# SYLLABUS

**We cover every topic of all grades in detail considering the variations in the syllabus of different states in the USA.**

NOTE: The syllabus can be modified according to the needs of the students or as per the school curriculum.

## SCIENCE

## MATHEMATICS

**Whole numbers & their Multiplication, Division.****Exponents and square roots.****Number theory.****Decimals Add Subtract, Multiply and Divide Decimal.****Fractions and mixed numbers and add, subtract multiply and divide fractions.****Integers, Operations with integers, Mixed Operations.****Rational Numbers.****Problem solving and estimation.****Ratios and rates.****Units of measurement.****Money, Consumer math.****Co-ordinate plane.****Expressions and properties, one-variable equations, one-variable inequalities, two-variable equations.****Two-dimensional figures.****Symmetry and transformations.****Three-dimensional figures.****Geometric measurement.****Data and graphs.****Statistics, probability.****Financial literacy.**

**NOTE: We cover every topics of all grades in details considering the variations in syllabus of different states in USA.****The syllabus can be modified according to the needs of the students or as per school curriculum.**

**SCIENCE PRACTICES AND TOOLS**

**Identify steps of the scientific method****Identify laboratory tools**

**DESIGNING EXPERIMENTS**

**Identify control and experimental groups****Identify independent and dependent variables****Identify the experimental question****Identify questions that can be investigated with a set of materials****Understand an experimental protocol about plant growth****Understand an experimental protocol about diffusion****Understand an experimental protocol about evaporation**

** **

**ENGINEERING PRACTICES**

**Identify parts of the engineering-design process****Evaluate tests of engineering-design solutions****Use data from tests to compare engineering-design solutions****Explore the engineering-design process: going to the Moon!**

**DENSITY**

**Calculate density, mass, and volume**

**ATOMS AND MOLECULES**

**What are atoms and chemical elements?****How are substances represented by chemical formulas and models?****Identify chemical formulas for ball-and-stick models****Describe the atomic composition of molecules****Classify elementary substances and compounds using chemical formulas****Classify elementary substances and compounds using models**

**CHEMICAL REACTIONS**

**Identify reactants and products****Count atoms and molecules in chemical reactions****Calculate amounts of reactants or products in chemical reactions****Describe energy changes in chemical reactions****Compare physical and chemical changes****Explore chemical structure and properties: soapmaking****Explore chemical structure and properties: food flavors**

**VELOCITY, ACCELERATION, AND FORCES**

**Calculate velocity from time and distance****Calculate distance from velocity and time****Calculate time from velocity and distance****Calculate velocity, distance, and time I****Calculate velocity, distance, and time II****Identify whether objects are accelerating****How does mass affect force and acceleration?****Predict forces using Newton’s third law****Balanced and unbalanced forces**

**KINETIC AND POTENTIAL ENERGY**

**Identify changes in gravitational potential energy****Use tables and graphs to identify patterns about kinetic energy****Explore energy transformations: roller coaster ride****Explore energy transformations: bike ride**

** **

**THERMAL ENERGY**

**Predict heat flow and temperature changes****Compare thermal energy transfers**

**PARTICLE MOTION AND ENERGY**

**How does particle motion affect temperature?****Particle motion and changes of state****How does particle motion affect gas pressure?****Identify how particle motion affects temperature and pressure**

** **

**WAVES**

**Compare amplitudes, wavelengths, and frequencies of waves****Compare energy of waves**

**SOLUTIONS**

**Compare concentrations of solutions****Diffusion across membranes**

**CLASSIFICATION AND SCIENTIFIC NAMES**

**Identify common and scientific names****Origins of scientific names****Use scientific names to classify organisms**

**BIOCHEMISTRY**

**Structure and function: carbohydrates, lipids, proteins, and nucleic acids****Understanding the chemistry of cellular respiration**

**CELLS**

**Understanding cells****Identify functions of plant cell parts****Identify functions of animal cell parts****Plant cell diagrams: label parts****Animal cell diagrams: label parts****Compare cells and cell parts**

**ANATOMY AND PHYSIOLOGY**

**Organization in the human body: the heart and the circulatory system****Science literacy: how does the nervous system produce phantom pain?**

**GENES TO TRAITS**

**Inherited and acquired traits: use evidence to support a statement****Genetics vocabulary: genotype and phenotype****Genetics vocabulary: dominant and recessive****Genetic variation in sexual reproduction****Complete and interpret Punnett squares****Use Punnett squares to calculate ratios of offspring types****Use Punnett squares to calculate probabilities of offspring types****Genes, proteins, and traits: understanding the genetic code****Describe the effects of gene mutations on organisms****How do genes and the environment affect plant growth?**

**ADAPTATIONS AND NATURAL SELECTION**

**How can animal behaviors affect reproductive success? Identify evidence to support a claim****Introduction to natural selection****Calculate the percentages of traits in a population****Calculate the averages of traits in a population****Construct explanations of natural selection**

** **

**FOSSILS**

**Compare fossils to modern organisms****Compare ages of fossils in a rock sequence**

**PLANT REPRODUCTION**

**Angiosperm and conifer life cycles****Moss and fern life cycles**

**PHOTOSYNTHESIS**

**How do plants use and change energy?****Identify the photosynthetic organism**

**ECOSYSTEMS**

**Describe populations, communities, and ecosystems****Identify ecosystems****Describe ecosystems**

**ECOLOGICAL INTERACTIONS**

**How does matter move in food chains?****Interpret food webs I****Interpret food webs II****Use food chains to predict changes in populations****Classify symbiotic relationships****Investigate primary succession on a volcanic island**

**CONSERVATION**

**Coral reef biodiversity and human uses: explore a problem****Coral reef biodiversity and human uses: evaluate solutions**

**NATURAL RESOURCES AND HUMAN IMPACTS**

**Evaluate claims about natural resource use: groundwater****Evaluate claims about natural resource use: fossil fuels**

** **

**ROCKS AND MINERALS**

**Identify rocks and minerals****Classify rocks as igneous, sedimentary, or metamorphic****Label parts of rock cycle diagrams****Select parts of rock cycle diagrams**

**PLATE TECTONICS**

**Label Earth layers****Label Earth features at tectonic plate boundaries****Describe tectonic plate boundaries around the world**

**TOPOGRAPHIC MAPS**

**Select parts of a topographic map**

**WATER CYCLE**

**Label parts of water cycle diagrams****Select parts of water cycle diagrams**

**WEATHER AND CLIMATE**

**Use data to describe climates****Explore air masses****Identify and compare air masses****How do air masses form?**

**CLIMATE CHANGE**

**The greenhouse effect**

**NATURAL HAZARDS**

**Analyze natural hazard maps**

**ASTRONOMY**

**Analyze models of the Earth-Sun-Moon system****Identify phases of the Moon****What causes the seasons on Earth?****Analyze data to compare properties of planets**

**UNITS AND MEASUREMENT**

**Choose customary units of distance, mass, and volume****Choose metric units of distance, mass, and volume****Estimate temperatures****Abbreviate length, speed, and acceleration units****Abbreviate temperature, mass, and volume units****Abbreviate force, energy, and electricity units**

**SCIENCE PRACTICES AND TOOLS**

**Identify steps of the scientific method****Identify laboratory tools**

**DESIGNING EXPERIMENTS**

**Identify control and experimental groups****Identify independent and dependent variables****Identify the experimental question****Identify questions that can be investigated with a set of materials****Understand an experimental protocol about plant growth****Understand an experimental protocol about diffusion****Understand an experimental protocol about evaporation**

**ENGINEERING PRACTICES**

**Identify parts of the engineering-design process****Evaluate tests of engineering-design solutions****Use data from tests to compare engineering-design solutions****Explore the engineering-design process: going to the Moon!**

**DENSITY**

**Calculate density, mass, and volume**

**ATOMS AND MOLECULES**

**What are atoms and chemical elements?****How are substances represented by chemical formulas and models?****Identify chemical formulas for ball-and-stick models****Describe the atomic composition of molecules****Classify elementary substances and compounds using chemical formulas****Classify elementary substances and compounds using models**

**CHEMICAL REACTIONS**

**Identify reactants and products****Count atoms and molecules in chemical reactions****Calculate amounts of reactants or products in chemical reactions****Describe energy changes in chemical reactions****Compare physical and chemical changes****Explore chemical structure and properties: soapmaking****Explore chemical structure and properties: food flavors**

**VELOCITY, ACCELERATION, AND FORCES**

**Calculate velocity from time and distance****Calculate distance from velocity and time****Calculate time from velocity and distance****Calculate velocity, distance, and time****Identify whether objects are accelerating****How does mass affect force and acceleration?****Predict forces using Newton’s third law****Balanced and unbalanced forces**

**KINETIC AND POTENTIAL ENERGY**

**Identify changes in gravitational potential energy****Use tables and graphs to identify patterns about kinetic energy****Explore energy transformations: roller coaster ride****Explore energy transformations: bike ride**

**THERMAL ENERGY**

**Predict heat flow and temperature changes****Compare thermal energy transfers**

**PARTICLE MOTION AND ENERGY**

**How does particle motion affect temperature?****Particle motion and changes of state****How does particle motion affect gas pressure?****Identify how particle motion affects temperature and pressure**

**WAVES**

**Compare amplitudes, wavelengths, and frequencies of waves****Compare energy of waves**

**SOLUTIONS**

**Compare concentrations of solutions****Diffusion across membranes**

**CLASSIFICATION AND SCIENTIFIC NAMES**

**Identify common and scientific names****Origins of scientific names****Use scientific names to classify organisms**

**BIOCHEMISTRY**

**Structure and function: carbohydrates, lipids, proteins, and nucleic acids****Understanding the chemistry of cellular respiration**

**CELLS**

**Understanding cells****Identify functions of plant cell parts****Identify functions of animal cell parts****Plant cell diagrams: label parts****Animal cell diagrams: label parts****Compare cells and cell parts**

**ANATOMY AND PHYSIOLOGY**

**Organization in the human body: the heart and the circulatory system****Science literacy: how does the nervous system produce phantom pain?**

**GENES TO TRAITS**

**Inherited and acquired traits: use evidence to support a statement****Genetics vocabulary: genotype and phenotype****Genetics vocabulary: dominant and recessive****Genetic variation in sexual reproduction****Complete and interpret Punnett squares****Use Punnett squares to calculate ratios of offspring types****Use Punnett squares to calculate probabilities of offspring types****Genes, proteins, and traits: understanding the genetic code****Describe the effects of gene mutations on organisms****How do genes and the environment affect plant growth?**

**ADAPTATIONS AND NATURAL SELECTION**

**How can animal behaviors affect reproductive success? Identify evidence to support a claim****Introduction to natural selection****Calculate the percentages of traits in a population****Calculate the averages of traits in a population****Construct explanations of natural selection**

**FOSSILS**

**Compare ages of fossils in a rock sequence**

**PLANT REPRODUCTION**

**Angiosperm and conifer life cycles****Moss and fern life cycles**

**PHOTOSYNTHESIS**

**How do plants use and change energy?****Identify the photosynthetic organism**

**ECOSYSTEMS**

**Describe populations, communities, and ecosystems****Identify ecosystems****Describe ecosystems**

**ECOLOGICAL INTERACTIONS**

**How does matter move in food chains?****Interpret food webs****Use food chains to predict changes in populations****Classify symbiotic relationships****Investigate primary succession on a volcanic island**

**CONSERVATION**

**Coral reef biodiversity and human uses: explore a problem****Coral reef biodiversity and human uses: evaluate solutions**

**NATURAL RESOURCES AND HUMAN IMPACTS**

**Evaluate claims about natural resource use: groundwater****Evaluate claims about natural resource use: fossil fuels**

**ROCKS AND MINERALS**

**Identify rocks and minerals****Label parts of rock cycle diagrams****Select parts of rock cycle diagrams**

**PLATE TECTONICS**

**Label Earth layers****Label Earth features at tectonic plate boundaries****Describe tectonic plate boundaries around the world**

**TOPOGRAPHIC MAPS**

**Select parts of a topographic map**

**WATER CYCLE**

**Label parts of water cycle diagrams****Select parts of water cycle diagrams**

**WEATHER AND CLIMATE**

**Use data to describe climates****Explore air masses****Identify and compare air masses****How do air masses form?**

** **

**CLIMATE CHANGE**

**The greenhouse effect**

**NATURAL HAZARDS**

**Analyze natural hazard maps**

**ASTRONOMY**

**Analyze models of the Earth-Sun-Moon system****Identify phases of the Moon****What causes the seasons on Earth?****Analyze data to compare properties of planets**

**UNITS AND MEASUREMENT**

**Choose customary units of distance, mass, and volume****Choose metric units of distance, mass, and volume****Estimate temperatures****Abbreviate length, speed, and acceleration units****Abbreviate temperature, mass, and volume units****Abbreviate force, energy, and electricity units**

**Whole numbers & their Multiplication, Division.****Exponents and square roots.****Number theory.****Decimals Add Subtract, Multiply and Divide Decimal.****Fractions and mixed numbers and add, subtract multiply and divide fractions.****Integers, Operations with integers, Mixed Operations.****Rational Numbers.****Problem solving and estimation.****Ratios and rates.****Units of measurement.****Money, Consumer math.****Co-ordinate plane.****Expressions and properties, one-variable equations, one-variable inequalities, two-variable equations.****Two-dimensional figures.****Symmetry and transformations.****Three-dimensional figures.****Geometric measurement.****Data and graphs.****Statistics, probability.****Financial literacy.**

**NOTE: We cover every topics of all grades in details considering the variations in syllabus of different states in USA.****The syllabus can be modified according to the needs of the students or as per school curriculum.**

**Number Theory****Integers, operations with integers.****Decimals, operations with decimals.****Fractions and mixed numbers, operations with fractions.****Rational numbers.****Exponents and square roots.****Roots, rates and proportions, proportional relationships.****Consumer math.****Problem solving and estimation.****Units of measurements.****Co-ordinate plane.****Number sequences.****Expressions and properties.****One-variable equations****One-variable inequalities****Two-variable equations.****Linear functions****Two-dimensional figures.****Transformations and congruence.****Pythagorean theorem.****Three-dimensional figure.****Geometric measurement.****Data and Graph.**

**NOTE: We cover every topics of all grades in details considering the variations in syllabus of different states in USA.**

**The syllabus can be modified according to the needs of the students or as per school curriculum.**

**Number Theory.****Integers****Operations with integers.****Rational numbers.****Operations with rational numbers.****Exponents and roots.****Scientific notation.****Ratios, rates and proportions.****Proportional relationship.****Percents****Consumer math.****Units of measurements.****Problem solving.****Co-ordinate plane.****Two-dimensional figures.****Transformations and congruence.****Transformation and similarity.****Pythagorean theorem.****Three-dimensional figures.****Geometric measurement.****Number sequences.****Expressions and properties.****One-variable equations.****One-variable inequalities.****Linear equations.****Functions.****System of linear equations.****Monomials and polynomials.****Data and graphs.****Statistics.****Probability.**

**Numbers**

**Compare and order rational numbers****Absolute value and opposites****Number lines****Convert between decimals and fractions****Convert between repeating decimals and fractions****Square roots****Cube roots****Sort rational and irrational numbers****Classify rational and irrational numbers****Properties of operations on rational and irrational numbers****Classify numbers**

**OPERATIONS**

**Add, subtract, multiply, and divide integers****Evaluate numerical expressions involving integers****Evaluate variable expressions involving integers****Add and subtract rational numbers****Multiply and divide rational numbers****Evaluate numerical expressions involving rational numbers****Evaluate variable expressions involving rational numbers**

**RATIOS, RATES, AND PROPORTIONS**

**Identify equivalent ratios****Write an equivalent ratio****Unit rates****Unit prices****Solve proportions****Solve proportions: word problems****Scale drawings: word problems**

**PERCENTS**

**Convert between percents, fractions, and decimals****Solve percent equations****Percent word problems****Percent of change****Percent of change: word problems****Percent of change: find the original amount word problems****Percent of a number: tax, discount, and more****Find the percent: tax, discount, and more****Multi-step problems with percents**

**MEASUREMENT**

**Convert rates and measurements: customary units****Convert rates and measurements: metric units****Unit prices with unit conversions****Multi-step problems with unit conversions****Precision****Greatest possible error****Minimum and maximum area and volume****Percent error****Percent error: area and volume**

**GEOMETRY**

**Perimeter****Area****Area and perimeter: word problems****Volume****Surface area****Similar figures: side lengths and angle measures****Similar triangles and indirect measurement****Dilations and scale factors****Area and perimeter of similar figures****Area between two shapes****Similar solids****Volume and surface area of similar solids****Perimeter and area: changes in scale****Surface area and volume: changes in scale****Perimeter, area, and volume: changes in scale****Pythagorean theorem****Pythagorean theorem: word problems****Converse of the Pythagorean theorem: is it a right triangle?****Special right triangles**

**COORDINATE PLANE**

**Coordinate plane review****Midpoint formula: find the midpoint****Midpoint formula: find the endpoint****Distance between two points**

**PROPERTIES**

**Properties of addition and multiplication****Distributive property****Simplify variable expressions using properties****Properties of equality****Identify equivalent equations**

**VARIABLE EXPRESSIONS AND EQUATIONS**

**Write variable expressions****Sort factors of variable expressions****Simplify variable expressions involving like terms and the distributive property****Identify equivalent linear expressions****Write variable equations****Does x satisfy the equation?****Which x satisfies an equation?****Solve equations using order of operations****Rearrange multi-variable equations**

**SOLVE EQUATIONS**

**Model and solve equations using algebra tiles****Write and solve equations that represent diagrams****Solve one-step linear equations****Solve two-step linear equations****Solve advanced linear equations****Solve equations with variables on both sides****Solve equations: complete the solution****Find the number of solutions****Create equations with no solutions or infinitely many solutions****Solve linear equations: word problems****Solve linear equations: mixed review**

** **

**SINGLE-VARIABLE INEQUALITIES**

**Graph inequalities****Write inequalities from graphs****Identify solutions to inequalities****Solve one-step linear inequalities: addition and subtraction****Solve one-step linear inequalities: multiplication and division****Solve one-step linear inequalities****Graph solutions to one-step linear inequalities****Solve two-step linear inequalities****Graph solutions to two-step linear inequalities****Solve advanced linear inequalities****Graph solutions to advanced linear inequalities****Graph compound inequalities****Write compound inequalities from graphs****Solve compound inequalities****Graph solutions to compound inequalities**

**ABSOLUTE VALUE EQUATIONS AND INEQUALITIES**

**Solve absolute value equations****Graph solutions to absolute value equations****Solve absolute value inequalities****Graph solutions to absolute value inequalities**

**MATRICES**

**Matrix vocabulary****Matrix operation rules****Add and subtract matrices****Multiply a matrix by a scalar****Add and subtract scalar multiples of matrices****Multiply two matrices****Properties of matrices**

**DATA AND GRAPHS**

**Interpret bar graphs, line graphs, and histograms****Create bar graphs, line graphs, and histograms****Interpret circle graphs****Interpret stem-and-leaf plots****Box plots**

**PROBLEM SOLVING**

**Word problems: mixed review****Word problems with money****Consecutive integer problems****Rate of travel: word problems****Weighted averages: word problems**

**NUMBER SEQUENCES**

**Identify arithmetic and geometric sequences****Arithmetic sequences****Geometric sequences****Evaluate variable expressions for number sequences****Evaluate recursive formulas for sequences****Identify a sequence as explicit or recursive****Write variable expressions for arithmetic sequences****Write variable expressions for geometric sequences****Write a formula for a recursive sequence****Convert a recursive formula to an explicit formula****Convert an explicit formula to a recursive formula****Number sequences: mixed review**

**RELATIONS AND FUNCTIONS**

**Relations: convert between tables, graphs, mappings, and lists of points****Domain and range of relations****Identify independent and dependent variables****Identify functions****Identify functions: vertical line test****Find values using function graphs****Evaluate a function****Evaluate a function: plug in an expression****Add and subtract functions****Multiply functions****Find the inverse of a function****Complete a function table from a graph****Complete a function table from an equation****Interpret the graph of a function: word problems****Interpret functions using everyday language****Rate of change: tables****Rate of change: graphs**

**DIRECT AND INVERSE VARIATION**

**Identify proportional relationships****Find the constant of variation****Graph a proportional relationship****Write direct variation equations****Write and solve direct variation equations****Identify direct variation and inverse variation****Write inverse variation equations****Write and solve inverse variation equations**

**LINEAR FUNCTIONS**

**Identify linear functions from graphs and equations****Identify linear functions from tables****Find the slope of a graph****Find the slope from two points****Find a missing coordinate using slope****Slope-intercept form: find the slope and y-intercept****Slope-intercept form: graph an equation****Slope-intercept form: write an equation from a graph****Slope-intercept form: write an equation****Slope-intercept form: write an equation from a table****Slope-intercept form: write an equation from a word problem****Linear equations: solve for y****Write linear functions: word problems****Complete a table and graph a linear function****Compare linear functions: graphs and equations****Compare linear functions: tables, graphs, and equations****Write equations in standard form****Standard form: find x- and y-intercepts****Standard form: graph an equation****Equations of horizontal and vertical lines****Graph a horizontal or vertical line****Point-slope form: graph an equation****Point-slope form: write an equation****Point-slope form: write an equation from a graph****Slopes of parallel and perpendicular lines****Write an equation for a parallel or perpendicular line****Transformations of linear functions**

**LINEAR INEQUALITIES**

**Does (x, y) satisfy the inequality?****Linear inequalities: solve for y****Graph a two-variable linear inequality****Linear inequalities: word problems****Is (x, y) a solution to the system of inequalities?****Solve systems of linear inequalities by graphing**

**SYSTEMS OF LINEAR EQUATIONS**

**Is (x, y) a solution to the system of equations?****Solve a system of equations by graphing****Solve a system of equations by graphing: word problems****Find the number of solutions to a system of equations by graphing****Find the number of solutions to a system of equations****Classify a system of equations by graphing****Classify a system of equations****Solve a system of equations using substitution****Solve a system of equations using substitution: word problems****Solve a system of equations using elimination****Solve a system of equations using elimination: word problems****Solve a system of equations using augmented matrices****Solve a system of equations using augmented matrices: word problems****Solve a system of equations using any method****Solve a system of equations using any method: word problems**

**EXPONENTS**

**Exponents with integer bases****Exponents with decimal and fractional bases****Negative exponents****Multiplication with exponents****Division with exponents****Multiplication and division with exponents****Power rule****Evaluate expressions using properties of exponents****Identify equivalent expressions involving exponents I****Identify equivalent expressions involving exponents II****Evaluate integers raised to positive rational exponents****Evaluate integers raised to rational exponents****Multiplication with rational exponents****Division with rational exponents****Power rule with rational exponents****Simplify expressions involving rational exponents**

**SCIENTIFIC NOTATION**

**Convert between standard and scientific notation****Compare numbers written in scientific notation****Add and subtract numbers written in scientific notation****Multiply numbers written in scientific notation****Divide numbers written in scientific notation**

**EXPONENTIAL FUNCTIONS**

**Evaluate an exponential function****Match exponential functions and graphs****Domain and range of exponential functions: graphs****Domain and range of exponential functions: equations****Exponential growth and decay: word problems****Compound interest: word problems**

** **

**MONOMIALS**

**Identify monomials****Multiply monomials****Divide monomials****Multiply and divide monomials****Powers of monomials**

**POLYNOMIALS**

**Polynomial vocabulary****Model polynomials with algebra tiles****Add and subtract polynomials using algebra tiles****Add and subtract polynomials****Add polynomials to find perimeter****Multiply a polynomial by a monomial****Multiply two polynomials using algebra tiles****Multiply two binomials****Multiply two binomials: special cases****Multiply polynomials**

**FACTORING**

**GCF of monomials****Factor out a monomial****Factor quadratics using algebra tiles****Factor quadratics with leading coefficient 1****Factor quadratics with other leading coefficients****Factor quadratics: special cases****Factor by grouping****Factor polynomials**

**QUADRATIC EQUATIONS**

**Characteristics of quadratic functions: graphs****Characteristics of quadratic functions: equations****Complete a function table: quadratic functions****Transformations of quadratic functions****Graph quadratic functions in vertex form****Solve a quadratic equation using square roots****Solve a quadratic equation using the zero product property****Solve a quadratic equation by factoring****Complete the square****Solve a quadratic equation by completing the square****Solve a quadratic equation using the quadratic formula****Using the discriminant****Graph quadratic functions in standard form****Match quadratic functions and graphs****Write a quadratic function from its vertex and another point****Systems of linear and quadratic equations**

**FUNCTIONS: LINEAR, QUADRATIC, EXPONENTIAL**

**Identify linear and exponential functions from graphs****Identify linear, quadratic, and exponential functions from graphs****Identify linear and exponential functions from tables****Identify linear, quadratic, and exponential functions from tables****Write linear, quadratic, and exponential functions****Linear functions over unit intervals****Exponential functions over unit intervals****Describe linear and exponential growth and decay**

**ABSOLUTE VALUE FUNCTIONS**

**Complete a function table: absolute value functions****Graph an absolute value function****Domain and range of absolute value functions: graphs****Domain and range of absolute value functions: equations****Transformations of absolute value functions**

**RADICAL EXPRESSIONS**

**Simplify radical expressions****Simplify radical expressions with variables****Simplify radical expressions involving fractions****Multiply radical expressions****Add and subtract radical expressions****Simplify radical expressions using the distributive property****Divide radical expressions****Simplify radical expressions: mixed review**

**RADICAL FUNCTIONS AND EQUATIONS**

**Evaluate a radical function****Domain and range of radical functions: graphs****Domain and range of radical functions: equations****Solve radical equations I****Solve radical equations II**

**RATIONAL FUNCTIONS AND EXPRESSIONS**

**Rational functions: asymptotes and excluded values****Simplify complex fractions****Simplify rational expressions****Multiply and divide rational expressions****Divide polynomials by monomials****Divide polynomials using long division****Add and subtract rational expressions****Solve rational equations****Evaluate rational expressions**

**TRIGONOMETRY**

**Trigonometric ratios: sin, cos, and tan****Find trigonometric ratios using a calculator****Inverses of trigonometric functions****Trigonometric ratios: find a side length****Trigonometric ratios: find an angle measure****Solve a right triangle**

**LOGIC**

**Identify hypotheses and conclusions****Counterexamples**

**PROBABILITY**

**Theoretical probability****Experimental probability****Find probabilities using two-way frequency tables****Find conditional probabilities using two-way frequency tables****Outcomes of compound events****Identify independent and dependent events****Probability of independent and dependent events****Counting principle****Permutations****Permutation and combination notation**

**STATISTICS**

**Identify biased samples****Mean, median, mode, and range****Quartiles****Identify an outlier****Identify an outlier and describe the effect of removing it****Mean absolute deviation****Variance and standard deviation****Interpret a scatter plot****Outliers in scatter plots****Match correlation coefficients to scatter plots****Calculate correlation coefficients****Scatter plots: line of best fit****Find the equation of a regression line****Interpret regression lines****Analyze a regression line of a data set**

**FUNCTIONS**

**Domain and range****Identify functions****Evaluate functions****Find values using function graphs****Complete a table for a function graph****Find the slope of a linear function****Graph a linear function****Write the equation of a linear function****Linear functions over unit intervals****Average rate of change****Add, subtract, multiply, and divide functions****Composition of functions****Identify inverse functions****Find values of inverse functions from tables****Find values of inverse functions from graphs****Find inverse functions and relations**

** **

**FAMILIES OF FUNCTIONS**

**Function transformation rules****Translations of functions****Reflections of functions****Dilations of functions****Transformations of functions****Describe function transformations**

**QUADRATIC FUNCTIONS**

**Find the maximum or minimum value of a quadratic function****Characteristics of quadratic functions****Graph a quadratic function****Match quadratic functions and graphs****Solve a quadratic equation using square roots****Solve a quadratic equation by factoring****Solve a quadratic equation by completing the square****Solve a quadratic equation using the quadratic formula****Using the discriminant**

**POLYNOMIALS**

**Divide polynomials using long division****Divide polynomials using synthetic division****Evaluate polynomials using synthetic division****Find the roots of factored polynomials****Write a polynomial from its roots****Rational root theorem****Complex conjugate theorem****Conjugate root theorems****Descartes’ Rule of Signs****Fundamental Theorem of Algebra****Match polynomials and graphs****Domain and range of polynomials****Factor sums and differences of cubes****Solve equations with sums and differences of cubes****Factor using a quadratic pattern****Solve equations using a quadratic pattern****Pascal’s triangle****Pascal’s triangle and the Binomial Theorem****Binomial Theorem I****Binomial Theorem II**

** **

**RATIONAL FUNCTIONS**

**Rational functions: asymptotes and excluded values****Solve rational equations****Check whether two rational functions are inverses**

**EXPONENTIAL AND LOGARITHMIC FUNCTIONS**

**Domain and range of exponential and logarithmic functions****Convert between exponential and logarithmic form****Solve exponential equations using factoring****Evaluate logarithms****Change of base formula****Product property of logarithms****Quotient property of logarithms****Power property of logarithms****Evaluate logarithms using properties****Solve exponential equations using logarithms****Solve logarithmic equations with one logarithm****Solve logarithmic equations with multiple logarithms****Exponential functions over unit intervals****Identify linear and exponential functions****Describe linear and exponential growth and decay****Exponential growth and decay: word problems****Compound interest: word problems**

**RADICAL FUNCTIONS**

**Domain and range of radical functions****Solve radical equations****Roots and Rational Exponents****Roots of integers****Roots of rational numbers****Find roots using a calculator****Evaluate rational exponents****Operations with rational exponents****Simplify radical expressions with variables****Nth roots****Simplify expressions involving rational exponents**

**SYSTEMS OF EQUATIONS**

**Solve a system of equations by graphing****Solve a system of equations by graphing: word problems****Classify a system of equations****Solve a system of equations using substitution****Solve a system of equations using substitution: word problems****Solve a system of equations using elimination****Solve a system of equations using elimination: word problems****Solve a system of equations using augmented matrices****Solve a system of equations using augmented matrices: word problems****Solve a system of equations in three variables using substitution****Solve a system of equations in three variables using elimination****Determine the number of solutions to a system of equations in three variables**

**SYSTEMS OF INEQUALITIES**

**Solve systems of linear inequalities by graphing****Solve systems of linear and absolute value inequalities by graphing****Find the vertices of a solution set****Linear programming**

** **

**NONLINEAR INEQUALITIES**

**Graph solutions to quadratic inequalities****Solve quadratic inequalities****Graph solutions to higher-degree inequalities****Solve higher-degree inequalities**

** **

**MATRICES**

**Matrix vocabulary****Matrix operation rules****Add and subtract matrices****Multiply a matrix by a scalar****Add and subtract scalar multiples of matrices****Multiply two matrices****Simplify matrix expressions****Properties of matrices****Solve matrix equations****Determinant of a matrix****Is a matrix invertible?****Inverse of a 2 x 2 matrix****Inverse of a 3 x 3 matrix****Identify inverse matrices****Solve matrix equations using inverses****Identify transformation matrices****Transformation matrices: write the vertex matrix****Transformation matrices: graph the image**

**TRIGONOMETRY**

**Convert between radians and degrees****Radians and arc length****Quadrants****Coterminal and reference angles****Find trigonometric ratios using right triangles****Find trigonometric ratios using the unit circle****Find trigonometric ratios of special angles****Find trigonometric ratios using reference angles****Inverses of trigonometric functions****Solve trigonometric equations****Trigonometric ratios: find a side length****Trigonometric ratios: find an angle measure****Solve a right triangle****Law of Sines****Law of Cosines****Solve a triangle****Area of a triangle: sine formula****Area of a triangle: Heron’s formula**

**TRIGONOMETRIC FUNCTIONS**

**Find properties of sine functions****Write equations of sine functions from graphs****Write equations of sine functions using properties****Graph sine functions****Graph translations of sine functions****Find properties of cosine functions****Write equations of cosine functions from graphs****Write equations of cosine functions using properties****Graph cosine functions****Graph translations of cosine functions****Graph sine and cosine functions****Graph translations of sine and cosine functions**

** **

**TRIGONOMETRIC IDENTITIES**

**Complementary angle identities****Symmetry and periodicity of trigonometric functions****Trigonometric identities I****Trigonometric identities II**

** **

**CONIC SECTIONS**

**Find properties of parabolas****Write equations of parabolas in vertex form****Graph parabolas****Find properties of circles****Write equations of circles in standard form****Graph circles****Find properties of ellipses****Find the eccentricity of an ellipse****Write equations of ellipses in standard form****Find properties of hyperbolas****Find the eccentricity of a hyperbola****Write equations of hyperbolas in standard form****Convert equations of conic sections from general to standard form**

** **

**REAL NUMBERS**

**Sort rational and irrational numbers****Classify rational and irrational numbers****Properties of operations on rational and irrational numbers**

**COMPLEX NUMBERS**

**Add and subtract complex numbers****Complex conjugates****Multiply and divide complex numbers****Add, subtract, multiply, and divide complex numbers****Absolute values of complex numbers****Powers of i****Complex Plane****Introduction to the complex plane****Graph complex numbers****Addition in the complex plane****Subtraction in the complex plane****Graph complex conjugates****Absolute value in the complex plane****Midpoints in the complex plane****Distance in the complex plane**

**POLAR FORM**

**Find the modulus and argument of a complex number****Convert complex numbers from rectangular to polar form****Convert complex numbers from polar to rectangular form****Convert complex numbers between rectangular and polar form****Match polar equations and graphs**

** **

**TWO-DIMENSIONAL VECTORS**

**Find the magnitude of a vector****Find the component form of a vector****Find the direction angle of a vector****Find the component form of a vector from its magnitude and direction angle****Graph a resultant vector using the triangle method****Graph a resultant vector using the parallelogram method****Add vectors****Subtract vectors****Find the magnitude and direction of a vector sum****Multiply a vector by a scalar****Find the magnitude of a vector scalar multiple****Determine the direction of a vector scalar multiple****Find a unit vector****Linear combinations of vectors**

** **

**THREE-DIMENSIONAL VECTORS**

**Find the magnitude of a three-dimensional vector****Find the component form of a three-dimensional vector****Add and subtract three-dimensional vectors****Scalar multiples of three-dimensional vectors****Find a three-dimensional unit vector****Linear combinations of three-dimensional vectors**

** **

**SEQUENCES AND SERIES**

**Find terms of a sequence****Find terms of a recursive sequence****Identify a sequence as explicit or recursive****Find a recursive formula****Find recursive and explicit formulas****Convert a recursive formula to an explicit formula****Convert an explicit formula to a recursive formula****Convert between explicit and recursive formulas****Identify arithmetic and geometric series****Introduction to sigma notation****Find the sum of an arithmetic series****Find the sum of a finite geometric series****Introduction to partial sums****Partial sums of arithmetic series****Partial sums of geometric series****Partial sums: mixed review****Convergent and divergent geometric series****Find the value of an infinite geometric series****Write a repeating decimal as a fraction**

** **

**PROBABILITY**

**Introduction to probability****Calculate probabilities of events****Combinations and permutations****Find probabilities using combinations and permutations****Find probabilities using two-way frequency tables****Identify independent events****Find conditional probabilities****Independence and conditional probability****Find conditional probabilities using two-way frequency tables****Find probabilities using the addition rule****Probability Distributions****Identify discrete and continuous random variables****Write a discrete probability distribution****Graph a discrete probability distribution****Expected values of random variables****Variance of random variables****Standard deviation of random variables****Write the probability distribution for a game of chance****Expected values for a game of chance****Choose the better bet****Find probabilities using the binomial distribution****Mean, variance, and standard deviation of binomial distributions****Find probabilities using the normal distribution I****Find probabilities using the normal distribution II****Find z-values****Find values of normal variables****Distributions of sample means****The Central Limit Theorem****Use normal distributions to approximate binomial distributions**

** **

**STATISTICS**

**Identify biased samples****Variance and standard deviation****Identify an outlier****Identify an outlier and describe the effect of removing it****Outliers in scatter plots****Match correlation coefficients to scatter plots****Calculate correlation coefficients****Find the equation of a regression line****Interpret regression lines****Analyze a regression line of a data set****Analyze a regression line using statistics of a data set****Find confidence intervals for population means****Find confidence intervals for population proportions****Interpret confidence intervals for population means****Experiment design****Analyze the results of an experiment using simulations**

**ALGEBRA REVIEW**

**Ratios and proportions****Scale drawings: word problems****Properties of exponents****Simplify radical expressions****Write variable expressions****Solve linear equations****Solve linear inequalities****Solve systems of linear equations****Solve a quadratic equation by factoring****Solve a quadratic equation using the quadratic formula****Distance formula****Distance to the origin in three dimensions****Construct the midpoint or perpendicular bisector of a segment**

**POINTS, LINES, LINE SEGMENTS, AND PLANES**

**Lines, line segments, and rays****Properties of planes, lines, and points****Describe intersections in a plane****Lengths of segments on number lines****Additive property of length****Midpoints****Congruent line segments****Perpendicular Bisector Theorem****Midpoint formula: find the midpoint****Midpoint formula: find the endpoint**

**ANGLES**

**Angle vocabulary****Angle measures****Identify complementary, supplementary, vertical, adjacent, and congruent angles****Find measures of complementary, supplementary, vertical, and adjacent angles****Angle bisectors****Construct an angle bisector****Construct a congruent angle****Proofs involving angles**

**PARALLEL AND PERPENDICULAR LINES**

**Identify parallel, intersecting, and skew lines and planes****Construct a perpendicular line****Transversals: name angle pairs****Transversals of parallel lines: find angle measures****Construct parallel lines****Proofs involving parallel lines I****Proofs involving parallel lines II**

**LINES IN THE COORDINATE PLANE**

**Coordinate plane review****Slopes of lines****Graph a linear equation****Equations of lines****Slopes of parallel and perpendicular lines****Equations of parallel and perpendicular lines****Find the distance between a point and a line****Find the distance between two parallel lines**

**INTRODUCTION TO TRIANGLES**

**Classify triangles****Triangle Angle-Sum Theorem****Exterior Angle Theorem****Exterior Angle Inequality**

**TWO-DIMENSIONAL FIGURES**

**Polygon vocabulary****Interior angles of polygons****Exterior angles of polygons****Review: interior and exterior angles of polygons****Construct an equilateral triangle or regular hexagon****Construct a square**

**THREE-DIMENSIONAL FIGURES**

**Parts of three-dimensional figures****Three-dimensional figure vocabulary****Nets and drawings of three-dimensional figures****Cross-sections of three-dimensional figures****Solids of revolution**

**Logic**

**Identify hypotheses and conclusions****Counterexamples****Conditionals****Negations****Converses, inverses, and contrapositives****Biconditionals****Truth tables**

**INTRODUCTION TO CONGRUENT FIGURES**

**Congruence statements and corresponding parts****Solve problems involving corresponding parts****Identify congruent figures**

**CONGRUENT TRIANGLES**

**SSS and SAS Theorems****Proving triangles congruent by SSS and SAS****ASA and AAS Theorems****Proving triangles congruent by ASA and AAS****SSS, SAS, ASA, and AAS Theorems****SSS Theorem in the coordinate plane****Proving triangles congruent by SSS, SAS, ASA, and AAS****Proofs involving corresponding parts of congruent triangles****Congruency in isosceles and equilateral triangles****Proofs involving isosceles triangles****Hypotenuse-Leg Theorem**

** **

**TRANSFORMATIONS**

**Classify congruence transformations****Translations: graph the image****Translations: find the coordinates****Translations: write the rule****Reflections: graph the image****Reflections: find the coordinates****Rotate polygons about a point****Rotations: graph the image****Rotations: find the coordinates****Compositions of congruence transformations: graph the image****Transformations that carry a polygon onto itself****Congruence transformations: mixed review****Dilations: graph the image****Dilations: find the coordinates****Dilations: scale factor and classification****Dilations and parallel lines**

**TRIANGLES**

**Midsegments of triangles****Triangles and bisectors****Identify medians, altitudes, angle bisectors, and perpendicular bisectors****Angle-side relationships in triangles****Triangle Inequality Theorem****Construct the circumcenter or incenter of a triangle****Construct the centroid or orthocenter of a triangle****Proofs involving triangles I****Proofs involving triangles II**

**QUADRILATERALS**

**Identify trapezoids****Classify quadrilaterals I****Classify quadrilaterals II****Find missing angles in quadrilaterals****Graph quadrilaterals****Properties of parallelograms****Proving a quadrilateral is a parallelogram****Properties of rhombuses****Properties of squares and rectangles****Properties of trapezoids****Properties of kites****Review: properties of quadrilaterals****Proofs involving quadrilaterals I****Proofs involving quadrilaterals II**

**SYMMETRY**

**Line symmetry****Rotational symmetry****Draw lines of symmetry**

**SIMILARITY**

**Similarity ratios****Similarity statements****Identify similar figures****Side lengths and angle measures in similar figures****Similar triangles and indirect measurement****Perimeters of similar figures****Similarity rules for triangles****Similar triangles and similarity transformations****Similarity of circles****Triangle Proportionality Theorem****Similarity and altitudes in right triangles****Areas of similar figures****Prove similarity statements****Prove proportions or angle congruences using similarity****Proofs involving similarity in right triangles****Prove the Pythagorean theorem**

**RIGHT TRIANGLES**

**Pythagorean theorem****Converse of the Pythagorean theorem****Pythagorean Inequality Theorems****Special right triangles**

**TRIGONOMETRY**

**Trigonometric ratios: sin, cos, and tan****Trigonometric ratios: csc, sec, and cot****Trigonometric ratios in similar right triangles****Trigonometric functions of complementary angles****Find trigonometric functions of special angles****Find trigonometric functions using a calculator****Inverses of trigonometric functions****Trigonometric ratios: find a side length****Trigonometric ratios: find an angle measure****Solve a right triangle****Law of Sines****Law of Cosines****Solve a triangle****Area of a triangle: sine formula****Area of a triangle: Law of Sines**

**AREA AND PERIMETER**

**Perimeter****Area of rectangles and squares****Area of parallelograms and triangles****Area of trapezoids****Area and perimeter in the coordinate plane I****Area and perimeter in the coordinate plane II****Area and circumference of circles****Area of compound figures****Area between two shapes****Area and perimeter of similar figures****Perimeter and area: changes in scale****Heron’s formula****Area and perimeter mixed review**

**SURFACE AREA AND VOLUME**

**Introduction to surface area and volume****Surface area of prisms and cylinders****Surface area of pyramids and cones****Surface area of spheres****Volume of prisms and cylinders****Volume of pyramids and cones****Volume of spheres****Introduction to similar solids****Surface area and volume of similar solids****Surface area and volume: changes in scale****Perimeter, area, and volume: changes in scale****Surface area and volume review**

**CIRCLES**

**Parts of a circle****Central angles and arc measures****Arc length****Convert between radians and degrees****Radians and arc length****Area of sectors****Circle measurements: mixed review****Arcs and chords****Tangent lines****Perimeter of polygons with an inscribed circle****Inscribed angles****Angles in inscribed right triangles****Angles in inscribed quadrilaterals I****Angles in inscribed quadrilaterals II****Construct a tangent line to a circle.****Construct an equilateral triangle inscribed in a circle****Construct a square inscribed in a circle****Construct a regular hexagon inscribed in a circle****Construct the inscribed or circumscribed circle of a triangle**

**CIRCLES AND PARABOLAS IN THE COORDINATE PLANE**

**Find the center of a circle****Find the radius or diameter of a circle****Write equations of circles in standard form from graphs****Write equations of circles in standard form using properties****Convert equations of circles from general to standard form****Find properties of circles from equations in general form****Graph circles from equations in standard form****Graph circles from equations in general form****Find the vertex of a parabola****Find the focus or directrix of a parabola****Find the axis of symmetry of a parabola****Write equations of parabolas in vertex form from graphs****Write equations of parabolas in vertex form using properties****Convert equations of parabolas from general to vertex form****Find properties of a parabola from equations in general form**

**MEASUREMENT**

**Convert rates and measurements: customary units****Convert rates and measurements: metric units****Convert square and cubic units of length****Precision****Greatest possible error****Minimum and maximum area and volume****Percent error****Percent error: area and volume****Calculate density, mass, and volume**

**PROBABILITY**

**Theoretical and experimental probability****Outcomes of compound events****Identify independent and dependent events****Probability of independent and dependent events****Counting principle****Permutations****Permutation and combination notation****Find probabilities using combinations and permutations****Find probabilities using two-way frequency tables****Identify independent events****Find conditional probabilities****Independence and conditional probability****Find conditional probabilities using two-way frequency tables****Geometric probability****Find probabilities using the addition rule**

**VECTORS**

**Compass directions and vectors****Find the magnitude of a vector****Find the component form of a vector****Find the component form of a vector given its magnitude and direction angle****Graph a resultant vector using the triangle method****Graph a resultant vector using the parallelogram method****Add vectors****Subtract vectors**

**VARIABLE EXPRESSIONS**

**Evaluate variable expressions involving integers****Evaluate variable expressions involving rational numbers****Simplify variable expressions using properties****Sort factors of single-variable expressions****Sort factors of multi-variable expressions**

**EQUATIONS**

**Solve linear equations****Solve linear equations: word problems****Solve equations: complete the solution****Solve absolute value equations****Graph solutions to absolute value equations****Solve multi-variable equations**

**INEQUALITIES**

**Graph a linear inequality in one variable****Write inequalities from graphs****Write a linear inequality: word problems****Solve linear inequalities****Graph solutions to linear inequalities****Solve absolute value inequalities****Graph solutions to absolute value inequalities****Graph a two-variable linear inequality****Graph solutions to two-variable absolute value inequalities****Graph solutions to quadratic inequalities****Solve quadratic inequalities**

**FUNCTIONS**

**Domain and range****Identify functions****Evaluate functions****Find values using function graphs****Complete a table for a function graph****Find the slope of a linear function****Graph a linear function****Write the equation of a linear function****Linear functions over unit intervals****Average rate of change****Graph an absolute value function****Domain and range of absolute value functions: graphs****Domain and range of absolute value functions: equations****Transformations of absolute value functions**

**SYSTEMS OF EQUATIONS**

**Is (x, y) a solution to the system of equations?****Solve a system of equations by graphing****Solve a system of equations by graphing: word problems****Find the number of solutions to a system of equations****Classify a system of equations****Solve a system of equations using substitution****Solve a system of equations using substitution: word problems****Solve a system of equations using elimination****Solve a system of equations using elimination: word problems****Solve a system of equations using any method****Solve a system of equations using any method: word problems****Solve a system of equations in three variables using substitution****Solve a system of equations in three variables using elimination****Determine the number of solutions to a system of equations in three variables****Solve a system of linear and quadratic equations****Solve a non-linear system of equations**

**SYSTEMS OF INEQUALITIES**

**Is (x, y) a solution to the system of inequalities?****Solve systems of linear inequalities by graphing****Solve systems of linear and absolute value inequalities by graphing****Find the vertices of a solution set****Linear programming**

**MATRICES**

**Matrix vocabulary****Matrix operation rules****Add and subtract matrices****Multiply a matrix by a scalar****Add and subtract scalar multiples of matrices****Multiply two matrices****Simplify matrix expressions****Properties of matrices****Solve matrix equations****Determinant of a matrix****Is a matrix invertible?****Inverse of a matrix****Identify inverse matrices****Solve matrix equations using inverses****Identify transformation matrices****Transformation matrices: write the vertex matrix****Transformation matrices: graph the image****Solve a system of equations using augmented matrices****Solve a system of equations using augmented matrices: word problems**

** **

**REAL NUMBERS**

**Sort rational and irrational numbers****Classify rational and irrational numbers****Properties of operations on rational and irrational numbers**

** **

**COMPLEX NUMBERS**

**Introduction to complex numbers****Add and subtract complex numbers****Complex conjugates****Multiply complex numbers****Divide complex numbers****Add, subtract, multiply, and divide complex numbers****Absolute values of complex numbers****Powers of i**

**FACTORING**

**Factor out a monomial****Factor quadratics using algebra tiles****Factor quadratics****Factor using a quadratic pattern****Factor by grouping****Factor sums and differences of cubes****Factor polynomials**

**QUADRATIC FUNCTIONS**

**Characteristics of quadratic functions: graphs****Characteristics of quadratic functions: equations****Complete a function table: quadratic functions****Transformations of quadratic functions****Graph a quadratic function****Solve a quadratic equation using square roots****Solve a quadratic equation using the zero product property****Solve a quadratic equation by factoring****Complete the square****Solve a quadratic equation by completing the square****Solve a quadratic equation using the quadratic formula****Using the discriminant****Match quadratic functions and graphs****Write a quadratic function from its zeroes****Write a quadratic function from its vertex and another point**

**POLYNOMIALS**

**Polynomial vocabulary****Add and subtract polynomials****Multiply polynomials****Divide polynomials using long division****Divide polynomials using synthetic division****Evaluate polynomials using synthetic division****Solve polynomial equations****Find the roots of factored polynomials****Write a polynomial from its roots****Rational root theorem****Complex conjugate theorem****Conjugate root theorems****Descartes’ Rule of Signs****Match polynomials and graphs****Domain and range of polynomials****Fundamental Theorem of Algebra****Pascal’s triangle****Pascal’s triangle and the Binomial Theorem****Binomial Theorem I****Binomial Theorem II**

**RADICAL FUNCTIONS AND EXPRESSIONS**

**Roots of integers****Roots of rational numbers****Find roots using a calculator****Simplify radical expressions with variables I****Simplify radical expressions with variables II****Nth roots****Multiply radical expressions****Divide radical expressions****Add and subtract radical expressions****Simplify radical expressions using the distributive property****Simplify radical expressions using conjugates****Domain and range of radical functions****Solve radical equations**

**RATIONAL EXPONENTS**

**Evaluate rational exponents****Multiplication with rational exponents****Division with rational exponents****Power rule****Simplify expressions involving rational exponents I****Simplify expressions involving rational exponents II**

**RATIONAL FUNCTIONS AND EXPRESSIONS**

**Rational functions: asymptotes and excluded values****Evaluate rational expressions I****Evaluate rational expressions II****Simplify rational expressions****Multiply and divide rational expressions****Add and subtract rational expressions****Solve rational equations**

**FUNCTION OPERATIONS**

**Add and subtract functions****Multiply functions****Divide functions****Composition of linear functions: find a value****Composition of linear functions: find an equation****Composition of linear and quadratic functions: find a value****Composition of linear and quadratic functions: find an equation****Identify inverse functions****Find values of inverse functions from tables****Find values of inverse functions from graphs****Find inverse functions and relations**

**FAMILIES OF FUNCTIONS**

**Function transformation rules****Translations of functions****Reflections of functions****Dilations of functions****Transformations of functions****Describe function transformations**

**VARIATION**

**Write and solve direct variation equations****Write and solve inverse variation equations****Classify variation****Write joint and combined variation equations I****Find the constant of variation****Write joint and combined variation equations II****Solve variation equations**

**LOGARITHMS**

**Convert between exponential and logarithmic form: rational bases****Convert between natural exponential and logarithmic form****Convert between exponential and logarithmic form: all bases****Evaluate logarithms****Evaluate natural logarithms****Change of base formula****Evaluate logarithms using a calculator****Identify properties of logarithms****Product property of logarithms****Quotient property of logarithms****Power property of logarithms****Properties of logarithms: mixed review****Evaluate logarithms using properties**

** **

**EXPONENTIAL AND LOGARITHMIC FUNCTIONS**

**Domain and range of exponential and logarithmic functions****Evaluate exponential functions****Match exponential functions and graphs****Solve exponential equations using factoring****Solve exponential equations using common logarithms****Solve exponential equations using natural logarithms****Solve logarithmic equations I****Solve logarithmic equations II****Exponential functions over unit intervals****Identify linear and exponential functions****Describe linear and exponential growth and decay****Exponential growth and decay: word problems****Compound interest: word problems****Continuously compounded interest: word problems**

**PARABOLAS**

**Identify the direction a parabola opens****Find the vertex of a parabola****Find the focus or directrix of a parabola****Find the axis of symmetry of a parabola****Write equations of parabolas in vertex form from graphs****Write equations of parabolas in vertex form using properties****Convert equations of parabolas from general to vertex form****Find properties of a parabola from equations in general form****Graph parabolas**

**CIRCLES**

**Find the center of a circle****Find the radius or diameter of a circle****Write equations of circles in standard form from graphs****Write equations of circles in standard form using properties****Convert equations of circles from general to standard form****Find properties of circles from equations in general form****Graph circles**

**ELLIPSES**

**Find the center, vertices, or co-vertices of an ellipse****Find the length of the major or minor axes of an ellipse****Find the foci of an ellipse****Write equations of ellipses in standard form from graphs****Write equations of ellipses in standard form using properties****Convert equations of ellipses from general to standard form****Find properties of ellipses from equations in general form**

**HYPERBOLAS**

**Find the center of a hyperbola****Find the vertices of a hyperbola****Find the length of the transverse or conjugate axes of a hyperbola****Find the equations for the asymptotes of a hyperbola****Find the foci of a hyperbola****Write equations of hyperbolas in standard form from graphs****Write equations of hyperbolas in standard form using properties****Convert equations of hyperbolas from general to standard form****Find properties of hyperbolas from equations in general form**

**ANGLE MEASURES**

**Convert between radians and degrees****Radians and arc length****Graphs of angles****Quadrants****Coterminal angles****Reference angles**

**TRIGONOMETRY**

**Pythagorean Theorem and its converse****Special right triangles****Trigonometric ratios: sin, cos, and tan****Trigonometric ratios: csc, sec, and cot****Trigonometric ratios in similar right triangles****Find trigonometric ratios using the unit circle****Sin, cos, and tan of special angles****Csc, sec, and cot of special angles****Find trigonometric functions using a calculator****Inverses of sin, cos, and tan****Inverses of csc, sec, and cot****Solve trigonometric equations I****Solve trigonometric equations II****Trigonometric ratios: find a side length****Trigonometric ratios: find an angle measure****Solve a right triangle****Law of Sines****Law of Cosines****Solve a triangle****Area of a triangle: sine formula****Area of a triangle: Law of Sines**

**TRIGONOMETRIC FUNCTIONS**

**Find properties of sine functions****Write equations of sine functions from graphs****Write equations of sine functions using properties****Graph sine functions****Graph translations of sine functions****Find properties of cosine functions****Write equations of cosine functions from graphs****Write equations of cosine functions using properties****Graph cosine functions****Graph translations of cosine functions****Graph sine and cosine functions****Graph translations of sine and cosine functions**

** **

**TRIGONOMETRIC IDENTITIES**

**Complementary angle identities****Symmetry and periodicity of trigonometric functions****Trigonometric identities I****Trigonometric identities II**

**SEQUENCES AND SERIES**

**Find terms of an arithmetic sequence****Find terms of a geometric sequence****Evaluate explicit formulas for sequences****Evaluate recursive formulas for sequences****Classify formulas and sequences****Write a formula for an arithmetic sequence****Write a formula for a geometric sequence****Write a formula for a recursive sequence****Sequences: mixed review****Identify arithmetic and geometric series****Introduction to sigma notation****Find the sum of an arithmetic series****Find the sum of a finite geometric series****Introduction to partial sums****Partial sums of arithmetic series****Partial sums of geometric series****Partial sums: mixed review****Convergent and divergent geometric series****Find the value of an infinite geometric series****Write a repeating decimal as a fraction**

**PROBABILITY**

**Introduction to probability****Calculate probabilities of events****Counting principle****Combinations and permutations****Find probabilities using combinations and permutations****Find probabilities using two-way frequency tables****Identify independent events****Probability of independent and dependent events****Find conditional probabilities****Independence and conditional probability****Find conditional probabilities using two-way frequency tables****Find probabilities using the addition rule**

**PROBABILITY DISTRIBUTIONS**

**Identify discrete and continuous random variables****Write a discrete probability distribution****Graph a discrete probability distribution****Expected values of random variables****Variance of random variables****Standard deviation of random variables****Write the probability distribution for a game of chance****Expected values for a game of chance****Choose the better bet****Find probabilities using the binomial distribution****Find probabilities using the normal distribution I****Find probabilities using the normal distribution II****Find z-values****Find values of normal variables****Distributions of sample means**

** **

**STATISTICS**

**Identify biased samples****Variance and standard deviation****Identify an outlier****Identify an outlier and describe the effect of removing it****Outliers in scatter plots****Find the equation of a regression line****Interpret regression lines****Analyze a regression line of a data set****Find confidence intervals for population means****Find confidence intervals for population proportions****Interpret confidence intervals for population means****Experiment design****Analyze the results of an experiment using simulations**

**FUNCTIONS**

**Find values of functions from graphs****Add, subtract, multiply, and divide functions****Composition of functions****Identify inverse functions****Find values of inverse functions from tables****Find values of inverse functions from graphs****Find inverse functions and relations**

** **

**FAMILIES OF FUNCTIONS**

**Function transformation rules****Translations of functions****Reflections of functions****Dilations of functions****Transformations of functions****Describe function transformations**

**TRIGONOMETRIC FUNCTIONS**

**Convert between radians and degrees****Quadrants****Coterminal and reference angles****Find trigonometric ratios using right triangles****Find trigonometric ratios using the unit circle****Find trigonometric ratios using reference angles****Inverses of trigonometric functions****Find properties of sine functions****Write equations of sine functions from graphs****Write equations of sine functions using properties****Graph sine functions****Find properties of cosine functions****Write equations of cosine functions from graphs****Write equations of cosine functions using properties****Graph cosine functions****Graph sine and cosine functions**

**EXPONENTIAL AND LOGARITHMIC FUNCTIONS**

**Domain and range of exponential and logarithmic functions****Convert between exponential and logarithmic form****Evaluate logarithms****Change of base formula****Product property of logarithms****Quotient property of logarithms****Power property of logarithms****Evaluate logarithms using properties****Describe linear and exponential growth and decay**

** **

**INTRODUCTION TO LIMITS**

**Find limits using graphs****Find one-sided limits using graphs****Determine if a limit exists**

** **

**CALCULATE LIMITS**

**Find limits using addition, subtraction, and multiplication laws****Find limits using the division law****Find limits using power and root laws****Find limits using limit laws****Find limits of polynomials and rational functions****Find limits involving factorization and rationalization****Find limits involving absolute value functions****Find limits involving trigonometric functions**

** **

**LIMITS INVOLVING INFINITY**

**Find limits at vertical asymptotes using graphs****Determine end behavior using graphs****Determine end behavior of polynomial and rational functions**

** **

**RATIONAL FUNCTIONS**

**Find the limit at a vertical asymptote of a rational function I****Find the limit at a vertical asymptote of a rational function II**

**CONTINUITY**

**Identify graphs of continuous functions****Determine continuity using graphs****Determine one-sided continuity using graphs****Find and analyze points of discontinuity using graphs****Determine continuity on an interval using graphs****Determine the continuity of a piecewise function at a point****Make a piecewise function continuous****Intermediate Value Theorem**

**INTRODUCTION TO DERIVATIVES**

**Average rate of change I****Average rate of change II****Find instantaneous rates of change****Velocity as a rate of change****Find values of derivatives using limits****Find the slope of a tangent line using limits****Find equations of tangent lines using limits**

**DERIVATIVE RULES**

**Sum and difference rules****Product rule****Quotient rule****Power rule I****Power rule II****Chain rule****Inverse function rule**

**CALCULATE DERIVATIVES**

**Find derivatives of polynomials****Find derivatives of rational functions****Find derivatives of trigonometric functions I****Find derivatives of trigonometric functions II****Find derivatives of exponential functions****Find derivatives of logarithmic functions****Find derivatives of inverse trigonometric functions****Find derivatives of radical functions****Find derivatives using the product rule I****Find derivatives using the product rule II****Find derivatives using the quotient rule I****Find derivatives using the quotient rule II****Find derivatives using the chain rule I****Find derivatives using the chain rule II**

** **

**DERIVATIVE STRATEGIES**

**Find derivatives using implicit differentiation****Find tangent lines using implicit differentiation****Find derivatives using logarithmic differentiation**

** **

**CALCULATE HIGHER DERIVATIVES**

**Find higher derivatives of polynomials****Find higher derivatives of rational and radical functions****Find second derivatives of trigonometric, exponential, and logarithmic functions****Find higher derivatives of exponential and trigonometric functions****Find higher derivatives of logarithmic and power functions**