Pre-AP Pre-Calculus

Explore polynomial functions, zeros and multiplicity, learn to factor and solve for zeros, analyze even and odd multiplicities, and predict graph behavior.

apply the rational root theorem to identify possible rational zeros using p over q, test candidates, and use long division to factor and find zeros like 1, -5, and -4.

Explore how rational functions are graphed by identifying vertical and horizontal (and oblique) asymptotes, x- and y-intercepts, and sign charts, then apply factorization and limits to analyze end behavior.

Learn to analyze and graph rational functions by hand, identify vertical and oblique asymptotes, intercepts, and end behavior using a sine chart.

Solve exponential and logarithmic equations with a circle of logs, by equating exponents to a common base and verifying solutions, such as x = -1 and x = 101.

Master solving exponential equations using logarithms, factoring, and domain checks to identify valid solutions, applying natural logs and log rules for clarity.

Explore angles and their measures in standard position, distinguishing positive (counterclockwise) and negative (clockwise) angles, and learn to find coterminal angles by adding or subtracting 360 degrees.

Explore radian and degree angles, memorize the unit circle, and learn to convert between degrees and radians while identifying quadrants and key angle measures.

Explore sine and cosine graphs and their transformations, including amplitude, period, and vertical and horizontal shifts, using the unit circle and graphing rules to derive equations.

Explore cosine and secant graphs, the reciprocal relationship, and how shifts, horizontal shrink, and vertical stretch transform period, domain, range, and asymptotes.

Explore other trig graphs and transformations by solving a height problem with tangent, labeling adjacent, opposite, and hypotenuse, and deriving height as 5 plus 120 tan 8°.

Apply tangent to two intermediate right-triangle trig scenarios to calculate horizontal distances from a 100-foot tower to a plane as the angle of elevation changes from 32° to 10°.

Explore inverse trig graphs by determining domains and ranges, and applying horizontal and vertical transformations to arc cosine, arc sine, and arc tangent.

Explore sum and difference formulas for sine, cosine, and tangent, memorize core identities like sin^2+cos^2=1, and apply addition rules to compute angles in degrees and radians using the unit circle.

Learn and apply the double-angle identities for sine, cosine, and tangent, using the unit circle and 3-4-5 and 5-12-13 triangles to compute theta and 2 theta values.

Apply the law of sines to ssa triangle problems, exploring acute, obtuse, and two-triangle cases, with a satellite distance scenario using 58 degrees and 52 degrees.

Compute component form and magnitude of vectors P and Q, then apply parallelogram addition and scalar operations. Verify with V = (-12,3), W = (8,16): result (-6,28) and magnitude sqrt(820).

Explore dot products and inner products to determine when vectors are orthogonal and the angles between them, using examples that show multiplying vectors yields zero for perpendicular pairs.

Learn to find the angle between two nonzero vectors using theta = arccos((u·v)/(|u||v|)), computing the dot product and magnitudes to obtain about 132.13 degrees.

Explore projectile motion with parametric equations, eliminate the parameter to get a y(x) relationship, and analyze a free-throw example using initial velocity, angle, and gravity to determine reach.

Master the polar coordinate plane by defining the pole and polar axis, expressing points as (r, theta), and using positive/negative r to plot equivalent coordinates.

Explore ellipses by mastering the center, major and minor axes, foci, and vertices; learn how a, b, c define orientation, eccentricity, and axis lengths for horizontal or vertical ellipses.

Derive hyperbola equations in standard form using a, b, and c via the Pythagorean relation, locate center, vertices, foci, and asymptotes, and practice graphing with a vertical transverse axis.

Explore hyperbola basics: determine center, vertices, and foci using a and b. Apply c^2 = a^2 + b^2 and analyze eccentricity for horizontal and vertical orientations.

Identify conics by transforming equations to general form and identifying ellipses, circles, parabolas, and hyperbolas. Use lcm to clear fractions, foil, and apply the discriminant B^2−4AC to detect rotated conics.

Explore sequences by comparing explicit and recursive rules, computing terms such as the hundredth term, and recognizing arithmetic sequences.

Explore arithmetic sequences by identifying the initial term and common difference, building recursive and explicit formulas, and generating the first five terms from examples.

Apply the geometric series sum formula, namely S = a1/(1 - r), to infinite sequences, and use arithmetic-series formulas to determine the number of terms.