Learning Objectives – PreCalculus Level
Students should also be able to explain the underlined terms.
6.1 A Convert angle measures between DMS and decimal form.
6.1 B Evaluate trig ratios using triangles and/or a calculator.
6.2 Solve triangles using trig ratios.
6.3 A Convert between radians and degrees.
6.3 B Determine coterminal angles.
6.3 B Calculate arc length.
6.4 A Determine trig ratios in the coordinate plane.
6.4 A Find reference angles.
6.4 B Find exact values of trig ratios for all special angles in the unit circle.
6.5 Simplify trig expressions using reciprocal and Pythagorean identities.
7.1-7.4 Graph trig functions.
7.1 Solve simple trig equations in the interval [0, 2  ]
8.1 Solve trig equations graphically (with a calculator).
8.2 Evaluate inverse trig functions.
8.3 Use algebraic techniques to solve trig equations.
9.1 Prove trig identities.
9.2 Use Sum and Difference identities to evaluate trig ratios.
9.3 Use Double Angle identities to evaluate trig ratios.
9.3 Use Half Angle identities to evaluate trig ratios.
10.1 Solve right triangles using Law of Cosines.
10.2 Solve right triangles using Law of Sines.
10.2 Find the area of a triangle given an angle and 2 adjacent sides.
10.2 Find the area of a triangle given its 3 sides.
10.3 Graph a complex number in the complex plane.
10.3 Find the absolute value of a complex number.
10.3 Change a complex number into polar form.
10.3 Multiply and divide numbers in polar form.
10.4 Calculate powers of complex numbers.
10.4 Calculate roots of complex numbers.
SECOND SEMESTER
1.2 Find the terms of a sequence.
1.2 Write a recursive formula for a sequence.
1.3 Identify arithmetic and geometric sequences.
1.3, 1.6 Write and apply explicit formulas for arithmetic and geometric sequences.
1.3 Use summation notation to represent a sum.
1.3, 1.6 Find partial sums of arithmetic and geometric sequences.
Chap 1 Can Do Calculus p. 76 Determine whether an infinite geometric series converges, and find
the sum if it does.
2.2 Solve quadratic equations by square roots, factoring, the quadratic formula, and completing the
square.
2.4 Solve absolute value equations.
2.4 Solve radical equations.
2.4 Solve fractional equations.
2.5 Solve inequalities algebraically.
2.5A Solve absolute value inequalities.
3.1 Determine whether a relation is a function, given its equation or table.
3.1 Use function notation to evaluate functions.
3.2 Determine whether a graph represents a function.
3.2 Analyze graphs to determine domain, range, local maxima and minima, inflection points, and
intervals where they are increasing, decreasing, concave up, and concave down.
3.2 Graph parametric equations by making a table.
3.4 Describe parent functions using graphs, tables, equations or verbal descriptions and find domain
and range.
3.4 Graph transformations of functions.
3.5 Add, subtract, multiply, and divide functions and find their domains.
3.5 Form composite functions and find their domains.
3.4A Algebraically and graphically, determine whether a relation is symmetric with respect to the xaxis, y-axis, origin, or none of these.
3.4A Determine whether a function is even, odd, or neither.
3.4A Use symmetry and/or odd/even characteristics to complete the graph of a relation.
3.6 Determine whether inverse relations are functions and whether functions are 1-1 from a table,
graph, or equation.
3.6 Verify functions are inverses using composition of functions.
4.5 Simplify square roots of negative numbers.
4.5 Add, subtract, multiply, divide, use powers with complex numbers.
4.1 Define a polynomial.
4.1 Divide polynomials using synthetic and long division.
4.1 Apply the Remainder Theorem, Factor Theorem, and the connections between remainders,
factors, zeros, and graphs.
4.1 Determine the maximum number of zeros of a polynomial.
Factor polynomials using any method, including grouping and cubes.
4.2 List all possible rational zeros of a polynomial.
4.2 Factor a polynomial completely.
4.2 Find all real zeros of a polynomial.
4.2 Find lower and upper bounds of zeros of a polynomial.
4.3 Analyze the graph of a polynomial function, including degree, end behavior, zeros, local extrema,
continuity and bounds.
4.4 Analyze the graph of a rational function, including domain, holes, vertical asymptotes, horizontal
asymptotes, slant asymptotes, x- and y-intercepts.
4.6 Find all zeros (real and complex) of a polynomial.
4.6 Factor a polynomial using only linear factors.
4.6 Determine the equation of a polynomial given its zeros or graph.
5.1 Define and apply rational exponents.
5.1 Simplify expressions containing radicals or rational exponents.
5.2 Graph and identify transformations of exponential functions.
5.3 Use exponential functions in real-life application problems.
5.4, 5.5A Evaluate logs of any base.
5.4, 5.5A Solve exponential and log equations by rewriting the equation in the other form.
5.5, 5.5A Use properties of logs to simplify expressions and solve equations.
5.4 Graph and identify transformations of log functions.
5.6 Solve log and exponential equations, including real-life applications.
10.5 Find the components and magnitude (norm) of a vector.
10.5 Add, subtract, and perform scalar multiplication with vectors.
10.6 Find a unit vector in the same direction.
10.6 Perform operations with vectors in component form.
10.6 Determine the direction angle of a vector or use it to find a vector’s components.
10.6A Find the dot product of two vectors.
10.6A Find the angle between two vectors.
10.6A Determine whether two vectors are parallel, perpendicular, or neither.
Class Notes Given the equation of a circle, write it in standard form, find the center, radius, and
graph it.
Class Notes Given the characteristics of a circle, determine its equation.
11.1, 11.4 Given the equation of a ellipse, write it in standard form, find the center, vertices, foci, and
graph it.
11.1, 11.4 Given the characteristics of a ellipse, determine its equation.
11.2, 11.4 Given the equation of a hyperbola, write it in standard form, find the center, vertices, foci,
asymptotes, and graph it.
11.2, 11.4 Given the characteristics of a hyperbola, determine its equation.
11.3, 11.4 Given the equation of a parabola, write it in standard form, find the vertex, directrix, foci,
axis, and graph it.
11.3, 11.4 Given the characteristics of a parabola, determine its equation.
11.4 Identify the conic, given its equation.
11.7 Given a set of parametric equations, eliminate the parameter.
B.1 Use Pascal’s triangle and expand binomial expressions.
Chap. 12 Can Do Calculus (p. 838) Decompose a fraction into a sum of partial fractions.
12.3 Add, subtract, and multiply matrices.
12.3 Define the identity matrix.
12.4 Find the inverse of a matrix.
12.4 Solve systems using inverses of matrices.
Class notes/ Alg 2 Solve systems using Cramer’s Rule.