Download 2013 Suggested Practice for SOL AII.3 Distributive Property

Spring 2012-2014
Student Performance Analysis
Algebra I
Standards of Learning
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Representing and Evaluating Cube Roots
and Square Roots
2012, 2013
SOL A.1
The student will represent verbal quantitative situations
algebraically and evaluate these expressions for given
replacement values of the variables.
2012 Suggested Practice for SOL A.1
Students need additional practice using replacement values
to evaluate expressions with cube roots and square
roots.
2013 Suggested Practice for SOL A.1
Students need additional practice evaluating expressions that
contain an absolute value.
Evaluate the following expressions:
a.
b.
2013 Suggested Practice for SOL A.1
Students need additional practice evaluating expressions with
cube roots, square roots, and the square of a number, particularly
when the replacement variable has a negative value.
Evaluate the following expressions:
a.
b.
c.
2012 Suggested Practice for SOL A.1
Students need additional practice translating expressions with
square and cube roots.
Translate into an algebraic expression:
a)
The quotient of the square root of x and five
b)
The cube root of the product of x and y, less twelve
c)
The sum of the square root of sixteen and the product of four and the cube root of eight
Translate into a verbal expression:
d)
e)
Five times the cube root of the product of 4 and x less the square root of y
A number y plus the cube root of a number x
2013 Suggested Practice for SOL A.1
Students need additional practice translating expressions.
Select each phrase that verbally translates this algebraic expression:
One fourth times the cube root of x less five.
One fourth times the cube root of x less than five.
Five subtract one fourth times the cube root of x.
Five less than one fourth times the cube root of x.
Express Square Roots and Cube Roots
in Simplest Radical Form
2012, 2013, 2014
SOL A.3
The student will express the square roots and cube roots of
whole numbers and the square root of a monomial algebraic
expression in simplest radical form.
2012 Suggested Practice for SOL A.3
Students need additional practice simplifying square roots of
monomial expressions and cube roots of whole numbers.
Completely simplify:
a)
b)
c)
d)
2013 Suggested Practice for SOL A.3
Students need additional practice simplifying the square root
of a monomial algebraic expression.
Write each expression in simplest radical form.
a.
b.
c.
2014 Suggested Practice for SOL A.3
Students need additional practice identifying expressions
that are in simplest radical form.
Identify each expression that is in simplest radical form.
Solving Linear and Quadratic Equations
2012, 2013, 2014
SOL A.4
The student will solve multistep linear and quadratic equations
in two variables, including
a)
solving literal equations (formulas) for a given variable;
b)
justifying steps used in simplifying expressions and solving equations, using
field properties and axioms of equality that are valid for the set of real
numbers and its subsets;
d)
solving multistep linear equations algebraically and graphically;
f)
solving real-world problems involving equations and systems of equations.
Graphing calculators will be used both as a primary tool in solving problems and to
verify algebraic solutions.
2012 Suggested Practice for SOL A.4a
Students need additional practice solving a literal equation
for a given variable.
Solve each equation:
a)
b)
2013 Suggested Practice for SOL A.4a
Students need additional practice solving literal equations.
The formula for the surface area (S) of a triangular prism is
where h is the height of the prism, p is the perimeter of the base, and B is the area
of the base. Solve the equation for the given variable:
a. Solve for h:
b. Solve for B:
2013 Suggested Practice for SOL A.4b
Students need additional practice solving multi-step equations with the
variable on both sides and with fractions. Students also need additional
practice justifying steps in solving a linear equation.
Solve for x:
What property justifies the work between each step?
2014 Suggested Practice for SOL A.4b
Students need additional practice justifying steps used to solve an
equation using the axioms of equality.
What property justifies the work between step 1 and step 2?
a.
b.
c.
d.
Commutative property of addition
Inverse property of addition
Addition property of equality
Associative property of addition
2013 Suggested Practice for SOL A.4d
Students need additional practice describing solutions to equations that
have the following solutions: x=0, an infinite number of real solutions,
and no real solutions.
Describe the solution to each equation.
a.
No real solutions
b.
x=0
c.
An infinite number of real solutions
2014 Suggested Practice for SOL A.4d
Students need additional practice determining solutions to equations
that have the following solutions: x=0, an infinite number of real
solutions, and no real solutions.
1. What is the solution to
?
There are an infinite number of real solutions.
2. What describes the solution to
a.
b.
c.
d.
There is an infinite number of real solutions.
There are no real solutions.
The only solution is 0.
The only solution is 5.
?
2014 Suggested Practice for SOL A.4d
Students need additional practice finding solutions to equations that contain
rational expressions.
Find the solution to the equation shown:
a.
b.
c.
d.
2014 Suggested Practice for SOL A.4d
Students need additional practice finding solutions to
equations that require computation with positive and negative
rational numbers.
Find the solution to the equation shown.
2014 Suggested Practice for SOL A.4f
Students need additional practice finding solutions to systems of equations
presented in a real-world situation.
James bought a total of 15 bottles of drinks for his team.
• Each drink was either a bottle of water or a bottle of juice.
• He spent $1.50 on each bottle of water.
• He spent $3.00 on each bottle of juice.
• James spent a total of $28.50.
How many bottles of juice did James buy?
Solving Multistep Inequalities
2012, 2013, 2014
SOL A.5
The student will solve multistep linear inequalities in two
variables, including
a) solving multistep linear inequalities algebraically and
graphically;
b) justifying steps used in solving inequalities, using axioms of
inequality and properties of order that are valid for the set
of real numbers and its subsets;
c) solving real-world problems involving inequalities;
2012 Suggested Practice for SOL A.5a
Students need additional practice solving multistep linear inequalities
which require a sign change.
Solve and graph on a number line:
2013 Suggested Practice for SOL A.5a
Students need additional practice solving multistep inequalities.
An inequality is solved as shown.
Between which two steps is an
error made? Explain the error.
The -3 was not distributed properly to
the second term.
2013 Suggested Practice for SOL A.5b
Students need additional practice identifying properties of inequality.
Given:
Using the given inequality, select all that illustrate the application of the
subtraction property of inequality.
Spring 2012 - 2014
Student Performance Analysis
Algebra II
Standards of Learning
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using the arrow keys or the mouse.
26
Identify Field Properties
2012, 2013
SOL AII.3
The student will perform operations on complex
numbers, express the results in simplest form using
patterns of the powers of i, and identify field
properties that are valid for the complex numbers.
2012 Suggested Practice for SOL AII.3
Students need additional practice identifying the field
properties that are valid for complex numbers.
Identify the property used in each of the following:
a)
Identity Property of Multiplication
b)
Distributive Property
c)
Associative Property of Addition
d)
Symmetric Property
e)
Transitive Property
2013 Suggested Practice for SOL AII.3
Students need additional practice identifying the field
properties that are valid for complex numbers.
Identify the property represented in each example.
a.
Inverse Property of Multiplication
b. 3i  2i  8  3i  8  2i
Commutative Property of Addition
c. If 3i  2i  5i , and 5i  11i  6i , then 3i  2i  11i  6i.
d. 3i(2i  4)  6  12i
Distributive Property
e. If 3i  8  w , then w  3i  8.
Symmetric Property
Transitive Property
2013 Suggested Practice for SOL AII.3
Identify the property used between each step:
Step 1:
Given
Step 2:
Distributive Property
Step 3:
Commutative Property of Addition
Step 4:
Substitution Property
Step 5:
Substitution Property
2014 Suggested Practice for SOL AII.3
Students need additional practice performing operations on
complex numbers involving radicals.
What number is equivalent toA
B
C
D
2014 Suggested Practice for SOL AII.3
Students need additional practice performing operations on
complex numbers involving radicals.
A
B
2014 Suggested Practice for SOL AII.3
Students need additional practice identifying the field
properties that are valid for complex numbers.
Identify the property that justifies each step of the
simplification shown.
STEPS
JUSTIFICATIONS
Given Expression
Commutative Property of Addition
Distributive Property
Substitution Property
Associative Property of Addition
Substitution Property
2014 Suggested Practice for SOL AII.1b
Students need additional practice simplifying and
performing operations on radical expressions.
Simplify the expression for positive x and y values.
a)
b)
2014 Suggested Practice for SOL AII.1c
Students need additional practice writing radical expressions
as expressions containing rational exponents and vice versa.
a. Write an expression in radical form equivalent to
b. Write an expression containing rational exponents
equivalent to
.
.
2014 Absolute Value Equations Suggested
Practice for SOL AII.4a
Students need additional practice solving absolute value
equations and inequalities algebraically and graphically.
a. Find the solution to:
b. Determine an ordered pair that is a solution to:
2014 Suggested Practice for SOL AII.4a
How many values of x will satisfy the absolute value
equation?
a.
one
b.
two
c.
zero
Extension: What value(s) of x would be the solutions to the
equations?
2014 Suggested Practice for SOL AII.4a
Graph the solutions to the problems shown.
a.
b.
Shapes of Functions
SOL AII.6
The student will recognize the general shape of function
(absolute value, square root, cube root, rational, polynomial,
exponential, and logarithmic) families and will convert
between graphic and symbolic forms of functions. A
transformational approach to graphing will be employed.
Graphing calculators will be used as a tool to investigate the
shapes and behaviors of these functions.
Analyzing Functions
SOL AII.7
The student will investigate and analyze functions algebraically
and graphically. Key concepts include
a)
domain and range, including limited and discontinuous
domains and ranges;
b)
zeros;
c)
x- and y-intercepts;
d)
intervals in which a function is increasing or decreasing;
e)
asymptotes;
f)
end behavior;
g)
inverse of a function; and
h)
composition of multiple functions.
Graphing calculators will be used as a tool to assist in investigation
of functions.