Integrated Math 2 | Final Exam Outline Review
Name:_______________________ Date:______________________
Instructions: With finals in the near future, this review outline will help support and prepare you for the
Integrated Math 2 mock final and the final examination for semester 1. During the course of Semester 1, we
have covered the following topics:
 Probability
 Quadratics Functions
 Structure of Expressions
 Quadratics Equations
You have learned a tremendous amount of information, and not all topics will be covered. This outline is here
to guide you on what you need to do in order to pass the examinations when you return from break.
Word of wisdom: attempt to solve every problem. If you cannot do one, at least you have tried. It is better to
have tried than to not have tried.
Word of wisdom #2: questions on this review might reappear on your exam.
Topics and Standards Covered:
Probability
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Estimating conditional
probability and
interpreting the meaning
of set data.
Examining conditional
probability using multiple
representation
Using sample to estimate
probabilities
Creating Venn diagrams
using data while
examining addition rules
of probability.
Examining independence
of events using two-way
tables.
Using data in various
representations to
determine independence.
Quadratic Functions
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Introduction to quadratics
using representations to
discover new types of
pattern and change.
Solidification of quadratic
functions in multiple
representations.
Examining the difference
between linear and
quadratic rate of change.
Focus on
maximum/minimum
points as well as
domain/range.
Examining quadratic
functions on various sized
intervals to determine rate
of change.
Comparing quadratic to
exponential functions to
distinguish the rate of
change.
Incorporating quadratics
with the understanding of
linear and exponential
functions.
Structure of Expressions
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Connecting
transformations to
quadratic functions and
parabolas.
Working with vertex form
of a quadratic, connecting
the components to
transformations.
Visual and algebraic
approaches to completing
the square.
Connecting the factored
and expanded form of a
quadratic.
Focus on the vertex and
intercepts for quadratics.
Building fluency in
rewriting and connecting
different forms of a
quadratic.
Quadratic Equations
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Examining values of
continuous exponential
functions between
integers.
Connecting radicals and
rules of exponents to
create meaning for rational
exponents.
Verifying that properties
of exponents hold true for
rational exponents.
Fluent in rewriting
between exponential and
radical forms of
expressions.
Developing quadratic
formula as a way for
finding x-intercepts and
roots of quadratics.
Examining how different
forms of a quadratic
expression can facilitate
the solving of quadratic
equations.
Solving quadratic
equation.
Surfacing the need for
complex numbers.
Extending the real and
complex numbers as
solutions for some
quadratics.
Examining the arithmetic
of real and complex
numbers.
1
Probability
Vocabulary:
 Independence
 Dependence
 Event
 Probability
 Union
 Intersection
Questions
Below is a two-way table depicting two states and their most liked sports. Fill out the
following probabilities being asked. Use a calculator.
California (C)
New York (NY)
Total
1.
2.
3.
4.
5.
6.
7.
Soccer (S)
8390
6747
15, 137
Total
18,680
26, 938
45, 618
What is the P(S)?
What is the P(B)?
What is the P(C)?
What is the P(NY)?
What is P(B and C)?
What is the P(S and NY)?
What is the P(S | C)?
Quadratic
Functions
Vocabulary:
 Quadratic
 Linear
 Maximum
 Minimum
 Rate of change
 Exponential
 Recursive Formula
 Explicit Formula
Basketball (B)
10,290
20,191
30, 481
Questions
Factor the following expressions
8. 𝑥 2 − 9
9. 𝑥 2 − 16
10. 12𝑥 2 − 20𝑥 − 8
11. 2𝑥 2 + 5𝑥 − 25
Plug in the following number into the functions:
𝑓(0), 𝑓(−1), 𝑎𝑛𝑑 𝑓(2).
2
12. 𝑓(𝑥) = 3𝑥 − 2𝑥 + 1
13. 𝑓(𝑥) = 7𝑥 − 2
14. 𝑓(𝑥) = (𝑥 − 3)(𝑥 + 1)
Classify the following functions as either linear, quadratic, or exponential:
15. 𝑓(𝑥) = 2𝑥 + 1
16. 𝑓(𝑥) = 𝑥 2 + 𝑥 + 1
17. 𝑓(1) = 1, 𝑓(𝑥) = 𝑓(𝑥 − 1) + 2
18. 𝑓(0) = 2, 𝑓(𝑥) = 𝑓(𝑥 − 2) + 2𝑛
2
Structure of
Expressions
Vocabulary
 Quadratic
functions
 Parabolas
 Vertex form
 Transformations
 Completing the
square
 Factored form
 Expanded form
 x-intercepts
 y-intercepts
Questions
Convert to Vertex Form (complete the square):
19. 𝑦 = 𝑥 2 + 2𝑥 − 8
20. 𝑦 = 𝑥 2 + 6𝑥 + 8
Convert to Standard Form (distribute):
21. 𝑦 = (𝑥 − 1)2 − 9
22. 𝑦 = (𝑥 − 3)2 − 1
Convert to Factored form (diamond):
23. 𝑦 = 𝑥 2 + 2𝑥 − 8
24. 𝑦 = 𝑥 2 + 6𝑥 + 8
Quadratic
Equations
Vocabulary:
 Exponential
function
 Integers
 Quadratics
 Radicals
 Exponents
 Rational exponents
 Quadratic formula
 Roots of quadratic
functions
 Complex numbers
 𝑖 2 = −1
 𝑖 3 = −𝑖
 𝑖4 = 1
 𝑖5 = 𝑖
Questions
Find the solutions to the given equations:
25. 𝑥 2 + 8𝑥 + 7 = 0
26. (𝑥 + 8)2 = 7
27. 3𝑥 2 − 11𝑥 + 3 = 0
Simplify the imaginary numbers:
28. 𝑖 7
29. 2𝑖 2 + 3𝑖 3 + 4𝑖 4
30. 10√−9 + 11(√−4)
31. 10 + (√−100)
2
Find the solutions to the following equations:
32. 5𝑥 2 − 2𝑥 + 4 = 0
33. 𝑥 2 + 4𝑥 − 12 = 0
34. 4𝑥 2 + 4𝑥 − 3 = 0
3