Las Vegas Math Tutor
Las Vegas Math Tutor

PRECALCULUS

PRECALCULUS

Functions

  1. A.1Domain and range
  2. A.2Identify functions
  3. A.3Evaluate functions
  4. A.4Find values using function graphs
  5. A.5Complete a table for a function graph
  6. A.6Find the slope of a linear function
  7. A.7Graph a linear function
  8. A.8Write the equation of a linear function
  9. A.9Linear functions over unit intervals
  10. A.10Average rate of change
  11. A.11Add, subtract, multiply, and divide functions
  12. A.12Composition of functions
  13. A.13Identify inverse functions
  14. A.14Find values of inverse functions from tables
  15. A.15Find values of inverse functions from graphs
  16. A.16Find inverse functions and relations

Families of functions

  1. B.1Function transformation rules
  2. B.2Translations of functions
  3. B.3Reflections of functions
  4. B.4Dilations of functions
  5. B.5Transformations of functions
  6. B.6Describe function transformations

Quadratic functions

  1. C.1Find the maximum or minimum value of a quadratic function
  2. C.2Characteristics of quadratic functions
  3. C.3Graph a quadratic function
  4. C.4Match quadratic functions and graphs
  5. C.5Solve a quadratic equation using square roots
  6. C.6Solve a quadratic equation by factoring
  7. C.7Solve a quadratic equation by completing the square
  8. C.8Solve a quadratic equation using the quadratic formula
  9. C.9Using the discriminant

Polynomials

  1. D.1Divide polynomials using long division
  2. D.2Divide polynomials using synthetic division
  3. D.3Evaluate polynomials using synthetic division
  4. D.4Find the roots of factored polynomials
  5. D.5Write a polynomial from its roots
  6. D.6Rational root theorem
  7. D.7Complex conjugate theorem
  8. D.8Conjugate root theorems
  9. D.9Descartes' Rule of Signs
  10. D.10Fundamental Theorem of Algebra
  11. D.11Match polynomials and graphs
  12. D.12Factor sums and differences of cubes
  13. D.13Solve equations with sums and differences of cubes
  14. D.14Factor using a quadratic pattern
  15. D.15Solve equations using a quadratic pattern
  16. D.16Pascal's triangle
  17. D.17Pascal's triangle and the Binomial Theorem
  18. D.18Binomial Theorem I
  19. D.19Binomial Theorem II

Rational functions

  1. E.1Rational functions: asymptotes and excluded values
  2. E.2Solve rational equations
  3. E.3Check whether two rational functions are inverses

Exponential and logarithmic functions

  1. F.1Domain and range of exponential and logarithmic functions
  2. F.2Convert between exponential and logarithmic form
  3. F.3Solve exponential equations using factoring
  4. F.4Evaluate logarithms
  5. F.5Change of base formula
  6. F.6Product property of logarithms
  7. F.7Quotient property of logarithms
  8. F.8Power property of logarithms
  9. F.9Evaluate logarithms using properties
  10. F.10Solve exponential equations using logarithms
  11. F.11Solve logarithmic equations with one logarithm
  12. F.12Solve logarithmic equations with multiple logarithms
  13. F.13Exponential functions over unit intervals
  14. F.14Identify linear and exponential functions
  15. F.15Describe linear and exponential growth and decay
  16. F.16Exponential growth and decay: word problems
  17. F.17Compound interest: word problems

Radical functions

  1. G.1Domain and range of radical functions
  2. G.2Solve radical equations

Roots and rational exponents

  1. H.1Roots of integers
  2. H.2Roots of rational numbers
  3. H.3Find roots using a calculator
  4. H.4Evaluate rational exponents
  5. H.5Operations with rational exponents
  6. H.6Simplify radical expressions with variables
  7. H.7Nth roots
  8. H.8Simplify expressions involving rational exponents

Systems of equations

  1. I.1Solve a system of equations by graphing
  2. I.2Solve a system of equations by graphing: word problems
  3. I.3Classify a system of equations
  4. I.4Solve a system of equations using substitution
  5. I.5Solve a system of equations using substitution: word problems
  6. I.6Solve a system of equations using elimination
  7. I.7Solve a system of equations using elimination: word problems
  8. I.8Solve a system of equations in three variables using substitution
  9. I.9Solve a system of equations in three variables using elimination
  10. I.10Determine the number of solutions to a system of equations in three variables

Systems of inequalities

  1. J.1Solve systems of linear inequalities by graphing
  2. J.2Solve systems of linear and absolute value inequalities by graphing
  3. J.3Find the vertices of a solution set
  4. J.4Linear programming

Nonlinear inequalities

  1. K.1Graph solutions to quadratic inequalities
  2. K.2Solve quadratic inequalities
  3. K.3Graph solutions to higher-degree inequalities
  4. K.4Solve higher-degree inequalities

Matrices

  1. L.1Matrix vocabulary
  2. L.2Matrix operation rules
  3. L.3Add and subtract matrices
  4. L.4Multiply a matrix by a scalar
  5. L.5Add and subtract scalar multiples of matrices
  6. L.6Multiply two matrices
  7. L.7Simplify matrix expressions
  8. L.8Properties of matrices
  9. L.9Solve matrix equations
  10. L.10Determinant of a matrix
  11. L.11Is a matrix invertible?
  12. L.12Inverse of a 2 x 2 matrix
  13. L.13Inverse of a 3 x 3 matrix
  14. L.14Identify inverse matrices
  15. L.15Solve matrix equations using inverses
  16. L.16Identify transformation matrices
  17. L.17Transformation matrices: write the vertex matrix
  18. L.18Transformation matrices: graph the image

Trigonometry

  1. M.1Convert between radians and degrees
  2. M.2Radians and arc length
  3. M.3Quadrants
  4. M.4Coterminal and reference angles
  5. M.5Find trigonometric ratios using right triangles
  6. M.6Find trigonometric ratios using the unit circle
  7. M.7Find trigonometric ratios using reference angles
  8. M.8Inverses of trigonometric functions
  9. M.9Solve trigonometric equations
  10. M.10Trigonometric ratios: find a side length
  11. M.11Trigonometric ratios: find an angle measure
  12. M.12Solve a right triangle
  13. M.13Law of Sines
  14. M.14Law of Cosines
  15. M.15Solve a triangle
  16. M.16Area of a triangle: sine formula
  17. M.17Area of a triangle: Heron's formula

Trigonometric functions

  1. N.1Find properties of sine functions
  2. N.2Write equations of sine functions from graphs
  3. N.3Write equations of sine functions using properties
  4. N.4Graph sine functions
  5. N.5Find properties of cosine functions
  6. N.6Write equations of cosine functions from graphs
  7. N.7Write equations of cosine functions using properties
  8. N.8Graph cosine functions
  9. N.9Graph sine and cosine functions

Trigonometric identities

  1. O.1Complementary angle identities
  2. O.2Symmetry and periodicity of trigonometric functions
  3. O.3Trigonometric identities I
  4. O.4Trigonometric identities II

Conic sections

  1. P.1Find properties of parabolas
  2. P.2Write equations of parabolas in vertex form
  3. P.3Graph parabolas
  4. P.4Find properties of circles
  5. P.5Write equations of circles in standard form
  6. P.6Graph circles
  7. P.7Find properties of ellipses
  8. P.8Find the eccentricity of an ellipse
  9. P.9Write equations of ellipses in standard form
  10. P.10Find properties of hyperbolas
  11. P.11Find the eccentricity of a hyperbola
  12. P.12Write equations of hyperbolas in standard form
  13. P.13Convert equations of conic sections from general to standard form

Real numbers

  1. Q.1Sort rational and irrational numbers
  2. Q.2Classify rational and irrational numbers
  3. Q.3Properties of operations on rational and irrational numbers

Complex numbers

  1. R.1Add and subtract complex numbers
  2. R.2Complex conjugates
  3. R.3Multiply and divide complex numbers
  4. R.4Add, subtract, multiply, and divide complex numbers
  5. R.5Absolute values of complex numbers
  6. R.6Powers of i

Complex plane

  1. S.1Introduction to the complex plane
  2. S.2Graph complex numbers
  3. S.3Addition in the complex plane
  4. S.4Subtraction in the complex plane
  5. S.5Graph complex conjugates
  6. S.6Absolute value in the complex plane
  7. S.7Midpoints in the complex plane
  8. S.8Distance in the complex plane

Polar form

  1. T.1Find the modulus and argument of a complex number
  2. T.2Convert complex numbers from rectangular to polar form
  3. T.3Convert complex numbers from polar to rectangular form
  4. T.4Convert complex numbers between rectangular and polar form
  5. T.5Match polar equations and graphs

Two-dimensional vectors

  1. U.1Find the magnitude of a vector
  2. U.2Find the component form of a vector
  3. U.3Find the direction angle of a vector
  4. U.4Find the component form of a vector from its magnitude and direction angle
  5. U.5Graph a resultant vector using the triangle method
  6. U.6Graph a resultant vector using the parallelogram method
  7. U.7Add and subtract vectors
  8. U.8Find the magnitude and direction of a vector sum
  9. U.9Multiply a vector by a scalar
  10. U.10Find the magnitude of a vector scalar multiple
  11. U.11Determine the direction of a vector scalar multiple
  12. U.12Find a unit vector
  13. U.13Linear combinations of vectors

Three-dimensional vectors

  1. V.1Find the magnitude of a three-dimensional vector
  2. V.2Find the component form of a three-dimensional vector
  3. V.3Add and subtract three-dimensional vectors
  4. V.4Scalar multiples of three-dimensional vectors
  5. V.5Find a three-dimensional unit vector
  6. V.6Linear combinations of three-dimensional vectors

Sequences and series

  1. W.1Find terms of a sequence
  2. W.2Find terms of a recursive sequence
  3. W.3Identify a sequence as explicit or recursive
  4. W.4Find a recursive formula
  5. W.5Find recursive and explicit formulas
  6. W.6Convert a recursive formula to an explicit formula
  7. W.7Convert an explicit formula to a recursive formula
  8. W.8Convert between explicit and recursive formulas
  9. W.9Identify arithmetic and geometric series
  10. W.10Introduction to sigma notation
  11. W.11Find the sum of a finite arithmetic or geometric series
  12. W.12Introduction to partial sums
  13. W.13Partial sums of arithmetic series
  14. W.14Partial sums of geometric series
  15. W.15Partial sums: mixed review
  16. W.16Convergent and divergent geometric series
  17. W.17Find the value of an infinite geometric series
  18. W.18Write a repeating decimal as a fraction

Probability

  1. X.1Introduction to probability
  2. X.2Calculate probabilities of events
  3. X.3Combinations and permutations
  4. X.4Find probabilities using combinations and permutations
  5. X.5Find probabilities using two-way frequency tables
  6. X.6Identify independent events
  7. X.7Find conditional probabilities
  8. X.8Independence and conditional probability
  9. X.9Find conditional probabilities using two-way frequency tables
  10. X.10Find probabilities using the addition rule

Probability distributions

  1. Y.1Identify discrete and continuous random variables
  2. Y.2Write a discrete probability distribution
  3. Y.3Graph a discrete probability distribution
  4. Y.4Expected values of random variables
  5. Y.5Variance of random variables
  6. Y.6Standard deviation of random variables
  7. Y.7Write the probability distribution for a game of chance
  8. Y.8Expected values for a game of chance
  9. Y.9Choose the better bet
  10. Y.10Find probabilities using the binomial distribution
  11. Y.11Mean, variance, and standard deviation of binomial distributions
  12. Y.12Find probabilities using the normal distribution
  13. Y.13Find z-values
  14. Y.14Find values of normal variables
  15. Y.15Distributions of sample means
  16. Y.16The Central Limit Theorem
  17. Y.17Use normal distributions to approximate binomial distributions

Statistics

  1. Z.1Identify biased samples
  2. Z.2Variance and standard deviation
  3. Z.3Identify an outlier
  4. Z.4Identify an outlier and describe the effect of removing it
  5. Z.5Outliers in scatter plots
  6. Z.6Match correlation coefficients to scatter plots
  7. Z.7Calculate correlation coefficients
  8. Z.8Find the equation of a regression line
  9. Z.9Interpret regression lines
  10. Z.10Analyze a regression line of a data set
  11. Z.11Analyze a regression line using statistics of a data set
  12. Z.12Find confidence intervals for population means
  13. Z.13Find confidence intervals for population proportions
  14. Z.14Interpret confidence intervals for population means
  15. Z.15Experiment design
  16. Z.16Analyze the results of an experiment using simulations