Accelerated Analysis Midterm Exam Review

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Accelerated Analysis Midterm Exam ReviewAccelerated Analysis Midterm Exam Review.doc12th GradePeriod 7-8 (Accelerated Analysis)

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Name ____________________________ Due Date __________________
Review for Accelerated Analysis Midterm Exam
You may use a calculator for highlighted topics
Unless otherwise indicated, problems are found on p. A-26 and A-27 in the
indicated section of the extra practice pages in the back of your textbook
Chapter 1 Concepts Problems
1.1
• Determine whether a relation is a function
• Identify domain and range of a relation or a function
• Evaluate functions
• Give domain restrictions in the denominator and under an even
root radical
#2
#6
p. 11 #48-50
1.2
• Perform operations with functions
• Perform composition of functions
#1
#2
1.3
• Graph linear equations using x- and y-intercepts
• Find slope of a line given two points
• Find zeros of linear functions and graph
p. 23 #5
p. 23 #31
p. 23 #35
1.4
• Write linear equations in point-slope, slope-intercept, and
standard forms
#5 Write eq
in all three
forms
1.5
• Write equations of parallel and perpendicular lines
#1
1.6
• Create scatter plots
• Write a predictions equation/equation for line of best fit
• Compute correlation coefficient to determine goodness of fit
#1
#3
#4
1.7
• Identify and graph piecewise functions: classic
Absolute value
step
#1
#2
#3
Name ____________________________ Due Date __________________
Review for Accelerated Analysis Midterm Exam
You may use a calculator for highlighted topics
Unless otherwise indicated, problems are found on p. A-28 and A-29 in the
indicated section of the extra practice pages in the back of your textbook
Chapter 2 Concepts Problems
2.1
• Solve systems of equations graphically
• Solve systems of equations algebraically via
Substitution and elimination
#2
#6
2.2
• Solve systems of equations involving three variable
algebraically
#3
2.3
• Solve a matrix equation including two equal matrices
• Add, subtract and multiply matrices
#3
#5, 6, 7, 9, 10
2.5
• Calculate determinant of a 2x2 and a 3x3 matrix
• Find the multiplicative inverse of a 2x2 matrix
• Find the multiplicative inverse of a 3x3 matrix
• Solve systems of equations using inverses of matrices
#1, 5
#9
#5 Find inverse on calc
#13
2.6
• Graph systems of inequalities
• Find the maximum/minimum value of a function defined for
a set of points of a convex polygon
#2
2.7
• Use Linear Programming to problem solve
• Recognize situations where there are alternate optimal
solutions or no solution
#1
p. 116 #9, 10, 11
Answers to Review for Accelerated Analysis Midterm Exam
Chapter 1 Answers
1.1 #2). {-3, -0.5, 0.5, 3}; {0.5, 3}; yes #6) 26 p. 11 #48) 5 t ≠ x
#49)
3 3 ≥ − ≤ x or x
#50) 7 7 > − < x or x
1.2 #1)
1 3
1 2
; 1 5 5 2 ; ; 2 5
2
2 3 2 2
− +

+ − + − − − +
x x
x
x x x x x x x

#2) 36 24 4 ; 3 4
2 2
+ − + − x x x
1.3 p. 23 #5)Check on graph calc #31) check on graph calc ; 2
#35) a.
4
1
c. check on graphing calc
1.4 #5)
4 2 ; 2
2
1
; ) 2 (
2
1
3 ) 2 (
2
1
1 · + + − · + − · − − − · − y x x y x y or x y
1.5 #1) None of these; slopes are neither the same nor opposite reciprocals
1.6 #1) see graph calc #3) y = 0.6125x-1178; r ≈ 0.99 #4) strong correlation; 53.7 million
1.7 #1) check on graph calc #2) check on graphing calc #3) check on graphing calc
Chapter 2 Answers
2.1 #2) (-1, 5); consistent & independent #6) (-1,5)
2.2 #3) (-1, 0, 3)
2.3 #3) (-4, -5) #5)
]
]
]



1 5
6 5
#6)
]
]
]





8 12 16
12 0 8
#7) impossible
#9 impossible #10)
]
]
]


− −
3 16
14 14
2.5 #1) 83 #5) 34 #9)
]
]
]
]




2
5
2
3
3 2
#5) inverse:
]
]
]
]
]
]
]
]








− −

17
5
17
3
17
3
34
9
17
1
34
19
34
7
17
3
34
11
#13)

,
`

.
|
−1 ,
2
5
2.6 #2) (0,3), (4,7), (4,2), (0,2); 6; -3
2.7 #1) 50 cars, 10 buses p. 116 #9) infeasible #10) unbounded
#11) alternate optimal solutions
Name ____________________________ Due Date __________________
Review for Accelerated Analysis Midterm Exam
You may use a calculator for highlighted topics
Unless otherwise indicated, problems are found on p. A-30 and A-31 in the
indicated section of the extra practice pages in the back of your textbook
Chapter 3 Concepts Problems
3.1
• Test for symmetry about the origin
• Test for line symmetry about the x-axis, y-axis, y=x, & y= – x
• Classify functions as odd or even
#1, 2
#4
Are #1 & 2 odd
functions?
Is #4 an even
function?
3.2
• Recognize and sketch parent graphs
• Recognize and sketch transformations of parent graphs
#1-5
3.3
• Graph Nonlinear inequalities
• Solve absolute value inequalities
#1, 2
#7, 10
3.4
• Graph functions and their inverses
• Determine inverses of relations and functions
#1, 2
#4, 6
3.5
• Use the continuity test to determine whether a function is
continuous or discontinuous
• Identify types of discontinuity: point, jump, infinite
• Identify end behavior of functions
• Determine Monotonicity (whether a function is Increasing or
decreasing on an interval)
#1
#5
#6, 7
#6 determine if
this function is
increasing or
decreasing over
intervals
3.6
• Find critical points and extrema: relative & absolute max/min,
• Identify a critical point as a max, min, or point of inflection
#1, 2
p. 177 #26,
# 27, 28
3.7
• Graph rational functions by determining point discontinuity
(holes) and asymptotes: vertical, horizontal, and slant
p.187
#31, 37, 39
Name ____________________________ Due Date __________________
Review for Accelerated Analysis Midterm Exam
You may use a calculator for highlighted topics
Unless otherwise indicated, problems are found on p. A-32 and A-33 in the
indicated section of the extra practice pages in the back of your textbook
Chapter 4 Concepts Problems
4.1
• Write a polynomial equation of least degree given roots
• State the number of complex roots of a polynomial function.
• Determine the roots of a polynomial equation
#8
4.2
• Solve quadratics by completing the square and quadratic
formula
• Use the discriminant to determine the nature of the roots
• Solve quadratic equations using the quadratic formula
#3, 4
#7, 8, 9
4.3
• Find the factors of polynomials using the Remainder and
Factor Theorems
#5, 6
4.4
• Identify all possible roots using the Rational Root Theorem
• Determine the number of positive and negative real roots of
a polynomial function using Descartes’ rule of signs
#4
#8
4.5
• Locate zeros of a polynomial using a table
• Approximate the zeros of a polynomial function by graphing
#1 (use table)
#4 (use graph, 2
nd
calc
zero…)
4.6
• Solve a rational equation…check for excluded/restricted
values
• Solve a rational inequality…test intervals
• Decompose a fraction into partial fractions
Solve:
2
1
6
5
) 2 ( 3
1

+ ·

+
a
a
a
a
#6
p. 248 #25
4.7
• Solve a radical equation…check for extraneous roots
• Solve a radical inequality…test intervals
p. 255 #17
Solve:
4 2 6
4
< − a
Chapter 3 Answers
3.1 #1) yes #2) no #4) y = x. y = -x …#1 is an odd function, #2 is not an odd
function, #4 is not an even function
3.2 #1) vertical translation up 2 units #2) vertical expansion by a factor of 3
#3) vertical translation down 3 units and horizontal translation left 4 units
#4) vertical compression by a factor of 2 and horizontal translation 1 unit right
#5)
5
2
1

]
]
]



− · x y
3.3 #1)see graphing calculator→ parabola, solid line, shade outside
#2)see graphing calculator→ “V” shape, dashed line, shade inside
#7) 5 1 ≤ ≤ − x #10) x < -5 or x > 3
3.4 #1) function→”V” shaped, vertex (0, -2), opens up; inverse→”V” shaped,
vertex (-2, 0), opens right
#2) function→parabola, vertex (0, 1), opens up; inverse→parabola,
vertex (1, 0), opens right
#4)
( ) yes
x
x f ;
4
5
1
+
·

#6) no x y ; 6 − t ·
3.5 #1) yes, function approaches 1 as x approaches 2 from both sides
#5) jump discontinuity #6)
∞ → ∞ →
−∞ → −∞ →
y x as
y x as
,
,
#7)
−∞ → ∞ →
−∞ → −∞ →
y x as
y x as
,
,
In #6, the function (to the nearest tenth) is:
increasing for x< -1.8 and for x > -0.2 and decreasing for -1.8 < x < -0.2
3.6 #1)abs max @ (-1,2) #2) rel min @ (-3,0), rel max @ (-1,3), abs min @ (2, -1)
p. 177 #26) pt of inflection #27) max #28) min
3.7 p. 187 #31) y = x + 3 #37) check on graphing calc→ hole @ x = -2, vertical
asymptote @ x = 2, horizontal asymptote @ y = 0 #39) check on graphing
calc→ hole @ x = 3,vertical asymptote @ x = -2,horizontal asymptote @ y = 1
Chapter 4 Answers
4.1 #8) 1 ; ; 0 2 2
2 3
odd x x x · + + +
4.2 #3)
2
17
2
3
t − #4) 7 2 t #7) 121; 2 real rational rts; x=-1,
4
7
#8) 44; 2 real irrational rts; w= 11 1t − #9) -263;2 imaginary;
24
263 5 i t
4.3 #5) 0; yes #6) 13; no
4.4 #4)
2
1
,
3
2
;
6
1
,
3
8
,
3
4
,
3
2
,
3
1
,
2
1
, 8 , 4 , 2 , 1 − t t t t t t t t t t
#8) 3 or 1;
1; 1
4.5 #1) -1 and 0, 2 and 3 #4)
3 . 1 , 3 . 0 ≈ x
4.6 Solve:
5
2
· a
#6) 0 < x < 3 or x > 6 p. 248 #25)
1
2
1 3
2


+
− y y
4.7 p. 255 #17) no real solution Solve:
43
3
1
< ≤a
Name ____________________________ Due Date __________________
Review for Accelerated Analysis Midterm Exam
You may use a calculator for highlighted topics
Unless otherwise indicated, problems are found on p. A-34 and A-35 in the
indicated section of the extra practice pages in the back of your textbook
Chapter 5 Concepts Problems
5.1
• Find coterminal angles for
° < ≤ ° 360 0 θ

• Find measures of reference angles
• Find the number of degrees in a given number of rotations
#9, 10
#13, 15
p. 281 #31, 33
5.2
• Identify reciprocal functions
• Find the values of Trig ratios for acute angles of a right
triangle: sin, cos, tan, sec, cos, cot
#1, 2
#5
5.3
• Use the unit circle to find the values of six trig functions for a
given angle
• Given one trig function value for
θ
, find the remaining trig
function values of θ if θ is an angle in standard position
whose terminal side lies in a given quadrant
p. 297 #25
p. 297 #33
5.4
• Use trig to find the measures of the sides of a right triangle
• Use trig to solve problems involving Angles of elevation and
depression
#3, 5
p. 326 #41
5.5
• Evaluate expressions containing inverse trig functions
• Solving a right triangle for a missing angle
• Solve right triangles
p. 309 #22, 27
#4, 5
p. 310 #37
5.6
• Solve triangles by using The Law of Sines
• Find the area of triangles
#3
#7
5.7
• Determine whether a triangle has zero, one or two solutions
(the ambiguous case)
#2, 3
5.8
• Solve triangles by using The Law of Cosines
#2
Name ____________________________ Due Date __________________
Review for Accelerated Analysis Midterm Exam
You may use a calculator for highlighted topics
Unless otherwise indicated, problems are found on p. A-36 and A-37 in the
indicated section of the extra practice pages in the back of your textbook
Chapter 6 Concepts Problems
6.1
• Change radians ↔ degrees
• Find Length of an arc
• Find Area of a sector
#3, 6
#13 (Find arc length
and area of sector)
6.2
• Find angular velocity and linear velocity
p. 355-356
#21, 29
6.3
• Graph a function for a given interval
• Know period, domain, range, x-int, y-int, max and min from
graphs of sine and cosine functions (see p. 360, 362)
p. 364 #31
6.4
• Find the amplitude and period for sine and cosine functions
• Write equations of sine and cosine functions given the
amplitude and period
#2, 3
#5, 7
6.5
• Find the phase shift and vertical translation for sine and
cosine functions
• Write equations of sine and cosine functions given the
amplitude, period, phase shift and vertical translation
p. 384 #23, 27
#4, 6
Chapter 5 Answers
5.1 #9) 130º; II #10) 295º; IV #13) 54º #15) 78º p. 281 #31) 720º #33) -2700º
5.2 #1)
5
6
#2) 0.4 #5)
2
3
cot ;
3
13
sec ;
2
13
csc ;
3
2
tan ;
13
13 3
cos ;
13
13 2
sin · · · · · · A A A A A A
5.3 p. 297 #25)
3 210 cot ;
3
3 2
210 sec ; 2 210 csc ;
3
3
210 tan ;
2
3
210 cos ;
2
1
210 sin · ° − · ° − · ° · °

· ° − · °
#33)
8
1
cot ; 65 sec ;
8
65
csc ; 8 tan ;
65
65
cos ;
65
65 8
sin − · · − · − · · − · θ θ θ θ θ θ
5.4 #3)c = 39.6 #5) b = 5.6 p. 326 #41) about 185.6 m
5.5 p. 309 #22)
5
4
#27)
5
21
p. A35 #4) A = 56.7º #5) B = 63.5º p. 310 #37) B = 55º, a =
5.6, c = 9.8
5.6 #3) A = 99º, b = 7.6, c = 5.4 #7) 37.9 units
2
5.7 #2) Ambiguous case - two solutions: B = 44.8º, C = 110.2º, c = 13.3 ; B = 135.2º, C = 19.8º, c =
4.8 #3) none
5.8 #2) A = 48.2º, B = 35.4º, C = 96.4º
Chapter 6 Answers
6.1 #3)
9
22π

#6) 75º #13) arc length = about 7.0 inches, area of sector =
inches sq about or 4 . 17
9
50π
6.2 p. 355-356 #21) 9.0 radians per second #29) 109.6 feet per second
6.3 p. 364 #31) check on graph calc…be in radian mode, set window
[ ] [ ] 1 , 1 0 , 6 − − by π
…take
part of graph
x
scl=
π
y
scl=1
from
π π 3 5 − − to
6.4 #2) 3; 4
π
#3)
π 8 ,
2
1
#5)
θ 6 sin 2 t · y
#7)
θ
π
4
cos 25 . 0 t · y
6.5 p. 384 #23)
2 ,
4
, 6 , 1 −
π
π
#27)
2 ,
2
, 4 , 4 − −
π
π

p. A-37 #4)
( ) 1 sin 2 − − t · π θ y
#6)
( ) 4 8 4 cos 20 + − t · π θ y

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