Download Test - LPS

DIFF PRECALCULUS PACING AND ASSESSMENT CARD – SEMESTER ONE
Student Name/ID:
_____Grade:______School:_____________________________
Year:___________
Teacher_________________________
Course Objectives
Diff
Precal
Section
Students will be able to use the distance formula.
Students will be able to use the midpoint formula.
Student will be able to graph equations by hand and using a calculator.
Students will be able to find intercepts from an equation.
Students will be able to tell if a graph is symmetric to the x-axis, y-axis, and/or the origin.
Students will be able to solve linear and quadratic equations.
Students will be able to solve absolute value and radical equations.
Students will be able to set up and solve interest problems, mixture problems, uniform motion problems, and
constant rate job problems.
Students will be able to use interval notation. Students will be able to use properties of inequalities.
Student will be able to solve linear inequalities, combined inequalities, and absolute value inequalities
algebraically and graphically.
Students will be able to calculate and interpret the slope of a line.
Students will be able to find equations of lines given two points, vertical lines, parallel and perpendicular lines.
Students will be able to use point-slope and slope y-intercept forms.
Students will be able to draw and interpret scatter diagrams and distinguish between linear and nonlinear
relations. Students will be able to use a calculator to fine the line of best fit.
Students will be able to write the standard form of the equation of a circle. Students will be able to graph a
circle by hand and using a calculator. Students will be able to find the center and radius from and equation of
a circle.
1.1
Students will be able to determine whether a relation represents a function. Students will be able to find the
value and domain of a function. Students will be able to identify the graph of a function.
Students will be able to find the average rate of change of a function. Students will be able to locate local
maxima, minima, determine where a function increases and decreases, and identify even and odd functions.
Students will be able to graph functions listed in the library. Students will be able to graph piecewise-defined
functions.
Students will be able graph functions using horizontal and vertical shifts, compressions and stretches, and
graph functions using reflections about the x or y axis..
Students will be able to form the sum, difference, product, and quotient of two functions.
Students will be able to form the composite function and find its domain.
Students will be able construct and analyze functions. Students will be able to solve real-world problems.
2.1
Students will be able to convert between degrees, minutes, seconds, and decimal forms of angles. Students
will e able to find the arc length of a circle. Students will be able to convert from degrees to radians and from
radians to degrees. Students will be able to find the linear speed of an object traveling in circular motion.
Students will be able to find the exact value of trig functions using a point on the unit circle. Students will be
able to find the exact values of quadrantal angles. Students will be able to find the exact value of the trig
functions of 45-60-30 angles. Students will be able to use a calculator to approximate values of the trig
functions.
Students will be able to determine domain, range, period and signs of trig functions. Students will be able to
find the value of thee trig functions utilizing fundamental identities. Students will be able to use even-odd
properties to find the exact value of the trig functions.
Students will be able to find the value of trig functions of acute angles. Students will be able to use the
Complementary Angle Theorem. Students will be able to solve right triangles and applied problems.
Students will be able to graph transformations of the sine and cosine functions.
6.1
Students will be able to graph transformations of the tangent and cotangent functions.
Students will be able to graph transformations of the secant and cosecant functions.
Students will be able to determine amplitude, period, and phase shift of a sinusoidal function. Students will be
able to find an equation for a sinusoidal graph and find a sinusoidal function from data.
6.5
Students will be able to establish trig identities.
7.1
Students will be able to use sum and difference formulas to find exact values.
Students will be able to use sum and difference formulas to establish identities
Students will be able to use double-angle and half-angle formulas to find exact values. Students will be able
to use double-angle and half-angle formulas to establish identities.
Students will be able to express products as sums and sums as products.
7.2
Students will be able to find exact and approximate values of inverse trig functions.
7.5
Students will be able to find the exact value of expressions involving inverse trig functions. Students will be
able to write a trig expression as an algebraic expression. Students will be able to establish identities
involving inverse trig expressions.
Students will be able to solve equations involving a single trig function.
Students will be able to solve trig equations that are quadratic in form. Students will be able to solve trig
equations using identities. Students will be able to solve trig equations linear in sine and cosine. Students will
be able to solve trig equations using a graphing calculator.
7.6
Students will be able to use the law of sines to solve SAA, SAS, and SSA triangles. Students will be able to
solve applies problems using the law of sines.
Students will be able to use the law of cosines to solve SAS and SSs triangles. Students will be able to solve
applies problems using the law of cosines.
Students will derive and be able to find the area of SAS and SSS triangles.
8.2
Students will be able to find an equation for an object in simple harmonic motion.
Students will be able to analyze simple harmonic motion and an object in damped motion
8.5
Date
Covered
Quiz
Scores
Test
Scores
Test:
1.2
1.3
1.4
1.5
1.6
Retest:
1.7
1.8
Test:
2.2
2.3
2.4
Retest:
2.5
2.6
Test:
6.2
6.3
8.1
Retest:
6.4
6.6
Test:
7.3
7.4
Retest:
7.7
7.8
Test:
8.3
8.4
Retest:
6/28/17
Course Objectives
Precal
Section
Students will be able to understand the proof of the Law of Sines and will be able to use the
computational applications to solve a variety of problems.
Students will be able to apply the Law of Cosines to solve acute and obtuse triangles and to
determine the area of a triangle in terms of the measures of sides and angles.
5.5
Students will be able to apply the arithmetic of vectors and use vectors to solve real world
problems. Key ideas include: component form of a vector, scalar multiplication, directed line
segments, speed, direction angle. standard position of a vector, equal vectors, standard unit
vectors i and j, equivalent line segments, terminal point, horizontal component, unit vector, initial
point, vector addition, length or magnitude (of a vector), velocity, linear combination.
Students will be able to calculate dot products; use dot products to find length; find the angle
between vectors; calculate projections of vectors; apply concepts to real-world problems involving
components of force and work.
Students will be able to plot points in the polar coordinate system; find several polar coordinates for
a point; convert points and equations from polar to rectangular coordinates and vice versa; find
distance using polar coordinates.
Students will be able to graph a variety of polar equations and determine the maximum r-value and
the symmetry of a graph.
Students will be able to represent complex numbers in trigonometric form and perform operations
on them; use De Moivre’s Theorem, find nth roots of nonzero complex numbers; find roots of unity.
Students will be able to define parametric equations, graph curves parametrically, and solve
application problems using parametric equations.
6.1
Students will be able to describe and produce the graphs of rational functions, identify their
horizontal and vertical asymptotes, and analyze their end behavior. Students will be able to model
real-world problems with rational functions and solve the resulting equations, identifying extraneous
solutions when they occur.
Students will be able to solve inequalities involving polynomials and rational functions by using both
algebraic and graphical techniques.
2.7
Students will be able to evaluate exponential expressions, and identify and graph exponential and
logistic functions.
Students will be able to use exponential growth, decay, and regression to model real-life problems.
Students will be able to convert equations between logarithmic form and exponential form, evaluate
common and natural logarithms, and graph common and natural logarithmic functions.
Students will be able to apply the properties of logarithms to evaluate expressions and graph
functions, and be able to re-express data.
Students will be able to apply the properties of logarithms to solve exponential and logarithmic
equations algebraically and solve application problems using these equations.
Students will be able to use exponential functions to solve business and finance applications
related to compound interest and annuities.
3.1
Students will be able to find the standard form equation, focus, and directrix of a parabola. Graph
by hand.
Students will be able to find the standard form equation, vertices, and foci of an ellipse. Graph by
hand.
Students will be able to find the standard form equation, vertices, and foci of a hyperbola. Graph by
hand.
Students will be able to draw three-dimensional figures and analyze vectors in space.
8.1
Students will be able to use the multiplication principle of counting, permutations, or combinations
to count the number of ways that a task can be done.
Students will be able to expand a power of a binomial using the binomial theorem or Pascal’s
triangle. Students will be able to find the coefficient of a given term of a binomial expansion.
Students will be able to identify a sample space and calculate probabilities and conditional
probabilities in sample spaces with equally likely or unequally likely outcomes.
Students will be able to express arithmetic and geometric sequences explicitly and recursively; use
sigma notation and basic summation formulas to find the sum of a finite series or a converging
infinite geometric series.
Students will be able to use the principle of mathematical induction to prove mathematical
generalizations.
9.1
Date
Coverd
5.6
6.2
6.4
6.5
6.6
6.3
2.8
3.2
3.3
3.4
3.5
3.6
8.2
8.3
8.6
9.2
9.3
9.4
9.5
Optional
Quiz
Scores
Test
Score