Advanced Precalculus practice tests and more

Each of the following topics has at least a practice test, read the description of each topic to see what will be on it. To access the pdf, click on the green link and the pdf will open in another tab.

Various Functions (Unit 1)

• Finding difference quotients

• Finding domain and range of functions

• Using functions to write various expressions

• Identifying whether functions are even or odd

• Writing piecewise functions

• Sketching transformations

Various Functions Practice Test

Various Functions Practice Test Answer Key

Polynomial Functions (Unit 2)

• Factoring complex polynomial functions using various techniques

• Using polynomial functions to solve word problems

• Graphing transformations of polynomial functions

• Creating polynomial functions given constraints

Polynomial Functions Practice Test

Polynomial Functions Practice Test Answer Key

Rational Functions (Unit 3)

• Application of rational functions using word problems

• Applying transformations to rational functions

• Finding rational functions given graphs

• Solving inequalities using breakpoints

• Designing rational functions with certain characteristics

• Graphing rational functions using asymptotes and intercepts

Rational functions practice test

Logarithmic and Exponential Functions (Unit 4)

• Modeling with logarithmic transformations (semi-log and log-log)

• Exponential and logarithmic growth and decay

• Interest (compound and continuous)

• Solving equations (solve exponential and logarithmic equations)

• Logarithmic properties (apply logarithmic properties to write equivalent expressions involving logarithms, prove properties of logarithms)

• Logarithmic functions (graph a logarithmic function using transformations: end behavior and transformations of the points (1,0) and (b,1) need to be accurately graphed)

• Exponential functions (find an equation for an exponential function from a table, graph an exponential function using transformations: end behavior and transformations of the points (0,1) and (1,b)

• Inverses of functions (find inverse of a function including restricting of domain, know the relationship between domain and range of inverse functions)

Logarithmic and Exponential functions practice test

Sequences and Sums (Unit 5)

• Determining whether sequences are arithmetic or geometric, and show using ratios or differences.

• Using arithmetic and geometric sequences to find terms, and solve for variables (ex. Insert 5 arithmetic means between 6 and 30 )

• Defining arithmetic and geometric sequence formulas

• Express sums using sigma notation, write out sums, and evaluate sum

• Apply knowledge of sequences and sums to real problems

• Use the principle of mathematical induction to prove mathematic rules

Sequences and sums practice test

Sequences and sums applied worksheet (word problems)

Probability and Combinations (Unit 6)

This section includes basic probability and more complicated probability ideas

• nCr and nPr word problems

• Card probability (ex. if you choose 3 cards from a stack, what’s the probability that it contains exactly 1 pair?)

• Circle combinations (ex. how many ways can you sit 4 girls around a circle?)

• Survey probabilities (30 people like vanilla, 20 like chocolate, 10 like Napoleon, 5 like all three, how many only like vanilla?)

• Choosing ball problems (ex. you have 3 red balls, 2 green balls, and 4 blue balls, if you don’t replace the balls, what’s the probability of choosing no green balls)

  Probability and combinations practice test

  Probability and combinations explanations (each concept explained in depth with examples)

Trigonometric functions (unit 7)

• Graph trigonometric functions using transformations

• Write equations for trigonometric functions given their graphs

• Find exact values of trigonometric functions using the unit circle and trigonometric properties.

• Apply trigonometric properties to solve problems.

• Apply angular and linear velocity to application problems

• Prove trigonometric identities

Trigonometric functions practice test (unit 7)

Trigonometric functions practice test answer key (unit 7)

Analytic Trigonometry (Unit 8)

• Proving trig identities.

• Finding exact values of inverse and regular trig functions.

• Find the domain and range of transformed inverse trig functions.

• Solving trigonometric equations and inequalities

• Application of analytic trigonometry concepts

  Analytic Trigonometry practice test (unit 8)

  Analytic Trigonometry practice test answer key (unit 8)
  
  

Applications of Trigonometry (Unit 9)

• Solving for angles and side lengths of triangles

• Applying trigonometry to complex word problems

• Finding areas of regions using trigonometry

• Deriving and proving formulas using trigonometry

Applications of Trigonometry practice test (Unit 9)

Applications of Trigonometry practice test answer key (Unit 9)

Polar Coordinates Part 1

• Converting between rectangular and polar coordinates

• Graphing polar coordinates and polar equations

• Finding symmetry for polar curves

• Finding points of intersection of polar curves and finding “phantom” solutions

• Converting from polar, exponential, and standard forms of complex numbers

• Using DeMoivre’s theorem

• Finding solutions to complex number equations using polar equations

Polar Coordinates Part 1 practice test

Polar Coordinates Part 1 practice test answer key

Polar Coordinates Part 2

• Magnitudes of vectors

• Determining if vectors are parallel, orthogonal or neither

• Determining equation types from parametric equations

• Solving word problems using parametric equations

Polar Coordinates Part 2 practice test

Polar Coordinates Part 2 practice test answer key

Final Exam Review

• A collection of 5 problems from each unit this year

Final Exam Review

Final Exam Review Answer Key