Benchmark Computation The student models, performs, and explains computation with complex numbers and polynomials in a variety of situations.

Transcription

1 Standard Number and Computation The student uses numerical and computational concepts and procedures in a variety of situations. Indicator/Objective Critical Vocabulary Knowledge Indicators The student will MA565X.NC.C.1 classify and perform operations with polynomials. MA565X.NC.C. evaluate radical expressions. MA565X.NC.C.3 simplify radical expressions by using the Properties of Radicals. MA565X.NC.C.4 add, subtract, multiply, and divide radical expressions. MA565X.NC.C.5 rewrite expressions, changing from exponential form to radical form. MA565X.NC.C.6 rationalize denominators. MA565X.NC.C.7 simplify rational expressions including complex fractions. MA565X.NC.C.8 perform operations with rational expressions. MA565X.NC.C.9 simplify and evaluate expressions involving exponents and logarithms. MA565X.NC.C.10 simplify expressions using matrix operations. MA565X.NC.C.11 write equivalent forms for exponential and logarithmic equations. Benchmark Computation The student models, performs, and explains computation with complex numbers and polynomials in a variety of situations. Essential Concepts/Skills Implementation Assessment Examples What Students Need to Know 1. Definition of square root and cube root.. How to evaluate an expression. 3. Know basic math skills. 4. Be familiar with a graphing calculator. 5. Have an understanding of exponents. 6. Be able to perform conversions with decimals and percents. 7. Be proficient at isolating variables. What Students Need to Do/Apply 1. Classify polynomials by degrees and number of terms and evaluates polynomials for specified values, and performs indicated operations. Evaluate radical expressions.. Convert from exponential form to logarithmic form and vice-versa using the properties of exponents and logarithms. Strategies Use cooperative learning techniques. Use Cognitive Tutor for exponents. Scope and Sequence Algebra students will perform and explain computational procedures using the set of complex numbers. They will simplify radical expressions, products and quotients of complex numbers, sums and products of complex numbers, and expressions involving exponents and logarithms. They will use the change-of-base formula to evaluate a logarithmic expression. Algebra 3/Trigonometry is typically a class for seniors. Pacing Considerations Radical expressions days Classify and perform operations with polynomials 1 week Simplify radical expressions days Rationalize denominators days Matrices days Exponential and logarithmic equations weeks 1. Write the following polynomial in standard form, identify the degree of the polynomial, and classify the polynomial by name based on the degree. f(x) = 5x 3 + 3x x 3 Evaluate f(-4) for the polynomial function: f(x) = x 3 +4x - 5x 1 Simplify and write your answer in standard form. (3x 7 8x x 7 ) + (x - 9x x 4 ) (18x x ) (4x + 3x 3 9x 5 ) ( )( 8 ) 3. (4( 3 90 ) ) ( ) 3 81x y xy (6 + 5 ) (3 0 ) 1

2 MA565X.NC.C.1 use the definitions of exponents and logarithms to simplify expressions (including common and natural logarithms). MA565X.NC.C.13 use the change-ofbase formula to evaluate a logarithmic expression. MA565X.NC.C.14 write a logarithmic expression as a single logarithm. MA565X.NC.C.15 evaluate natural exponential and logarithmic functions using a calculator. Vocabulary Students Know and Use linear quadratic cubic quartic degree monomial binomial trinomial polynomial coefficient term standard form evaluate square root cube root rational exponent radicand index Properties of Radicals exponential form radical form rationalize denominator least common denominator Algebra III/Trigonometry Curriculum ( ) 5. Rewrite the expression (9x y 6 ) 1/4 in radical form. 6. Simplify Simplify the expression. x + 4x x + 4 x + 3 x 9 x 3 x 8. 3x 10 + x + 4x 1 x Evaluate log Let A = 6 7 and B = 1 3 6, A + B 11. Write 6 4 = 196 in equivalent logarithmic form. 13. Evaluate the logarithm using the change-of-base formula: log Write the following as one logarithmic expression: log 3 x + log log 3.

3 logarithmic functions common logarithms natural logarithms logarithm properties row by column scalar determinant matrix inverse Algebra III/Trigonometry Curriculum 15. Evaluate the following using a calculator. Round your answer to the nearest hundredth. e 3.4 = 3

4 Standard Algebra The student uses algebraic concepts and procedures in a variety of situations. Benchmark Patterns The student recognizes, describes, extends, and explains the general rule of a pattern in a variety of situations. Indicator/Objective Critical Vocabulary Knowledge Indicators The student will MA565X.A.P.1 find the formula (either explicit or recursive) and indicated term of an arithmetic and geometric sequence. MA565X.A.P. evaluates given arithmetic and geometric series. MA565X.A.P.3 use Pascal s Triangle and/or combinations to find an indicated term of a binomial expansion. MA565X.A.P.4 use the binomial theorem to expand (x + y) n. Essential Concepts/Skills Implementation Assessment Examples What Students Need to Know 1. Pascal s Triangle.. Recognize arithmetic and geometric sequences. What Students Need to Do/Apply 1. Use given terms of a sequence to write a recursive or explicit formula and then use the formula to find a specified term. Strategies Use cooperative learning strategies. Scope and Sequence Geometry students identified, stated, and continued patterns using geometric figures as well as algebraic patterns including consecutive number patterns. Algebra 3/Trigonometry is typically a class for seniors. Pacing Considerations Series and sequence 3 weeks Binomial expansion theorem 3 days 1. Find the explicit formula for the arithmetic sequences 4, 7, 10, What is the value of the 9 th term?. Use the formula to evaluate the following arithmetic series Find the 5 th term of (x + y) Use the binomial theorem to expand (x + 3) Find the 18 th term of (x + y) 13. MA565X.A.P.5 use the binomial theorem to find an indicated term of (x + y) n. Vocabulary Students Know and Use sequence geometric sequence arithmetic sequence explicit formula recursive formula Pascal s Triangle combinations binomial theorem 4

5 Standard Algebra The student uses algebraic concepts and procedures in a variety of situations. Indicator/Objective Critical Vocabulary Knowledge Indicators The student will MA565X.A.V.1 solve quadratic equations by completing the square, quadratic formula, factoring, and taking the square root. MA565X.A.V. use the discriminant to classify the roots of a quadratic equation. MA565X.A.V.3 solve rational equations using algebra, tables, or graphs. MA565X.A.V.4 solve radical equations. MA565X.A.V.5 solve logarithmic and exponential equations using algebra and graphing. MA565X.A.V.6 solve systems of equations using matrices. Vocabulary Students Know and Use extraneous solutions discriminant imaginary numbers complex roots conjugate domain inverse functions matrix equations Algebra III/Trigonometry Curriculum Benchmark Variable, Equations, and Inequalities The student uses variables, symbols, complex numbers, and algebraic expressions to solve equations and inequalities in a variety of situations. Essential Concepts/Skills Implementation Assessment Examples What Students Need to Know 1. Solve linear equations.. Recognize quadratic equations. 3. Find common denominators. 4. Factor polynomials. 5. How to manipulate radical expressions. 6. Find the inverse of a matrix. What Students Need to Do/Apply 1. Use the definitions of exponential and logarithmic functions to solve equations. Strategies Use the graphing calculator to check results. Scope and Sequence Algebra students will solve linear equations and inequalities, systems of linear and quadratic equations, exponential and logarithmic equations, radical equations, and equations and inequalities with absolute value quantities containing one variable. They will use matrices to solve systems of equations. Algebra 3/Trigonometry is typically a class for seniors. Pacing Considerations Quadratic equations weeks Classify the roots of a quadratic equation 1 week Rational equations using algebra, tables or graphs 1 week Radical equations 1 week Logarithmic and exponential equations 3 days Systems of equations using matrices days 1. Solve by factoring. x 18x + 81 = 0 Solve by completing the square.. x 4x 17 = 0 Solve by using the quadratic formula. x + 9x + 14 = 0. Find the discriminant and determine the number of real solutions. Solve the equation over complex numbers. 3x 5x + 4 = 0 x + 8x 19 = 0 4x 1x + 9 = 0 3. Solve the rational equation. Check your solution. x = 14 x x+ x + x 4. Solve Algebraically. Check by graphing. x + 5 = x 1 4 x + 6 = 3 x 7 x - 1 = x Solve for x: log 5 (5x 6) = log 5 x. 6.Use matrices to solve the following system of equations. 9x y = 3 x 3y = 5 5

6 Standard Algebra The student uses algebraic concepts and procedures in a variety of situations. Benchmark Functions The student analyzes functions in a variety of situations. Indicator/Objective Critical Vocabulary Knowledge Indicators The student will MA565X.A.F.1 identify and evaluate rational functions. MA565X.A.F. find the inverse of a quadratic function. MA565X.A.F.3 find the domain of a radical function both from a graph and algebraically. MA565X.A.F.4 graph and interpret exponential and logarithmic functions. MA565X.A.F.5 find all solutions of polynomial functions. MA565X.A.F.6 write and evaluate exponential expressions to model growth and decay situations. Vocabulary Students Know and Use undefined quadratic function inverse index domain factors roots synthetic division long division remainder theorem factor theorem multiplicity complex zeros Essential Concepts/Skills Implementation Assessment Examples What Students Need to Know 1. How to solve and graph equations.. How to use a graphing calculator. What Students Need to Do/Apply 1. Interchange the x and y.. Solve an equation for y. 3. Graph both the original equation and the inverse. 4. Graph and interpret exponential and logarithmic functions. 5. Graph and interpret exponential and logarithmic functions with transformations. 6. Apply the factor theorem to polynomial functions to determine solutions and factors. 7. Divide polynomial functions using long and synthetic division. 8. Apply the remainder theorem to prove or disprove a solution to polynomial functions and find the values of the polynomial functions at a given location. 9. Write a polynomial in standard form given the zeros and multiplicity. Strategies Graphing calculator. Scope and Sequence Algebra students will continue to evaluate and analyze functions. They will simplify composite functions, graph and interpret exponential and logarithmic functions, and find the inverse of functions. Algebra 3/Trigonometry is typically a class for seniors. Pacing Considerations Evaluate rational functions 1- days Inverse of a quadratic function 1 day Domain 1 day Interpret exponential and logarithmic functions 1 week Solutions of polynomial functions weeks 1. Determine if the following is a rational function. If it is, find the domain. If it is not, explain why. f(x) = f(x) = x + 3x+ 1 x 9 x+ 1 x + 1. Find the inverse of the following. Then graph both the original equation and the inverse. y = x + x - 8 y = x - x y = x - 8x Find the domain for the following: f(x) = 3x 1 f(x) = f(x) = x 9 4x 9 4. Graph f(x) = 5log x. For what domain values is the function producing positive values? 6

7 Graph f(x) 3 x + 8. If x represents time and f(x) represents an increase in population. Explain the meaning of the y intercept. 5. Write the factors and roots of f(x) = x 3 + x 5x 50 (x + 1) is a factor of f(x) = 3x 3 + x 3x 1. Find all factors and roots of the polynomial by using synthetic or long division. Solve for all roots of the polynomial. f(x) = x 4 x 3 5x x 6 Write a polynomial function, P, in factored form and in standard form by using the given information. P is of degree 4; P(0) = 1; zeros: 1 (multiplicity ), (multiplicity 6. A high school has 1,350 students in In 000 the same high school has 1,000 students. Based on this information, what is the equation needed to predict future growth or decay in this schools population? The value of a new home in 1984 is $65,000. In 003, the same home is appraised at $143,000. What is the equation needed to predict the value of the home in 010? Radon is a radioactive gas with a half-life of about 3.8 days. This means that only half of the original amount of radon gas will be present after about 3.8 days. Using the 7

8 exponential decay function A = Pe -kt, find the value of k to the nearest hundredth and write the function for the amount of radon remaining after t days. 8

9 Standard Geometry The student uses geometric concepts and procedures in a variety of situations. Indicator/Objective Critical Vocabulary Knowledge Indicators The student will MA565X.G.GFP.1 use the Pythagorean Theorem to solve for a missing side of a right triangle. MA565X.G.GFP. calculate the sin, cos, tan, sec, csc, cot for an angle. MA565X.G.GFP.3 use inverse trig functions to calculate angle measurements. MA565X.G.GFP.4 use trig ratios to solve right triangle application problems using angles of elevation and depression. MA565X.G.GFP.5 use Law of Sines and law of cosines to solve non-right triangles. MA565X.G.GFP.6 use the area formulas ½ absinc and Heron s to find the area of non-right triangles. Algebra III/Trigonometry Curriculum Benchmark Geometric Figures and Their Properties The student recognizes geometric figures and compares and justifies their properties of geometric figures in a variety of situations. Essential Concepts/Skills Implementation Assessment Examples What Students Need to Know 1. How to solve linear equations and proportions.. Know how to find the area of a triangle. 3. Angle measurement in degrees. 4. Plotting points on a coordinate plane. What Students Need to Do/Apply 1. Apply the Pythagorean Theorem.. Find the trigonometric ratios for a given right triangle. 3. Recognize what pattern of given information is provided and whether or use Law of Sines or cosines to solve. 4. Use trig ratios to evaluate any size angle, positive or negative. 5. Use a wooden double cone to show all conic sections. 6. Use the graphing calculator to graph circle, ellipses, parabolas, and hyperbolas. Scope and Sequence Algebra students will continue to use the Pythagorean theorem to find the missing measure in a right triangle. They will evaluate trigonometric functions and use inverse trigonometric functions to calculate angle measures. They will use Law of Sinus and Cosines to solve non-right triangles. They will convert from degree measure to radian measure and classify conic sections by model equations and graphs. Algebra 3/Trigonometry is typically a class for seniors. Pacing Considerations Right triangle trig 1 week Law of Sines etc. 3 weeks Rotational trig weeks Radian measure 1 week Classifying conic sections 1 day 1,. Given right triangle ABC where a = 6, b = 10, and angle B = 90º, find: side c sin A sec C m C 5 3. Given tanθ =, find different 4 angle measurements for θ between 0º and 360º. 4. A recovery vehicle 300 yards from the landing target sites the hot air balloon hovering over the landing target at an angle of elevation of 4º. How high above the target is the balloon? Truck 300 yds. Target MA565X.G.GFP.7 use Law of Sines to solve S.S.A. ambiguous triangle. MA565X.G.GFP.8 construct a unit circle in degrees with a radius of 1 and multiples of 30 degrees and 45 degrees labeled. MA565X.G.GFP.9 use degree triangle ratios and degree triangle ratios to find (cos x, sin x) for each angle. Strategies SOHCAHTOA acronym for remembering. sinθ = opposite leg/hypotenuse. cosθ = adjacent leg/hypotenuse. tanθ = opposite leg/adjacent leg. Show the bow tie. Sketch 4 congruent triangles on the unit circle all having the same size reference angle. Show the 5. An airplane flies from Ft. Myers to Sarasota, a distance of 150 miles, and then turns through an angle of 50º and flies to Orlando, a distance of 100 miles. How far is it by direct route from Ft. Myers to Orlando? (Give answer to the nearest hundredth of a mile.) Ft. Myers 150 miles Sarasota 50 Orlando 100 miles 9

10 MA565X.G.GFP.10 compute the trig ratios for any angle using the calculator. Give exact answers for special angles. MA565X.G.GFP.11 given one trig ratio and the quadrant the angle is located in, find the other trig ratios for that angle. MA565X.G.GFP.1 calculate trig ratios using radian measure and apply this skill to real-world applications. MA565X.G.GFP.13 classify a conic section by model, equation and graph. MA565X.G.GFP.14 convert between degree and radian angle measure. Vocabulary Students Know and Use adjacent leg opposite leg hypotenuse sine cosine tangent secant cosecant cotangent inverse function angle of elevation angle of depression non-right triangle patterns for given information: A.S.A., A.A.S., S.S.S., S.A.S. and special case S.S.A. Law of Sines Law of Cosines area formulas rotational angles in standard position quadrants initial side of angle Algebra III/Trigonometry Curriculum (cos θ, sin θ ) of all 4 angles have the same absolute value. Use wax paper to show circle, ellipse, parabola, and hyperbolas. 6. Find the area of triangle ABC to the nearest hundredth, if angle A = 30º, angle B = 110º and side b = 8 cm. 7. Given obtuse triangle ABC with angle A = 60º, side a = 9 in. and side b = 10 in., find the measurement of angle B. Round your answer to the tenths place. Use the unit circle to find an exact value for: 9. sin -10º 10. cos 600º Given cosθ = and 5 90 o <θ <180 o find an exact value for the csc θ. 1. Find the 8 cos 3 π. 13. Classify the conic represented by each equation and use a graphing calculator to graph.. x ( y + ) + = x y + = ( x ) y =

11 terminal side of angle definitions of the six trig functions on coordinate plane, x, y, and r positive and negative angles reference angles coterminal angles radian measure angular velocity linear velocity conic parabola ellipse hyperbola circle point line standard form general form Algebra III/Trigonometry Curriculum x y = x y x y = 0 x y x y = 0 x y x y + + = A central angle intercepts an arc 16 cm in length. Find the measure of the angle in radians, if the circle has a 13 cm radius. 14. Find the radian measure of a 00 angle. 11

12 Standard Geometry The student uses geometric concepts and procedures in a variety of situations. Indicator/Objective Critical Vocabulary Knowledge Indicators The student will MA565X.G.AP.1 graph a rational function, write equations for its asymptotes, and identify any holes in the graph. MA565X.G.AP. graph and interpret polynomial functions. MA565X.G.AP.3 graph a circle, given the equation in standard form. MA565X.G.AP.4 write an equation for a circle given sufficient information. MA565X.G.AP.5 write and graph the standard and general equation of a parabola. MA565X.G.AP.6 graph an ellipse given an equation in standard form. MA565X.G.AP.7 write the equation of an ellipse in standard form given sufficient information. MA565X.G.AP.8 graph a hyperbola given the equation in standard form. MA565X.G.AP.9 write the equation of a hyperbola given sufficient information. MA565X.G.AP.10 find the real roots/zeros of a quadratic function by locating the x-intercepts of a graph and using a table of values. Algebra III/Trigonometry Curriculum Benchmark Geometry from an Algebraic Perspective The student uses an algebraic perspective to analyze the geometry of two- and three-dimensional figures in a variety of situations. Essential Concepts/Skills Implementation Assessment Examples What Students Need to Know 1. Factoring of polynomials.. Constructing a table of values, with or without a graphing calculator. 3. Identifying the degree of a polynomial. 4. Multiply binomials using FOIL. 5. Graph a function using a graphing calculator. What Students Need to Do/Apply 1. Factor numerator and denominator of function if possible.. Find the domain. 3. Look for holes. 4. Define vertical asymptotes. 5. Identify horizontal asymptotes, using degree of numerator and denominator. 6. Graph the function using a table of values after sketching asymptotes. 7. Sketch any holes in the graph. 8. Write a rational function given asymptotes and holes. 9. Locate local and absolute maximums and minimums of polynomial functions. 10. Locate the intercepts of polynomial functions. 11. Describe the end behaviors of polynomial functions. 1. Identify and describe increasing and decreasing intervals of polynomial functions. 13. Graph a circle, given the equation in standard form, centered at the origin Scope and Sequence Algebra students continue to recognize and examine two- and threedimensional figures and their attributes including graphs of functions on a coordinate plane. They will also graph rational functions, write equations for the asymptotes, and identify holes in the graph. They will graph and interpret polynomial functions as well as find the complex roots/zeros of a quadratic function. They will be expected to recognize and graph circles, ellipses, parabolas, and hyperbolas. Algebra 3/Trigonometry is typically a class for seniors. Pacing Considerations Rational function 3 days Polynomial functions days Circle in standard form 1 day Equation for a circle 1 day Standard and general equation of a parabola days Graph an ellipse in standard form 1 day Ellipse given sufficient information 1 day Graph a hyperbola 1 day Hyperbola given sufficient information 1 day Real roots/zeros of a quadratic function 1 day Find the domain of the rational function. Identify all asymptotes and holes in the graph, and then sketch the graph using a table of values. 3x + x 8 1. f(x) = x 3x 10. Write a rational function with the given asymptotes and holes, has a vertical asymptote at x = 3, no horizontal asymptote, and a hole at x = 3. Without graphing, identify the end behaviors of the polynomial function: f(x) = -4x 5x 3 + x + 3x Graph the polynomial on the calculator and identify the maximums, minimums, increasing and decreasing intervals. f(x) = x 3 + 4x 7x 4 3. Graph the following equation for a circle. ( x 1) + ( y+ 3) = 5 4. Find the equation of a circle in standard form. Radius is 15 and the center is (5, -6). 1

13 Vocabulary Students Know and Use numerator denominator domain asymptote hole degree local maximum local minimum absolute maximum absolute minimum roots end behaviors turning points increasing and decreasing intervals intercepts infinity: interval notation algebraic notation vertex maximum minimum axis of symmetry x-intercept(s) y-intercept real roots/zeros Algebra III/Trigonometry Curriculum and in all four quadrants. 14. Graph the circle given the equation in general form (complete the square) finding the center and radius. 15. Using the graphing calculator graph the equation of a circle in standard form. 16. Determine whether the graph opens left, right, up, or down from the equation. 17. Write the standard form given focus, directrix, axis of symmetry, and vertex from a diagram. 18. Write the standard from given the vertex, focus, and directrix. 19. Graph the parabola given the equation in standard form labeling the focus, directrix and vertex. 0. Graph the parabola given the equation in general form (complete the square) labeling the focus, directrix, and vertex. 1. Graph an ellipse from an equation in standard form. Label the center, vertices, foci and co-vertices.. Graph an ellipse from an equation in general form (completing the square). Label the center, vertices, foci and co-vertices. 3. Using the graphing calculator graph an ellipse from standard form. 4. Locate the vertex (maximum or minimum) by using the following strategies: a. Finding Vertex: (-b/(a), f(-b/(a)). b. Vertex Form: y = a(x-h) + k. 5. Use the graphing calculator to locate the vertex and the intercepts. 5. For each of the following functions, find: vertex maximum/minimum axis of symmetry x- and y-intercepts real roots/zeros f(x) = (4-x)(6-x) g(x) = + 3x 5x h(x) = (x+3) Graph completely and label all parts. ( x ) ( y+ 5) + = x + 4y + 6x 8y+ 9 = 0 ( x 4) ( y+ ) + = Write an equation of an ellipse with the given information. Foci (, 8) and (10, 8). Vertices (-4, 8) and (14, 8). 8. Graph using a graphing calculator. Label all parts for the graphs of the following. ( y 4) ( x+ ) = ( x ) ( y+ 5) = x 6y 18 0 x y + = 13

14 6. Write the equation for the axis of symmetry using the equation y = - b/(a). 7. Given foci, vertices and/or covertices, write an equation in standard form. 8. Given the graph, write the equation in standard form. 9. Graph a hyperbola from an equation in standard form. Label the center, vertices, foci and co-vertices. 30. Graph a hyperbola from an equation in general form (completing the square). Label the center, vertices, foci and co-vertices. 31. Using the graphing calculator graph a hyperbola from standard form. 3. Find the real roots/zeros of a quadratic function by locating the x- intercepts of a graph and using a table of values. 9. Write an equation of a hyperbola with the given information. Vertices (, 8) and (10, 8). Foci (-4, 8) and (14, 8). 10. Find the real roots for the function h(x) = (x+3) + 1 Strategies Provide students with a graphic organizer. Demonstrate using push-pins for foci and string. 14

15 Standard Geometry The student uses algebraic concepts and procedures in a variety of situations. Benchmark Transformational Geometry The student recognizes and applies transformations on two- and three-dimensional figures in a variety of situations. Indicator/Objective Critical Vocabulary Knowledge Indicators The student will MA565X.G.TG.1 find the transformation of quadratic, cubic, radical, and absolute functions both from a graph and algebraically. MA565X.G.TG. graph sinusoidal equations by hand and with the graphing calculator. Vocabulary Students Know and Use index square root cube root domain horizontal and vertical translations reflection period amplitude vertical shift Essential Concepts/Skills Implementation Assessment Examples What Students Need to Know 1. How to graph.. Parent function of a graph. What Students Need to Do/Apply 1. Graph the functions: y=sin x and y=cos x.. Graph, by hand, one cycle of various sin and cos equations with b values of 1/, 1, and and a variety of different amplitudes and vertical shifts. 3. Use the graphing calculator to compare and contrast graphs with different amplitudes but the same period, or different vertical shifts but like amplitude and period (transformations). Strategies Modeling parent functions y=sin x and y=cos x, with carousel, swing, pendulum or Ferris wheel problems. Do these supplemental handouts as a class or in small groups. Labeling the x-axis in 30 increments, works well when graphing by hand. Stress patterns and transformations on the basic parent function. Ensure that students can first graph well by hand before allowing them to use the graphing function of the Scope and Sequence Algebra students continue to apply their knowledge of transformational geometry to problem solving situations. They continue to study transformations when working with functions and conic sections. They will find the transformation of quadratic, cubic, radical, and absolute functions, both from a graph and algebraically. Algebra 3/Trigonometry is typically a class for seniors. Pacing Considerations One week Sinusoidal equations weeks 1. Describe the transformation applied to parent function. Then graph each transformed function. g(x) = 3 x 1 g(x) = x g(x) = x 5 + g(x) = 5 + ( x 3) 3 g(x) = (x + ) Identify the transformations to the graph of f(x) = sin x to form the graph of g(x) = 3 + sin x. Write a new equation, g(x), whose graph is similar to the graph of f(x) = 3 + sin x except it is translated units downward on the coordinate plane.. Graph one cycle of each of the following sinusoidal equations: y = 3 sin x y = cos x y = 1 + sin 1/x 15

16 calculator. Initially, allow time for students to practice graphing in class in small groups or on individual white boards. Show a sinusoidal graph on the overhead calculator screen and have student write the equation. They can use their own calculators to check the accuracy of the equation they write. 16

17 Standard Data The student uses concepts and procedures of data analysis in a variety of situations. Benchmark Statistics The student models and evaluates real-world problems involving polynomial functions. Indicator/Objective Critical Vocabulary Knowledge Indicators The student will MA565X.D.S.1 analyze information generated by a table of data using the following: a. graph. b. domain and range. c. regression equation. d. interpreting values. e. prediction. f. minimum and maximum. Vocabulary Students Know and Use graph domain range regression equation interpreting values prediction minimum maximum Essential Concepts/Skills Implementation Assessment Examples What Students Need to Know 1. Graphing calculator functions: list, window, calculate min, max, intersection; find algebraic regression models.. Draw picture and problem solve; reasonable solution. What Students Need to Do/Apply 1. Students will apply and interpret information from the real world. Strategies Use the graphing calculator to find regression equations. Scope and Sequence Algebra students will continue to use data analysis in real-world problems with rational number data sets to make accurate inferences and predictions, and to analyze decisions. They will use expressive equations for scatter plots to approximate lines of best fit. Algebra 3/Trigonometry is typically a class for seniors. Pacing Considerations days November Section The average amount, A, that an individual gave to charity in 1990 is modeled by A = 0.014x x x for 5 < x < 100, where x = income in 1,000 s. If $000 was given to charity, what was the income?. An open box is to be made from a 10 by 1 piece of cardboard by cutting x-in. sq. from each corner and folding up the sides. Write a function giving the volume of the box in terms of x. Sketch the graph of the function and use it to approximate the value of x that produces the greatest volume. 3. Yearly from the amounts of farm exports in billions of dollars were: 39.4, 43.1, 4.9, 46.3, 56.3, 60.5, 57.1, 5.0. Graph and find the best-fit algebraic model for this data (lowest possible degree that has a reasonable fit). 17