Algebra II Mathematics Content Standards
Students will:
1.0
Solve equations and inequalities involving absolute value
2.0
Solve systems of linear equations and inequalities (in two or three variables) by substitution,
with graphs, or with matrices
3.0
Add, subtract, multiply and divide polynomials
4.0
Factor polynomials including sum and difference of two cubes
5.0
Demonstrate knowledge of how real and complex numbers are related both arithmetically and
graphically
6.0
Add, subtract, multiply, and divide complex numbers
7.0
Add, subtract, multiply, divide, reduce, and evaluate rational polynomial expressions, including
those with negative exponents
8.0
Solve and graph quadratic equations over the complex number system, including word
problems
9.0
Determine how the graph of a parabola as a, b, and c vary in the equation
10.0
Graph quadratic functions and determine the maxima, minima, and zeros of the function; find a
polynomial function given the zeros.
11.0
Prove and apply simple laws of logarithms; understand and use the relationship between
exponents and logarithms to solve problems
12.0
Know the laws of fractional exponenets, understand exponential functions, and use these
functions in problems involving exponential growth and decay
13.0
Use logarithmic properties to change base
14.0
Use the properties of logarithms to simplify logarithmic numeric expressions and use the
definition of logs to approximate values
15.0
Determine whether specific algebraic statements are always, sometimes, or never true
16.0
Explain how the geometry of the graph of a conic section depends upon the coefficients of its
quadratic equation
17.0
Complete the square to transform the equation of a conic into standard form, recognize the
type of conic given, and graph it
18.0
Use the fundamental counting principle to compute combinations and permutations
19.0
Use combinations and permutations to compute probabilities
20.0
Know and use the binomial theorem to expand binomial expressions raised to positive integer
powers
21.0
Apply mathematical induction to prove general statements about the positive integers
22.0
Find the general term and sums of arithmetic series, finite geometric series, and infinite
geometric series
23.0
Derive the summation formulas for arithmetic series, finite geometric series, and infinite
geometric series
24.0
Solve problems involving composite and inverse functions, and perform arithmetic operations
on functions
25.0
Use properties from number systems to justify steps in combining and simplifying functions
NAME_______________________________________ DATE____________________
. Algebra II Content Standards Worksheet
3x  y  17
1.0 Solve and graph: 3  2 x  4
2.0 Solve by graphing, substitution & matrices:
3.0 Let A= 2 x  3x  4 x  1 and B= 2 x  1 . Find A+B, A-B,
3
AB and
2
2 x  y  3
b gb2x  4x  6g
4.0 Factor completely: 8a  b
3
3
2
A
B
6.0 If A  3  4i  and B  2  i  , find A+B, A-B, AB and
5.0 Solve and graph in the complex plane:
bx  4gbx  9g 0
tc
t  1h

7.0 Simplify
2
2
A
B
2
t2  4
3t 2
t


2
2
2t  t  1 2t  3t  2 st
4 st
8.0 Graph y  2 x  5x  2 . Label vertex, y-int, and x-int.
2
9.0 Find an equation of a parabola with vertex (4, -5)
10.0 (a) Find the maximum height of a ball thrown from a
opening down, congruent to the graph of y  4 x  3x  2 .
105 ft high building at an initial velocity of 14 m/s using the
2
formula h  ho  vt  4.9t . (b) Find a polynomial with zeros
2
1, -i , and -3
11.0 Prove log a x  log a y  log a
x
y
then solve
12.0 A certain isotope has a half-life of 5,325 years. How
much of a 14 gram sample is left after 2,700 years?
log 3 x  log 3 2  4
13.0 Convert log 3 4 into base 6.
14.0 Simplify to find exact numerical values for log
15.0 Is the following true for all real numbers x, some real
b1 x g  1  x
ax  2 f
2
16.0 Graph
4

ay  3f
2
25
2
b
b .
 1 . Label foci, asymptotes and
2
numbers x, or no real numbers x?
1 x
eccentricity if applicable.
17.0 Write in standard form and graph
18.0 How many ways can a student answer a 10 question
4 x  9 y  16 x  18 y  11  0 .
multiple choice (A-B-C-D) test?
2
2
19.0 In a club consisting of eight upper classmen and 4
20.0 Find the 7th term of
under classman, what is the probability that the two co-
bx  3g.
12
chairs will both be upper classmen?
21.0 Use mathematical induction to show that
22.0 Find the 27th term and the sum of (a)
n n 1
1  2  3  4...n  b2 g
14  17  20...230 (b) 2  6  18...9565938 (c)
23.0 Derive the summation formulas for Arithmetic Series,
24.0 If f  x   2 x  1 and g x  
Finite Geometric Series, Infinite Geometric Series.
27  9  3...
f g
x
4
, find (a) f  g  x  and (b)
25.0