Sutherland
Pre-Calculus
Strand Title: Algebraic Standard
Content Standard # Relationships: Students will generalize, represent and analyze
relationships using algebraic symbols
MA 12.3.1
Unit Outcomes
MA 12.3.1 (a) Represent, interpret, and analyze functions with
graphs, tables, and algebraic notation, and convert among these
representations (e.g., linear, non-linear)
- Apply integral and rational zeros theorem
- Will locate limits of functions as values of (x) approach from
both sides of the functions
MA 12.3.1 (b) Identify domain and range of functions
represented in either symbolic or graphical form (e.g., linear,
non-linear, sine and cosine)
MA 12.3.1 (d) Identify characteristics of linear and non-linear
functions
MA 12.3.1 (e) Graph linear and non-linear functions (sine and
cosine)
MA 12.3.1 (f) Compare and analyze the rate of change by using
ordered pairs, tables, graphs, and equations
MA 12.3.1 (g) Graph and interpret linear inequalities
MA 12.3.1 (h) Represent, interpret and analyze functions and
their inverses.
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Students will explore the symmetry of a function and its
inverse function.
Students will also predict the inverse linear equation from its
original
MA 12.3.1 (i) Determine if a relation is a function (through
graphs, equations, and ordered pairs)
3/9/16
Vocabulary
Function
Integral zeros theorem
Rational zeros theorem
Limit of a function
Domain
Range
Sine
Cosine
Inverse functions
Symmetry of a function
Derivative of function
Radical functions
Quadrantal angles
Coterminal angles
Suggested Resources
Sutherland
Pre-Calculus
Additional:
-
Students will determine the slope of a line tangent to a
curve at a given point
The students will apply the definition of a derivative to
differentiate functions
The students will utilize the following theorems to find a
derivative of a function: Derivative of a Constant, Derivative
of a Power, Multiple of a Power, and Derivative of a Sum
Students will apply the first and second derivatives of a
function to determine the velocity and acceleration of an
object
Students will solve radical functions utilizing algebraic
methods
Students will compute exact values for sine and cosine
functions using the definition of sine and cosine
Students will determine values for the six trigonometric
functions using special and quadrantal angles
Students will use scientific calculators for finding
approximate values of the six trig functions, their angles and
coterminal angles
District Assessment
3/9/16
Sutherland
Pre-Calculus
Strand Title: Algebraic Standard
Content Standard # Modeling in Context: Students will model and analyze quantitative
relationships.
MA 12.3.2
Unit Outcomes
MA 12.3.2 (a) Model contextualized problems using various
representations (e.g., graphs, tables, one variable equalities,
one variable inequalities, linear equations in slope intercept
form, inequalities in slope intercept form, system of linear
equations with two variables)
MA 12.3.2 (b) Represent a variety of quantitative relationships
using linear equations, and one variable inequalities
Vocabulary
Exponential function
Absolute value function
Piecewise function
Exponential growth
MA 12.3.2 (c) Analyze situations to determine the type of
algebraic relationship (e.g., linear, non-linear)
MA 12.3.2 (d) Model contextualized problems using various
representations for non-linear functions (e.g., quadratic,
exponential, square root, absolute value, and piecewise
functions)
- Students will compare and contrast the similarities between
the different families of functions
- Students will represent patterns of exponential growth and
decay, along with their significance to real-life situations and
science
District Assessment
3/9/16
Suggested Resources
Sutherland
Pre-Calculus
Strand Title: Algebraic Standard
Content Standard # Procedures: Students will represent and solve equations and inequalities
MA 12.3.3
Unit Outcomes
MA 12.3.3 (d) Multiply and divide polynomials (dividing
polynomials by binomials)
MA 12.3.3 (e) Factor Polynomials (binomial: difference of
squares, trinomials, and factoring by grouping)
MA 12.3.3 (i) Solve quadratic equations (factoring, graphing,
quadratic formula)
- Apply synthetic substitution /division and remainder
theorem to determine zeros
Vocabulary
Synthetic subsitution
Synthetic division
Remainder theorem
Composition
Logarithm
MA 12.3.3 (j) Add, subtract, and simplify rational expressions
(determine the domain and range after operation)
MA 12.3.3 (k) Multiply (distributive property and FOIL method),
divide, and simplify rational expressions
MA 12.3.3 (l) Evaluate polynomial and rational expressions and
expressions containing radicals and absolute values at specified
values of their variables
MA 12.3.3 (n) Combine functions by composition, as well as by
addition, subtraction, multiplication, and division (determine
domain and range after operation)
MA 12.3.3 (o) Solve an equation involving several variables for
one variable in terms of the others
MA 12.3.3 (p) Analyze and solve systems of two linear
equations in two variables algebraically and graphically
Additional:
-
Students will display solutions to quadratic inequalities with
and without the use of graphing calculators
Students will solve exponential and logarithmic equations
by applying the change of base formula, the definitions of a
logarithmic functions and exponential functions
District Assessment
3/9/16
Suggested Resources
Sutherland
Pre-Calculus
Strand Title: Data Analysis/Probability Standard
Content Standard # Display and Analysis: Students will formulate a question and design a
survey or an experiment in which data is collected and displayed in a
MA 12.4.1
Unit Outcomes
variety of formats, then select and use appropriate statistical methods to
analyze the data.
MA 12.4.1 (a) Interpret data represented by the normal
distribution and formulate conclusions
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Students will display the normal bell curve, labeling the
mean and three standard deviations from the mean
Students will compile results from real world applications
utilizing the empirical rule (68%, 95%, 99.7%)
MA 12.4.1 (b) Compute, identify and interpret measures of
central tendency (mean, median, mode) when provided a graph
or data set
Vocabulary
Normal distribution
Normal bell curve
Empirical rule
Variance
Standard deviation
Outliers
Box and whisker plot
z-scores
MA 12.4.1 (c) Explain how sample size and transformations of
data affect measures of central tendency
MA 12.4.1 (d) Describe the shape and determine spread
(variance, standard deviation) and outliers of a data set
-
Graph the normal curve and also a box and whisker plot
(finding the five number summary and then graphing)
MA 12.4.1 (e) Explain how statistics are used and misused in
the real world
-
Students will find situations where statistics are skewed in
advertising…
MA 12.4.1 (f) Create scatter plots, analyze data patterns and
describe relationships in paired data
-
Students will utilize the TI 83 graphing calculator’s
regression program to explore possible methods for
representing data in a linear or quadratic form
Students will compute the correlation coefficient of paired
data with the TI 83 to determine how two variables are
related to one another
3/9/16
Suggested Resources
Sutherland
Pre-Calculus
MA 12.4.1 (g) Explain the impact of sampling methods, bias and
the phrasing of questions asked during data collection and the
conclusions made thereafter
-
Students will justify a chosen random sampling technique
to gather data to eliminate bias.
Additional
-
Students will refer to a list of (z) scores in the
appendix of the textbook to compute areas
(probability) under a curve
Students will determine class rank and
percentiles in relation to other values in a
normally distributed group of data when given
specific information
District Assessment
3/9/16
Sutherland
Pre-Calculus
Strand Title: Data Analysis/Probability Standard
Content Standard # Predictions and Inferences: Students will develop and evaluate
inferences to make predictions.
MA 12.4.2
Unit Outcomes
MA 12.4.2 (a) Compare data sets and evaluate conclusions
using graphs and summary statistics
-
Students will apply hypothesis testing (95% and 99%
confidence intervals) to accept or reject a hypothesis
MA 12.4.2 (b) Support inferences with valid arguments
Vocabulary
Hypothesis testing
Inference
Correlation coefficient
Linear regression
MA 12.4.2 (c) Develop linear equations for linear models to
predict unobserved outcomes using linear regression and
correlation coefficient
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The use of the TI 83 statistics program will be utilized to
find the linear models when given a set of data
Suggested Resources
District Assessment
3/9/16
Sutherland
Pre-Calculus
Strand Title
Content Standard # Probability: Students will apply and analyze concepts of probability.
MA 12.4.3
Unit Outcomes
MA 12.4.3 (a) Construct a sample space and a probability
distribution
MA 12.4.3 (b) Identify dependent and independent events and
calculate their probabilities
MA 12.4.3 (e) Determine the relative frequency of a specified
outcome of an event to estimate the probability of the outcome
Vocabulary
Sample space
Probability distribution
Independent events
Dependent Events
Relative Frequency
Suggested Resources
District Assessment
3/9/16