Download Algebra II Bloom`s Taxonomy Unit 1: Equations and Inequalities

Algebra II Bloom’s Taxonomy Unit 1: Equations and Inequalities
Knowledge – Comprehension – Application – Analysis – Synthesis - Evaluation
God cares about numbers. He knows them all. He has recorded many for our
information. Genesis 5:1-32, Numbers 3:14-39, Psalm 147:4, Luke 12:7
1. Describe the subsets of the real number system.(K)
Irrational numbers, rational numbers, integers, whole numbers, and natural numbers
2. List the steps for the order of operations.(S)
Parenthesis, exponents, multiplication and/or division from left to right, addition
and/or subtraction from left to right.
3. How can you simplify an expression using like terms?(App)
Combine like terms
4. How do the solutions in a compound inequality using “and” differ from those
of a compound inequality using “or”?(An)
When graphing the solutions of an “and” inequality, the graph will go towards each
other, in an “or” inequality, the graph will go in the opposite directions.
5. Compare solving linear inequalities with solving linear equations.(An)
The process for solving both types will be the same, but with inequalities, when you
multiply or divide by a negative number, you must reverse the inequality sign.
6. What is the absolute value of a number?(K)
The distance a number is from zero on a number line, there will be two values that
are the same distance from zero.
7. How are absolute value inequalities containing a “<” or “” symbol solved
differently from those containing a “” or “” symbol?(K, An)
Absolute value inequalities with a “<” or “” symbol will be solved as an “and”
problems and those with a “” or “” symbol will be solved as an “or” problem.
Bonus (5 pts.)
Psalms 147 :4 He determines the number of the stars and calls them each by name.
Algebra II Bloom’s Taxonomy Unit 2: Linear Equations and Functions
Knowledge – Comprehension – Application – Analysis – Synthesis – Evaluation
God has at various times commanded men to count, measure, and record their findings.
Exodus 30:11-16, Numbers 1:1-46, Revelation 21:15-17
1. Explain the process for graphing an equation.(S)
Get y by itself, plot b first; then from b, plot m (rise/run)
2. Compare the slopes of parallel lines and the slopes of perpendicular lines.(K, C)
Get y by itself, compare the slopes of the two lines. Parallel lines will have the
same slope, perpendicular lines will have slopes that are the negative reciprocals.
3. Explain what the x-intercept and the y-intercept are.(K)
The x- and y-intercepts are the points on the x- and y-axis that the graph crosses.
4. Identify the point-slope form and the two-point form.(K)
Point-slope form is used when you are given the slope and one point. Substitute into
the form y  y1  m( x  x1 ) . The two-point form is used when you are only given
two points, you must find slope using the slope formula and then choose one of the
points and substitute into the point-slope form.
5. What are the steps to graphing a linear inequality?(S)
Same steps as graphing a linear equation, but the line will either be solid or dashed and
you will shade a half-plane. Use a test point to determine which half-plane to shade.
6. What is the difference between a half-plane for a “<” or “>” inequality and one
for a “” or “” inequality?(An)
A half-plane with the “<” or “>” will be a dashed line, a half-plane with the
“” or “” will be a solid line.
7. For the graph of y  a x  h  k , tell how to find the vertex, the direction the
graph opens, and the slopes of the branches.(An)
To find the vertex you would use the ordered pair (h,k); remember h is always the
opposite of how it appears in the absolute value symbols. The direction of the graph
will be determined by a. If a is positive it will open up, if a is negative it will open
down. The slopes of the branches will be determined by │a│. If 0 < │a│ < 1 the
graph will be wider, if │a│ > 1 the graph will be narrower.
Bonus (5 pts.)
Exodus 30:21a “When you take a census of the Israelites to count them…”
Algebra II Bloom’s Taxonomy Unit 3: Systems of Linear Equations and
Inequalities
Knowledge – Comprehension – Application – Analysis – Synthesis – Evaluation
God is concerned that men not place too much confidence in numbers or size. Numbers
are not everything! Judges 7:2-7, I Kings 18:17-41, John 6:9-13
1. Describe how to use a graph to determine how many solutions there are for a
system of linear equations.(An)
Solve both equations for y, graph each equations see if the graphs intersect, coincide,
or are parallel.
2. How do you know when a linear system has no solution?(An)
The graphs are parallel, algebraically, the variables cancel and you get a false
statement.
3. How do you know when a linear system has infinitely many solutions?(An)
The graphs coincide, algebraically, the variables cancel and you get a true statement.
4. What is the procedure used to graph a system of linear inequalities?(S)
Solve both equations for y, graph each equation.
5. Explain the term ordered triple.(K)
A point in a three-dimensional plane.
6. Write the general form of a linear equation in three variables. How is the
solution of such an equation represented?(K,C)
ax + by + cz = d; the solution will be an ordered triple.
7. How do you decide if a linear system in three variables has one, infinitely many,
or no solutions?(An)
If you can solve the system and get a value for (x, y, z), there is one solution which is
a plane. If the variables cancel and you get a false statement, there is no solution. If
the variables cancel and you get a true statement, there are infinitely many solutions.
Bonus (5 pts.)
Judges 7:2a “You have too many men. I cannot deliver Midian into their hands, or Israel
would boast against me”
Algebra II Bloom’s Taxonomy Unit 4: Quadratic Functions
Knowledge – Comprehension – Application – Analysis – Synthesis – Evaluation
God uses the concept of measurement to express men's failures and His plans for man.
Jeremiah 30:11, John 3:34, 35, 2 Corinthians 10:13, Ephesians 4:7-16
1. How do you determine whether the graph opens up or down?(An)
If “a” is positive the graph will open up, if “a” is negative the graph opens down.
2.
Give the vertex form and the intercept form of a quadratic function.(K)
Vertex form y  a x  h 2  k Intercept form y  a( x  p)( x  q)
3.
What is the standard form for a quadratic equation?(K)
y  ax 2  bx  c
4.
What is it called when you eliminate the radical in the denominator?(K)
Rationalizing the denominator
5.
How do you know when a radical expression is simplified?(An)
No radicand has a perfect square other than 1 and there is no radicand in the
denominator.
6.
Apply addition and subtraction rules to complex numbers.(App)
Addition and rules for real numbers is the same for complex numbers, combine
like terms.
7.
In the quadratic formula, what is the expression b 2  4ac under the radical
sign called?(K)
The discriminant.
8.
Describe how the discriminant can generate three different types of
solutions.(An)
If the discriminant is positive you will have 2 real solutions, if it is equal to zero
you will have 1 real solution, if it is negative you will have no real solutions but
instead, two imaginary solutions.
Bonus (5 pts.)
II Corinthians 10:13 We, however, will not boast beyond proper limits, but will confine
our boasting to the sphere of service God himself has assigned to us, a sphere that also
includes you.
Algebra II Bloom’s Taxonomy Unit 5: Polynomials and Polynomial Functions
Knowledge – Comprehension – Application – Analysis – Synthesis – Evaluation
God created the number concept. He initiated numbers back in the beginning .
Genesis 1:5, 8, l3, 19, 23, 31
1. How does the power of a power property of exponents differ from the product
of powers property?(An)
A power of a power property has you multiply the exponents, the product of
powers property has you add the exponents.
2.
When evaluating a polynomial function, put the function in standard form,
identify the leading coefficient, the constant term, the degree of the
polynomial and the name of the polynomial. (E) Given  2x  5x3  7
Standard form: 5x 3  2x  7 , Leading Coefficient: 5, Constant Term: - 7, Degree
of the Polynomial: 3, the name of the polynomial: cubic.
3.
What is the difference between direct substitution and synthetic substitution?
(An)
Direct substitution puts the value into each variable and then you simplify the
expression. Synthetic substitution has you divide using only the coefficients.
4.
Which term of the polynomial function is most important in determining the
end behavior of the function?(K)
The highest degree.
5.
Demonstrate, by using examples, of a function that is considered to be a
polynomial function compared to one that is not a polynomial function.(S, E)
Polynomial Function:  2x  5x3  7
Not a polynomial function: 3x  4x 2  1
6.
Before trying to factor any polynomial, what should you look for first?(K)
Look for a common factor.
7.
How can you shorten your search for the rational zeros?( An)
List all the factors of the constant over the factors of the leading coefficient.
Bonus (5 pts.)
Genesis 1:5 God called the light “day,” and the darkness he called “night.” And there
was evening, and there was morning—the first day
Algebra II Bloom’s Taxonomy Unit 6: Rational Exponents and Radical
Functions
Knowledge – Comprehension – Application – Analysis – Synthesis – Evaluation
Man's ability to understand and work with numbers is a gift from God. Job 32:8, 9,
1Corinthians 2:14-16
1. b is the nth root of a”, can you write this as a radical?(C)
b
2.
a
When is
n
n
x n  x, and when is
x n  x, when x is odd,
n
n
x n  x ? (An, E)
x n  x when x is even.
3.
Describe the conditions that must exist for radicals to be added or subtracted.
(K, An)
In order for radicals to be added or subtracted they need to have the same radicands
4.
When are two functions f and g inverses of each other?(An, E)
When f ( g ( x))  x and g ( f ( x))  x
5.
Describe the steps for finding the inverse of a relation.(K, S)
Switch places with x and y and solve for y.
6.
Explain how to use the horizontal line test to determine if an inverse relation
is an inverse function.(An)
If an inverse relation is an inverse function, you will not be able to draw a
horizontal line through the graph and intersect the graph in more than one point.
7.
How do the “h” and the “k” effect the graphs of radical functions?(An)
The “h” will shift the graph horizontally and the “k” will shift it vertically.
Bonus (5 pts.)
I Corinthians 2:15a “The person with the Spirit makes judgments about all things”