Instructional Unit Conic Sections Pre Calculus #312 Unit Content Objective Performance Performance Task State Standards

Transcription

1 Instructional Unit Conic Sections Conic Sections The student will be -Define conic sections -Homework E -Ellipses able to create conic as conic slices and -Classwork -Hyperbolas sections based on by their components -Quiz -Parabolas their definitions. -Create an ellipse with -Calculator -Graphing physical operations -Conversion to standard form manipulatives -Create a parabola by Conic Sections The student will be -Graph all three conic -Homework E, -Ellipses able to graph conic sections with their -Classwork H -Hyperbolas sections. components given -Quiz -Parabolas standard or -Calculator -Graphing non-standard form operations -Conversion to standard form -Graph Monday, August 11, 2003 Page 1 of 12

2 Instructional Unit Discrete Mathematics Discrete Mathematics The student will be -Work recursively on -Homework F, -Arithmetic and Geometric Sequences able to work with the home screen of -Classwork C, -Recursive and Explicit Definitions sequences in the calculator -Quiz Q -Golden Ratio recursive or explicit -Create sequences -Calculator -Finite and Infinite Series form. from explicit and operations -Permutations and Combinations recursive formulas -Binomial Theorem -Probability and vice versa -Problem-solve with sequences -Recognize convergent sequences -Investigate the golden ratio based on converging sequences Discrete Mathematics The student will be -Find the value of a -Homework F, -Arithmetic and Geometric Sequences able to work with series -Classwork D, -Recursive and Explicit Definitions finite and infinite -Write a series in -Quiz A, -Golden Ratio series. summation notation -Calculator D -Finite and Infinite Series and expanded form operations -Permutations and Combinations -Problem solve with -Binomial Theorem series -Probability Monday, August 11, 2003 Page 2 of 12

3 Instructional Unit Discrete Mathematics Discrete Mathematics The student will be -Determine if a -Homework F, -Arithmetic and Geometric Sequences able to apply the situation is a -Classwork A, -Recursive and Explicit Definitions principles of combination or -Quiz B, -Golden Ratio combinatorics and permutation -Calculator C, -Finite and Infinite Series probability. -Compute operations D, -Permutations and Combinations combinations and E -Binomial Theorem permutations -Probability -Calculate probabilities -Compare probability to odds -Use area model for probability -Recognize Monday, August 11, 2003 Page 3 of 12

4 Instructional Unit Exponential, Logistic, and Logarithmic Functions Exponential, Logistic, and Logarithmic The student will be -Graph exponentials of -Homework A, Functions able to graph and any base with -Classwork C, -Graphing exponentials solve exponential transformations -Quiz F, -Exponential modeling and regression functions. -Solve exponentials -Calculator B, -Population growth and decay graphically operations B, -Financial applications -Recreate exponential C, -Logarithmic modeling and regression growth and decay with D, -Logarithm operations manipulatives A, -Graphing log functions -Model population B, -Applications of the natural number e growth and decay D, E, N, Q, R, S, C Monday, August 11, 2003 Page 4 of 12

5 Instructional Unit Exponential, Logistic, and Logarithmic Functions Exponential, Logistic, and Logarithmic The student will be -Compare logistic to -Homework A, Functions able to use and exponential growth -Classwork C, -Graphing exponentials graph logistic -Create a logistic -Quiz F, -Exponential modeling and regression regression on the -Calculator B, -Population growth and decay calculator operations D, -Financial applications -Use logistic model to B, -Logarithmic modeling and regression predict future values C, -Logarithm operations D, -Graphing log functions -Applications of the natural number e A, B, D, E, Q, R, S Exponential, Logistic, and Logarithmic The student will be -Apply logarithmic -Homework A, Functions to able to graph and properties -Classwork F, -Graphing exponentials solve logarithmic -Solve logarithmic -Quiz B, -Exponential modeling and regression functions. equations -Calculator D, -Population growth and decay -Eliminate extraneous operations E, -Financial applications solutions N, -Logarithmic modeling and regression -Solve exponential S -Logarithm operations -Graphing log functions -Applications of the natural number e equations algebraically -Convert exponential to logarithmic and vice versa -Graph logarithmic functions Monday, August 11, 2003 Page 5 of 12

6 Instructional Unit Exponential, Logistic, and Logarithmic Functions Exponential, Logistic, and Logarithmic The student will be -Derive the formula -Homework A, Functions able to derive, for compound interest -Classwork A, -Graphing exponentials solve, and apply -Quiz F, -Exponential modeling and regression financial formulas. -Solve compound and -Calculator A, -Population growth and decay continuous interest operations B, -Financial applications equations for any N -Logarithmic modeling and regression variable -Logarithm operations -Use TMV solver for -Graphing log functions -Applications of the natural number e annuities -Compare returns on various investments Exponential, Logistic, and Logarithmic The student will be -Graph y=x, y=x^2, -Homework F, Functions able to graph the ten y=x^3, y=1/x, -Classwork B, -Graphing exponentials basic functions in y=sqrt(x), y=e^x, -Quiz E, -Exponential modeling and regression their simple and y=ln(x), y=sin(x), -Calculator S, -Population growth and decay complex forms. y=cos(x), y=abs(x) operations T -Financial applications -Graph -Logarithmic modeling and regression transformations a,b,c, -Logarithm operations and d in -Graphing log functions y=a*f(b(x+c))+d -Applications of the natural number e Monday, August 11, 2003 Page 6 of 12

7 Instructional Unit Functions Functions The student will be -Graph data by hand -Homework C, -Determine domain and range able to model data and with the graphing -Classwork F, -End behavior with an appropriate calculator -Quiz A, -Symmetry function. -Choose an -Calculator Q, -Continuity appropriate function to operations R, -Boundedness model the data H, -Ten Basic Graphs -Perform a regression D, -Transformations intuitively and with B -Composition calculator -Inverses -Modeling data -Make predictions based on the regression equation -Determine accuracy of prediction Functions The student will be -Determine domain -Homework B, -Determine domain and range able to describe a and range given a -Classwork E, -End behavior function using the graph, equation or -Quiz O, -Symmetry appropriate table -Calculator P, -Continuity mathematical -Find local and operations F, -Boundedness terminology. absolute extrema J -Ten Basic Graphs -Identify increasing or -Transformations decreasing intervals -Composition -Prove symmetry -Inverses -Modeling data algebraically -Recognize removable, jump, and infinite discontinuity -Find the inverse of one-to-one functions Monday, August 11, 2003 Page 7 of 12

8 Instructional Unit Limits Limits The students will be -Understand the -Homework F, -Identify limits from a graph able to evaluate the definition of a limit -Classwork S -Sided limits limits of functions. -Evaluate both -Quiz -Determine limit from equation one-sided and -Calculator two-sided limits operations -Evaluate limits given a graph or equation Limits The students will be -Define both in words Q, -Identify limits from a graph able to find and and symbolically a A -Sided limits verify end behavior horizontal asymptote -Determine limit from equation models for various -Apply properties of functions, calculate the limit as x limits as x approaches both approaches both positive and negative positive and infinity negative infinity, and identify vertical -Define a vertical asymptote using the concept of a limit -Determine both a right and left end behavior model of a Monday, August 11, 2003 Page 8 of 12

9 Instructional Unit Matrices Matrices The student will be -Add, subtract, and -Homework F, -Solving systems of equations able to perform multiply matrices -Classwork G, -Matrix multiplication applications operations and -Solve systems of -Quiz I -Determinants applications with equations with inverse -Calculator -Reduced row eschelon form matrices. matrices and reduced operations -Inverse matrices row eschelon form -Matrices on the calculator -Perform all matrix operations by hand and with calculator -Apply matrix multiplication to problem situations Monday, August 11, 2003 Page 9 of 12

10 Instructional Unit Polynomial and Rational Functions Polynomial, Rational, and Power The student will be -Find the zeros of a -Homework F, Functions able to graph and function by identifying -Classwork B, -Graphing polynomials solve polynomial possible rational zeros -Quiz A, -Solving polynomials with rational and equations and and then using -Calculator E, complex solutions inequalities. synthetic and long operations H, -Solving rational equations division to determine N, actual zeros S -Verify complex zeros of a function -Graph by hand using zeros, multiplicity, and end behavior -Recognize hidden zeros on the calculator -Test the regions on a number line to determine solution to inequality Monday, August 11, 2003 Page 10 of 12

11 Instructional Unit Polynomial and Rational Functions Polynomial, Rational, and Power The student will be -Find and cancel -Homework A, Functions able to graph and common denominators -Classwork F, -Graphing polynomials solve rational -Quiz A, -Solving polynomials with rational and equations. -Eliminate extraneous -Calculator B, complex solutions solutions operations C, -Solving rational equations -Find areas of A, discontinuity and B, identify them as E, removable or infinite Q, -Find end behavior R, asymptotes S -Test the regions on a number line to determine solution to inequality -Recognize magnification data as rational Monday, August 11, 2003 Page 11 of 12

12 Instructional Unit Vectors, Parametric and Polar Equations Vectors, Parametric and Polar Equations The student will be -Graph rosette curves -Homework F, -Vector operations able to graph polar -Classwork T -Vector applications equations. -Quiz -Graphing parametrics -Calculator -Parametric applications operations -Graphing in polar coordinates Vectors, Parametric and Polar Equations The student will be -Add and subtract -Homework F, -Vector operations able to perform vectors -Classwork A, -Vector applications operations and -Scalar multiplication -Quiz B, -Graphing parametrics applications with -Dot product -Calculator D -Parametric applications vectors. -Apply vector operations -Graphing in polar coordinates applications to real-life solutions Vectors, Parametric and Polar Equations The student will be -Graph parametric -Homework F, -Vector operations able to graph and equations by hand and -Classwork A, -Vector applications apply parametric calculator -Quiz C, -Graphing parametrics equations. -Create parametric -Calculator B, -Parametric applications equations to model operations E, -Graphing in polar coordinates objects with linear, B, quadratic, and circular E. motion F, -Apply parametric I, equations to solve B motion problems Monday, August 11, 2003 Page 12 of 12