Memorize Me’s, Backgrounders, & How2’s

Here are all the existing Acumen Tutoring MemorizeMe™, Backgrounder™, and How2™ documents as downloadable PDFs.

These are free for anyone to use: teachers, individuals, whomever; in particular, you don't need to be an Acumen Tutoring student, so help yourself.

All I require is:

• Don't remove the Acumen Tutoring logo, web address or copyright notice.
• Don't directly email or otherwise distribute these to other teachers or tutors.
  You can give them the link to this page and let them download whatever they want.

Note that eventually I'll be charging for these, so enjoy them while you can!

Bug reports: If you notice an error in one of the documents, please tell me about it at:

john@acumen-tutoring.com

Algebra

MemorizeMe’s

• Divisibility Rules - Quickly determine if a number is divisible by 2, 3, 4, 5, 6, 8, or 9
• Graphing Quadratic Equations - Standard, Vertex, and Intercept forms
• Midpoint & Distance formulas - Midpoint and distance formulas, point-slope, slope-intercept, and standard forms
• Percentages - Percent change, profit margins, discounts.
• Special-Case Factoring - a² - b² and the like

Algebra2

A lot of these are useful for Precalc, as well.

Backgrounders

• Combinations, Permutations, and Probability
• Operations - Cayley tables, etc.
• Set Theory - Sets, subsets, intersections, unions
• Solving Equation Word Problems - Steps to solving word problems

MemorizeMe’s

• Advanced Factoring - Rational zero test, Descarte’s Rule of Signs, upper and lower bounds rules
• Complex Numbers - A summery of how to peform arithmetic on numbers that include i.
• Conic Sections (1) - Alg2 version: Circles, ellipses, parabolas, hyperbolas; version 1: a = semi-major axis
• Conic Sections (2) - Alg2 version: Circles, ellipses, parabolas, hyperbolas; version 2: a = Horizontal axis
• Exponents and Logarithms - Log and exponent properties; growth, decay, interest, half life
• Graphing Logs and Exponents - Parent functions and transformations
• Graphing Parent Functions and Transformations - Shift, reflect, stretch, and shrink
• Graphing Polynomials - Leading coefficients and degrees, multiplicity.
• Graphing Quadratic Functions - Vertex, Axis of Symmetry, etc.
• Graphing Rational Expressions - Horizontal, vertical, and slant asymptotes for rational expressions
• Midpoint & Distance formulas - Midpoint and distance formulas, point-slope, slope-intercept, and standard forms
• Sequences - Arithmetic and geometric sequences

Calculus

• Area Under a Curve - The limit calculation of the area under a curve and the formal definition of an integral
• Common Derivatives - Derivatives for common trig, exponential, and log functions
• Common Integrals - Trig, exponential, and log functions; Integration by parts
• Definitions & Theorems - Definitions of continuous, differentiable; IVT, MVT, EVT, and Rolle's
• ε-δ Proofs of Limits, 1 - for linear functions
• ε-δ Proofs of Limits, 2 - for quadratic functions
• Limits - Strategy for determining limits
• Limits and derivatives - Definition of derivative; L’Hôpital’s Rule

AP Calc BC

• Euler's Method - Approximating solutions to differential equations
• Homogeneous Differential Equations - Recognizing and solving homogeneous differential equations
• Linear Differential Equations - Solving First-Order Linear Differential Equations
• Newton's Method - Approximating solutions to functions
• p- and Power Series - P-series and power series; what are they and are they friendly?
• Parametric Equations - Derivatives, arc length, areas of revolution
• Polar Coordinates - The Calculus version: includes derivatives, etc.
• Polar Coordinates: Areas and Arc Lengths - Area under a curve, arc length, surfaces of revolution
• Series: Testing for Convergence - Integral test, root test, nth-term test, etc.
• Series: Choosing a Test for Convergence - How to decide among the many tests for convergence.
• Taylor and Maclaurin Series - How to construct Taylor and Maclaurin polynomials
• Trigonometric Integrals - Integrating powers of trig functions
• Trigonometric Substitution - Replacing square roots with trig functions
• Volumes & Surfaces - Volumes of revolution, Surfaces of revolution, arc length

Multi-variable Calculus

• Directional derivatives and gradients
• Multivariable Extrema - Critical points, relative extrema, Lagrange variables
• Lines and Planes - Equations, distances, etc.
• Surfaces in Space - Ellipsoids, Hyperbolic paraboloids, etc.
• Tangents and Normals - Tangent and Normal vector functions
• Tangent Planes - Tangent planes and normal lines

Chemistry

How2’s

MemorizeMe’s

• Acids & Bases - pH, pOH, [H], [OH], conjugate acids/bases
• Accuracy and Precision - Accuracy, precision, and measurement
• Electrochemical Cells - i.e., Batteries
• Gas Laws - Ideal gas, Combined gas laws, Rate of effusion, etc.
• Kinetics - Reaction rates, rate laws, etc.
• Lewis Diagrams - How to create Lewis diagrams (includes formal charges)
• Metric Units - Metric prefixes & the most commonly-used unit conversions
• Naming Compounds - Naming rules for ionic & molecular compounds
• Organic Chemistry - Naming rules for organic compounds
• Redox - Oxidation states, Balancing redox reactions, Electrochemistry
• Significant Figures - Rules for figuring out significant figures
• Solutions and Concentration - Molarity, molality, % concentration, changes to melting and boiling points
• Thermochemistry - Specific heat, heats of fusion and vaporization
• VSEPR - Determining molecular shapes

AP Computer Science

MemorizeMe’s

• Acumen Utilities Documentation - Describes the CInputGetter and CRandom classes.
• Conditional execution and Loops - Loops and if..else operations
• Strings - Java class methods for parsing, changing, and otherwise working with String objects.

Geometry

MemorizeMe’s

• Algebraic Postulates - Transitivity, Symmetry, etc.
• Areas of Plane Figures - Areas of rectangles, triangles, parallelograms, etc.
• Circles, Chords, and Tangents - All the circle-related theorems
• Logic - Induction, deduction, conditional statements
• Parallel Lines Theorems - Corresponding angles, alternate interior angles, etc.
• Polygons - Parallelograms and their friends
• Theorems and Postulates - A list of the names of commonly-used theorems and postulates
• Transformations - Translation, rotation, reflection, dilation
• Triangle Centers - Centroid, circumcenter, incenter, orthocenter
• Triangle Theorems - SAS, ASA, CPCTC, etc.
• Trigonometry - Sines, cosines, tangents, Pythagoras
• Volumes & Surface Areas - Three-dimensional solids, such as cones and prisms

Physics

MemorizeMe’s

Note that several of these have more-advanced versions in the "AP Physics" section.

• Circuits - Ohm's law, series & parallel, etc.
• Circular Motion - Angular velocity, radians, centripetal force
• Electrostatics - Force between charges, electric fields.
• Gravity - Gravitational force and acceleration, orbital velocities
• Mechanical Energy - Potential and kinetic energy, work, power
• Metric Units - Metric prefixes & the most commonly-used unit conversions
• Motion - Accelerated motion: position, velocity, acceleration, and time; this is the version for regular physics.
• Momentum and Impulse - Collisions and projectiles.
• Resonance - Harmonics, open and closed cylinders, etc.
• Waves - Frequency, wavelength, period

AP Physics

MemorizeMe’s

• Electrostatics Basics Electric fields, electric flux, etc.
• Gravity - Gravitational force and acceleration, orbital velocities; this is the version for AP physics.
• Kinematics - Accelerated motion: position, velocity, acceleration, and time; this is the version for AP physics.
• Rotational Dynamics - Angular momentum, moment of inertia, etc.
• Simple Harmonic Motion - Springs and pendulums (pendula?)

Precalculus

How2’s

• Graphing Sine & Cosine Functions - How to graph sin & cos, step-by-step

MemorizeMe’s

• Area Under a Curve - Area under a curve, summation values and properties
• Conic Sections (1) - Precalc version: Circles, ellipses, parabolas, hyperbolas; version 1: a = semi-major axis
• Conic Sections (2) - Precalc version: Circles, ellipses, parabolas, hyperbolas; version 2: a = Horizontal axis
• Exponents and Logarithms - Log and exponent properties; growth, decay, interest, half life
• Graphing Parent Functions and Transformations - Shift, reflect, stretch, and shrink
• Graphing Rational Expressions - Horizontal, vertical, and slant asymptotes for rational expressions
• Graphing Trigonometric Functions - Parent functions and their transformations
• Laws of Sines, Cosines, etc. - Law of Sines, Law of Cosines, trigonometric form of complex numbers
• Polar Coordinates - Polar-Rectangular conversion; Common curves, etc.
• Reduced Row-Echelon Solutions - Solving systems of equations using the reduced row-echelon technique
• Trigonometric Identities - Co-function formulas, product-to-sum, etc.
• Trigonometric Identities - Tactics - How to approach simplifying trig identities.
• Vectors - Dot and cross products, projections, etc.

Statistics

MemorizeMe’s

• Binomial Distributions - Probabilities, mean, etc.
• Chi-squared - Goodness-of-fit, independence, homogeneity
• Comparing two populations - CI, significance testing, etc.
• Confidence Intervals - CI, standard error, etc.
• Basics: Describing Data and Normal Distributions - Quartiles, Normal distribution, Standard deviation, Z-scores.
• Geometric Distributions - Probabilities, mean, etc.
• Hypotheses testing - Null and alternate hypotheses, levels of significance, etc.
• Organizing a Problem - 4-Step procedure.
• Power calculation - Calculating power for a test
• Probability - So, what are the odds?
• Regression - Linear regression, coefficient of correlation, etc.
• Sampling Distributions - Probabilities associated with normally-distributed data.
• Sampling Terminology - Sampling types and attributes, bias, etc.

Copyright © 2015-2016 John Deubert