Guide PreCalculus: Sequences & Series (Quick Review Notes)

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  2. Series | Precalculus | Math | Khan Academy
  3. Precalculus Unit 09 – Sequences and Series

The sequence is arithmetic 9. Find the first term. Find the first three terms. Find a formula for the nth term. If there are 12 layers, how many telephone poles does the pile contain? If it is geometric express the nth term of the sequence in the standard form —3, 9, —27, 81, —; Find the fifth term. Use an infinite geometric series to approximate the total distance the ball travels, after being dropped from 3 m above the ground, until it comes to rest. The first row of the auditorium has 16 seats, the second row has 24 seats, the third row has 32 seats, and so on, increasing by 8 seats each row for a total of 50 rows.

Find the number of people that can be accommodated in the sixteenth row. Math , Algebra , Algebra 2. Arithmetic Sequences and Series - Bundle.


Students will practice identifying the first term and the common difference in the. Worksheets , Test Prep , Task Cards. Arithmetic Sequences and Series - Task Cards. Arithmetic Sequences and Series - Task Cards This set contains 26 task cards with arithmetic sequence and series problems. Worksheets , Task Cards. Arithmetic Sequences and Series - Word Problems. This set contains 16 task cards featuring arithmetic sequence and series related real-life word problems with multiple choice, accompanied by pictures.

The activity includes word problems with varying levels of difficulty that help students to practice how to solve real-life problems involving arit. Math , Algebra , Word Problems. This test comes in 3 different versions. Forms A and B are equal in difficulty. Form C assesses the same concepts as the other forms, but it is intended for students with IEP accommodations. Form C is roughly half the length with slightly easier questions. The following topics are assessed on all 3. Examinations - Quizzes , Assessment.

Arithmetic Sequence and Series. Skoolmaths - Interactive Maths Lessons. In this lesson, learners will be able to: Math , Math Test Prep , Algebra 2. Arithmetic Sequences and Series Lesson Plan. This is the complete lesson plan that goes along with my Arithmetic Series worksheet. This is meant to be the beginning of an arithmetic and geometric sequences and series unit. The lesson plan includes warmup and closure activities, along with ideas for direct instruction and how to present the n.

Lesson Plans Individual , Minilessons. The World of Algebra. This is an Algebra II lesson that covers writing rules and finding sums of arithmetic sequences and series. Review for Arithmetic Sequences and Series. A review packet for students being assessed on the basics of arithmetic sequences and series. Answer key is included. Algebra , Graphing , Algebra 2.

Review Stations for Arithmetic Sequences and Series. Solving Exponential and Logarithmic Equations. Application of Exponential and Logarithmic Functions. Sine and Cosine Values of Special Angles. Computations of Inverse Trigonometric Functions. Addition and Subtraction Formulas.

Word Problems and Applications of Trigonometry. Variables, Equations, and Algebra. Midpoint, Distance, the Pythagorean Theorem and Slope. Put the Rational and Irrational Numbers Together. Affects the Output of a Function or a Dependent Variable. A Coefficient is a Multiplicative Factor on a Variable. Example of Something More Complex. Find the Midpoint of Arbitrary Values a and b. Arbitrary Pair of Points Example. Distance Between Arbitrary a and b. Slope is the Rate of Change.

Positive Slope and Negative Slope. Intervals Show x-values; Write in Parentheses. Variation Direct and Inverse. Positive and Negative Coefficients on the Controlling Term. Roots Zeros of Polynomials. Factoring Quadratics, Check Your Work. Square Roots and Equations. Taking the Square Root to Find the Value of x. Getting the Positive and Negative Answers. Polynomials that are Easy to Solve. Making Complex Polynomials Easy to Solve. Steps to Completing the Square. Add to Both Sides to Complete the Square.

Solving Quadratics with Ease. Follow Format to Use Formula. What the Discriminant Tells Us: Using the Quadratic Formula. Looking at the Axis of Symmetry and Vertex for other Parabolas. Switching Forms by Completing the Square. Incredibly Minor Note on Grammar. The Intermediate Value Theorem. U between a and b.

Intermediate Value Theorem, Proof Sketch. But Graph is Defined as Continuous. Finding Roots with the Intermediate Value Theorem. Picking a and b to be of Different Signs. Using Roots and Division to Factor. How It Works to Divide Polynomials. Polynomial Long Division In Action. Which Method Should We Use. Advantages of Synthetic Method. Advantages of Long Division. Fundamental Theorem of Algebra. Definition of a Rational Function. Domain of a Rational Function. Investigating a Fundamental Function.

What Occurs at the Zeroes of the Denominator. Idea of a Vertical Asymptote. Definition of a Vertical Asymptote. Vertical Asymptotes and Graphs. Drawing Asymptotes by Using a Dashed Line. Not All Zeros Give Asymptotes. How to Find Vertical Asymptotes. Factor Numerator and Denominator. Draw Graph Find Points as Necessary. Logarithms as Inverse of Exponentiation. Example of Taking an Exponent or Logarithm of an Equation.

Applications of Exponential Functions. Natural Exponential Growth Model. Applications of Logarithmic Functions.

Series | Precalculus | Math | Khan Academy

What Logarithms are Useful For. Graphing Sine and Cosine Functions. All Students Take Calculus. All Angles and Quadrants. Amplitude and Period of a Sine Wave. Distance from Middle to Peak. Distance from Peak to Peak.

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Phase Shift and Vertical Shift. Find Sine Wave Given Attributes. Find Cosine Wave Given Attributes.

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  • Tangent and Cotangent Functions. Graph Tangent and Cotangent Functions. Tangent and Cotangent of Angles. Secant and Cosecant Functions. Values of Secant and Cosecant. Graph of Cosecant Function. Inverse Trigonometric Function Domains and Ranges. Arcsines of Common Values. Odd, Even, or Neither. Arccosines of Common Values. Arctangents of Common Values. Find Angle Given Cosine and Quadrant. Given Tan Find Sec. Given Sec Find Tan. Derive the Formula for cos A-B. Use Addition and Subtraction Formulas. Use cos A-B and Cofunction Identities. Convert to Radians and use Formulas. Prove Trigonometric Identity using Double Angle.

    Prove Trigonometric Identity using Half-Angle. Prove the Half-Angle Formula for Tangents. Trigonometry in Right Angles. Find All Angles in a Triangle. Find Lengths of All Sides of Triangle. Length of Third Side and Area of Triangle. Finding the Area of a Triangle.

    Area of Triangle with Three Sides. Area of Triangular Field. Roads to a Town.

    Systems of Linear Equations. Understand the Relationship Between Solutions and the Graph. Systems of Linear Inequalities. Refresher--Stick to Basic Operations.

    Precalculus Unit 09 – Sequences and Series

    Solutions are Best Found Through Graphing. Variables in Objective Function have Constraints. Critical Solution is at the Vertex of the Overlap. Dot Product - Geometric Interpretation. Cross Product - Geometric Interpretations. Not All Matrices Are Invertible. Minors and Cofactors - Cofactors. Determinant of Larger Matrices. Alternative Method for 3x3 Matrices. Finding the Inverse of Larger Matrices. General Inverse Method - Step 1. General Inverse Method - Step 2. General Inverse Method - Step 3. Interchange the Locations of Two Rows. Multiply or Divide a Row by a Nonzero Number.

    Sequences and Series

    Row Operations - Keep Notes! Gauss-Jordan Elimination - Idea. Gauss-Jordan Elimination - Idea, cont. Gauss-Jordan Elimination - Method. Gauss-Jordan Elimination - Method, cont.

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    Cramer's Rule - 2 x 2 Matrices. Cramer's Rule - n x n Matrices. Solving with Inverse Matrices. Solving Inverse Matrices, cont. The Mighty Graphing Calculator. Another Way to Name the Same Point: Polar Form of Complex Numbers. Convert Rectangular to Polar Form. Convert Polar to Rectangular Form. Multiply Two Complex Numbers. Convert Between Rectangular and Polar Forms. Simplify Expression to Polar Form. Towards an Arithmetic Series Formula. General Formula for Arithmetic Series. Formula for Infinite Geometric Series. Formal Definition of a Limit. The Adventure of the Delta-Epsilon Limit.

    The Adventure of the Delta-Epsilon, cont. Limit of a Function at Infinity. Evaluating Limits at Infinity. Does the Function Grow Without Bound? The Vertical Change Divided by the Horizontal. Idea of Instantaneous Slope. What is the Tangent Line for a Circle? Towards a Derivative - Average Slope. Towards a Derivative - Average Slope, cont. Towards a Derivative - General Form. Towards a Derivative - General Form, cont. Towards a Derivative - Limits! Towards a Derivative - Checking Our Slope. Definition of the Derivative.

    Notation for the Derivative. Area Under a Curve Integrals. Various Methods for Choosing Rectangles. Rectangle Method - Right-Most Point. Rectangle Method - Maximum Upper Sum. More Rectangles, Better Approximation.