# Scope and Sequence of Secondary Math

## Fundamentals of Math

### Whole Numbers

Comparing and ordering; Estimating; Operations; Exponents; Roots of perfect squares

### Decimals

Comparing and ordering; Rounding; Approximating square roots; Operations; Estimating square roots; Scientific notation

### Number Theory

Divisibility; Factors; Prime and composite numbers GCD and LCM; Converting to and adding in other number bases

### Fractions

Equivalent fractions; Mixed numbers; Comparing and ordering; Operations; Order of operations

### Rational numbers

Ratio and proportion; Solving proportions; Scale drawings; Decimals as rational numbers; Finding a percent (part) of a number; Finding the percent; Finding the whole amount

### Using percents

Enlargement and reduction; Sales tax; Discounts; Sale price; Simple interest; Commission; Percent change

### Measurements

Customary units of length; Capacity, and weight; SI (metric) units of length, capacity, and mass; Renaming metric units; Time zones; Temperature conversions; Precision

### Geometry

Measuring angles; Pairs of angles; Perpendicular and parallel lines; Transversal of parallel lines; Polygons; Circle; Perimeter and circumference; Pythagorean theorem; Congruent and similar figures

### Area and Volume

Area of quadrilaterals, triangles, and circles; Areas of similar figures; Surface area of prisms, cylinders, and pyramids; Volume of prisms and cylinders

### Probability and statistics

Fundamental principle of counting; Permutations; Probability; Mean, median, mode; Circle, bar, and line graphs; Histograms; Box–and–whisker plots; Stem–and–leaf diagrams

### Integers

Ordering; Operations; Applying order of operations; Expansion to and properties of the real numbers

### Algebra

Evaluating expressions; Solving one–and two–step equations; Solving one–and two–step inequalities

### Relations and functions

Coordinate plane; Functions and function rules; Graphing linear functions; Slope; Translation of figures on a plane

### Logic and set theory

Statements and negations; Compound and conditional statements and negations; Truth tables; Sets and subsets; Union and intersection of sets; Finite and infinite sets

## Pre–Algebra

### Integers

Absolute value; Operation ; Exponents; Order of operation; Scientific notation

### Expressions

Real–number properties; Evaluating and simplifying expressions; Translating word phrases; Rounding and estimating results of operations

### Equations

Solving two–step equations; Removal of parentheses; Subsets of the real numbers; Irrational numbers; Solving linear inequalities; Applying equations and inequalities

### Number Theory

Prime factorization; GCD and LCM; Arithmetic and geometric sequences; Number bases other than 10, including hexadecimal; Operations in other bases

### Rational Numbers

Forms of ordering fractions and decimals; Decimal equivalents of fractions; Conversion of repeating decimals to fractions; Ratios and proportions; Subsets and properties of real numbers

### Operations on rational numbers

Operations; Evaluating and simplifying expressions; Solving equations involving rationals; Operations in scientific notataion

### Percents

Solving percent equations; Applying percents; Scales; Discount, markup, commissions, tips, and interest (including compound); Percent change

### Applications

Equations with variables on both side; Writing and solving equations and inequalities

### Relations and functions

Coordinate plane; Functions; Graphing linear functions and linear inequalities; Slope; Direct variation

### Statistics and probability

Population and sample; Mean, median, and mode; Scatterplot; Quartiles; Box–and–whisker; Stem–and–leaf; Histograms; Choosing the correct type of graph; Permutations; Combinations; Probability

### Radicals

Square roots; Radical equations; Equations with radicals; Equations of the form *ax ^{2}+b=c*; Pythagorean theorem; Operations with radicals; Cube roots

### Geometry

Pairs of angles; Polygons; Perimeter and circumference; Congruence and similarity; 30—60 and 45—45 right triangle ratios; Distance and midpoint formulas; Symmetry and transformation

### Areas and volume

Areas of quadrilaterals, triangles, and circles; Relation of lengths and areas of similar regions; Surface areas of prisms, cylinders, pyramids, cones, and spheres

### Polynomials

Definition of a polynomial; Operations with polynomials, including multiplying binomials and dividing a polynomial by a monomial

## Algebra 1

### Operations

Review of the real number system, number lines, absolute value, arithmetic operations of integers and rational numbers, exponents, and order of operations

### Variables and equations

Using variables, algebraic expressions, and formulas; Writing and solving linear equations

### Using algebra

Solving literal equations and proportions; Applying equations to applications involving similar figures, percentages, money, motion, and mixtures

### Solving inequalities

Linear inequalities, including conjunctions, disjunctions; Absolute-value equations and inequalities

### Relations and functions

Representing relationships between data, using graphs, equations, and tables; Direct and inverse variations; Graphing absolute value functions

### Linear functions

Graphs, slopes, and intercepts of linear equations; Determining the equation of a line; Parallel and perpendicular lines; Correlation and lines of fit; Graphing linear inequalities

### Systems of equations and inequalities

Solving systems graphically, by substitution, and by elimination; Applications of systems

### Exponents

Products, quotients, and powers of exponential expressions; Scientific notation; Graphing exponential functions; Exponential growth and decay

### Polynomials

Classification, evaluation, operations, special patterns

### Factoring

Common monomials, trinomials, special patterns

### Radicals

Simplification and operations with radicals; Pythagorean theorem; Distance and midpoint formulas; Solving radical equations and graphing radical functions; Applications

### Quadratic Equations

Solving by factoring, taking roots, completing the square, and the quadratic formula; Graphing parabolas and finding zeros; Applications

### Rational expressions and equations

Simplification and operations with rational expressions; Solving rational equations; Applications

## Geometry

### Foundations of Geometry

Sets; definitions; incidence postulates and theorems; segment and angle measure; circles; polygons; polyhedrons

### Reasoning and Proof

Inductive and deductive reasoning; truth tables; proofs using angles and segments; bisectors; constructions

### Parallel and Perpendicular Lines

Characteristics; proofs; constructions; and coordinate geometry

### Congruent Triangles

Angles in triangles; congruence postulates and theorems; flow-chart proofs; right triangles; midsegments

### Relationships in Triangles

Circumcenter; incenter; orthocenter; centroid; indirect proof; triangle inequalities; constructions

### Quadrilaterals

Classification; characteristics; proofs; analytic geometry related to trapezoids; kites; parallelograms; squares; rectangles; and rhombii

### Area

Postulates; polygons; Pythagorean Theorem; special triangles; regular polygons; and circles

### Circles

Chords; tangents; arc length; sectors; inscribed angles; secants; constructions; graphs

### Surface Area and Volume

Nets; prisms; cylinders; pyramids; spheres; non-Euclidean geometry; perspective

### Transformations and Symmetry

Reflections; translations; rotations; dilations; invariants; symmetry; applications

### Similarity

Triangles; right triangles; proportions; chords and tangents of circles; golden ratio

### Trigonometry

Basic ratios; solving right triangles; applications; vectors; areas; identities

## Algebra 2

### Operations

Real and complex numbers; Polynomial; Matrix; Function

### Linear equations

Solving equations and inequalities; Absolute value equations and inequalities; Distance on number lines; Word problems; Compound inequalities

### Linear relations

Graphs of linear functions; Slopes; Special functions; Linear inequalities; Distances and midpoints; Modeling with linear regressions

### Systems

Solved graphically and algebraically; Systems of inequalities; Systems of three variables; Problem solving; Linear programming

### Matrices

Organizing data; Operations; Determinants; Solving systems using Cramer's Rule and inverse matrices; Transformations

### Quadratic equations

Solving by factoring, taking roots, completing the square, and the quadratic formula; Using the discrimiant; Complex roots; Quadratic inequalities

### Polynomial functions

Roots, graphing, and modeling with quadratic and polynomial functions; Problem solving; Rational root, remainder, and factor theorems; Fundamental theorem of algebra

### Radicals, Exponents, and Logarithms

Rational exponents; Inverse functions; Simplifying expressions; Solving equations, graphing and modeling with radical, exponential, and logarithmic functions; Natural and common logarithms

### Rational Expressions

Simplifying; Solving equations; Graphing; Variations

### Trigonometry

Right triangle and coordinate plane trigonometry; Special triangles and the unit circle; Radians; Graphs of trigonometric functions; Inverse functions

### Trigonometric Identities

Law of Siens; Law of Cosines; Problem solving; Proving identities; Trigonometric equations

### Sequences and Series

Explicit and recursive formulas; Arithmetic and geometric sequences and series; Summation notataion

### Probability and Statistics

Counting principles; Theoretical and experimental probabilities; Independent, dependent, and mutually exclusive events; Binomial distribution, descriptive statistics, representing data; Normal distributions; Making inferences

### Analytic Geometry

Circles; Parabolas; Ellipses; Hyperbolas; Systems of quadratic relations

## Precalculus

### Analyzing functions

Relations; linear, quadratic, power, and piecewise functions; continuity, transformations, and operations of functions, parametric representations and modeling with functions

### Radical, polynomial, and rational functions

Describing zeros, asymptotes, and end behavior of radical, polynomial, and rational functions and solving related equations and inequalities

### Exponential and logarithmic functions

Graphing, applying properties, solving equations, and modeling

### Trigonometric functions

Angle and arc measures; trigonometric functions in a right triangle, for other angles, and of real numbers; graphs of trig functions; inverse trig functions

### Trigonometric identities and equations

Derive and verify identities; use identities to solve equations; derive and apply the law of sines and law of cosines

### Vectors, polar graphs, and complex numbers

Describe and perform operations on 2-D and 3-D vectors; graph polar coordinates and equations; represent and perform operations on complex numbers in polar form

### Systems and matrices

Using Gaussian elimination; determinants, and inverse matrices to solve systems of equations and inequalities; decomposing into partial fractions

### Analytic geometry

Analyzing parabolas, ellipses, circles, and hyperbolas; rotated conics; parametric and polar representations

### Sequences and series

Recursive and explicit formulas; arithmetic and geometric sequences; summations; the binomial theorem; mathematical induction

### Descriptive statistics

Counting principles and basic probability; graphic representations; measures of central tendency and variability; normal distributions

### Inferential statistics

Probability distributions; the central limit theorem; confidence intervals; hypothesis testing; research studies

### Limits, derivatives, and integrals

Limit theorems; tangents to the curve; derivative theorems including product, quotient, and chain rules; area under a curve and integration; the fundamental theorem of calculus

## Consumer Math

### Math skills

Fractions, decimals, integers; problem solving using proportions and percent; solving linear equations; negative exponents to prepare for finance formulas

### Measurement

Customary and SI (metric) units; conversion within and between systems using dimensional analysis; perimeter, circumference, area, volume, and capacity

### Income

Calculating hours worked from clock times, gross pay including overtime; payroll deductions, including FICA and federal withholding; buying and selling stocks and bonds, including brokerage fees

### Budgeting

A standardized budget; an annual budget; reducing annual budget to monthly or weekly; emergency adjustments; revising the annual budget

### Banking

Checking accounts and deposits; overdraft penalties and protection; service charges; reconciling a bank statement; simple interest; compounding interest; interest on savings using the minimum balance or daily interest methods; effective interest rate; savings programs with regular deposits

### Borrowing

Simple interest loans; add-on loans and annual percentage rate; discount loans; amortized loans; how credit cards work; how interest is calculated and payments are applied to credit accounts

### Transportation

Calculating the finance charge and monthly payment for a new car; depreciation; leasing costs including residual value, mileage penalty; car insurance; cost of gas, oil, and tires; scheduled maintenance and repair costs

### Food

Store specials and coupons; unit prices; calculating freezer payback periods; consumer price index; calorie counting; finding the calories expended in activities

### Clothing

Planning for seasonal buying; calculating discounts including multiple ones; online shopping; internet buying tips; savings from making clothing; retail marketing of clothing, returns, net profit and gross profit margin; markup rate and breakeven point for retailer

### Housing

Renting; buying a house, including down payments, closing costs, points, and monthly payments; owner’s equity; building a house, including converting dimensions to scale for a set of plans; finding the area of rectangular lots in acres; calculating the amount of shingles needed from a house plan, allowing for pitched roofs

### Maintaining a home

Real-estate tax based on millage rates; homeowner’s insurance; calculating utility charges for electricity, gas, water, and sewer; communications; calculating house repairs, maintenance, and home improvements

### Life and health insurance

Mortality tables; term, whole-life, and universal life insurance; health insurance, including payout of benefits; Social-Security retirement benefits

### Income taxes

General principles of calculating federal income taxes; 1040EZ, 1040A, and 1040, including extra schedules A and B and Form 2441 for childcare benefits

### Vacations

Costs of food and lodging; cost of transportation; getting around at the site; travel times across time zones; economizing admissions