Download B. Apply properties of exponents (5.1)

ALGEBRA II WITH TRIGONOMETRY
MIDTERM EXAM REVIEW – PART I
Work on separate paper! Copy down the original problem first.
CHAPTER 1 –EQUATIONS
A.
B.
C.
D.
E.
F.
G.
H.
I.
AND
INEQUALITIES
Apply Properties of Real Numbers (1.1)
Apply properties of exponents (5.1)
Evaluate and Simplify Algebraic Expressions (1.2)
Solve Linear Equations (1.3)
Rewrite Formulas and Equations (Literal Equations) (1.4)
Use Problem Solving Strategies and Models (1.5)
Solve Linear Inequalities (1.6)
Solve Absolute Value Equations and Inequalities (1.7)
Perform Operations with Complex Numbers (4.6)
PROBLEM SET
1)
2)
Simplify the following expressions until there are no negative exponents or
parentheses and each base is used only once.
a)
3x–2(xy)3
c)
9x 2 (x 3 y)2
(6x)2 y 1
b)
d)
y0(x2z)3
(2y)2 (y 4 z)2
4z 2 y 2
Which of the following classifications apply to each of these numbers:
Real, Rational, Integer, Imaginary, Complex
a)
c)
e)
g)
-0.05
2/3
-15
0
b)
d)
f)
h)
0.666…
4 + 8i
-5i
2 7
1
3)
4)
5)
State the name of the property for each example
a) -18  1 = -18
b)
c) 2x + 5 = 5 + 2x
e) -29  (4  x) = (-29  4)  x
d)
f)
Simplify each numerical expression.
a)
2(-1 + 3) - 42  8
b)
c)
(|-3| + |7| - |6|) (5|2|- |-7|)
d)
a)
63
b)
c)
256
d)
e)
12  5 24  11 75
i)
k)
13


6 3 5  6

5
6 2
f)
162
32
8  5 63
h)
18  12
j)
2 5
8
l)
4 3
92 3
2 + 7i
b)
3 – 5i
Solve for x and y.
a)
8)
7
2
2
 150
Give the conjugate of each number.
a)
7)
2(3 + 18  9) – 7
4  (6  9)2
8(3  7)  2
Simplify each radical expression.
g)
6)
1
=1
7
7a(b + 3c) = 7ab + 21ac
8+0=8
7 
5x + 2yi = 15 + 4i
b)
3x – 7yi = 2 + -14i
Simplify each expression involving complex numbers.
a)
c)
e)
g)
(2 + 9i) + (4 - 11i)
i2(4 + i)
(3 + 4i)(2 – 5i)
(4 – i)²
b)
d)
f)
h)
(2 + 3i) – (8 + 2i)
8i(1 + 2i)
(12 – 5i)(12 + 5i)
i267
2
i15
5
6i
i)
k)
m)
9)
j)
l)
5
7  2i
n)
Solve
a) 3(5 - a) – a = -4(a - 4)
2
5
3
c)
x-7= x+
3
6
4
e) A = P + Prt for t
g) S = L - rL for L
i)
| 5r - 8 | = 2
k)
2
x 3
7
b)
d)
f)
h)
j)
x 5
l)
x 3
(3i)2(8i)
26
 12i
3  4i
2  5i
15(x - 2) = -13(x + 1) + 11
x  2 2x  1 10  x


4
3
6
2
V = r h for h
6x – 3b = 12ax for x
| 3x + 2 | = 13
3
2m

4
3

5
m

1
2
10) Solve and graph on a number line, give interval notation.
a)
c)
5x - 2 < 13
1  3x  16  20
b)
d)
-2x - 1  5
2x  7  5 and 2x  6  12
e)
g)
| 2x - 1 | < 3
| 3x - 5 | > 9
f)
h)
| -3x -2 |  4
| -2x - 3 | > 7
CHAPTER 2 – LINEAR EQUATIONS
A.
B.
C.
D.
E.
F.
G.
H.
I.
AND
FUNCTIONS
Represent Relations and Functions (2.1)
Find Slope and Rate of Change (2.2)
Graph Equations of Lines (2.3)
Write Equations of Lines (2.4)
Model Direction Variation (2.5)
Model Inverse and Joint Variation (8.1)
Draw Scatter Plots and Best-Fitting Lines (2.6)
Use Absolute Value Funs and Transformations (2.7) plus extension on Piecewise
Graph Linear Inequalities in Two Variables (2.8)
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PROBLEM SET
1)
Consider the relation { (-5, -9), (-2, -3), (0, 1), (4, 9), (7, 15) }.
a) State the domain.
b) State the range.
c) Is the relation a function? Why or why not?
d) What is the rule?
e) Describe the relation in a mapping.
2)
A line has a slope of
3)
In 1990 Marc earned $42,360 per year, and he now earns $61,800. What is the
rate of change for Marc’s salary per year?
4)
If f(x) = 4x – 3 and g(x) = 2 – 7x2, evaluate each of the following.
2
and contains the points (3, -4) and (6, y). What is y?
3
a) f(-6)
c) f(2a)
5)
b)
d)
g(2)
f(g(-4))
b)
2x + 3y – 12 = 0
Find the x- and y-intercepts for:
a)
-3x + 4y = -2
6)
Write a linear equation using the given information.
2
a) slope of
and a y-intercept of 4. (Write in standard form.)
3
b) through the points (-6, -1) and (3, 2).
c) through the points (4, 3) and (0, -5). (Write in general form.)
d) horizontal line through the point (3, -7).
e) vertical line through the point (-2, -4).
f) through the point (3, -2) and perpendicular to 2x – 3y = 6.
7)
y
The piecewise function f(x) is defined as:
 1
  x 1
x  2
 2
f (x)  
 2x  3 2  x  0

3
x0
a)
f(5) =
b)
f(-4) =
c)
graph f(x) on the grid to the right
x
4
8)
Graph on these grids
a)
2x + 3y = 6
b)
y
5x - 2y = -4
y
x
c)
5x + 3y < 6
x
d)
y
6x – 2y  8
y
x
e)
f(x) = |x – 3| + 5
y
x
f)
f(x) = |2x + 6|
y
x
x
5
9)
The following chart shows the data of time spent studying and grade earned on last
years Algebra II midterm in one class.
a)
b)
c)
Hours
spent
studying
Midterm
Grade
Make a scatter plot on the grid below using these data and find the equation
for the line of best fit two ways: sketch and find the equation of a line and do
regression on your graphing calculator
What score would you expect a student to receive if he or she studied 2.75
hours?
How many hours would you expect someone to study to receive a perfect score?
.5
.5
1
1
50 72 55 64
1.25 1.5 1.75
68
74
75
2
2
2
82 77 94
2.25 2.5 2.5 2.75
85
88
98
96
3
3.5
61
97
y
x
10) Solve each of the following variation problems.
a) x and y vary directly. If x = 2 and y = 5, find the constant of variation and
write an equation relating x and y.
b) x and y vary inversely. If x = 7 and y = 9, find the constant of variation and
write an equation relating x and y.
c) If w varies jointly as x and y, and w = 28 when x = 4 and y = 21, find w when x = 12
and y = 17.
d) If y varies inversely as the square of x, and y = 50 when x = 4, find y when x = 5.
6