Livingston County Schools
Pacing Guide
Pre-Calculus
Length of time
16 days
15 days
Unit Name
Linear Relation and Functions
Systems of Linear Equations
and Inequalities
Overview
After completing this unit, students will
determine whether a given relation is a
function, identify the domain and range of a
relation or function, evaluate functions,
perform operations with functions, find
composite functions, iterate functions using
real numbers, graph linear equations, find xand y-intercepts, find the slope of a line
through two points, find zeros of functions,
write linear equations, write linear equations
of parallel and perpendicular lines, draw and
analyze scatter plots, write a prediction
equation, identify and graph piecewise
functions including greatest integer, step and
absolute value and graphing linear
inequalities.
Assessed Standards
Math
After completing this unit, students will be
able to solve systems of equations graphically
and algebraically, solve systems of equations
involving three variables algebraically, model
data using matrices, add, subtract and
multiply matrices, find determinants and
Math
F.IF.1, F.IF.2, F.IF.4, F.IF.9, F.IF.6,
F.IF.7, A.CED.2, F.BF.1
ELA/Literacy
Science
A.REI.6, A.REI.11, A.REI.5,
A.REI.12, A.CED.2
15 days
Polynomial and Rational
Functions
multiplicative inverses and use linear
programming to solve problems.
ELA/Literacy
Science
After completing this unit, students will be
able to determine roots of polynomial
equations, apply the Fundamental Theorem
of Algebra, solve quadratic equations, use the
discriminant to describe roots of quadratic
equations, use the Remainder and Factor
Theorem, find zeros of polynomials and solve
radical equations.
Math
F.IF.4, F.IF.6, A.CED.1, F.IF.8, F.IF.9,
F.BF.3, A.CED.2, A.SSE.1, A.SSE.2,
A.APR.3, N.CN.1, N.CN.2, N.CN.7,
N.CN.8, A.REI.4, F.IF.5, A.APR.1,
A.APR.6, A.APR.2, A.REI.11,
ELA/Literacy
Science
30 days
The Trigonometric Functions
After completing this unit, students will be
able to convert decimal degree measure to
degrees, minutes and seconds and vice versa,
find the number of degrees in a given
rotation, identify angels that are coterminal,
find values of trigonometric ratios for acute
angles of right triangle, find the six
trigonometric functions using the unit circle,
find the values of the six trigonometric
functions of an angle in standard position
given a point on its terminal side, use
trigonometry to find the measures of the
sides of right triangles, evaluate inverse
trigonometric functions, find missing angle
measurements, solve right triangles, use the
law of sines to solve triangles, use the law of
Math
G.SRT.8, G.MG.1, G.SRT.7,
G.SRT.11
ELA/Literacy
Science
20 days
15 days
10 days
Graphs of Trigonometric
Functions
Trigonometric Identities and
Equations
The Nature of Graphs
cosines to solve triangles and find the area of
triangles if the measures of the three sides
are given.
After completing this unit, students will
change from radian measure to degree
measure and vice versa, find the length of an
arc given the measure of the central angle,
find the area of a sector, use the graphs of
the sine and cosine functions, find the
amplitude and period for the sine and cosine
functions, write equations of sine and cosine
functions given the amplitude and period,
find the phase shift and the vertical
transformation for the sine and cosine
functions and graph tangent, cotangent,
secant, and cosecant functions, write
equations of trigonometric functions and
graph inverse trigonometric functions.
After completing this unit, students will be
able to identify and use reciprocal identities,
quotient identities, Pythagorean identities,
symmetry identities, opposite-angle
identities, use the basic trigonometric
identities to verify other identities, find
numerical values of trigonometric identities,
use the sum and difference identities for the
sine, cosine and tangent functions and use
the double-and half-angle identities.
After completing this unit, students will be
able to use algebraic test to determine if the
graph of a relation is symmetrical, classify
functions as even or odd, identify
transformations of simple graphs, sketch
Math
G.SRT.8, G.MG.1, G.SRT.7,
G.SRT.11
ELA/Literacy
Science
Math
G.SRT.8, A.CED.4, A.SSE.3
ELA/Literacy
Science
Math
F.BF.3, F.BF.4, F.IF.4
10 days
10 days
Exponential and Logarithmic
Functions
Conic Sections
graphs of related functions, determine
inverses of relations and functions, graph
functions and their inverses, determine
whether a function is continuous or
discontinuous, identify the end behavior of
functions, determine whether a function is
increasing or decreasing on an interval, find
the extrema of a function, graph rational
functions and determine vertical and
horizontal asymptotes.
After completing this unit, students will be
able to use the properties of exponents,
evaluate and simplify expressing containing
rational exponents, solve equations
containing rational exponents, graph
exponential functions, use the number e,
evaluate expressions involving logarithms,
solve equations and inequalities involving
logarithms, graph logarithmic functions and
inequalities, solve equations and inequalities
using common logarithms and find natural
logarithms.
After completing this unit, students will be
able to find the distance and midpoint
between two points on a coordinate plane,
prove geometric relationships among points
and lines, use and determine the standard
and general forms of the equation of a circle,
graph circles, use and determine the
standard and general forms of the equation
of an ellipse, graph ellipses, use and
determine the standard and general form of
the equation of a hyperbola, graph
ELA/Literacy
Science
Math
F.LE.4, F.IF.7, F.BF.1, A.SSE.1
ELA/Literacy
Science
Math
G.GPE.1, G.GPE.2, F.IF.8, A.REI.11,
A.REI.7, F.TF.1, F.TF.2, G.GPE.3
ELA/Literacy
Science
15 days
Statistics and Data Analysis
hyperbolas, use and determine the standard
and general forms of the equation of a
parabola and graph parabolas.
After completing this unit, students will be
able to draw, analyze and use bar graphs and
histogram, organize data into a frequency
distribution table, find the mean, median,
and mode of a set of data, find measures of
central tendency in a frequency distribution
table, find the interquartile range, the semiinterquartile range, mean deviation, and
standard deviation of a set of data, use the
normal distribution and find the standard
error of the mean to predict the mean of a
population with a certain level of confidence.
Math
S.IC.1, S.IC.2, S.IC.3, S.IC.4, S.IC.5,
S.IC.6
ELA/Literacy
Science
Math
ELA/Literacy
Science
Math
ELA/Literacy
Science