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Student Name________________________________ Instructor Name_________________________________
High School or Vocational Center_________________________________________Grade________________
COMPETENCY RECORD FOR ARTICULATION
Muskegon Community College
Mathematics
Please check below each skill the student has mastered as described, with 80 percent accuracy, or with an A or
B grade. The skills needed for articulation of each course are listed.
MTH 112
Trigonometric Functions with Coordinate Geometry
4 Credit Hours
Task
Satisfactory
Trigonometric functions based on the unit circle; applications using other circles
1. Be able to find, on a unit circle, the terminal point for a given
angle and the reference number for a given terminal point.
2. Be able to find the sine, cosine, tangent, cotangent, secant, and
cosecant of a given angle using the unit circle.
3. Be able to find the values of the six basic trigonometric functions
π π π π
for these special angles (in radians): 0, , , , , and π .
6 4 3 2
4. Be able to identify which of the six basic trigonometric functions
are even functions and which are odd functions.
5. Be able to use the fundamental trigonometric identities
(reciprocal and Pythagorean identities) to simplify an expression.
6. Be able to convert angle measurement between degrees and
radians.
7. Be able to determine the length of the arc of a circle, given an
angle and radius.
8. Be able to determine the area of a circular sector, given an angle
and radius.
Trigonometric functions based on the right triangle; applications using
other triangles
1. Be able to find trigonometric functions of a right triangle using
adjacent sides, opposite sides, and/or the hypotenuse.
MTH 112 - 6/9/08
Unsatisfactory
Task
Satisfactory
Unsatisfactory
2. Be able to find the trigonometric ratios of the special right
triangles (30-60-90 and 45-45-90).
3. Be able to solve a right triangle.
4. Be able to use the reference angle to evaluate a trigonometric
function.
5. Be able to determine the area of a triangle.
6. Be able to use the Law of Sines to solve a triangle.
7. Be able to use the Law of Cosines to solve a triangle.
8. Be able to Heron’s Formula to find the area of a triangle.
1
s ( s − a )( s − b)( s − c) where s= (a+b+c) is the
2
semiperimeter (half the perimeter) of a triangle with sides a, b,
and c.
Area =
Trigonometric graphs
1. Be able to graph the six basic trigonometric functions.
2. Be able to graph transformations of six basic trigonometric functions
including: changes in amplitude, phase shift, and/or period.
Analytic trigonometry, inverse trigonometric functions, complex number forms
1. Be able to prove and use the following identities and formulas to
find trigonometric values and solve trigonometric equations:
Cofunctions identities
Addition and subtraction formulas; sums of sines and cosines
Double-angle identities
Half-angle identities (and related formulas for lowering
powers)
Product-sum identities
2. Be able to solve trigonometric equations by factoring.
3. Be able to graph the inverse trigonometric functions.
4. Be able to find the composition of trigonometric functions and
their inverses.
5. Be able to evaluate the inverse trigonometric functions.
6. Be able to find the points of intersection for two trigonometric
functions.
7. Be able to find the trigonometric form of complex numbers,
including modulus and argument.
MTH 112
2
Task
Satisfactory
Unsatisfactory
8. Be able to perform multiplication and division of complex
numbers.
9. Be able to find the power of a complex number using
DeMoivre’s Theorem: If z=r(cosθ + i sin θ), then for any integer
n,
zn = rn(cos nθ + i sin nθ )
10. Be able to find the nth roots of a complex number:
If z = r (cos θ + i sin θ), and n is a positive integer, then z has the
n distinct nth roots:
1 
 θ + 2kn 
 θ + 2kn 
r n cos
 + i sin 
 for k = 0, 1, 2, ..., n - 1
 n 
  n 
Vectors
1. Be able to identify the initial and terminal points of a vector.
2. Be able to find the sum and difference of two vectors.
3. Be able to find perform scalar multiplication of a vector.
4. Be able to find the analytic form of a vector and i-j form of a vector.
5. Be able to find the magnitude (norm or length) of a vector.
6. Be able to apply the vector addition and scalar multiplication
properties of vectors.
7. Be able to break down a vector into its horizontal and vertical
components.
MTH 112
3
Task
Satisfactory
Unsatisfactory
Analytic geometry
1. Be able to graph and find the equation of a parabola with vertex at
origin.
2. Be able to find the focus and directrix of a paraola.
3. Be able to graph and find the equation of an ellipse with center at
origin.
4. Be able to find the foci of an ellipse.
5. Be able to find the eccentricity of an ellipse.
6. Be able to graph and find the equation of a hyperbola with center at
origin.
7. Be able to find the vertices and asymptotes of a hyperbola.
8. Be able to find important values (foci, directrix, vertices,
asymptotes) for conic functions subjected to horizontal and vertical
shifts.
9. Be able to graph and find the general equation of a shifted conic
section.
10. Be able to the XY-coordinates of a conic equation after the rotation
of axes.
11. Be able to use the general conic equation
Ax2 + Bxy + Cy2 + Dx + Ey + F =0
to eliminating the xy term in an equation.
12. Be able to use the general conic equation to identify a conic by its
discriminant.
Polar coordinates and equations
1. Be able to plot polar points.
2. Be able to convert between polar and rectangular coordinates.
3. Be able to graph polar equations.
4. Be able to recognize the common polar curves: circles, spirals,
limaçons, roses, and lemniscates.
5. Be able to find the polar equation of a conic and use it to sketch the
conic.
Parametric equations
1. Be able to graph a parametric curve.
2. Be able to convert between parametric equations and rectangular
functions.
3. Be able to convert bewteen polar equations and parametric forms.
MTH 112
4
Task
Satisfactory
Unsatisfactory
Sequences and series
1. Be able to find the terms in a non-recursive and recursive sequence.
2. Be able to identify the Fibonacci sequence.
3. Be able to compute the partial sum of a sequence.
4. Be able to use the sigma (Σ) notation of sums and apply the
properties of sums.
5. Be able to find the terms and partial sums of an arithmetic sequence.
6. Be able to find the terms and partial sums of a geometric sequence.
7. Be able to find the next term in an infinite series.
8. Be able to find the sum of an infinite geometric series.
Mathematical induction
1. Be able to distinguish betwen a conjecture and a mathematical proof.
2. Be able to demonstrate the principles of mathematical induction by
doing a simple proof.
Binomial theorem
1. Be able to generate expanded binomial coefficients using factorials:
n
n!
  =
 r  r!(n − r )!
2. Be able to expand a binomial using Pascal’s triangle.
3. Be able to expand a binomial using the Binomial Theorem
4. Be able to find the general term of binomial expansion:
 n  r n-r
The term that contains ar in the expansion of (a+b)n is 
 ab
n − r 
Instructor’s Signature _____________________________________________________Date ______________
MTH 112
5