ALGEBRA I (SEMESTER 2)
(Integrated Algebra - Revised August 2008)
I. Graphing Linear and Nonlinear Functions (4 weeks)
A. Functions
1. Definition of a function
2. Determine when a relation is a function by examining multiple representations (ordered
pairs, mappings, equations, and graphs)
3. Vertical Line Test
B. Identify and graph linear functions
C. Identify and graph absolute value functions
1. Explore Vertical and Horizontal Shifts
D. Graph linear inequalities
E. Equations of a Line
1. Explain slope as a rate of change between dependent and independent variables. Including:
Calculate rates using appropriate units and solve problems involving conversions within
measurement systems.
2. Determine slope of a line, given the coordinates of two points on a line.
3. Write the equation of a line, given the coordinates of two points on a line.
4. Write an equation of a line, given its slope and the coordinates of a point on the line.
5. Write the equation of a line parallel to the x-axis or y-axis.
6. Determine the slope of a line, given its equation in any form.
7. Determine if two lines are parallel or perpendicular, given their equations in any form.
8. Given an equation of a line, write an equation for a line parallel or perpendicular to the given
equation.
9. Given an equation of a line, determine whether a given point is on a line.
10. Determine whether a given point is in the solution set of a system of linear equalities.
*** Please be advised – graphs must be accompanied by a table of values***
(The Graphing Linear and Nonlinear Functions unit includes, but is not limited to the following references to the New York State Learning Standard for Mathematics – Revised by the New York State Board of Regents March 15th, 2005 - A.A.3, A.G.6, A.G.7, A.A.32-A.A.40, A.M.1, A.M.2, A.A.10, A.CM.11)
II. Graphing Quadratic Functions (2 weeks)
A. Graphs of Quadratics
1. Identify quadratic graphs
2. Graphing quadratic equations of the form y = ax2, y = ax2 + c, and y = ax2 + bx + c.
(Optional inclusion of a parabola in the vertex form y = (x – h)2 + k)
3. Determine the vertex and axis of symmetry of a parabola given either the equation or the graph.
4. Investigate how changing the coefficients of a function affects its graph. For example, compare the
graphs of quadratics in the form y = ax2, by changing the sign on a. and the value of a
5. Find the roots of a parabolic function graphically (integral solutions only).
6. Understand the relationship between the roots of a quadratic equation, the factors of a quadratic
expression, and the x-intercepts of the parabola.
(The Quadratic Functions unit includes, but is not limited to the following references to the New York State Learning Standard for Mathematics – Revised by the New York State Board of Regents March 15th, 2005 - A.A.8, A.A.26, A.A.27, A.A.41, A.A.28, A.R.8, A.G.4, A.G.5, A.G.8-A.G.10, A.A.11, A.G.1)
III. Systems of Equations (1-2 weeks)
A. Solve systems of linear equations and inequalities with rational coefficients in two variables
graphically.
B. Solve systems of two linear equations in two variables algebraically. (may have already been covered
in semester 1)
C. Solve a system of one linear and one quadratic equation in two variables (the quadratic is a parabola
and the solutions should be integers)
D. Solve systems of linear and quadratic equations graphically (integer solutions only).
IV. Exponential Functions (2 weeks)
A. Exponential Expressions
1. Evaluate exponential expressions
B. Exponential Function Graphs
1. Identify exponential functions
i. y = abx explore what a, b and x represent
2. Graph exponential functions
C. Solving Exponential Functions
1. Solve Exponential Equations with the same base
2. Solve Exponential Equations with powers of the same base.
3. Analyze and solve verbal problems that involve exponential growth and decay.
(The Exponential Functions unit includes, but is not limited to the following references to the New York State Learning Standard for Mathematics – Revised by the New York State Board of Regents March 15th, 2005 – A.G.4, A.N.6, A.A.9)
V. Right Triangles (3 weeks)
A. Radicals
1. Simplify
2. Four arithmetic operations using radicals (leaving answers in simplest radical form)
3. Rationalizing
B. Pythagorean Theorem
C. Special Right Triangles
1. Derivations of the Relationships between the sides of a 45-45-90 and a 30-60-90
D. Right Triangle Trigonometry
1. Find the sine, cosine, and tangent ratios of an angles of a right triangles, given the
lengths of the sides
2. Determine the measure of an angle of a right triangle, given the lengths of any two sides
of the triangle
3. Find the measure of a side of a right triangle, given an acute angle and the length of
another side
4. Right Triangle Trigonometry applications using Angle of Depression and/or Angle of
Elevation.
(The Right Triangles unit includes, but is not limited to the following references to the New York State Learning Standard for Mathematics – Revised by the New York State Board of Regents March 15th, 2005 - A.A.42 -A.A.45, A.N.2, A.N.3, A.R.6, A.CN.6)
VI. Statistics (2 weeks)
A. Making Sense of Data
1. Categorize Data as qualitative or quantitative.
2. Determine whether the data to be analyzed is univariate or bivariate.
3. Determine when collected data or display of data may be biased.
4. Evaluate published reports and graphs that are based on data by considering: experimental design,
appropriateness of the data analysis, and the soundness of the conclusions.
5. Understand the difference between correlation and causation and identify variables that might have
a correlation.
6. Identify and describe sources of bias and its effect
7. Recognize how linear transformations of one-variable data affect the data’s mean, median, mode,
and range.
B. Measures of Central Tendency Vs Measures of Dispersion
1. Mean, Median, Mode and Range –
2. Compare and contrast the appropriateness of difference measure of central tendency for a given
data set.
3. Quartiles and Percentiles
4. The 5 Number Summary – Minimum, Q1, Median (Q2), Q3, and Maximum
C. Graphical Representations - Construct, Analyze, and Interpret
1. Histogram
2. Cumulative Frequency Histogram
3. Box-and-Whisker Plot
4. Scatterplot
a. Construct manually a reasonable line of best fit for a scatterplot and determine the equation of a
line.
b. Using the line of best fit to make a prediction involving interpolation and/or extrapolation.
The Statistics unit includes, but is not limited to the following references to the New York State Learning Standard for Mathematics – Revised by the New York State Board of Regents March 15th, 2005 - A.S.1-A.S.17)
VII. Probability (2 weeks)
A. The Counting Principle
1. Use the counting principle to determine the number of possible events
B. Conditional Probability
1. Sample Spaces and Tree Diagrams
2. Determine the number of elements in a sample space and the number of favorable events.
3. Calculate the probability of an event and its complement.
4. Determine empirical probabilities based on specific sample data.
5. Determine, based on calculated probability of a set of events, if:
i. some or all are equally likely to occur
ii. one is more likely to occur than another
iii. whether of not an event is certain to happen or not to happen
6. Calculate the probability of:
i. a series of independent events
ii. a series of dependent events
iii. two mutually exclusive events
iv. two events that are not mutually exclusive
C. Permutations
1. Determine the number of possible arrangements.
2. Calculate Permutations using the notation nPr.
(The Probability unit includes, but is not limited to the following references to the New York State Learning Standard for Mathematics – Revised by the New York State Board of Regents March 15th, 2005 - A.S.18-A.S.23, A.N.7, A.N.8)
NOTE: For ALGEBRA I Semesters 1 and 2 : The objectives stated in the Problem Solving, Reasoning and Proof, Communication, Connections, and Representation Strands are not necessarily listed specifically in any of units, as these ideas and objectives, are embedded within the teaching strategies used by our teaching staff.
