Walter’s current tutoring subjects are listed at the left. You
can read more about
Walter’s qualifications in specific subjects below.
Algebra 1 is dealing with the use of integers, and rational and irrational numbers. Also, it deals with taking the opposite, finding the reciprocal, taking a root, and the rules of exponents & fractional powers, absolute values. linear equations and inequalities with a single variable, word problems, graph a linear equation and compute the x- and y-intercepts, sketch the region defined by linear inequality, verify that points lies on a line when given an equation of the line, linear equations in the point-slope formula, parallel lines and perpendicular lines, systems of two linear equations with two variables algebraically, systems of two linear inequalities in two variables.
Algebra 1 further deals with adding, subtracting, multiplying, and dividing polynomials, factoring second- and simple third-degree polynomials including finding a common factor for all terms in a polynomial, the difference of two squares, and perfect squares of binomials, adding, subtracting, multiplying, and dividing rational expressions and functions, solving a quadratic equation by factoring or completing the square, solve rate problems, work problems, and percent mixture problems, understanding what a relation is and what a function is, determine whether a given relation defines a function, and determine the domain and the range of independent and dependent variables.
Algebra 1 finishes up dealing with the quadratic formula by completing the square, using the quadratic formula to find the roots of a second-degree polynomial, to solve quadratic equations to graph quadratic functions, determining whether the graph of a quadratic function will intersect the x-axis in 0, 1, or 2 points, and apply quadratic equations to physical problems like the motion of an object under the force of gravity.
Algebra 2 continues to use and expand all the rules, axioms and laws from Algebra 1 and Geometry. It investigates absolute value equations and inequalities, systems of linear equations and inequalities, polynomials operations including long division, factoring of polynomials, and how to add, subtract, multiply, and divide real and complex numbers. Also, Algebra 2 investigates how to add, subtract, multiply, divide, reduce, and evaluate rational expressions with monomial and polynomial denominators and simplify complicated rational expressions, and solve and graph quadratic equations by factoring, completing the square, or using the quadratic formula.
Algebra 2 explores quadratic functions and determine the maximum, minimum, and zeros of the function, simple laws of logarithms, understand that exponents and logarithms are inverses and to solve problems involving logarithms and exponents, know the laws of fractional exponents, understand exponential functions, and use these functions in problems involving exponential growth and decay, use the definition of logarithms to translate between logarithms in any base. Algebra 2 also shows how to understand and use the properties of logarithms to simplify logarithmic numeric expressions, how to determine whether a specific algebraic statement involving rational expressions, radical expressions, or logarithmic or exponential functions is sometimes true, always true, or never true, and delves into the geometry of the graph of a conic.
Algebra 2 finishes up with quadratic equations and graphs of circles, ellipses, parabolas, and hyperbolas, how to the compute combinations and permutations and how to use them to compute probabilities, knowing and applying the binomial theorem, and knowing the general term and the sums of the arithmetic series and of both the finite and the infinite geometric series.
Elementary Math explores large numbers (such as 345, 8006, and 11,947), and the adding, subtracting, multiplication, and dividing of whole numbers, fractions, decimals, and integers. It delves into the properties of and the relationships between geometric figures (such as square, trapezoids, triangles, etc). Elementary Math also goes into determining the length and the area to determine the volume of simple geometric figures. It further shows how to use grids, tables, graphs, and charts to record and analyze data.
Elementary continues on with the usage of the mean, median, and mode of data sets and how to calculate the range of that data set. It uses the addition and multiplication of fractions to calculate the probabilities for compound events and works with ratios and proportions and it shows how to compute percentages like for sales tax or simple interest. Elementary Math explores pi (3.14 or 22/7) and its relationship to the formulas for the circumference and area of a circle. It shows what is to come in Algebra by introducing the variable in formulas involving geometric shapes and ratios and solving one-step linear equations.
Elementary Math delves into the factoring of the numerator and the denominator of fractions and into the properties of exponents. It works on the Pythagorean Theorem and uses said theorem to compute the length of an unknown side. It delves into the calculation of the surface area and volume of basic 3-D objects and shows how to understand how area and volume change with a change in scale. Elementary Math explores how to convert between different measurement units and between fractions, decimals, and percents. It looks into the links between ratios and proportions, computes percents of increase and decrease, and computes simple and compound interest. And finally, Elementary Math probes the graphing of linear functions and the purpose of slope and its relationship to ratios.
Geometry explores congruence and similarity and how triangles are congruent or similar, and how to use the concept of corresponding parts of congruent triangles. It also deals with solving proofs including proofs by contradiction.
Geometry looks into the properties of parallel lines, the properties of quadrilaterals, and the properties of circles with emphasis on how to deal with problems involving the perimeter, circumference, area, volume, lateral area, and surface area of most of the basic shape one would deals with in one’s life. Also, it gets into how to find the measures of sides, interior angles and exterior angles of triangles and the relationships between angles in polygons by use of complementary, supplementary, vertical, and exterior angles, and explores the Pythagorean theorem and uses it to determine distance and to find missing lengths of sides of right triangles.
Geometry concludes its exploration with how to draw, by hand, angle bisectors, perpendicular bisectors, and the line parallel to a given line through a point off the line. Then, it goes on to use the definitions of the basic trigonometric functions defined by the angles of a right triangle to solve for an unknown length of a side of a right triangle which given an angle and a length of a side. Finally, Geometry it delves into problems on the subject of relationships between chords, secants, tangents, inscribed angles, and inscribed and circumscribed polygons of circles.
Pre-Algebra is to prepare the student for the study of algebra. This includes the review of natural numbers, new types of numbers like integers, fractions, decimals and negative numbers, the factorization of natural numbers, understanding and use of the Associative Property and Distributive Property, Simple (integer) roots and powers.
Pre-Algebra also includes the basics of equations and what to do with them, and movement over the standard 4-quadrant Cartesian coordinate plane. Pre-algebra sometimes include subjects from geometry, especially subjects that further understanding of algebra in applications to area and volume. Equations will be seen and used throughout one’s math career.
Learning and understanding the basics of Pre-Algebra is an integral part of "getting off on the right foot" when dealing with math so that one will better understand, work with, and solve equations when they have addition and/or subtraction in them.
Pre-Calculus deals with the basic fundamentals of Calculus just like Pre-Algebra explores the basic fundamentals of Algebra. It delves into the concepts of sets (what they are and how they work), real numbers and complex numbers (such as pi, 105, and 2i -7). It expands upon solving inequalities and equations, the properties of functions, and goes over composite, polynomial, and rational functions.
Pre-Calculus further explores fundamentals of Trigonometry such as its functions and their inverses, and the various trigonometric identities. It investigates conic sections, polar coordinates (graphing on a sphere) and the purpose and use of exponential and logarithmic functions. It goes into the use and calculation of sequences and series, the binomial theorem (expanding a binomial expression that is to an exponent greater than 3), the necessity of vectors, parametric equations (such as x = t, y = f(t)), matrices and determinants.
Lastly, Pre-Calculus starts students on the path of limits that will be dealt with further in Calculus.
Trigonometry looks into the concepts of angles and how to measure them both in degrees and radians and how to convert between them, how to use the sine and cosine as y- and x-coordinates of points on the unit circle, develop familiarity with the graphs of the sine and cosine functions, investigates the identity of cos2 (x) + sin2 (x) = 1, and show that this identity is equivalent to the Pythagorean theorem, and uses it to prove other trigonometric identities.
Trigonometry explores the graph of the functions of f(t) = A sin (Bt + C) and f(t) = A cos (Bt + C) and interpret A, B, and C in terms of amplitude, frequency, period, and phase shift, defines the tangent, cotangent, secant and cosecant functions and can graph them, discovers the tangent of the angle that a line makes with the x-axis is equal to the slope of the line, defines and graphs the inverse trig functions, and calculate, by hand, the values of trig functions and their inverses at various standard points.
Trigonometry also explores the addition formulas and proofs for Sines and Cosines, the half-angle and double-angle formulas for Sines and Cosines and they can be used to prove and/or simplify other trig identities, how to determine unknown sides or angles in right triangles, dives into the Law of Sines and the Law of Cosines and apply those laws to solve problems, and researches the area of a triangle when given only one angle and the two adjacent sides.
Trigonometry concludes with investigating polar coordinates and how they can determine them on a point given in rectangular coordinates and vice versa, examining the idea of complex numbers, looking into DeMoivre’s theorem and how one can use said theorem to derive nth roots of a complex number given in polar form, and shows how to use trigonometry in a variety of applications and word problems.