COURSE DESCRIPTION:
Polynomial and rational functions , exponential and logarithmic functions,
trigonometric functions, analytic trigonometry, vectors, complex numbers ,
elementary theory of equations, linear systems, matrices, and analytic geometry.
COURSE COMPETENCIES:
During this course, the student will be expected to:
1. Analyze mathematical functions.
1.1 Define a function.
1.2 De termine if a relation is a function.
1.3 Find the domain and range of a function.
1.4 Determine minimum and maximum values of a function .
1.5 Determine whether functions are increasing, decreasing or constant.
1.6 Determine whether functions have even or odd properties.
2. Graph functions .
2.1 Identify common functions .
2.2 Identify transformations.
2.3 Combine functions using addition, subtraction, multiplication, or division.
2.4 Define an inverse function.
2.5 find inverse function.
3. Use polynomial functions.
3.1 Define a polynomial function.
3.2 Determine the standard form of a quadratic function .
3.3 Determine the vertex and any x-intercepts of a quadratic function.
3.4 Find zeros of a polynomial function.
3.5 State the fundamental Theorem of Algebra.
3.6 apply the intermediate value, remainder, factor, and rational root theorems
to find polynomial roots.
4. Identify rational functions.
4.1 Define a rational function.
4.2 Identify any horizontal and vertical asymptotes.
4.3 Graph a rational function.
5. Use exponential functions.
5.1 Define exponential functions.
5.2 Graph exponential functions.
5.3 Solve exponential equations.
6. Use logarithmic functions.
6.1 Define logarithmic functions.
6.2 Apply the properties of logarithms.
6.3 Graph logarithmic functions.
6.4 Solve logarithmic equations.
6.5 Apply exponential and logarithmic functions to problems involving interest,
growth and decay.
7. Use trigonometric functions for oblique triangles.
7.1 Apply the Law of Sines and Law of Cosines.
7.2 Find the area of SAS triangles.
7.3 Find the area of SSS triangles using heron’s formula.
8. Use vectors in the plane.
8.1 Perform scalar multiplication and vector addition.
8.2 Find the dot product of two vectors .
8.3 Apply properties of the dot product.
8.4 Find the angle between two vectors.
8.5 Find vector components using projection of one vector onto another.
9. Use the trigonometric form of complex numbers.
9.1 Find the trigonometric form of a complex number.
9.2 Find the modulus of a complex number.
9.3 Multiply and divide complex numbers.
9.4 Find powers and roots of complex numbers.
10. Solve systems of equations.
10.1 Use the substitution and elimination methods to solve a system of
equations.
10.2 Identify whether a system of equations has zero, one, or infinitely many
solutions .
10.3 Use row-echelon form and back-substitution to solve a system of equations.
10.4 Solve nonsquare systems of equations using a parameter.
10.5 Decompose a fraction into partial fraction equivalents .
11. Use matrices.
11.1 Use Gaussian Elimination with back-substitution to solve a system of
equations using row operations on matrices.
11.2 Use Gauss-Jordan Elimination to solve a system of equations.
11.3 Perform the operations of matrix addition, scalar multiplication, and
matrix multiplication.
11.4 Determine the inverse of a nonsingular matrix.
11.5 Solve a system of equations using the inverse matrix.
11.6 Find the determinant of a square matrix.
11.7 Use Cramer’s Rule to solve a linear system of equations.
12. Analyze conic sections using rectangular coordinates .
12.1 find the standard equation of a parabola, an ellipse , and a hyperbola .
12.2 Find the vertex, focus, and directrix of a parabola.
12.3 Find the center, vertices, foci, and eccentricity of an ellipse.
12.4 Find the center, vertices, foci, and asymptotes of a hyperbola.
12.5 Classify a conic from its general equation.
13. Analyze conic sections using polar coordinates.
13.1 Convert coordinates and equations from rectangular to polar and vice versa.
13.2 Graph polar equations by testing for symmetry.
13.3 Identify and graph a conic by examining the polar form of the equation.
14. Graph points, lines, vectors and surfaces in space.
14.1 Plot points, find distances between points, and find midpoints of segments.
14.2 Write equations of spheres.
14.3 Find dot products of vectors and angles between vectors.
14.4 Find cross products of vectors.
15. Find limits.
15.1 Use properties and operations of limits.
15.2 Find limits by direct substitution, dividing out, and rationalizing.
15.3 Find slopes by use of tangents lines, the limit definition of slope, and
derivatives.
15.4 Find limits at infinity and limits of sequences.
15.5 Find limits of summations .
