex: ( –3, –28)
axis of symmetry: x = −3
PTS:
OBJ:
NAT:
TOP:
KEY:
1
DIF: L2
REF: 4-2 Standard Form of a Quadratic Function
4-2.1 To graph quadratic functions written in standard form
CC A.CED.2| CC F.IF.4| CC F.IF.6| CC F.IF.7| CC F.IF.8| CC F.IF.9| CC F.BF.1
4-2 Problem 1 Finding the Features of a Quadratic Function
Graph functions expressed symbolically | standard form | vertex of a parabola | axis of symmetry
6
ID: A
34. ANS:
minimum value: –62
range: y ≥ −62
PTS:
OBJ:
NAT:
TOP:
KEY:
35. ANS:
1
DIF: L2
REF: 4-2 Standard Form of a Quadratic Function
4-2.1 To graph quadratic functions written in standard form
CC A.CED.2| CC F.IF.4| CC F.IF.6| CC F.IF.7| CC F.IF.8| CC F.IF.9| CC F.BF.1
4-2 Problem 1 Finding the Features of a Quadratic Function
standard form | minimum value | maximum value
PTS: 1
DIF: L2
REF: 4-2 Standard Form of a Quadratic Function
OBJ: 4-2.1 To graph quadratic functions written in standard form
NAT: CC A.CED.2| CC F.IF.4| CC F.IF.6| CC F.IF.7| CC F.IF.8| CC F.IF.9| CC F.BF.1
TOP: 4-2 Problem 2 Graphing a Function of the Form y=ax^2+bx+c
KEY: standard form
36. ANS:
y = (x − 6) 2 − 24
PTS:
OBJ:
NAT:
TOP:
KEY:
1
DIF: L2
REF: 4-2 Standard Form of a Quadratic Function
4-2.1 To graph quadratic functions written in standard form
CC A.CED.2| CC F.IF.4| CC F.IF.6| CC F.IF.7| CC F.IF.8| CC F.IF.9| CC F.BF.1
4-2 Problem 3 Converting Standard Form to Vertex Form
standard form | vertex form
7
ID: A
37. ANS:
PTS: 1
DIF: L4
REF: 4-2 Standard Form of a Quadratic Function
OBJ: 4-2.1 To graph quadratic functions written in standard form
NAT: CC A.CED.2| CC F.IF.4| CC F.IF.6| CC F.IF.7| CC F.IF.8| CC F.IF.9| CC F.BF.1
TOP: 4-2 Problem 4 Interpreting a Quadratic Graph
KEY: standard form
38. ANS:
(x + 10)(x + 7)
PTS: 1
DIF: L2
REF: 4-4 Factoring Quadratic Expressions
OBJ: 4-4.1 To find common and binomial factors of quadratic expressions
NAT: CC A.SSE.2| N.5.c| A.2.a
TOP: 4-4 Problem 1 Factoring ax^2+bx+c when a=+/-1
KEY: factoring | quadratic expression
39. ANS:
−4x(3x + 5)
PTS: 1
DIF: L2
REF: 4-4 Factoring Quadratic Expressions
OBJ: 4-4.1 To find common and binomial factors of quadratic expressions
NAT: CC A.SSE.2| N.5.c| A.2.a
TOP: 4-4 Problem 2 Finding Common Factors
KEY: factoring | greatest common factor
40. ANS:
(7x + 3)(7x − 3)
PTS: 1
DIF: L2
REF: 4-4 Factoring Quadratic Expressions
OBJ: 4-4.2 To factor special quadratic expressions
NAT: CC A.SSE.2| N.5.c| A.2.a
TOP: 4-4 Problem 5 Factoring a Difference of Two Squares
KEY: difference of two squares | factoring
41. ANS:
–6, –3
PTS:
OBJ:
NAT:
TOP:
KEY:
1
DIF: L2
REF: 4-5 Quadratic Equations
4-5.1 To solve quadratic equations by factoring
CC A.SSE.1.a| CC A.APR.3| CC A.CED.1| A.2.a| A.4.a| A.4.c
4-5 Problem 1 Solving a Quadratic Equation by Factoring
Zero-Product Property
8
ID: A
42. ANS:
–2, –3
PTS: 1
DIF: L2
REF: 4-5 Quadratic Equations
OBJ: 4-5.2 To solve quadratic equations by graphing
NAT: CC A.SSE.1.a| CC A.APR.3| CC A.CED.1| A.2.a| A.4.a| A.4.c
TOP: 4-5 Problem 3 Solving a Quadratic Equation by Graphing
KEY: zero of a function
43. ANS:
5.17 seconds
PTS: 1
DIF: L2
REF: 4-5 Quadratic Equations
OBJ: 4-5.1 To solve quadratic equations by factoring
NAT: CC A.SSE.1.a| CC A.APR.3| CC A.CED.1| A.2.a| A.4.a| A.4.c
TOP: 4-5 Problem 4 Using a Quadratic Equation
44. ANS:
3, – 3
PTS: 1
DIF: L2
REF: 4-6 Completing the Square
OBJ: 4-6.1 To solve equations by completing the square
NAT: CC A.REI.4.b| A.2.a| A.4.c| A.4.g
TOP: 4-6 Problem 1 Solving by Finding Square Roots
45. ANS:
69
3
±
10
10
PTS: 1
DIF: L3
REF: 4-6 Completing the Square
OBJ: 4-6.1 To solve equations by completing the square
NAT: CC A.REI.4.b| A.2.a| A.4.c| A.4.g
TOP: 4-6 Problem 5 Solving by Completing the Square
KEY: completing the square
9
ID: A
46. ANS:
y = (x − 2) 2 − 2
vertex: (2, – 2)
y-intercept: (0, 2)
PTS: 1
DIF: L3
REF: 4-6 Completing the Square
OBJ: 4-6.2 To rewrite functions by completing the square
NAT: CC A.REI.4.b| A.2.a| A.4.c| A.4.g
TOP: 4-6 Problem 6 Writing in Vertex Form
47. ANS:
5
±
4
PTS:
OBJ:
NAT:
TOP:
48. ANS:
3i
73
4
1
DIF: L3
REF: 4-7 The Quadratic Formula
4-7.1 To solve quadratic equations using the Quadratic Formula
CC A.REI.4.b| A.2.a| A.4.c| A.4.e| A.4.f
4-7 Problem 1 Using the Quadratic Formula
KEY: Quadratic Formula
PTS: 1
DIF: L2
REF: 4-8 Complex Numbers
OBJ: 4-8.1 To identify, graph, and perform operations with complex numbers
NAT: CC N.CN.1| CC N.CN.2| CC N.CN.7| CC N.CN.8| N.5.f| A.4.g
TOP: 4-8 Problem 1 Simplifying a Number using i
KEY: imaginary number | imaginary unit
49. ANS:
4(9 + 2i)
PTS:
OBJ:
NAT:
TOP:
50. ANS:
33
− −
34
PTS:
OBJ:
NAT:
TOP:
KEY:
1
DIF: L3
REF: 4-8 Complex Numbers
4-8.1 To identify, graph, and perform operations with complex numbers
CC N.CN.1| CC N.CN.2| CC N.CN.7| CC N.CN.8| N.5.f| A.4.g
4-8 Problem 4 Multiplying Complex Numbers
KEY: complex number
21
i
34
1
DIF: L3
REF: 4-8 Complex Numbers
4-8.1 To identify, graph, and perform operations with complex numbers
CC N.CN.1| CC N.CN.2| CC N.CN.7| CC N.CN.8| N.5.f| A.4.g
4-8 Problem 5 Dividing Complex Numbers
complex number | complex conjugates
10