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Caltech Y Rise Program

Rise Program students will often work on both math and science, but sometimes need more help in one area. Tutors select the subjects they are most comfortable tutoring. For possible topics associated with each subject check the table below.

Math

Math 1

Domain, Range, End Behavior, Linear Functions, Interior/Exterior Angles, Inequalities, graphing, Absolute Value, Geometric Sequences, Piecewise Functions, Slope, Triangles, Parallel/Perpendicular lines, Triangle Congruency Tests, Transversal, Angle Bisectors, Logarithms, Change of Base, Fractions, Radicals, Exponents, Binomial Expansion, Polynomials, Long Division, Factoring, Substitution/Elimination, System of Linear Equations, Arithmetic, Transformations, Simplifying Expressions, Box and Whisker, Histogram, Cross-multiply

Math 2

Adding/Multiplying Polynomials, Composite Shapes, Adding Areas, Factoring/FOIL, Quadratic Equation, Exponentials, Fractions, Negative Numbers, Exponents, Imaginary Numbers, Square Roots, Piecewise Functions, Integers, Inequality, Line Plotting, Absolute Value, Chi-Square Test, Domain/Range, Rational Equation, Solving Linear Equation, Functions, Vertexes, Parabolas, Graphing Functions, Order of Operations

Algebra 1

One-variable linear equations, One-variable linear inequalities , Units of measurement in modeling, Two-variable linear equations, Functions, Linear equations, Sequences, Systems of linear equations, Two-variable linear inequalities, Absolute value equations, functions, and inequalities, Expressions with rational exponents and radicals, Exponential functions, Polynomials, Polynomial factorization, Quadratic equations and functions, Rational and irrational numbers

Geometry

Circumference, Chords/Arc/Sector, Angles in Circles, Tangent line, Area of Quadrilaterals, Lateral and Surface Area of Solids, Vectors: Addition, Translation, Reflections, Symmetry, 2D/3D Postulates, If-then Statements, Converse/Inverse/Contrapositive, Proofs, Congruency/Similarity, Right Triangle Trig, Reference Angles, Cofunctions, Complementary Angles, Sin/Cos Graphs, Trig Functions, Similar Triangles, Ratios/Proportions, Altitudes, Geometric Means, Special Right Triangles, Angle Bisectors, Midpoints, Cross-Multiplication, Incenter/Orthocenter/Circumcenter/Centroid, Polygon Angle measures, Transversal Angles, Reflections/Translations

Algebra 2

Geometric/Arithmetic Series, Trig, Algebraic Expressions, Factoring, Exponent, Logarithms, Inverses, Exponential Growth/Decay, Pascal's Triangle, Long Division, Synthetic Division, Polynomials in Standard Form, Adding/Subtracting Rational Expressions, Solving Absolute Value Expressions, Square Roots/Radical, Functions, Rational Operations/Equations, Extraneous Roots, Domain/Range, Piecewise, Simplifying Radicals, Quadratic Formula, Parabola, Complex Numbers, Combinatorics
Finding roots of equations, Factorials, Combination/Permutation, Standard Deviation, Circles/Tangents, Rational Root Theorem, Completing the Square, x,y-intercepts, System of Equations, Fractions, Inequality, Completing the Square, Arithmetic/Geometric Means

Pre-Calculus

Trig Functions, Reference Angles, Unit Circle, Even/Odd Functions, Graphing Functions, Translations, Domain/Range, Angular vs. Linear Speed, Conterminal Functions, Factoring/Expanding, Intercepts, Finding Roots, Parent Functions, System of Equations/Inequalities, Linear Programming, Maxima/Minima, Matrices, Completing the Square, Linear Regression, Probability, Circular Permutations, Combinations/Permutation, Logarithmic Equation/Percent Change, Law of Cosines, Triangles, Linear/Quadratic/Exponential/Power Functions, Matrix Algebra, Summation, Sequences, Parabola, Complex Numbers, Radians, Arc lengths, Polar Equations, IVT, Rational Functions, End Behavior/one-to-one, Compound Interest, Piecewise Functions, Symmetry, Transforming Functions, Using a graphing calculator, Synthetic Division, Composite Functions, Sketching Polynomials, Quadratic Formula

Calculus

Integrals, Slope Fields, Differential Equations, Integrals, Riemann Series, Area between Functions, Optimization, L'Hospital Rule, Differentiation, Maxima/Minima, Continuity, One-sided limits, Chain Rule, Implicit Differentiation, Rolle's Theorem, Increasing/Decreasing Functions, Second Derivative Test

Statistics

Random Variables, Expected Value, Standard Deviation, Normal Distribution, Confidence Interval, Probability, Variance, Binomial Distribution, Geometric Distribution, Normal cdf, Hypothesis Testing, Pascal's Triangle, z-score, Linear Regression, Extrapolation/Leverage/Influential Points, Experimental methods, Chi-Squared, Residuals, p-values, Box and Whisker Plot, Correlation Coefficient, Bar Graph, Mean, Median , Histograms, Scatter Plot, Outliers, Correlation, Regression
Predictions

 

Science

Physical Science

Solar System, Sun and Stars, Force: Friction, Gravity, Velocity/Distance, Astronomy, Chemistry, Planets, Rates, Dimensional Analysis, Thermal Energy, Acceleration, Energy Transformation/Transfer, Work, Free Body Diagrams, Newton’s First Law, Newton’s Second Law, Kinetic Energy, Electric Fields, Waves, Frequency, Period, EM Waves, States of Matter, Black Hole, Penrose Diagram, Proteins/Carbohydrates, DNA, Naming Compounds, Phase Changes, Electron Orbitals and Quantum Mechanics, Electron Geometry

Biology

Mitosis, Meiosis I/II, Monohybrid/Dihybrid, Incomplete/Co-Dominance, Cell Cycle, Digestive System, Excretory System, Nervous System, Cardiac System, Evolution, Protein Synthesis, Cellular Basis of Inheritance, DNA replication, Transcription, Translation, Central Dogma of Biology, Fluid Mosaic Model, Eukaryotes/Prokaryotes, Organelles, Homeostasis, Cell to Organism, Cellular Respiration/Photosynthesis, Nutrition, Ecology, Organs, Immune System, Muscular System, Biochemistry, Cell Structure, Ecology/Population/Food Webs, Sickle Cell, Transfusion, Diffusion/osmosis/active transport, PCR, Gel Electrophoresis, Plasmids/Restriction Enzymes, Glycolysis, Pedigrees, Chromosome Maps, Evolution, Animal Development, Taxonomy/Cladistics, Building macromolecules, Endocrine System

Chemistry

Balancing Equations, Isotopes, Periodic Table, States of Matter, pH scale, Bohr Model, Combustion Reaction, Ideal Gas Law, Predicted Yields, Le Chateliers Principle, Reaction Rates, Equilibrium Constants, Strong/Weak Acids, Thermochemistry, Enthalpy Calculations (w/ phase changes), sig figs, Scientific, Notation, Radical equations, Units, Molar mass, Avogadro’s Number, Convert mole to gram to particles, Stoichiometry, Heat Diagrams, Lewis Dot Diagrams, Periodic Trends, Dimensional Analysis, Tire Pressure/Thread Depths, Molarity, Colorimetry, Calorimetry, Ionic/Covalent; Polar/Nonpolar Bonds, Radioactivity, Limiting Reagents, Chemical Reactions, Boiling/Melting Points, VSEPR, Organic Nomenclature, Polyatomic Ions, Nuclear Decay, Oxidation Numbers, Quantum, Naming Compounds, STP

Physics

Circular Motion, Dimensional Analysis, Rotational Motion, Torque, Force Diagrams, Gravity, Universal Gravitation, Sound, Vibration/Waves, Polarization, Spectroscopy, Lenses, Focal Length, Kinetic Energy, Thermal Expansion, Heat Capacity, Work, Energy Conversion, Thermodynamics, Doppler Effect, Vectors, Center of Gravity, Bouyancy, Density, Momentum/Impulse, Potential Energy, Force/Acceleration, Air Resistance, Newton's Laws, Mechanical Advantage, Percent uncertainty/Error, Projectile Motion, Electron Geomtry , Properties of solutions, Nuclear Reactions, Collisions, Keplers Laws, Power, Pulleys

Environmental Science

Renewable Resources/Alternative Energy, Coal/Fossil Fuel Sourcing and Clean up, Ozone Layers, Toxins, Climate and Water, Oceans, Atmosphere, Deforestation, Urbanization, Biodiversity, Mass Extinction, Electrochemistry, Thermodynamics, Equilibrium Constants, Ecology, Natural/Artificial Selection/Evolution, Nitrogen Cycle, Invasive Species

 

 

Contact Information

The Caltech Y
Rise Tutoring Program
Phone: (626) 395-6163
Email: ljackman@caltech.edu