Algebra 1-2

ThinkTank Learning builds its classes to mimic the local high school curriculum. For this reason, there may be some variations from one center to the next, but the general list of topics in our Algebra 1-2 class (also called Algebra 1 in some districts) includes: writing and evaluating expressions; correctly applying the order of operations; representing functions as rules, tables, and graphs; identifying and manipulating real numbers; solving equations of one variable; identifying and understanding the various ways to represent a linear equation; plotting data and creating best-fit lines to interpolate and extrapolate; correctly manipulating and solving inequalities; introducing exponents – including negative, zero, and fractional exponents; identifying, classifying, adding, subtracting, multiplying and factoring polynomials; graphing quadratic functions – including identifying the axis of symmetry, vertex, and zeroes; simplifying and graphing radical functions; simplifying and graphing rational functions; and basic probability – including mutual exclusivity, dependence and independence, and compound events.

Algebra 3-4

ThinkTank Learning builds its classes to mimic the local high school curriculum. For this reason, there may be some variations from one center to the next, but the general list of topics in our Algebra 3-4 class (also called Algebra 2 in some districts) includes: interpreting terms, factors, and coefficients in a polynomial or an expression; apply basic factoring techniques to second- and third-degree polynomials; mastering the standard and vertex forms of quadratic expressions; utilizing the properties of exponents to manipulate exponential functions; demonstrating basic laws of logarithms; determine the sum of basic arithmetic and geometric series; manipulating polynomials, rational expressions, and complex numbers; mastering the Binomial Theorem of expansion, exploring Pascal’s Triangle, and introducing combinations and permutations.

Of all the classes in the standard California math progression, this one most widely varied from one school to the next. Some schools combine it with geometry, others combine it with trigonometry, while still others combine it with math analysis. The topics listed here are the ones specified in the California state math standards. These standards are the foundation for our class, and we build from there to blend with the local curriculum.

Calculus

ThinkTank Learning builds its classes to mimic the local high school curriculum. For this reason, there may be some variations from one center to the next, but the general list of topics in our Trigonometry class includes: measuring angles in degrees and radians, and converting one form into the other; relate sine and cosine to the unit circle and understand the periodic functions; explore and prove trigonometric identities; understanding and interpreting the general form of a sinusoidal function; understanding and caculating values for the inverse trigonometric functions; using the addition formulas for sines and cosines to simplify expressions; applying the half-angle and double-angle formulas to simplify expressions; mastering the law of sines and law of cosines to determine the length of the unknown leg of a triangle; converting Cartesian coordinates into Polar coordinates and back; understanding complex numbers and how to represent them in polar form; and applying DeMoivre’s Theorem to find all “n” roots of an “n-th” degree polynomial.

Chemistry

ThinkTank Learning builds its classes to mimic the local high school curriculum. For this reason, there may be some variations from one center to the next, but the general list of topics in our Chemistry class includes: grasping the organization of the periodic table, including trends in atomic number, atomic mass, atomic size, and ionization states; understanding the development of the modern atomic theory, including models proposed and advances made by Dalton, Rutherford, Millikan, Bohr, Heisenberg, and Shroedinger; identifying compounds as covalent or ionic and naming them using modern conventions; drawing Lewis dot structures for individual atoms as well as compounds and understanding how to develop these structures into drawings of molecules; describing chemical reactions by writing and balancing chemical equations; understanding the origin of the mole and its use in calculations; calculating percent yield and identifying limiting reagent in a reaction; studying the basic gas laws and developing the ideal gas law from them; correctly applying the concepts of standard temperature and pressure (STP) in calculations involving gas systems – including working in the Kelvin scale of temperature; studying the properties of acids and bases – including the origins and meaning of the pH scale; understanding the properties of solutions and how their behavior changes with temperature, pressure, surface area, and other factors; exploring basic thermodynamics – including exothermic vs endothermic reactions, heat of fusion, heat of vaporization, and heat of solution; studying basic reaction kinetics – including rate of reaction and impact of temperature, concentration, pressure, and catalysts; expanding reaction kinetics to include reverse-reactions and the origins of equilibrium; introducing basic organic chemistry and the naming trends of simple carbon chains; and introducing fundamental nuclear processes and the attributes and differences between the most common types of radiation.

Geometry

ThinkTank Learning builds its classes to mimic the local high school curriculum. For this reason, there may be some variations from one center to the next, but the general list of topics in our Geometry class includes: using postulates to identify congruent segments, angles and figures; naming, measuring, and classifying angles; identifying the midpoint of a segment and measuring a segment; developing simple logical arguments based on deducting reasoning and the laws of logic; using angle relationships to prove lines are parallel; finding the distance between parallel lines without measuring; classifying and measuring triangles; using ratios, proportions, and geometric identities to apply scale measurement and recognize similar figures; mastering the Pythagorean theorem and exploring special triangles; exploring the properties of quadrilaterals; investigating the properties of circles – including tangents, secants, chords, arcs and subtended angles; applying formulas to measure areas in common shapes; and identifying and measuring 3-dimensional figures and spaces.

Pre-Calculus

ThinkTank Learning builds its classes to mimic the local high school curriculum. For this reason, there may be some variations from one center to the next, but the general list of topics in our Pre-Calculus class includes: complex numbers in polar form (often introduced in Trigonometry); identifying the roots of a quadratic and understanding how roots differ from zeroes; recognizing polynomial, rational, exponential, or logarithmic functions from an equation, a table, or a graph of the function; exploring the composite of functions and how f(g(x)) is not the same as g(f(x)); examining a function to identify the maxima and minima, its asymptotes, and limits; and the applications of exponential growth, especially in populations and economics.

Trigonometry

ThinkTank Learning builds its classes to mimic the local high school curriculum. For this reason, there may be some variations from one center to the next, but the general list of topics in our Trigonometry class includes: measuring angles in degrees and radians, and converting one form into the other; relate sine and cosine to the unit circle and understand the periodic functions; explore and prove trigonometric identities; understanding and interpreting the general form of a sinusoidal function; understanding and caculating values for the inverse trigonometric functions; using the addition formulas for sines and cosines to simplify expressions; applying the half-angle and double-angle formulas to simplify expressions; mastering the law of sines and law of cosines to determine the length of the unknown leg of a triangle; converting Cartesian coordinates into Polar coordinates and back; understanding complex numbers and how to represent them in polar form; and applying DeMoivre’s Theorem to find all “n” roots of an “n-th” degree polynomial.

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