Math Analysis Standards
Unit 1 – Matrices MA.14 (2 blocks)

MA 14
o Learning Objectives
 Add, subtract, and multiply matrices with and without the use of a calculator
 Multiply matrices by a scalar
 Model problems with a system of no more than three linear equations.
 Express a system of linear equations as a matrix equation.
 Solve a matrix equation
 Find the inverse of a matrix
 Verify the commutative and associative properties for matrix addition and
multiplication.
Unit 2 – Functions MA.1 – MA. 3 (6 blocks)



MA 1
o Learning Objectives
 Identify a polynomial function, given an equation or graph
 Identify a rational function given an equation or graph
 Identify domain, range, zeros, upper and lower bounds,
y-intercepts, symmetry, asymptotes, intervals for which the function is increasing or
decreasing, points of discontinuity, end behavior, and maximum and minimum
points, given a graph of a function.
 Sketch the graph of a polynomial function
 Sketch the graph of a rational function
 Investigate and verify characteristics of a polynomial or rational function, using a
graphing calculator.
MA 2
o Learning Objectives
 Find the composition of functions
 Find the inverse of a function algebraically and graphically
 Determine the domain and range of the composite function.
 Determine the domain and range of the inverse of a function
 Verify the accuracy of sketches iof functions, using a graphing utility.
MA 3
o Learning Objectives
 Describe continuity of a function
 Investigate the continuity of absolute value, step, rational, and piece-wise defined
functions.
 Use transformations to sketch absolute value, step, and rational functions
 Verify the accuracy of sketches of functions, using a graphing utility
Unit 3 – Exponential and Logarithmic Functions MA 9 (6 blocks)

MA 9
o Learning Objectives
 Identify exponential functions from an equation or a graph.
 Identify logarithmic functions from an equation or a graph
 Define e, and know its approximate value.
 Write logarithmic equations in exponential from and vice versa
 Identify common and natural logarithms
 Use laws of exponents and logarithms to solve equations and simplify expressions
 Model real-world problems, using exponential and logarithmic functions
 Graph exponential and logarithmic functions, using a graphing utility, and identify
asymptotes, intercepts, domain, and range
Unit 4 – Trig


T.6 - T.7
(5 blocks)
T.6
o
Learning Objectives
 State the domain and range given a trig function in standard form
 Determine the amplitude, period, phase shift, and vertical shift of a given trig
function in standard form
 Sketch the graph of a given trig function using transformations
o
Learning Objectives
 Identify the domain and range of inverse trig functions
 Recognize the graphs of the inverse trig functions
T.7
Unit 5 - Trig Part II T.5 and T.8


T.5
o
Learning Objectives
 Verify basic trig identities and make substitutions, using the basic identities
o
Learning Objectives
 Solve trig equations with restricted domain solutions
 Solve trig equations with infinite domain solutions
 Solve trig inequalities
 Verify algebraic solutions using a graphing utility
 Check for reasonableness of results
T.8
Unit 6 – Triangle Trig

(4 blocks)
MA.13
(3 blocks)
MA. 13
o Learning Objectives
 Solve and create problems using trig functions
 Solve and create problems , using the Pythagorean Theorem
 Solve and crea problems,using the Law os Sines and the Law of Cosines
 Sole real world problems using vectors
Unit 7 – Conic Sections

MA.8
(4 blocks)
MA. 8
o Learning Objectives
 Identify the type of conic given its graph or equation
 Write the equation of a conic in standard form given the general form of the
equation
 Graph a circle, a parabola, a hyperbola, and an ellipse given the equation of the
conic in standard or general form
Unit 8 – Polar Coordinates and Graphs

(4 blocks)
MA.10
o Learning Objectives
 Recognize polar equations (rose, cardioids, limacon, lemniscates, spiral, and circle) ,
given the graph or the equation.
 Determine the effects of changes in the parameters of polar equations on the graph ,
using a graphing utility.
 Convert complex numbers from rectangular form to polar form and vice versa
 Find the intersection of the graphs of two polar equations, using a graphing utility.
Unit 9 – Vectors

MA.10
MA.11
(4 blocks)
MA.11
o Learning Objectives
 Use vector notation
 Perform the operations of addition, subtraction, scalar multiplication, and inner
(dot) product on vectors.
 Graph vectors and resultant vectors
 Express complex numbers in vector notation
 Define unit vector, and find the unit vector in the same direction as a given vector.
 Identify properties of vector addition, scalar multiplication, and dot product
 Find vector components
 Find the norm (magnitude) of a vector.
 Use vectors in simple geometric proofs
 Solve real-world problems using vectors
Semester 2
Unit 10 – Parametric Equations

MA. 12
(2 blocks)
MA 12
o Learning Objectives
 Graph parametric equations, using a graphing utility
 Use parametric equations to model motion over time
 Determine solutions to parametric equations, using a graphing utility
 Compare and contrast traditional solution methods with parametric methods
Unit 11 – Sequences and Series/Mathematical Induction MA. 5 – 6 (4 blocks)


MA 5
o Learning Objectives
 Use and interpret the notation: , n, nth, and an

Given the formula, find the nth term, an , for an arithmetic or geometric sequence

Given the formula, find the sum, S n , if it exists, of an arithmetic or geometric series.



Model and solve problems, using sequence and series information.
Distinguish between a convergent and divergent series
Discuss convergent series in relation to the concept of a limit
MA 6
o Learning Objectives
 Compare inductive reasoning and deductive reasoning
 Prove formulas/statements, using mathematical induction
Unit 12 – Binomial Theorem




(2 blocks)
MA 4
o Learning Objectives
 Expand binomials having positive integral exponents
 Use the Binomial Theorem, the formula for combinations, and Pascal’s Triangle to
expand binomials.
Unit 13 – Limits

MA.4
MA.3 , MA. 7, LCPS Calc 1.1 – 1.3
(8 blocks)
MA 7
o Learning Objectives
 Verify intuitive reasoning about the limit of a function, using a graphing utility.
 Find the limit of a function algebraically and verify with a graphing utility
 Find the limit of a function numerically, and verify with a graphing utility
 Use limit notation when describing end behavior of a function
MA 3
o Learning Objective
 Given the equation or graph of a function, determine if the function is continuous or
discontinuous.
LCPS Calc 1.1 Limits of Functions (including one-sided limits)
o Learning Objectives
 Describe the limit process
 Calculate limits algebraically
 Estimate limits from graphs or tables of data
LCPS Calc 1.2 Asymptotic and unbounded behavior
o Learning Objectives
 Discuss asymptotes in terms of graphical behavior
 Describe asymptotic behavior in terms of limits involving inifinity
 Compare relative magnitudes of functions and their rates of change (for example,
contrasting exponential growth, polynomial growth, and logarithmic growth)

LCPS Calc 1.3 Continuity as a property of functions
o Learning Objectives
 Determine if a function is continuous using limits
 Interpret graphs geometrically using Intermediate Value Theorem and Extreme
Value Theorem
Unit 14 – Differentiation



LCPS Calc 2.1 – 2.6
(13 blocks)
LCPS Calc 2.1 Concept of the derivative
o Learning Objectives
 Explain the derivative of function graphically, numerically, and analytically
 Interpret the derivative as an instantaneous rate of change
 Define the derivative as the limit of the difference quotient
 Determine the relationship between differentiability and continuity
LCPS Calc 2.2 Derivative at a point
o Learning Objectives
 Determine the slope of a curve at a point…including points at which the tangent line
is vertical or at which no tangents occur.
 Discuss the instantaneous rate of change as the derivative of the average rate of
change
 Approximate rate of change from graphs and tables of values
LCPS Calc 2.3 Derivative of a function
o Learning Objectives
 Compare and contrast the graphs of f and f  and discuss their corresponding

characteristics
Determine the relationship between the increasing and decreasing behavior of f
and the sign of f  .

 Interpret the Mean Value Theorem geometrically
 Translate verbal descriptions into equations involving derivatives and vice versa
LCPS Calc 2.4 Second derivatives
o Learning Objectives
 Compare and contrast the graphs of f , f  , and f  and discuss their corresponding



characteristics
Determine the relationship between the concavity of f and the sign of f  .
 Discuss the meaning of points of inflection
LCPS Calc 2.5 Applications of derivatives
o Learning Objectives
 Analyze curves …include the notion of monotonicity and concavity
 Find minimums and maximums on an interval and determine if those values are
relative or absolute extrema
 Model rates of change
 Use implicit differentiation to find the derivative of an inverse function
 Interpret the derivative as a rat of change in varied applied contexts, including
velocity, speed, and acceleration
LCPS Calc 2.6 Computation of derivatives
o Learning Objectives

Calculate the derivative of basic functions, including power, exponential,
logarithmic, trigonometric, and inverse trigonometric functions
Use derivative rules for sums, products, and quotients of functions to calculate the
derivative of a more complex function
Apply the chain rule to calculate the derivative of a function when applicable

Use implicit differentiation to find the derivative of function when applicable


Unit 15 – Applications of differentiation

LCPS Calc 2.5 (14 blocks)
LCPS Calc 2.5 Applications of derivatives
o Learning Objectives
 Analyze curves …include the notion of monotonicity and concavity
 Find minimums and maximums on an interval and determine if those values are
relative or absolute extrema
 Model rates of change
 Use implicit differentiation to find the derivative of an inverse function
 Interpret the derivative as a rat of change in varied applied contexts, including
velocity, speed, and acceleration