LEARN · EXPLAIN · REVISE
Targeted skill lessons
Read the idea, work independently, then explain what changed.
Six themes, four independent skills each. Start with an eight-question check or a 40-minute lesson.
Quadratics
Eight-question checkVertex form and completing the square
Explain turning points, symmetry and constrained optima through a square.
3 examples · 10 exercises · 40 minutesRoots and completeness of solutions
Choose a root method, then check reality, location and the original domain.
3 examples · 10 exercises · 40 minutesQuadratic signs and solution sets
Use roots to partition a line, then retain endpoint and domain conditions.
3 examples · 10 exercises · 40 minutesQuadratic extrema on restricted intervals
Compare admissible vertex and endpoints, including open and moving intervals.
3 examples · 10 exercises · 40 minutesTrigonometry
Eight-question checkUnit-circle coordinates and signs
Read sine and cosine as coordinates, retaining angle direction and quadrant information.
3 examples · 10 exercises · 40 minutesIdentity choice and domain preservation
Transform expressions with a purpose, explain excluded angles and test tempting false rules.
3 examples · 10 exercises · 40 minutesAmplitude, period and phase in models
Read parameters as observable changes and reconstruct models without hiding ambiguity.
3 examples · 10 exercises · 40 minutesComplete trigonometric solution sets
Solve a transformed angle, recover every branch and intersect the original interval.
3 examples · 10 exercises · 40 minutesVectors
Eight-question checkVectors as displacements
Translate, add and scale arrows; distinguish a journey from its net displacement.
3 examples · 10 exercises · 40 minutesCoordinates, bases and division
Convert arrows to coordinates, recover unknown endpoints and test when a basis actually determines coordinates.
3 examples · 10 exercises · 40 minutesDot products and constrained projection
Connect signed projection, angle and squared distance; distinguish a line projection from a nearest point on a segment.
3 examples · 10 exercises · 40 minutesVector proofs in triangles
Turn geometric hypotheses into vector equations; prove midpoint, centroid and orthocenter properties with their assumptions visible.
3 examples · 10 exercises · 40 minutesConics
Eight-question checkEllipse: definition, axes and constraints
Build an ellipse from a distance sum, identify its major direction and distinguish a genuine ellipse from boundary loci.
3 examples · 10 exercises · 40 minutesHyperbola: branches and asymptotes
Keep signed and absolute focal differences separate; inspect degree loss when a line is parallel to an asymptote.
3 examples · 10 exercises · 40 minutesParabola: focus and directrix
Derive a parabola from equal distances, track orientation under translation and use the definition in a distance optimization.
3 examples · 10 exercises · 40 minutesConic intersections, chords and inverse problems
Solve line–conic systems with degree and domain checks; use Vieta for midpoint loci and reconstruct a chord from its midpoint.
3 examples · 10 exercises · 40 minutesCalculus
Eight-question checkRates and tangent meaning
Derive tangent slope from shrinking secants, then connect slope, point and local approximation.
3 examples · 10 exercises · 40 minutesDerivative rules and domains
Choose power, product, quotient or chain rules from the expression structure, retaining domains.
3 examples · 10 exercises · 40 minutesMonotonicity and constrained extrema
Use derivative sign changes, endpoints and feasible domains to distinguish local extrema from global optima.
3 examples · 10 exercises · 40 minutesCurvature, inflections and derivative graphs
Verify a concavity change at a point on the curve, distinguishing inflections from stationary points.
3 examples · 10 exercises · 40 minutesProbability and statistics
Eight-question checkConditions, partitions and posterior probability
Identify the conditioning group, verify partitions, and update priors with observed evidence.
3 examples · 10 exercises · 40 minutesDistribution means, variances and dependence
Compute weighted moments and apply shifts/scales with correct units and dependence conditions.
3 examples · 10 exercises · 40 minutesChoosing binomial, hypergeometric and normal models
Choose a model from its assumptions and support before computing its probability or moments.
3 examples · 10 exercises · 40 minutesPaired data, fitted lines and responsible prediction
Calculate a least-squares line from paired centered data and interpret residuals and units.
3 examples · 10 exercises · 40 minutes