SYLLABUS

• 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