PreCalculus and PreCalculus Honors Review and Test Prep Bundle

PreCalculus and PreCalculus Honors Review and Test Prep Bundle

GREAT RESOURCE for FINAL EXAM REVIEW for a Pre-Calculus Course.

Do your students need more hands-on activities in Pre-Calculus or Pre-Calculus Honors? This bundle has it all!

In this bundle I have included 19 resources for a Regular PreCalculus different stations of worksheets based on topics taught in PreCalculus and 11 resources for a PreCalculus Honors class that I created for my PreCalculus Students. Please read the descriptions below to see what you would be purchasing! 28 of the resources are worksheets and 2 of the resources is a Self Checking Google Sheet!

-----------------------------Non-Honors PreCalculus Resources----------------------------

1: Find the errors in students work & correct them in PreCalculus

-Piecewise functions

-Operations on Functions

-Transformations of Functions

-Even, Odd, or Neither Algebraically & Graphically

-Complete the Square to Identify the Vertex

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2: Domain Algebraically & Graphically Review in PreCalculus

-4 questions on solving for the domain of a rational function algebraically

-4 questions on identifying the domain of functions graphically

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3: Transformations of Functions

Students will be required to know the rules for transformations of functions, such as what constitutes as a vertical stretch, vertical compression, horizontal stretch, horizontal compression, reflection in the x-axis, reflection in the y-axis, vertical shift up or down, horizontal shift left or right, etc.

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4: Even, Odd, Neither of Functions Algebraically & Graphically (includes inverses and one to one functions)

-Scaffolded/graphic organizer at the top of the page on even, odd, neither of functions

-Algebraically and Graphically determine if a function is even, odd, or neither

-Determine if a function has an inverse

-Determine if a function is one-to-one

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5: Function Operations & Composition of Functions in PreCalculus

-Function Operations

-Compositions of Functions

-End Behavior of functions

-Rational functions, quadratic functions, linear functions

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6: Piecewise Functions in PreCalculus

-Evaluating Piecewise Functions

-Graphing Piecewise Functions WITHOUT A CALCULATOR

-Identify domain and range

-Intervals where the function is increasing, decreasing, or constant

-Identify where the function is continuous over an interval

-Write the absolute value function as a piecewise function

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7: Condensing, Expanding, Solving, etc. of Exponential & Logarithmic Functions in PreCalculus

Students will be able to condense and expand logarithmic functions. Solve exponential and logarithmic equations. Students will need to convert from log form to exponential form or from exponential form to log form. Students will need to recognize when to reject a solution when solving logarithmic equations.

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8: Graphing Exponential & Logarithmic Functions AND Applications in PreCalculus

Students will be able to graph exponential and log equations, identifying the asymptotes and solving for the x-intercept and y-intercept, if they exist.

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9: The Unit Circle: Evaluating Trigonometric Functions in PreCalculus

Students will evaluate trigonometry functions by using right triangle trigonometry with SOH CAH TOA. Students will need to identify the location of an angle and evaluate the trig function and decide if its value is negative or positive using the acronym All Students Take Calculus. Students will need to construct right triangles given a point, and identify trig ratios of the triangle.

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10: Graphing Trigonometric Functions in PreCalculus

Students will graph all 3 trig functions: sine, cosine, and tangent. The graphs will contain a vertical shift, phase shift, amplitude, and a frequency where students will need to factor out the frequency from the parenthesis to identify the appropriate phase shift.

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11: Solving for Roots using the Rational Root Theorem in PreCalculus

-6 questions on using the Rational Root Theorem to solve for roots of a polynomial function

-Students will need to use long division or synthetic division to test the possible rational roots on the polynomial equation.

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12: Solving for Roots using the Descartes Rule of Signs and the Rational Root Theorem in PreCalculus

-At the top of the page you will see a summary of what Descartes Rule of Signs is; example provided.

-Using Descartes’s Rule of Signs (List the possible number of positive and negative real zeros for the function)

-Using the Rational Root Theorem (List the possible rational roots)

-Find the roots

-Describe the nature of the roots (real vs imaginary, rational vs irrational)

-Write the factorization of the polynomial function

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13: Simplifying Rational Expressions: Multiplying/Dividing & Adding/Subtracting in PreCalculus

-Steps to evaluating and/or solving complex rational expressions or equations

1) Factor if possible

2) Identify LCD

3) Multiply numerator and denominator by LCD

4) Simplify completely

-5 questions total

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14: Simplifying Complex Fractions & Solving Rational Equations

- Steps to evaluating and/or solving complex rational expressions or equations

1) Factor if possible

2) Identify LCD & determine which values x cannot equal.

3) Multiply numerator and denominator by LCD

4) Check for extraneous solutions.

-6 questions total on simplifying complex fractions and solving rational equations which may contain extraneous solutions.

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15: Law of Sines and Law of Cosines

Use the Law of Sines or Law of Cosines to solve for a specific side of angle. 2 questions pertain to application problems with two triangle trigonometry and forces.

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16: The Ambiguous Case and the Area of a Triangle using Trigonometry

Students will need to use the formula for the area of a triangle to solve for the area. Students need to know what an equilateral and isosceles triangle are as well as their properties. Students will need to determine if 0, 1, or 2 distinct triangles can be created from a given set of information.

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17: Proving Trigonometric Identities using the Pythagorean Identities, Double Angle Identities, Reciprocal Identities, and Sum/Difference Identities

Students will prove trig identities true by working with the left hand side and right hand side separately.

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18: Solving First & Second Degree Trigonometric Equations using Trig Identities Review in Pre-Calculus

Students will solve trigonometric equations by substituting in for trig identities in order to solve the equation. Students will answer in terms of radians. Students will need to know the appropriate quadrant in which their solution lies. Students will need to understand when to reject an answer for sine and cosine since their values can only fall between -1 and 1 from the unit circle.

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19: Evaluating Trig Functions and Find the Remaining Trig Functions Given a Point for Pre-Calculus

In this resource you will find that the first google sheet contains 4 questions when given a point on the terminal side of the angle θ in standard form, students will need to find the exact values of the trigonometric functions of the given angle θ. In the second google sheet, there are 5 questions that pertain to given one trigonometric ratio and the quadrant that the triangle is in, students will need to find the exact values of the five remaining trigonometric functions of the angle θ.

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--------------------------------PreCalculus Honors Resources--------------------------------

20: Domain Algebraically & Graphically in Pre-Calculus Honors

12 questions total. 8 questions on Solving for the Domain of Rational Functions Algebraically. 4 questions on Identifying the Domain of Functions Graphically. Students will identify discontinuities in graphs, such as a removable discontinuity.

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21: Finding Errors and Correcting Them in Pre-Calculus Honors

-Graphing Piecewise Functions

-Simplifying the Difference Quotient

-Transformations of Functions

-Proving functions are inverses of each other using a composition of functions

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22: Function Operations, Composition of Functions, Simplifying the Difference Quotient, & Inverses of Functions in Pre-Calculus Honors

-Arithmetic Function Operations

-Compositions of Functions

-Simplifying the Difference Quotient

-Proving rational functions are inverses of each other using a composition of functions

-Evaluating function operations using graphs of functions

-State the domain and range of graphs of functions

-Identify from a graph if the function is one-to-one, explain!

-Graph the inverse of a given function and write its piecewise function

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23: Piecewise Functions in Pre-Calculus Honors

-Evaluating Piecewise Functions

-Graphing Piecewise Functions WITHOUT A CALCULATOR

-Identify domain and range

-Intervals where the function is increasing, decreasing, or constant

-Identify where the function is continuous over an interval

-Write the absolute value function as a piecewise function

-Graph the absolute value of a quadratic function and write its piecewise function

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24: Transformations of Functions in Pre-Calculus Honors

Students will be required to know the rules for transformations of functions, such as what constitutes as a vertical stretch, vertical compression, horizontal stretch, horizontal compression, reflection in the x-axis, reflection in the y-axis, vertical shift up or down, horizontal shift left or right, etc.

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25. Arithmetic Operations on Functions & Composition of Functions in Pre-Calculus Honors

-Google Sheets Activity. Self-Checking. Cells will turn GREEN if CORRECT.

-Arithmetic Function Operations

-Compositions of Functions

-Simplifying the Difference Quotient

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26. Graphing Higher Order Polynomials in Pre-Calculus Honors

Graphic organizer on page 1.

5 questions total with multiple parts.

Students will be able to perform the following skills:

1) Solve for the value of the leading coefficient given two roots and a point on the quadratic function, from there, students will then write the equation of the quadratic in vertex form by completing the square.

2) Students will algebraically determine the roots and y-intercept of the polynomial function without the use of a calculator.

3) Students will determine the following with a calculator: Extrema (relative/absolute max/min) & inflection points

4) Students will provide an accurate graph of the polynomial function by using their knowledge of end behavior based on the leading coefficient and whether the function has an even or odd degree.

5) Students will write the equation of the cubic polynomial in factored form given a graph.

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27. Intermediate Value Theorem in Pre-Calculus Honors

Graphic organizer on page 1.

5 questions total with multiple parts.

Students will be able to perform the following skills:

1) Use the three criteria of the intermediate value theorem to apply to given scenarios

• determine if the function (polynomial function or rational function) is continuous over the interval
• determine if IVT guarantees a root on the given interval and why.
• Show whether or not x=c exists on the interval for f(c)=#. Solve using algebraic means.

2) Given a graph, determine if the function is continuous on the given interval

3) Create a test question: Create a polynomial and a small interval of x-values and see if the intermediate value theorem applies.

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28. Optimization: Maximum Area & Maximum Volume in Pre-Calculus Honors

6 questions total with multiple parts.

Students will be able to perform the following skills:

1) 3 different scenarios to find the maximum area of a two-dimensional shape by using the axis of symmetry formula of a quadratic function

2) Find the dimensions and maximum area of a rectangle inscribed with its base on the x-axis and its upper corners on the parabola.

3) Find the dimensions and maximum volume for an open topped box. State an appropriate domain for the dimensions.

4) Given the length and width of the inscribed rectangle under the parabola, write the equation of the parabola in standard form. Students will need to solve for the leading coefficient by utilizing the vertex point and the dimensions of the rectangle.

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29. Simplifying Complex Fractions and Solving Rational Equations Review in Pre-Calculus Honors

Students will be required to utilize the following skills:

1) Identify the LCD in order to simplify the fraction and combine like terms

2) Simplify trinomial expressions where a≠1

3) Simplify expressions using the sum of cubes or difference of cubes formula

4) Solve rational equations by identifying the values in which the denominator cannot equal 0. Be sure to check for extraneous solutions.

-6 questions total on simplifying complex fractions and solving rational equations which may contain extraneous solutions.

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30. Multiply, Divide, Add, Subtract Rational Expressions Review in Pre-Calculus Honors

1) Students will be required to simplify rational expressions by means of multiplication, division, addition, and subtraction.

2) Students will need to be able to factor expressions which contain a difference of perfect squares.

3) Students will need to be able to factor trinomial expressions where a≠1

4) Students will be required to apply the formulas for the sum of cubes and difference of cubes when simplifying their rational expressions.

6 questions total.

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Each worksheet/station takes about 15-20 minutes.

NO PREP NEEDED! Answer key and DETAILED SOLUTIONS provided for all!

I use these stations at the end of each quarter as a cumulative review. Great for final exam review for a non-Honors Pre-Calculus or Honors Pre-Calculus course!

SUGGESTION:

Use pocket folders for each station.

Put the answer key in left-hand pocket.

Leave copies of the station activity in the right hand pocket. When students are working in their stations, they can check their work with the answer key. I do this in my classroom and it is extremely effective.

Please leave feedback!