Download I. Chapter 1 –Equations and Inequalities

ALGEBRA II
WITH
TRIGONOMETRY: MIDTERM EXAM REVIEW 2012
Directions: Complete ALL questions for full credit. Do all work on notebook paper and/or
graph paper. You may print free graph paper online (google “free graph paper”). The due
dates for each of the 4 sections will be listed on SchoolWires. 4 HW points each
chapter.
I. CHAPTER 1 –EQUATIONS
A.
B.
C.
D.
E.
F.
G.
H.
AND
INEQUALITIES
Apply Properties of Real Numbers (1.1)
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
Simplify:
1)
2(-1 + 3) - 428
2)
2(3 + 189) - 7
4)
43x - 3y + 2 for x=5, y = -3
Evaluate:
3)
2t3 - 4t + 3 when t = 2
Solve:
5)
3(5 - a) = -4(a - 4)
6)
15(x - 2) = -13(x + 1) + 11
7)
A = P + Prt for t
8)
V = r2h for h
9)
S = L - rL for L
10) | 5r - 8 | = 2
11) | 3x + 2 | = 13
MPH 1/05 (REVISED 1/10 MD)
Page 1 of 7
ALGEBRA II
WITH
TRIGONOMETRY: MIDTERM EXAM REVIEW 2012
Solve and graph:
12) 5x - 2 < 13
13) -2x - 1  5
14) | 2x - 1 | < 3
15) | -3x -2 |  4
16) | 3x - 5 | > 9
17) | -2x - 3 | > 7
Simplify each expression.
18)
162
19)
20)
150 - 8 6
21)
3 27
2 6
2+4 3
5 -1
Simplify:
22)
- 144
23)
- 28 +
- 63
24) i15
25) (3i)(2i)
26) (2 + 3i) + (5 - 4i)
27) (2 + 3i) - (5 - 4i)
28) (2 + 3i)(5 - 4i)
29)
30) (3i)5
31) (4 -5i)2
(2 + 3i)
(5 - 4i)
32) Show that each decimal can be written as a rational number.
a)
0.32
b)
1.125
c)
0 .45
d)
2.236
MPH 1/05 (REVISED 1/10 MD)
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ALGEBRA II
II.
WITH
TRIGONOMETRY: MIDTERM EXAM REVIEW 2012
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 Functions and Transformations (2.7)
Graph Linear Inequalities in Two Variables (2.8)
PROBLEM SET
Find the x- and y-intercepts for:
1)
-3x + 4y = -2
2)
2x + 3y – 12 = 0
3)
Write the equation of the line in standard form for the line with slope of
y-intercept of 4.
-2
and a
3
4)
Write the equation of the line in standard form for the line through the points
(-6, -1) and (3, 2).
5)
Write the equation of the line in general form for the line through the points
(4, 3) and (0, -5).
6)
Write the equation of the horizontal line through the point (3, -7).
7)
Write the equation of the vertical line through the point (-2, -4).
Graph:
8)
2x + 3y = 6
10) 5x + 3y < 6
MPH 1/05 (REVISED 1/10 MD)
9)
5x - 2y = -4
11) 6x – 2y  8
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ALGEBRA II
WITH
TRIGONOMETRY: MIDTERM EXAM REVIEW 2012
Solve each of the following variation problems.
12) x and y vary directly. If x = 2 and y = 5, find the constant of variation and
write an equation relating x and y.
13) x and y vary inversely. If x = 7 and y = 9, find the constant of variation and
write an equation relating x and y.
14) 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.
15) If y varies inversely as the square of x, and y = 50 when x = 4, find y when x = 5.
Graph and analyze the following scatter plot.
The manager of a band has kept track of the price of tickets and the attendance at the
band’s recent concerts.
Price ($)
6
Attendance 213
Concert Attendance by Ticket Sales
5
8.5
8
10
5.5
256
155
194
160
267
7
258
7.5
210
8
235
16) Make a scatter plot of the data using price as the independent variable.
17) Find the correlation coefficient and the equation of the line of best fit. Draw the
line of best fit on your scatter plot.
18) Predict the attendance at a concert where the price of tickets is $9. How accurate
do you think your prediction is?
Graph the function.
19) y = - 4 x + 2 - 3
MPH 1/05 (REVISED 1/10 MD)
20) f(x) = 2x + 2 - 6
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ALGEBRA II
WITH
TRIGONOMETRY: MIDTERM EXAM REVIEW 2012
21) 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.
22) 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?
III. CHAPTER 3 – LINEAR SYSTEMS
A.
B.
C.
D.
E.
AND
MATRICES
Solve Linear Systems by Graphing (3.1)
Solve Linear Systems Algebraically (3.2)
Graph Systems of Linear Inequalities and Linear Programming (3.3)
Solve Systems of Linear Equations in Three Variables (3.4)
Perform Basic Matrix Operations (3.5)
PROBLEM SET
Solve the system:
1)
ì- 2x + 3y = 5
í
î 3x - 2y = 0
3)
ì5z + y - z = 6
ï
íx + y + z = 2
ï
î3x + y = 4
2)
ì2x - 5y = -4
í
î 4x + 3y = 5
5)
ì6x - 2y > 2
í
î x+y³3
Graph:
4)
1
ì
ïy £ x + 4
í
2
ïî x + 2y > 4
MPH 1/05 (REVISED 1/10 MD)
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ALGEBRA II
WITH
TRIGONOMETRY: MIDTERM EXAM REVIEW 2012
Solve by writing a system of equations.
6)
A nut wholesaler sells a mix of peanuts and cashews. The wholesaler charges $2.80
per pound for peanuts and $5.30 per pound for cashews. The mix is to sell for $3.30
per pound. How many pounds of peanuts and how many pounds of cashews should be
used to make 100 pounds of the mix?
7)
Given the system of constraints and objective quantity shown below, graph the
feasible region. Identify the vertices and determine the maximum and minimum
values of the objective quantity.
Objective Quantity
C = 3x + 6y
ì x³0
ï y³0
ï
Constraints í
ïx + 4 y £ 1
ïî x + y £ 2
Use matrices A, B, and C to evaluate the matrix expression, if possible. If not possible,
state the reason.
é2 - 5ù
A= ê
ú
ëê3 - 1 ûú
8)
A+B
10) 3A + C
MPH 1/05 (REVISED 1/10 MD)
é- 6 - 2 9 ù
C= ê
ú
ëê 1 - 4 - 1úû
é- 4 3 ù
B= ê
ú
ëê 8 10 ûú
9)
B – 2A
11)
2
C
3
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ALGEBRA II
IV.
WITH
TRIGONOMETRY: MIDTERM EXAM REVIEW 2012
CHAPTER 4 – QUADRATIC FUNCTIONS
A.
B.
C.
D.
E.
F.
G.
AND
FACTORING
Graph Quadratic Functions in Standard Form (4.1)
Graph Quadratic Functions in Vertex or Intercept Form (4.2)
Solve x2 + bx + c = 0 by Factoring (4.3)
Solve ax2 + bx + c = 0 by Factoring (4.4)
Solve Quadratic Equations by Finding Square Roots (4.5)
Complete the Square (4.7)
Use the Quadratic Formula and the Discriminant (4.8)
PROBLEM SET
Factor:
1)
x2 - 7x + 6
2)
x3 - 8
3)
4y3 + 108
4)
3x3 - 24x2 + 21x
5)
8x3 + 27
6)
4x2 + 12x + 9
7)
x2 - 81
8)
64x3 - 27
9)
15x3 + 10x2 + 6x + 4
10) k3 + 4k2 – 9k – 36
Solve:
11) 3x2 - 24 = 0
12) 5x2 + 19x = 125 + 19x
13) x2 - 10x - 4 = 0
14) -2x2 + 3x -7 = -9
15) x2 + 5x + 7 = 0
16) 2x2 - 2x = -3
For each of the following, find: the vertex, axis of symmetry, y-intercept, and xintercepts. Then graph the function.
17) y = x2 - 4x + 3
MPH 1/05 (REVISED 1/10 MD)
18) y = 2x2 - x - 6
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