One-Year Algebra Outline
I.
Real Numbers – 9 days
1. Properties of Real Numbers (  2 days)
a. Commutative
b. Associative
c. Identity
d. Inverse
e. Distributive
f. Zero Property
g. Closure
2. Operations with Radicals (  5 days)
a. Simplify radicals
1. perfect square radicand
2. radicand with a perfect square factor (no variable)
b. Add and subtract like and unlike radicands
c. Multiply radicals (include use of distributive property)
d. Divide radicals
3. Review and Assessment (  2 days)
II.
Polynomials – 15 days
1. Operations With Monomials and Polynomials (  9 days)
a. Add and subtract monomials
b. Add and subtract polynomials
c. Multiply and divide monomials (include negative exponents)
d. Distributive Property (include combining like terms)
e. Multiply two binomials
f. Multiply two polynomials
g. Multiply and divide monomial expressions with a common base using
the properties of exponents (use integers as exponents)
h. Divide a polynomial by a monomial
2. Scientific Notation (  2 days)
a. Convert to scientific notation
b. Convert from scientific notation to standard form
c. Compute products and quotients involving scientific notation
d. Solve word problems involving products and quotients
3. Review and Assessment (  2 days)
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One-Year Algebra Outline
III.
Linear Equations – 18 days
1. Translate Among Verbal, Written, and Algebraic ( 2 days)
a. Represent words with mathematical expressions and equations (and
vice versa)
b. Distinguish between algebraic expressions and algebraic equations
c. Write algebraic equations to represent a situation
2. Solve Linear Equations (  15 days)
a. Solve one-and two-step equations with one unknown (include
fractions and decimals)
1. Combine like terms
2. Use Distributive Property
3. Variables on opposite sides of the equal sign
3. Variable in the denominator
4. Equations with an infinite number of solutions
such as 2x+4 = 2(x+2)
5. Equations with no solutions such as x + 4 = x + 5
b. Solve an algebraic proportion with one unknown that results in a linear
equation
c. Determine whether a value is a solution to a given linear equation
d. Solve literal equations for a given variable (Ex: pq + r = n, solve for q)
e. Analyze and solve word problems whose solution requires solving a
linear equation with one unknown (consecutive integer, perimeter, etc.)
f. Solve algebraic problems arising from situations that involve fractions,
decimals, percents (decrease/increase and discount), rates, and
proportionality/direct variation
g. Absolute value equations
3. Review and Assessment ( 2 days)
IV.
Linear Inequalities – 4 days
1. Solve Linear Inequalities (  3 days)
a. Solve linear inequalities with one variable (include multiplying and
dividing by a negative number)
b. Translate among verbal, written and algebraic
1. Represent words with mathematical inequalities
2. Write algebraic inequalities that represent a situation
c. Determine whether a given value is a solution to a linear inequality with
one variable
d. Analyze and solve word problems whose solution requires solving a
linear inequality with one variable
2. Review and Assessment  1 day
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One-Year Algebra Outline
V.
Graphs of Linear Equations and Inequalities – 14 days
1. Graphs of Lines (  10 days)
a. Graph a line using a table of values
b. Define of a function
1. Ordered pairs
2. Vertical line test
c. Determine whether a given point is on a line, given an equation
( Ex: Given (3, 2) is on the graph of x + 3y = k, find k )
d. Solve for an unknown in an equation (or for a coordinate) given a point
on a graph
( Ex: Given (k, 7) is on the graph of x – 7y = 10, find k )
e. Slope
1. Define slope as the rate of change
2. Find slope between two points using the formula and using a
graph
3. Identify different slopes (positive, negative, zero and undefined)
f.
Intercepts (x and y)
1. Find the x- and y-intercepts
2. Write an equation and graph lines parallel to the axes
3. Graph a line using the x and y intercepts (optional)
g. Slope-Intercept Form
1. Write the equation of a line given its slope and
y-intercept
2. Convert an equation into slope-intercept form
3. Graph equations using slope-intercept form (include
investigating and generalizing how changing the slope and yintercept affects the graph)
4. Determine if two lines are parallel, given their equations in any
form
5. Write the equation of a line, given the coordinates of two points
on the line
h. Write the equation of a line given the slope and the coordinates of a
point. (point-slope form)
i.
Write the equation of a line, given the coordinates of two points
the line
2. Graphs of Linear Inequalities (  2 days)
a. Determine if reference line is dashed or solid
b. Determine where to shade
3. Review and Assessment (  2 days)
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One-Year Algebra Outline
VI.
Systems of Linear Equations and Inequalities – 10 days
1. Systems of Equations (  6 days)
a. Solve algebraically and check
1. substitution method
2. elimination method
b. Solve graphically and check
c. Solve word problems
2. Systems of Inequalities (  2 days)
a. Solve graphically
b. Determine whether a given point is in the solution set
3. Review and Assessment (  2 days)
VII. Factoring and Algebraic Fractions – 11 days
1. Factoring (  4 days)
a.
b.
c.
d.
e.
f.
Factor algebraic expressions using the GCF
Factor a trinomial into two binomials, given a = 1
Factor a trinomial into two binomials, given a >1 (optional)
Identify and factor the difference of two perfect squares
Factor a trinomial into binomials that requires factoring out a GCF first
Factor a trinomial into two binomials that requires factoring out a
negative GCF first (Ex: –x2 – 3x – 4)
2. Algebraic Fractions (  5 days)
a. Find the value for which an algebraic fraction is undefined
1. monomial and binomial denominators
2. factorable binomial denominators
b. Simplify fractions with polynomials in the numerator and denominator by
factoring both and reducing to lowest terms
c. Add or subtract fractional expressions
1. like and unlike monomial denominators
2. like binomial denominators
d. Multiply and divide algebraic fractions and express the product or
quotient in simplest form
1. monomial divided by monomial
2. polynomial divided by monomial
3. polynomial divided by polynomial
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One-Year Algebra Outline
2. Algebraic Fractions (continued)
e. Divide a polynomial by a monomial or binomial, where the quotient has
no remainder
1. monomial divided by monomial
2. polynomial divided by monomial
3. polynomial divided by polynomial
3. Review and Assessment (  2 days)
VIII. Non-linear Functions – 17 days
1. Graph Quadratic Equations (  2 days)
a. Recognize general form of a quadratic
b. Determine the axis of symmetry using the formula or from the graph
c. Determine the vertex algebraically or graphically
d. Find the table of values for an equation
e. Graph the equation
2. Solve Quadratic Equations (  7 days)
a. Identify the relationship between the roots of a quadratic equation and
the x-intercepts on the graph of the parabola
b. Find the roots of a parabolic function graphically (integer solutions)
c. Identify the relationship between the number of roots and the number of
x-intercepts
d. Understand and apply the multiplication property of zero to solve
quadratic equations whose coefficients and roots are integers
e. Analyze and solve word problems that involve quadratic equations
f. Solve algebraic proportions with one unknown that result in quadratic
equations
3. Solve Systems of Linear and Quadratic Equations (  2 days)
a. Solve graphically
b. Solve algebraically using substitution
4. Exponential Functions (  2 days)
a. Identify and graph an exponential function (given an un known in the
base or as an exponent )
b. Analyze and solve word problems that involve exponential growth and
decay
5. Absolute Value Functions (  1 day)
a. Identify and graph an absolute value function
6. Review and Assessment (  3 days)
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One-Year Algebra Outline
X.
Plane and Solid Geometry – 12 days
1. Perimeter (  2 days)
NOTE: Include problems that use algebra to find perimeter of the following
figures:
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
k.
Triangle
Rectangle
Square
Parallelogram
Rhombus
Trapezoid
Circle
Semi-Circle
Quarter- Circle
Other Regular Polygons
Figures composed of polygons and/or circles or sectors of a circle
2. Area (  4 days)
NOTE:
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
k.
Include problems that use algebra to find area of the
following figures:
Triangle
Rectangle
Square
Parallelogram
Rhombus
Trapezoid
Circle
Semi-Circle
Quarter-Circle
Figures composed of polygons and/or circles or sectors of a circle
Shaded regions
3. Volume (  2 days)
a. Cube
b. Rectangular Prism
c. Cylinder
4. Surface Area ( 2 days)
a. Cube
b. Rectangular Prism
c. Cylinder
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One-Year Algebra Outline
5. Relative Error (  1 day)
a. Calculate the relative error in measuring square and cubic units, where
there is an error in the linear measure
6. Review and Assessment (  1 day)
IX.
Right Triangles – 10 days
2. Pythagorean Theorem (  2 days)
a. Determine if a triangle is a right triangle
b. Find the third side (radical, rational and irrational) of a right triangle,
given two sides
c. Solve word problems
3. Trigonometric Functions (  5 days)
a.
b.
c.
d.
e.
f.
Sine
Cosine
Tangent
Inverse Trigonometric Functions
Find all sides and angles of a right triangle using trig. and/or
Pythagorean Theorem
Solve word problems (include angle of elevation and depression)
4. Review and Assessment (  3 days)
XI.
Set Theory and Probability – 13 days
1. Set Theory (  2 days)
a. Review subsets of Real Numbers
b. Use set builder and/or interval notation ( Ex: {x | x > 4} )
c. Define and solve problems using the following:
1. roster notation
2. subset
3. universal set
4. complement
5. null set
6. intersection
7. union
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One-Year Algebra Outline
2. Probability (  7 days)
a. Define and solve problems using the following:
1.
2.
3.
4.
5.
6.
7.
8.
9.
sample space
simple probability of a single event
probability with “and” (single event)
probability with “or” (single event)
complement
empirical probability (based on specific sample data)
impossible events
certain events
Fundamental Counting Principle
b. Analyze a set of events to determine when:
1. some or all are equally likely to occur
2. one is more likely to occur
3. an event is certain to happen or not to happen
c. Conditional Probability
4. with replacement
5. without replacement
d. Probability of a series of independent and dependent events
1.
2.
3.
4.
and
or
mutually exclusive
not mutually exclusive
3. Permutations (  1 day)
a. Review definition of factorial
b. Formula
Factorials (  1 day)
a. Define factorial
b. Evaluate factorials
c. Simplify expressions with factorials (rational, algebraic)
4. Review and Assessment (  2 days)
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One-Year Algebra Outline
XII. Statistics and Regression – 14 days
1. Categorize Data (  1 day)
a.
b.
c.
d.
Qualitative
Quantitative
Univariate
Bivariate
2. Measures of Central Tendency
e.
f.
g.
h.
i.
j.
(  2 days)
Mean
Median
Mode
Appropriate choice of measure
Range
Recognize how linear transformations of one-variable data affect the
data’s mean, median, mode and range
3. Histograms (  2 days)
a.
b.
c.
d.
Generate a frequency table
Construct a frequency histogram
Construct a cumulative frequency histogram
Analyze data from a frequency table, histogram, cumulative frequency
table or cumulative frequency histogram
4. Percentiles (  1 day)
a. Definition
b. Find the percentile rank of a value in a set of a data
c. Find the first, second and third quartiles
5. Box-and-whisker Plot (  2 days)
a. Define as a five-number summary (minimum, maximum, quartiles)
b. Construct a box-and-whisker plot
c. Analyze data from a box-and-whisker plot
6. Biased Data (  1 day)
a. Evaluate reports and graphs for accuracy, appropriateness,
experimental design and soundness of the conclusion
b. Identify and describe sources of bias and its effect, drawing conclusions
from data
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One-Year Algebra Outline
7. Scatterplots (  3 days)
a.
b.
c.
d.
e.
Construct a scatterplot
Identify the independent and dependent variables
Find the relationship between the variables (positive, negative, none)
Understand the difference between correlation and causation
Identify variables that might have a correlation but not a causal
relationship
f. Construct manually a line of best fit
g. Determine the equation of a line of best fit
h. Interpolation and extrapolation
8. Review and Assessment ( 2 days)
XIII. Regents Review – 15 days
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