Study, study, study! Use your old tests, quizzes, take home test, etc. to study! The list of topics for our exam is below:
And bring a pencil!
PreCalculus Final Exam Review Guide!
I. The
Format
·
50 multiple choice questions WITH a graphing
calculator (50%)
·
25 open ended questions; must show work, NO calculator
(50%)
II. Topics
Covered (everything we’ve learned! J )—Sections
4.1 through 5.4 in your textbook
·
Converting angle measures (radians/degrees)
·
Complements/Supplements
·
Coterminal Angles
·
Sketching angles/determine which quadrant a terminal
side falls in
·
Solve a triangle (find all missing sides and angles
using SOHCAHTOA or special triangles)
·
Find the six trig functions (given one of them, given
a triangle with 2 sides, or given a coordinate pair)
·
Graphing trigonometric functions
o Changes to
amplitude (a), period (2pi/b), and vertical shifts (d)
·
Find missing sides/angles of a triangle using SOHCAHTOA
(word problems)
·
Simplify/Verify trig identities
o Factor,
find a common denominator, substitute, etc.
o Know the
reciprocal, quotient, and Pythagorean identities—none of these will be provided
o Factoring:
factor out a common factor, diamond method, differences of squares, grouping
o Dividing
fractions! “Keep, change, change” or “keep, change, flip”
·
Inverse/Arc problems; for example, “Evaluate
arcsin(1/2)”—“the angle whose sine is ½”
o Know the
restrictions for domain/range
o Compositions
of inverse/arc problems; for example, “tan(arcsin1/2)” or arcsin(cos2pi/3)
·
Solving trig equations
o Including
solving equations WITH factoring
o Remember
that square roots are positive or negative?
·
Sum and difference formulas
o Split up an
angle measure (in degrees) and use these formulas to evaluate
o “U and V”
type problems
o Given the
expanded formula, work backwards to write as a single angle and evaluate
·
Double
angle formulas
·
Evaluating trig functions given an angle; for example,
“Evaluate sin(2pi/3) or csc(pi/4)
·
Graph arcsine, arccos, or arctan and state the domain
and range
·
Use a graphing calculator to evaluate trig expressions
and trig inverses
o Check the
mode!
o Make sure
your reciprocal identities!
·
Find the coordinates of a point on the unit circle;
for example, find the coordinates for a 135° angle
·
Use SOHCAHTOA to define ratios of sides of a triangle
·
Determine a quadrant given information about the sign
(+/-) of sine, cosine, tangent
·
Graphing trig functions
o Write the
equation of a trig function given the graph
o Write the
equation of a trig function given amplitude, period, and/or vertical shift
o Identify
the graph given a function
o Find the
amplitude/period/vertical shift given a graph or equation
·
Domain and Range
o Sine,
cosine, tangent
o Reciprocal
functions (secant, cosecant, cotangent)
o Inverse
functions (arcsine, arccosine, arctangent)
§ Make sure
you know the restrictions on the range
·
Use the graphs of sine, cosine, tangent and the
horizontal line test to determine the restrictions!
