Umiejętności z podstawy programowej

Mathematics: analysis and approaches

Number and algebra16

• Scientific notation3 zad.
• Arithmetic patterns and totals39 zad.
• Geometric patterns and totals38 zad.
• Interest and depreciation models8 zad.
• Integer powers and introductory logarithms3 zad.
• Direct algebraic arguments31 zad.
• Rational powers and logarithm rules42 zad.
• Convergent geometric totals12 zad.
• Finite binomial expansions15 zad.
• Counting and generalized binomial expansions41 zad.
• Decomposing rational expressions12 zad.
• Complex coordinates and conjugates46 zad.
• Polar and exponential complex forms29 zad.
• Complex roots and powers37 zad.
• Induction, contradiction and counterexamples22 zad.
• Linear systems and solution sets12 zad.

Functions16

• Straight-line relationships5 zad.
• Functions, domains and ranges17 zad.
• Representing functions graphically27 zad.
• Reading graph features and intersections9 zad.
• Composition and inverse functions37 zad.
• Quadratic forms and geometry6 zad.
• Quadratic solutions and discriminants53 zad.
• Linear-over-linear rational functions16 zad.
• Exponential and logarithmic functions17 zad.
• Analytic and numerical equation solving18 zad.
• Basic graph transformations16 zad.
• Polynomial factors and root relations60 zad.
• Higher rational graphs and asymptotes26 zad.
• Parity and restricted inverses10 zad.
• Comparing functions through inequalities11 zad.
• Modulus and composite graph changes14 zad.

Geometry and trigonometry18

• Spatial measures and right-triangle geometry36 zad.
• Triangle relationships and area32 zad.
• Trigonometric modelling of positions5 zad.
• Radians, arcs and sectors36 zad.
• Unit-circle values and ambiguous triangles7 zad.
• Basic trigonometric identities21 zad.
• Periodic graphs and models27 zad.
• Trigonometric equations on intervals16 zad.
• Reciprocal and inverse trigonometric functions20 zad.
• Compound-angle relationships15 zad.
• Trigonometric symmetry arguments0 zadań
• Vector arithmetic and geometric proof16 zad.
• Dot products and vector angles32 zad.
• Vector lines and motion20 zad.
• Relationships between spatial lines9 zad.
• Cross products and geometric areas26 zad.
• Representing planes20 zad.
• Plane intersections and angles28 zad.

Statistics and probability14

• Sampling, data quality and outliers3 zad.
• Frequency and cumulative displays7 zad.
• Location, spread and transformed data19 zad.
• Correlation and predicting y from x20 zad.
• Events and expected counts12 zad.
• Combined-event diagrams and probabilities37 zad.
• Discrete probability models and means28 zad.
• Binomial models23 zad.
• Normal probabilities with known parameters25 zad.
• Predicting x from y7 zad.
• Conditional probability and independence tests25 zad.
• Standardization and unknown normal parameters15 zad.
• Bayesian updating5 zad.
• Random-variable moments and densities50 zad.

Calculus19

• Limits and the meaning of a derivative9 zad.
• Derivative signs and monotonicity3 zad.
• Differentiating integer powers7 zad.
• Tangent and normal equations25 zad.
• Antiderivatives and introductory area2 zad.
• Elementary derivatives and differentiation rules48 zad.
• Second derivatives and linked graphs23 zad.
• Extrema, inflections and optimization69 zad.
• Calculus of motion45 zad.
• Elementary integration techniques19 zad.
• Definite integrals and regions35 zad.
• First-principles and higher derivatives1 zad.
• Indeterminate limits16 zad.
• Implicit derivatives and related rates32 zad.
• Further elementary derivatives and integrals20 zad.
• Substitution and integration by parts19 zad.
• Revolution volumes and areas against y17 zad.
• First-order differential equations56 zad.
• Maclaurin expansions and series operations34 zad.