Page 1 of 9 Close Window Print Page Layout Show Standards View Paragraph Format View Course Description MATH 3 (MASTER MAP) School: Binghamton High School Teacher: Master Map Email: Course #: 203 Grade Level: 10, 11 MONTH/YEAR ESSENTIAL QUESTIONS CONCEPTS/SKILLS/STANDARDS September What two subsets 1.1 Use a number line to graph 2006 of the real numbers and order real numbers. combine to form all of the real Identify properties of and use numbers? operations with real numbers. CONTENT Equations and Inequalities Linear Equations and Inequalities ASSESSMENT AREAS OF INTERACTION When converting units with unit analysis, how do you choose whether to use a particular conversion factor or its reciprocal? difference between an expression and an 1.2 Evaluate expressions (p.18 Activity 1.2). 1.3 Use tables to solve equations (p.25 Activity 1.3). 1.4 Review common formulas. Rearrange the literal equation in terms of specified variable(s). 1.5 Set up and use a problem solving plan. order of operations? Do you have to follow these to get the correct answer? What does it mean for algebraic expressions to be equivalent? What is a transformation of an How can rewriting an equation help you solve them? Employ different strategies. 1.6 Solve simple inequalities. Solve compound inequalities. 1.7 Solve absolute value equations and inequalities. Apply absolute value to real life. What process do you follow to 2.1 Identify a relation. display the solution set of an Sketch and evaluate a function. inequality? 2.2 Calculate slope. Relate slope to real life. 2.3 Sketch the graph of a linear equation in slope-intercept form. Sketch the graph of a linear equation in standard form. What is a formula? Technology- use a graphing Describe a real-life calculator. situation where you would need to be
Page 2 of 9 able to solve the area formula of a circle for r. relationship between a verbal model and an algebraic model? After you have set up and solved an algebraic model for a problem description, what remains to be done? difference between a linear equation and a linear inequality? What are the different signs used to represent an inequality? How does solving a linear equation differ from simplifying a linear question? How do the solutions in a compound inequality using "and" differ from those of a compound inequality using "or"? Which type of variable, independent or dependent, corresponds to values in a function's range? When is a relation a function? What does it mean for two lines to be perpendicular? How can you tell from a line's graph if it has positive, negative, or zero slope? name
Page 3 of 9 of the point on a line where its y- value is zero? October 2006 How can you tell from the graph of a line that it is the graph of a direct variation? 2.4 Write the equation of a line; *given the slope & intercept *given 2 points *given slope and a point *perpendicular/parallel line Systems of Linear Equations and Inequalities How do you determine that a set of data values exhibits direct variation? How do you find the constant of variation? How do you use the best fitting line to make a prediction? If the points of a scatter plot all lie on a horizontal line, what kind of relation does this show? If the phone company charges in 6 second blocks, what will the graph of the charges look like? How are the solution to a linear system and a solution to a linear equation related? How can you use a graph to determine how many solutions there are for a system of equations? What does it mean to "substitute" when solving a system of equations? Write an equation for a direct variation. Discover the concept for the "line of best fit" (p 99). 2.5 Use a scatter plot to identify the correlation shown by a set of data. Estimate the best-fitting line for a set of data. Use technology to calculate the linear regression (p107). 2.7 Sketch piecewise function. Use a piecewise function to model real-life quantities. Use technology to graph a piecewise function. 3.1 Use a graphing calculator to solve a system of equations 3.2 Combine equations in a linear system (p147 November 2006 When using the linear combination method for solving a linear system, why would you want to have the coefficients of one of the variables be opposites Give an example of 5.1 Sketch the graph of a a quadratic quadratic function. Quadratic Functions
Page 4 of 9 equation in vertex form. vertex of the graph of this What is a factor in relationship to an expression? What is standard form of a quadratic Show how a quadratic function is used in everyday life. 5.2 Identify the factors of a quadratic expression. Interpret the zeros of a quadratic function. 5.4 Compute using complex numbers. Quadratic Formula Quadratic Inequalities What must be true about a quadratic equation before you can solve it? zero product property? If a function is graphed, what do the x-intercepts represent? What are the three special factoring patterns you look for when factoring a quadratic? How can you find the maximum or minimum value of a quadratic function? For what purpose would you use the product or quotient properties of square roots when solving quadratic equations using square roots? Write a quadratic equation that you would solve by using square roots and show how to solve it. Why would you choose to solve this equation using square roots rather than factoring? How do you know if a radical expression is simplified? Why do you multiply both numerator and Define the value of the absolute value of a complex number. Use technology to find maximums and minimums. 5.6 Solve equations with the quadratic formula. Use the quadaratic formula in real life. 5.7 Graph and solve quadratic inequalities in 2 variables. Graph and solve quadratic inequalities in 1 variable. 5.8 Write quadratic Use technology to find quadratic models.
Page 5 of 9 denominator of the fraction by the complex conjugate of the denominator? How is the complex plane different from the coordinate plane? What steps do you follow when you add, subtract, multiply and divide complex numbers? How are the discriminant and the graph of a quadratic equation related? quadratic formula and what is it used for? How do use the discriminant to determine the number of solutions of a quadratic What is a quadratic inequality in one variable? procedure used to solve a quadratic inequality in two variables? What is a bestfitting quadratic model? December 2006 How do you find a quadratic model for a data set without using a graphing calculator? Which properties of exponents require you to check that two or more bases are the same before applying that property? 6.1 Use properties of exponents to Exponents evaluate and simplify expressions involving. Nth roots Use exponents and scientific notation to solve real-life Power Functions and Function operations Can you find the quotient of two radicals with different indices? 7.1 Evaluate Nth roots of real Inverse Functions Radical Equations
Page 6 of 9 Why or why not? How is the composition of functions different from the product of functions? When are two functions f and g inverses of one another? What is an extraneous solution and how can you tell if a solution is extraneous? numbers using both radical notation and rational exponent notation. Use properties of nth roots to solve real-life 7.2 Use properties of rational exponents to evaluate and simplify expressions. Use properties of rational exponents to solve real-life 7.3 Perform operations with power Use power functions and functions to solve real-life Explore inverse 7.4 Find the inverse of linear Find inverses of nonlinear Graph inverse 7.6 Solve equations that contain radicals or rational exponents. Use radical equations to solve real-life January 2007 Why are the y- values of an exponential growth function either always greater than or less than the asymptote of the function? What property of exponents is related to the product property of logarithms? What does the change of base allow you to do? What does it mean to exponentiate both sides of an 8.1 Graph exponential Use exponential growth functions to model real-life situations. Explore exponential Growth and Decay. 8.2 Graph exponential decay Use exponential decay functions to model real-life situations. Logarithmic 8.4 Evaluate logarithmic equations Graph logarithmic 8.5 Use properties of logarithms. Use properties of logarithms to solve real-life 8.6 Solve exponential equations. How can you use a line to determine Solve logarithmic equations. an exponential model for a set of 8.7 Model data with exponential points (x, y)? to Exponential Growth Exponential Decay Logarithmic functions properties Exponential equations Models of exponential and power functions
Page 7 of 9 February 2007 determine a power model for a set of points? When is a rational expression simplified? procedure for multiplying and dividing rational expressions involving polynomials? When is crossmultiplyng appropriate to solve a rational Give an example. standard equation for a circle whose center is at the origin and whose radius is the length r? Model data with power 9.4 Multiply and divide rational expressions. Use rational expressions to model real-life quantities. 9.5 Add and subtract rational expressions. Simplfy complex fractions. 9.6 Solve rational equations. Use rational equations to solve real-life 10.3 Graph and write equations of circles. Use circles to solve real-life problems 10.4 Graph and write equations of an ellipse. Use ellipses in real-life situations. Rational expressions operations Complex fractions simplify Rational equations Circles Ellipses Hyperbolas Conics Classify conics Describe the steps 10.5 Graph and write equations in graphing a circle for hyperbolas. on a graphing calculator. Inverse Variation In a standard equation for an ellipse, how can you tell which axis is the major axis and which axis is the minor axis? 10.6 Write and graph an equation of a parabola with its vertex at (h, k) and an equation of a circle, ellipse, or hyperbola with its center at (h, k). Classify a conic from its equation. March 2007 Which terms in a general seconddegree equation are used to find the discriminant and determine what type of conic the equation represents? What are the relationships of the sine, cosine, and tangent ratios to the cosecant, secant, and cotangent ratios? How can you convert an angle measured in degrees to radian measure? 13.1 Use trigonometric relationships to evaluate trigonometric functions of acute angles. Use trigonometric functions to solve real-life 13.2 Measure angles in standard position using degree measure and radian measure. Calculate arc lengths and areas of sectors. Right Triangle Trigonometry Angle measure degrees radians Arc length Sector area Inverse trigonometric functions Law of Sines
Page 8 of 9 reference angle for a non-quadrantal angle? Which quadrantal angle angles coincide with the x- axis? with the y- axis? What are you finding when you take the inverse of the sine, cosine, or tangent functions? minimum amount of information that needs to be given in order to use the law of sines to solve a triangle? 13.3 Evaluate trigonometric functions of any angle. Use trigonometric finctions in reallife 13.4 Evaluate inverse trigonometric 13.5 Use the law of sines to find the sides and angles of a triangle. Ambiguous Case p. 800 and supplement Find the area of any triangle using trig formula. 13.6 Use the law of cosines to find the sides and angles of a triangle. Area af a triangle Law of Cosines April 2007 What given information indicates using the law of cosines to solve a triangle? relationship between period an frequency? How is frequency related to cycle? How do you find the amplitude and period of a sine, cosine, or tangent function from its What is a double angle formula? What are some of the uses of doubleand half-angle formulas? How do you verify a trigonometric identity? 14.1 Graph sine and cosine Graph tangent Translate and reflect trig graphs. p 839 14.3 Use trigonometric identities to simplify trigonometric expressions and to verify other identities. 14.4 Solve a trigonometric equation. Solve real-life trigonometric equations. 14.6 Evaluate trigonometric functions of the sum or difference of two angles. Use sum or difference in real-life Trigonometric graphs Trigonometric Identities Trigonometric Equations Sum and Difference Formulas Double- and halfangle formulas What are the three techniques that you might use to solve a trigonometric What is a trigonometric sum formula? What are some of 14.7 Evaluate expressions using double- and half-angle formulas. Use double- and half-angle formulas to solve real-life
Page 9 of 9 May 2007 the uses of the sum and difference formulas? When is finding the mean or median more useful than finding the standard deviation? 7.7 Use measures of central tendency and measures of dispersion to describe data sets. 12.7 Calculate probabilities using normal distributions. 11.1 Write rules for geometric How can you sequences and find the sums of determine the geometric series. common ratio of a geometric 12.2 Use combinations to count sequence from 2 the number of ways an event can consecutive terms? happen. Statistics Measures of central tendencies Normal Distribution Sequences and Series Combinations and the Binomial Theorem relationship between Pascal's Triangle and the Binomial Theorem? Use the Binomial Theorem to Binomial expand a binomial that is raised to Distribution a power. 12.6 Find binomial probablilities and analyze distributions.