Final Exam Study Guide based off of standards released by DPI.
NAME:______________________________________________
N-RN.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.
1)
2)
3)
4)
5)
Simplify: x0 ∙ 643/2
Solve for x: (20x)(2012) = 2045
Solve for x: (5x)/(530) = 550
Solve for x: x1/3 − 5 = 0
6)
A-SSE.1 Interpret expressions that represent a quantity in terms of its context.
b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as
the product of P and a factor not depending on P. Note: At this level include polynomial expressions
7) Solve the following equation: 12(10)3x + 2 = 120
A-SSE.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing
it as a difference of squares that can be factored as (x2 – y2)(x2 + y2).
8) Re-write the following equation in standard form: y=5(x + 2)2 – 4
9) Re-write the following equation in factored form: y = x2 + 2x – 8
10)
A-APR.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations
of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
Note: At this level, add and subtract any polynomial and extend multiplication to as many as three linear expressions.
11) Add: 4x2 +(−12xy) + 9y2 + 25x2 + 4xy + (−32y2)
12) Multiply: (4x – 7xy)(2y + 3x)
13) Subtract. (10a3 + 5b2 – 5c + 10) – (15 + 5c – 15b2 + 10a3)
14)
A-APR.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph
of the function defined by the polynomial. Note: At this level, limit to quadratic expressions.
15) Find the zeros of the following cubic function: y = (x + 3) (x – 5) (x + 2)
16) Write a quadratic function with a graph that meets the following conditions: x-intercepts at (2, 0)
and (6, 0) with a minimum at (4, -8)
17)
HSA-CED.A.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from
linear and quadratic functions, and simple rational and exponential functions.
Note: At this level extend to quadratic and inverse variation (the simplest rational) functions and use common logs to solve
exponential equations.
18) There are 60 students going on a field trip to the chocolate factory. The students are from three
different classes. Mrs. Hooper's class has 24 students and Mr. Gomez's class has 18 students.
Which of the equalities correctly describes the students and could be used to solve for how many
students are from Mr. Anderson's class? (Let A = the number of students in Mr. Anderson's class.)
a. A + 18 = 24
b. A + A + A = 60
c. 60 – 18 = A – 24
d. 24 + 18 + A = 60
19) A total of 66 people attended a field trip to a chocolate factory for a tour. A maximum of 15 people
are allowed to tour at one time. Which equation correctly describes how many tour groups to
organize? (Let g = the number of groups.)
a. (A)
(B)
(C)
(D)
HSA-CED.A.2 : Create equations in two or more variables to represent relationships between quantities; graph equations on
coordinate axes with labels and scales.
Note: At this level extend to simple trigonometric equations that involve right triangle trigonometry.
20)
21)
HSA-REI.A.2: Solve simple rational and radical equations in one variable, and give examples showing how extraneous
solutions may arise.
Note: At this level, limit to inverse variation.
22)
23)
4
𝑥−7
4
𝑥+2
=
6
𝑥
+ 3=
9
𝑥+2
24)
25)
26)
HSA-REI.B.4.B: Solve quadratic equations in one variable.
b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic
formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives
complex solutions and write them as a ± bi for real numbers a and b.
Note: At this level, limit solving quadratic equations by inspection, taking square roots, quadratic formula, and factoring when
lead coefficient is one. Writing complex solutions is not expected; however recognizing when the
7
27) √𝑥 = 15
28) 4𝑥 5 − 20 = 40
29) (4 + 𝑥)
30)
5⁄
2
− 5 = 15
31)
32)
Solve the following quadratic equations by factoring, taking the square root, or using the quadratic
formula and match to its solutions:
_____ 1) x2 – 3x – 28 = 0
_____ 2) 2x2 - 5 = 3x
_____ 3) 6x2 - 72 = 0
_____ 4) 5x – 24 = - x2
_____ 5) 2x2 = - 9x – 7
_____ 6) x2 + 2x – 120 = 0
A. x = 2.5 and x = -1
B. x= -8 and x = 3
C. x= = -1 and x = -3.5
D. x = 3.46 and x = -3.46
E. x = 10 and x = -12
F. x = -4 and x = 7
HSA-REI.D.10: Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate
plane, often forming a curve (which could be a line). Note: At this level, extend to quadratics.
33)
Dr. Frankenstein thinks he knows more than you about what is true and false in the world just because
he's a doctor. (Just because he brought a corpse back to life, he thinks he's hot stuff.) He says that the
equation y = 17x + 1 also includes the point (1, 8). Is Dr. Frankenstein right or wrong?
(A) He's right
(B) He's wrong
(C) We need more information before we can say if he's right or wrong
(D) None of the above
34)
The Kooky Dough Company makes cookie dough, but it takes a little time for it to start reeling in the
dough. The equation y = 2x – 8 models the profits y after making x pounds of cookie dough. What are the x
and y coordinates of their break-even point?
(A) (4, 0)
(B) (0, 4)
(C) (2, 0)
(D) (0, 2)
35)
HSG-GMD.B.4 : Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify threedimensional objects generated by rotations of two-dimensional objects.
36)
HSG-GMD.B.4: Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify threedimensional objects generated by rotations of two-dimensional objects.
HSG – CO.A. 2:Represent transformations in the plane using, e.g., transparencies and geometry software; describe
transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations
that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
37)
38)
39)
40)
SG-CO.B.8: Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in
terms of rigid motions.
41) Which pair of triangles is congruent by ASA?
a)
b)
c)
d)
42) By which of the following postulates could you say the triangles below are congruent.
A. SAS
B. ASA
C. SSS
D. Not congruent
̅̅̅̅ ≅ 𝐴𝐶
̅̅̅̅ , and D is the midpoint of segment BC.
43) In the figure to the right, 𝐴𝐵
Is ΔADB ≅ ΔADC? If so, which congruence postulate states that they are congruent?
44) In the figure to the right, ∠𝐴 ≅ ∠𝐷, ∠𝐵𝐶𝐷 ≅ ∠𝐵𝐶𝐴.
Which congruence postulate states that they are congruent?
Write the congruence statement (Δ??? ≅ Δ???)
45) In the figure to the right, is ΔPQR≅ ΔKMN?
If so, which congruence postulate states that they are congruent?
46) In the figure to the right, ∠CBD and ∠CBA are right angles, and
CD ≅ CA. Is ΔCBD≅ ΔCBA? If so, which
congruence postulate states that they are congruent?
HSG-SRT.C.6: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to
definitions of trigonometric ratios for acute angles.
47)
HSG.SRT.C.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
48)
49)
50)
51)
52)
53) A girl 5.5 ft tall holds a string that is 50 ft. and is attached to a kite. If the string makes an angle of
elevation of 57o, how high is the kite off of the ground? Round to the nearest tenths.
54)
55)
56)
57)
HSG.GPE.B.6: Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
58)
HSS-IC.A.2: Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a
model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model?
59) The plastic arrow on a spinner for a child’s game stops rotating to point at a color that will
determine what happens next. Which of the following probability assignments are not possible?
a)
b)
c)
d)
Red
0.25
0.10
0.20
0.30
Probabilities of….
Yellow
Green
0.25
0.25
0.20
0.30
0.30
0.20
0.25
0.20
Blue
0.25
0.40
0.50
0.25
60)
S-CP.9 (+) Use permutations and combinations to compute probabilities of compound events and solve problems.
61) A captain and co-captain for a soccer team are chosen from a hat with the names of all 10
members in the hat. Determine the probability that Abbie is chosen as captain Morgan as cocaptain.
A)
1
B)
10
1
C)
5
1
1
D) 45
90
62) There are 25 kids in a class and the teacher is choosing four students to help the secretary move
books. If the teacher randomly chooses 4 students, what is the probability that Jason, Alexis,
Michael, and Madison will be selected?
A)
1
303600
1
B) 12650
C)
1
4
D) 25
100
63) What is the probability that 5 books placed randomly on a shelf will be placed alphabetically?
A)
1
120
B)
1
5
C)
1
2
D)
1
24
HSG-MG.A.1 : Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a
human torso as a cylinder).
64) Real-World Objects are listed and/or pictured below. Name the geometric 2-D or 3-D figure(s)
that best represent(s) each object. Be as specific as possible.
1. Stop sign
2. Yield sign
3. Orange (the fruit)
4. Soup can
5. Mattress for your bed
6. Tree trunk
7. Birthday Cake
8. Children’s party hat
9. Trailer part of a tractor-trailer
truck
10. The Pentagon (in DC)
11. Megaphone (ignore
handle)
12. Bird house (as pictured)
HSF-IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function
notation in terms of a context.
Note: At this level, extend to quadratic, simple power, and inverse variation functions.
65)
66)
67)
HSF-IF.B.4: For a function that models a relationship between two quantities, interpret key features of graphs and tables in
terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features
include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and
minimums; symmetries; end behavior; and periodicity.
Note: At this level, limit to simple trigonometric functions (sine, cosine, and tangent in standard position) with angle measures of
180° (𝜋 𝑟𝑎𝑑𝑖𝑎𝑛𝑠) or less. Periodicity not addressed.
68)
69)
70)
HSF-IF.C.7.B : Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using
technology for more complicated cases.
b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
Note: At this level, extend to simple trigonometric functions (sine, cosine, and tangent in standard position)
71)
72) f(x) = √𝑥 − 3
A) Describe in words the transformations
B) Identify the Domain
C) Identify the Range
D) Identify the End Behavior
E) Graph the function
3
73) f(x) = √𝑥 + 4
A) Describe in words the transformations
C) Identify the Range
B) Identify the Domain
D) Identify the End Behavior
E) Graph the function
74) f(x) = − √𝑥
A) Describe in words the transformations
3
C) Identify the Range
E) Graph the function
B) Identify the Domain
D) Identify the End Behavior
1
75) f(x) = 2 √𝑥
A) Describe in words the transformations
B) Identify the Domain
C) Identify the Range
D) Identify the End Behavior
E) Graph the function
HSF-IF.C.7.E: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using
technology for more complicated cases.
e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions,
showing period, midline, and amplitude.
Note: At this level, extend to simple trigonometric functions (sine, cosine, and tangent in standard position)
76)
77) What is the amplitude of the graph of the equation y = 2sin(3x)?
A. 3
B. 2
C. 0
D. 6
78) What is the midline of the graph of the equation y = 1 + 4cos(x)
A. y = 4
B. y = 1
C. x = 1
D. x = 4
HSF-IF.C.8.A: Write a function defined by an expression in different but equivalent forms to reveal and explain different
properties of the function.
a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and
symmetry of the graph, and interpret these in terms of a context.
Note: At this level, completing the square is still not expected.
79) Factor: x 2 – 3x – 28.
a. (x + 7)(x - 4)
b. (x - 7)(x + 4)
c. (x + 7)(x + 4)
d. (x - 7)(x - 4)
80) What are the solutions for the equation: 𝑦 = x 2 – 3x – 28.
81) Factor: 2𝑥 2 + 8𝑥
a. 2x(x + 4)
b. (x + 4)(2x + 2)
82) What are the solutions for the equation: 𝑦 = 2𝑥 2 + 8𝑥
c. x(2x + 8)
d. 2(𝑥 2 + 4𝑥)
83) Solve: 4x2 - 9 = 0
a. (2x + 3)(2x + 3)
b. x = -1.5 and x = 1.5
c. x = 1.5
d. (2x – 3)(2x + 3)
84) What are the vertex and the axis of symmetry of the quadratic function: 𝑦 = −2𝑥 2 + 6𝑥 − 3?
a. (-1.5, -1.5); y = -1.5
b. (-1.5, -1.5); x = -1.5
c. (1.5, 1.5); y = 1.5
d. (1.5, 1.5) x = 1.5
HSF-IF.C.9: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in
tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another,
say which has the larger maximum.
Note: At this level, extend to quadratic, simple power, and inverse variation functions.
85)
86)
87) Heidi Semaj jumped off of a cliff into the ocean while vacationing in Acapulco. Heidi’s height as a function of
time could be modeled by the function h(t) = − 16t2 +16t + 52, while Semaj’s height could be modeled by h(t) =
-16t2 + 12t + 52 where t is the time in seconds and h is the height in feet. Whose jump was higher and by how
much?
A. Heidi by 2.75 ft
B. Semaj by 2.75 ft
C. Heidi by 1.75 ft
D. Semaj by 1.75 ft
HSF-BF.B.3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both
positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects
on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for
them. Note: At this level, extend to quadratic functions and, k f(x).
88) Label the six functions as “even”, “odd”, or “neither”.
a) y = 𝑥 5 − 2𝑥 2
b) 𝑦 = 4𝑥 2 − 3
c) 𝑦 = 𝑥 3 + 𝑥
a) ____________________
b) ____________________
c) ________________
d) y = 𝑥 5 − 2𝑥 3
e) 𝑦 = 4𝑥 2 − 𝑥
f) 𝑦 = 𝑥 4 + 2𝑥 2
d) ____________________
89)
e) ____________________
f) ________________
90)
91)