AP Intermediate Mathematics (BIEAP) study plan

Solve quadratic equations, inequalities, and quadratic expressions in one and two variables without error

Apply the factor and remainder theorems to factor polynomials of degree 3 and 4

Solve systems of linear equations using Cramer's rule and matrix inversion

Prove and use the laws of indices and logarithms, including change of base

Expand and use the binomial theorem for positive integral indices, including general term extraction

Compute permutations and combinations and apply them to counting problems

Sum arithmetic and geometric progressions, including infinite GP convergence conditions

State and apply the principle of mathematical induction to simple series and divisibility results

Convert between degrees and radians and evaluate all six trigonometric ratios at standard angles

Prove and apply compound-angle and multiple-angle identities

Solve trigonometric equations over a stated interval and list all solutions

Apply sine and cosine rules to triangle problems, including the ambiguous case

Transform equations between general and standard forms for lines, circles, parabolas, ellipses, and hyperbolas

Find foci, eccentricity, directrix, and axes for each conic

Compute distances, midpoints, and areas using coordinate geometry formulas

Determine tangents and normals to circles and conics at a given point

Evaluate limits using standard forms, L'Hôpital's rule, and algebraic manipulation

Differentiate sums, products, quotients, and composites using the chain rule

Differentiate implicit and parametric functions and logarithmic differentiation

Apply derivatives to tangents, normals, maxima, minima, and rates of change

Integrate standard functions and apply substitution and integration by parts

Evaluate definite integrals and use them to compute areas and volumes of revolution

Decompose rational functions into partial fractions and integrate them

Distinguish which integration technique applies to a given integrand before starting

Classify differential equations by order and degree and solve separable and homogeneous equations

Solve first-order linear equations using an integrating factor

Add, subtract, and scale vectors and compute dot and cross products

Apply scalar triple product and vector geometry to angle and area problems

Compute mean, median, mode, variance, and standard deviation for grouped and ungrouped data

Apply basic probability rules, conditional probability, and Bayes' theorem to word problems

Find direction cosines, direction ratios, and equations of lines and planes in 3D

Compute angles and shortest distances between lines and planes in 3D