David M. Lee
IL Certified K-12 Math Tutor

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These topics are comprehensively explained for easy understanding in my guide

PRE-ALGEBRA  ----14 questions
--place value
--types of numbers such as integers, rational, irrational, whole and imaginary.
--clock problems
--basic operations of numbers (addition, subtraction, multiplication and division)
--order of operations
--number theory, divisibility rules, factors and multiples
--prime and composite numbers
--prime factorization
--lowest common multiples (LCM) and greatest common factor (GCF)
--fractions and reducing fractions to lowest terms
--adding, subtracting, multiplying and dividing fractions
--complex fractions
--improper fractions and mixed numbers
--evaluating expressions or solving for x using fractions
--decimals, converting fractions to decimals and operations with decimals
--ratio, proportion and percent
--application of percents
--percent increase and percent decrease
--basic statistics---organization of data, averages, range, median and mode
--average formula (needs use of Algebra)
--permutations, combinations and the fundamental counting principle
--simple probability
--data collection
--Number problems and multi-step problem solving
--Negative and positive numbers
--working with inequalities
--absolute value
--scientific notation
--rational vs. irrational numbers
--geometric and arithmetic sequences


--constants and variables
--similar terms and simplification
--equations including linear equations with one variable
--average formula
--evaluating algebraic expressions by substituting in values for variables and solving
--polynomials and roots of polynomials
--operations with polynomials
--difference of squares
--sum and differences of cubes
--factoring trinomials in the form of Ax2 + Bx + C = 0
--quadratic equations and finding solutions by factoring
--quadratic formula
--quadratic inequalities
--completing the square
--word problems using algebra
--rules of exponents and radicals
--square and cube roots and approximations
--simplifying radicals
--operations with radicals
--systems of equations
--solving systems of linear equations by substitution
--using variables to express functional relationships
--matrix multiplication
--real v. Imaginary numbers
--complex numbers


--graphing and plotting points
--relationship between equations and graphs
--graphing inequalities
--applying the quadratic formula
--distance formula using coordinates
--mid point formula using coordinates
--linear equations
--equation of lines
--slope-intercept form Y = mX + b
--finding slope given only two points
--slopes of parallel and perpendicular lines
--conic sections and all the formulas
--functions (exponential, logarithmic and inverse)
--systems of equations or linear algebra
--graphing inequalities
--sequence and series
--progressions and patterns
--binomial theorem        
--algebraic problems involving inequalities and absolute value

GEOMETRY 14 questions

--parallel and perpendicular lines
--theorems involving transversals and parallel lines
--angles and types of angles
--types of triangles
--triangle inequality theorem and other formulas involving triangles
--quadrilaterals, esp. trapezoids. Every ACT has a trapezoid question
--30-60-90 right triangles
--45-45-90 right triangles
--Pythagorean triples
--perimeter and area
--circles---must know formula for area of circle
--triangles within circles
--difference of areas of inscribed and circumscribed squares about circles.
--similarity and congruence
--sum of exterior angles of regular polygon theorem
--number of diagonals in polygon theorem
--3 dimensional figures.

TRIGONOMETRY only 4 questions
--Converting degrees to radians
--Values of special angles
--graphs of trigonometric functions and interpreting their behavior
--inverse trigonometric functions
--trigonometric identities
--applying trigonometric functions to right triangles

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Specializing in ACT Math Test Prep