I
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)
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
a. Solve an algebraic proportion with one unknown that results in a linear equation
b. Determine whether a value is a solution to a given linear equation
c. Solve literal equations for a given variable (Ex: pq + r = n, solve for q)
d. Analyze and solve word problems whose solution requires solving a linear equation with one unknown (consecutive integer, perimeter, etc.)
e. Solve algebraic problems arising from situations that involve fractions, decimals, percents (decrease/increase and discount), rates, and proportionality/direct variation
f. 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
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 y-intercept 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 on 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)
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. Factor algebraic expressions using the GCF
b. Factor a trinomial into two binomials, given a = 1
c. Factor a trinomial into two binomials, given a >1 (optional)
d. Identify and factor the difference of two perfect squares
e. Factor a trinomial into binomials that requires factoring out a GCF first
f. 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
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)
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. Triangle
b. Rectangle
c. Square
d. Parallelogram
e. Rhombus
f. Trapezoid
g. Circle
h. Semi-Circle
i. Quarter- Circle
j. Other Regular Polygons
k. Figures composed of polygons and/or circles or sectors of a circle
2. Area ( ( 4 days)
NOTE: Include problems that use algebra to find area of the
following figures:
a. Triangle
b. Rectangle
c. Square
d. Parallelogram
e. Rhombus
f. Trapezoid
g. Circle
h. Semi-Circle
i. Quarter-Circle
j. Figures composed of polygons and/or circles or sectors of a circle
k. 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
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. Sine
b. Cosine
c. Tangent
d. Inverse Trigonometric Functions
e. Find all sides and angles of a right triangle using trig. and/or Pythagorean Theorem
f. 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
2. Probability ( ( 7 days)
a. Define and solve problems using the following:
1. sample space
2. simple probability of a single event
3. probability with “and” (single event)
4. probability with “or” (single event)
5. complement
6. empirical probability (based on specific sample data)
7. impossible events
8. certain events
9. 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. and
2. or
3. mutually exclusive
4. 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)
XII. Statistics and Regression – 14 days
1. Categorize Data ( ( 1 day)
a. Qualitative
b. Quantitative
c. Univariate
d. Bivariate
2. Measures of Central Tendency ( ( 2 days)
e. Mean
f. Median
g. Mode
h. Appropriate choice of measure
i. Range
j. Recognize how linear transformations of one-variable data affect the data’s mean, median, mode and range
3. Histograms ( ( 2 days)
a. Generate a frequency table
b. Construct a frequency histogram
c. Construct a cumulative frequency histogram
d. 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
7. Scatterplots ( ( 3 days)
a. Construct a scatterplot
b. Identify the independent and dependent variables
c. Find the relationship between the variables (positive, negative, none)
d. Understand the difference between correlation and causation
e. 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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