# High School Equivalency Exam Prep – Mathematics ### Course Overview

This course focuses on Mathematical reasoning, including precision and fluency in executing and applying core computations, as well as learning to apply quantitative and algebraic reasoning skills within a wide range of academic, real-life, and workplace contexts. Specific areas include the following:
• Basics of mathematics
• Fractions, decimals, percents, and probability
• Basics of Geometry, perimeter, area, surface area, and volume
• Pre-Algebra
• Integers, rational numbers, and properties of Algebra
• Algebra
• Expressions, order of operations, and sets
• Absolute value, square roots, squares, and irrationals
• Equations and their applications
• Graphing, inequalities, and systems of equations
• Polynomials and operations with polynomials
• Rational expressions
This course is taught by award-winning Acellus Master Teacher, Patrick Mara. This course was developed by the International Academy of Science. Learn More

### Scope and Sequence

Unit 1 – Introduction and Basic Foundation This unit covers addition, subtraction, multiplication, and division of whole numbers; divisibility rules; prime and composite numbers; greatest common factors; prime factorization, place value; estimating; order of operations; powers of ten; formulas; and variables. Unit 2 – Fractions This unit discusses ratios; rates; proportions; improper and mixed fractions; simplifying fractions; least common multiples; adding, subtracting, multiplying, and dividing fractions and mixed numbers. Unit 3 – Decimals and Percents This unit covers adding, subtracting, and multiplying decimals, as well as dividing decimals by whole numbers, comparing and ordering decimals, forms and types of percent, and simple interest. Unit 4 – Probability This unit covers basic probability, mean, median, mode, and range, frequency tables, pictographs, bar graphs, and broken line graphs. Unit 5 – Geometry Basics This unit discusses planes, points, and lines, geometry symbols, angles, the sum of the angles of a triangle, classifying triangles, congruent versus similar triangles, quadrilaterals, and other polygons. Unit 6 – Geometry – Perimeter and Area This unit discusses length in relation to perimeter; area of parallelograms; triangles and trapezoids; square roots and the Pythagorean Theorem; circle vocabulary; circumference: finding C, and finding r and d; area of a circle: finding A, and finding r and d; and area of irregular figures. Unit 7 – Geometry – Surface Area and Volume This unit explains cross sections as well as both surface area and volume of prisms, pyramids, cylinders, and composite figures. Unit 8 – Pre-Algebra This unit discusses comparing and ordering integers; absolute value; adding, subtracting, multiplying, and dividing integers; order of operations with integers; the zero, identity, cummutative, associative, and distributive properties; and basic graphing: ordered pairs and the coordinate plane. Unit 9 – Beginning Algebra This unit covers comparing, ordering, adding, subtracting, multiplying and dividing rational numbers; expressions versus equations; order of operations with and without variables; and decimals and fractions in rational numbers. Unit 10 – Foundations of Algebra This unit covers verbal and algebraic expressions; order of operations; basic properties of algebra; the distributive property; integers and sets of numbers; integer arithmetic; absolute value; adding and subtracting integers; comparing, ordering, adding, subtracting, multiplying, and dividing rational numbers; square roots; squares; and irrationals. Unit 11 – Equations and Their Applications This unit discusses one-step equations using addition, subtraction, multiplication, and division; properties of equality; two-step equations with manipulatives; complement and supplement problems; clearing fractions and decimals; number problems; perimeter and angle problems; multi-step equations; and literal equations. Unit 12 – More Applications with Equations This unit covers solving proportions, similar triangles, percents as a special kind of ratio, simple interest, and percent of increase or decrease. Unit 13 – Foundations of Graphing This unit explains ordered pairs and relations, graphing linear equations, definitions of a function and of slope, calculating slope, rate of change, and point-slope formula. Unit 14 – Inequalities and Systems of Equations This unit discusses solving inequalities using addition, subtraction, multiplication, and division; multi-step inequalities; and solving systems of equations by substitution, addition, and multiplication. Unit 15 – Polynomials This unit covers polynomial terminology; polynomials with algebra tiles; adding, subtracting, multiplying, and dividing polynomials with algebra tiles; and multiplying polynomials by monomials. Unit 16 – More Operations with Polynomials This unit discusses multiplying polynomials, multiplyig binomials using FOIL, special binomial products, factoring polynomials, binomial factors, factoring using FOIL, and using the zero product property to solve equations. Unit 17 – Rational Expressions This unit discusses simplifying rational expressions, dividing a polynoal by a binomial, and rules of exponents.