Algebra I CC. Table Of Contents

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2 Algebra I CC Table Of Contents I. RELATIONSHIPS BETWEEN QUANTITIES & REASONING 1. Topic A: Overview of Graphs A. Quadratic Functions (L- B. Exponential Functions (L- C. Graphing World Problems (L- & MOD 5 (L Topic B: Expressions A. Properties of Number (L-6,7) B. Add and Subtract Polynomials (L-8) C. Multiply and Divide Polynomials (L-9( Topic C: Equations & Inequalities A. Order of Operations (L-10) B. Number Line (L C. Solving Linear Equations (L-12,1 i. One Step 43 ii. Two Steps 43 iii. Variables on Both Sides 46 iv. Equations with Parentheses 47 v. Equations with Fractions 49 vi. Equations with Decimals D. Solving System (L-5) E. Solving Linear Inequalities (L-14,15,16,18) F. Rearranging Formula (L-19) G. Algebraic Linear Systems (L H. Linear World Problems (L-20,24,25) i. Ratio and Percent 75 ii. Consecutive Integers 81 iii. Value Problems (Coin Problems) 86 iv. Mixture Problems 88 v. Distance/Time Problems 91 vi, Fixed and Variable Cost 92 vii. Average Rate of Change 95 viii. Simultaneous Equations 97 ix. Cost/Revenue 99 x. Miscellaneous Algebra I. Algebraic Linear and Quadratic System (MOD 5 L-8)

3 II. STATISTICS 1. Topic A: Central Tendency Graphing (Univariate) A. Interpreting Statistical Graphs (L- B. Measures of Central Tendency (L-2, Topic B: Variability & Comparing Distributions (Univariate) A. Summarize Measures of Central Tendency & Interpret Mean & Standard Deviations (L-4,5,6) B. Box Plots and Interquartile Range (L-7) C. Comparing Distributions of Various Statistical Graphs (L-8) Topic C: Categorical Data on Two Variables A. Summarizing Bivariate Categorical Data (L-9) B. Summarizing Bivariate Categorical Data with Relative Frequencies )L-10) C. Conditional Relative Frequencies (L Topic D: Numeration on Two Variables A. Relationship between Two Variables (L-12,1 B. Modeling with a Line (L-14,15,16) C. Interpreting and Analyzing Residuals (L-15,17,18) D. Analyzing Data and Correlation (L-19,20) and MOD 5 (L-7) III. LINEAR & EXPONENTIAL FUNCTIONS 1. Topic A: Linear & Exponential Sequences A. Explicit Versus Recursive Arithmetic Sequances (L-1, & MOD 1 (L-26,27) B. Arithmetic Versus Geometric (L- C. Compound Growth (L-4,5,6) and MOD 5 (L-5,6,9) D. Compound Decay (L-7) and MOD 5 (L-5,6,9) Topic B: Functions and their Graphs A. 1-1 Correspondence (L-9) 173 B. Definition/Evaluation of Domain and Range Using Tables (L-10) 174 C. Graphing Functions (L-11,1 i. Linear Functions a. Slope Forumla 179 b. As a Rage of Change 181 c. Graph using Point/Slopes, X-Intercepts 184 d. Writing Equations of Lines 188 e. Types of Line (Parallel, Perpendicular ) 190 D, Interpreting and Comparing Graphs (L-13,1 & MOD 5 (L-2,8) 193 E. Evaluate Functions 198 F. Inverses 203 G. Algebraic Compositions 205

4 3. Topic C: Transforming Functions A. Shifting and Compressing Graphs (L-17,18,19,20) Topic D: Using Functions & their Graphs A. Graphing Systems of Equations (L-16) i. Two Linear Equations (MOD 1 L-5,21,2 211 ii. Linear and Quadratic 216 iii. Two Quadratic Equations 222 iv. Linear and Exponential 226 v. Exponential and Quadratic 228 B. Systems of Inequalities i. Two Linear Inequalities 232 ii. Linear and Quadratic 243 iii. Two Quadratic Inequalities 246 C. Word Problems Involving Systems of Equations (L-21,22,2 249 D. Piecewise Functions (L-15,2 and MOD 1 (L- and MOD 5 (L- 251 IV. POLYNOMIAL & QUADRATIC EXPRESSIONS 1. Topic A: Quadratic Expressions A. Multiplying & Factoring (L-1,2,3, i. FOIL 255 ii. Factoring a. Common Factor 257 b. DOTS 257 c. Trinomials 260 d. Lead Coefficients 263 e. Group Factor B. Solving Simple Quadratic Equations (L-5,6) C. Word Problems (L-7) D. Quadratic Graph & Symmetry (L-8,9,10) i. Axis of Symmetry 272 ii. Turning Point (Max/Min) 273 iii. Roots 275 iv. World Problems Topic B: Solving Quadratics A. Completing the Square (L-11,12,1 B. Quadratic Formula (L-14,15) C. Vertex Form of Quadratic Graphs (L-16) D. Standard Form of Quadratic Graphs

5 3. Topic C: Transformations & Modeling A. Graphing Absolute Values, Cubes, Square Roots, and Cube Roots (L-18) B. Shifts & Other Transformations (L-19,20,2 C. Comparing Graphs & their Applications (L-2 D.Extended World Problems (L-23, V. A SYNTHESIS OF MODELING WITH EQUATIONS & FUNCTIONS 1. Topic A: Elements of Modeling A. Analyzing a Graph B. Analyzing a Data Set C. Analyzing a Verbal Description D. Modeling a Context from a Verbal Description Topic B: Completing the Modeling Cycle A. Modeling a Context from a Graph B. Modeling from a Sequence C. Modeling a Context from Data VI. REMEDIAL REVIEW 1. Topic A: Radicals A. Simplification B. Adding and Subtracting C. Multiplying and Dividing Topic B: LCD and GCF Topic C: Pythagorean Theorem Topic D: Linear Inequality Graphs Topic E: Area and Perimeter of Polygons Topic F: Conversion Units Topic G: Relative Error Topic H: Probability Topic I: Undefined Fractions Topic J: Absolute Value Topic K: Scientific Notations 363

6 12. Topic L: Mixed Algebra Rev A. Add and Subtract Monomials B. Multiply and Divide Monomials C. Exponents D. Add and Subtract Fractions E. Multiply and Divide Fractions 13. Topic M: Histograms 14. Topic N: Volume and Surface Area 15. Topic O: Number Theory 16. Topic P: Basic Trigonometry

7 MOD 1: RELATIONS BTWN QUANTITIES & REASONING 1. Overview of Graphs B. Exponential Functions (L A population that initially has 20 birds approximately doubles every 10 years. Which graph represents this population growth? Which function is shown in the table below? What is the equation of the graph shown below? Theresa is comparing the graphs of and. Which statement is true? The y-intercept of is (0,, and they-intercept of is (0,5). Both graphs have a y-intercept of (0,, and is steeper. Both graphs have a y-intercept of (0,, and is steeper. Neither graph has a y-intercept. y = 2 x y = 2 x x = 2 y x = 2 y

8 MOD 1: RELATIONS BTWN QUANTITIES & REASONING 1. Overview of Graphs B. Exponential Functions (L The breakdown of a sample of a chemical compound is represented by the function, where represents the number of milligrams of the substance and t represents the time, in years. In the function p(t), explain what 0.5 and 300 represent The table below represents the function F. The quation that represents this function is On the axes below, for, graph

9 MOD 1: RELATIONS BTWN QUANTITIES & REASONING 3. Equations & Inequalities F. Rearranging Formula (L-19) The formula for the sum of the degree measures of the interior angles of a polygon is. Solve for n, the number of sides of the polygon, in terms of S Michael borrows money from his uncle, who is charging him simple interest using the formula I = Prt. To figure out what the interest rate, r, is, Michael rearranges the formula to find r. His new formula is r equals Michael borrows money from his uncle, who is charging him simple interest using the formula I = Prt. To figure out what the interest rate, r, is, Michael rearranges the formula to find r. His new formula is r equals If, what is x expressed in terms of y and z? The distance a free falling object has traveled can be modeled by the equation, where a is acceleration due to gravity and t is the amount of time the object has fallen. What is t in terms of a and d? The equation for the volume of a cylinder is. The positive computations. value of r, in terms of h and V, is 787. If, what is x expected in terms of a and b? The formula for the volume of a cone is. The radius, r, of the cone may be expressed as 788. The formula for the volume of a right circular cylinder is. The value of can be expressed as 786. Tim ate four more cookies than Alice. Bob ate twice as many cookies as Tim. If x represents the number of cookies Alice ate, which expression represents the number of cookies Bob ate? 2 + (x + 2x + 4 2(x + 4(x At the beginning of her mathematics class, Mrs. Reno gives a warm up problem. She says, I am thinking of a number such that 6 less than the product of 7 and this number is 85. Which number is she thinking of? Shoe sizes and foot length are related by the formula S = 3F 24, where S represents the shoe size and F represents the length of the foot, in inches. a Solve the formula for F. b To the nearest tenth of an inch, how long is the foot of a person who wears a size 10 shoe? 783. Solve for r in terms of C and p: C = 2pr 782. Solve for D in terms of C and p: C = pd 781. Solve for R in terms of I, P, and T: I = PRT

10 MOD 2: STATISTICS 2. Variability & Comparing Distributions (Univariate) B. Box Plots and Interquartile Range (L-7) During the last 15 years of his baseball career, Andrew hit the following number of home runs each season. 35, 24, 32, 36, 40 32, 40, 38, 36, 33, 11, 20, 19, 22, 8 State and label the values of the minimum, 1st quartile, median, 3rd quartile, and maximum. Using the line below construct a box-and-whisker plot for this set of data Which statistic can not be determined from a box plot representing the scores on a math test in Mrs. DeRidder's algebra class? the lowest score the median score the highest score the score that occurs most frequently Corinne is planning a beach vacation in July and is analyzing the daily high temperatures for her potential destination. She would like to choose a destination with a high median temperature and a small interquartile range. She constructed box plots shown in the diagram below The box-and-whisker plot shown below represents the number of magazine subscriptions sold by members of a club. Which statistical measures do points B, D, and E represent, respectively? minimum, median, maximum first quartile, median, third quartile first quartile, third quartile, maximum median, third quartile, maximum The box-and-whisker plot below represents a set of grades in a college statistics class. Which destination has a median temperature above 80 degrees and the smallest interquartile range? Ocean Beach Whispering Palms Serene Shores Pelican Beach Which interval contains exactly 50% of the grades?

11 MOD 2: STATISTICS 4. Numeration on Two Variables B. Modeling with a Line (L-14,15,16) The data collected by a biologist showing the growth of a colony of bacteria at the end of each hour are displayed in the table below. Write an exponential regression equation to model these data. Round all values to the nearest thousandth. Assuming this trend continues, use this equation to estimate, to the nearest ten, the number of bacteria in the colony at the end of 7 hours The table below shows the number of grams of carbohydrates, x, and the number of Calories, y, of six different foods A cup of soup is left on a countertop to cool. The table below gives the temperatures, in degrees Fahrenheit, of the soup recorded over a l0-minute period. Write an exponential regression equation for the data, rounding all values to the nearest thousandth Which calculator output shows the strongest linear relationship between x and y? Which equation best represents the line of best fit for this set of data? All of the following statements about residuals are correct exept they are differences between observed and estimated values of y. their sum will always equal zero even if there are outliers. they can only be positive numbers. they are used to determine the legitimacy of a model Lin Reg y = a + bx a = b = r =.8643 Lin Reg y = a + bx a =.7 b = 24.2 r =.8361 Lin Reg y = a + bx a = 2.45 b =.95 r =.6022 Lin Reg y = a + bx a = 2.9 b = 24.1 r =.8924

12 MOD 3: LINEAR & EXPONENTIAL FUNCTIONS 1. Linear & Exponential Sequences A. Explicit Versus Recursive Arithmetic Sequances (L-1, & MOD 1 (L-26,27) Each day Toni records the height of a plant for her science lab. Her data are shown in the table below. The plant continues to grow at a constant daily rate. Write an equation to represent h(n), the height of the plant on the nth day Which recursively defined function represents the sequence 3, 7, 15, 31,...? A pattern of blocks is shown below Which recursively defined function has a first term equal to 10 and a common difference of 4? If the pattern of blocks continues, which formula(s) could be used to determine the number of blocks in the nth term? If a sequence is defined recursively by and for, then f( is equal to The third term in an arithmetic sequence is 10 and the fifth term is 26. If the first term is, which is an equation for the nth term of this sequence? I and II I and III II and III III, only A sunflower is 3 inches tall at week 0 and grows 2 inches each week. Which function(s) shown below can be used to determine the height, f(n), of the sunflower in n weeks? Write the n th term of the arithmetic sequence an = {4, 7, 10, 13, 16,...} What are the first three terms of the recursive sequence defined below. I and II II, only III, only I and III Find the third term in the recursive sequence, where.

13 MOD 3: LINEAR & EXPONENTIAL FUNCTIONS 4. Using Functions & their Graphs A. Graphing Systems of Equations (L-16) iii. Two Quadratic Equations The graph representing a function is shown below On the provided set of axes, graph the following equations and circle the points at which the two functions intersect. y = x 2 + 2x - 4 y = -x 2-5x + 1 Which function has a minimum that is less than the one shown in the graph? On the provided set of axes, graph the following equations and circle the points at which the two functions intersect a Draw the graph of y = x 2 + 4x including all values of x such that 1 x 5. b On the same set of axes, draw the graph of y = x 2 including all values of x such that 3 x 3. c How many points do the graphs drawn in parts a and b have in common? y = x 2-5x + 4 y = -x 2 + 2x + 3

14 MOD 4: POLYNOMIAL & QUADRATIC EXPRESSIONS 1. Quadratic Expressions A. Multiplying & Factoring (L-1,2,3, ii.b. Factoring - DOTS Which expression is equivalent to? The expression is equivalent to If the area of a rectangle is expressed as, then the product of the length and the width of the rectangle could be expressed as When factored completely, the expression is equivalent to Factor completely: ax 2 16a Which is not a factor of 2x 2 32? x x 4 x Which expression is the complete factorization of 32 18y 2? 2(16 9y 2 ) 2(3y + (3y 2(4 3y) 2 2(4 3y)(4 + 3y) Factor completely: 3x 3 y 12xy Factor completely: x Factor completely: 5x 2 y 3 180y Factor completely: 2x 3 98x Factor completely: 3x 3 y 2 147x Factor completely: 3x Factor completely: 4x 3 36x What are the factors of y 3 4y? y(y (y y(y + (y x(x x(x + (x (y 2 + l)(y y(y + (y When factored completely, x 3 9x is equivalent to 2(x 5)(x 5) 2(x 5)(x + 5) (x + (x x(x Written in simplest factored form, the binomial 2x 2 50 can be expressed as x (x 5)(x + 5) 2x(x 50) Which is not a factor of 2x 2 32? x 4 x Which expression is the complete factorization of? 2(16 9y 2 ) 2(3y + (3y 2(4 3y) 2 2(4 3y)(4 + 3y) When is factored, it is equivalent to. What is a value for b? The expression 100n 2 1 is equivalent to (10n + (10n (10n (10n (50n + (50n (50n (50n The expression 9a 2 64b 2 is equivalent to (9a 8b) (a + 8b) (9a 8b) (a 8b) (3a 8b )(3a + 8b) (3a 8b)(3a 8b) Which expression is equivalent to 64 x 2? (8 x)(8 x) (8 x)(8 + x) (x 6y)(x 6y) (x 18y)(x 18y) (x + 6y)(x 6y) (x + 18y)(x 18y) (x 8)(x 8) (x 8)(x + 8) The expression x 2 36y 2 is equivalent to

15 MOD 4: POLYNOMIAL & QUADRATIC EXPRESSIONS 3. Transformations & Modeling D. Extended World Problems (L-23, Given that, find g(x) if A contractor has 48 meters of fencing that he is going to use as the perimeter of a rectangular garden. The length of one side of the garden is represented by x, and the area of the garden is 108 square meters. Determine, algebraically, the dimensions of the garden in meters A landscaper is creating a rectangular flower bed such that the width is half of the length. The area of the flower bed is 34 square feet. write and solve an equation to determine the width of the flower bed, to the nearest tenth of a foot On the provided set of axes, draw the composite transformation of the graph y = log(x) when it is shifted down by a factor of 1 unit and reflected about the y-axis On the provided set of axes, draw the composite transformation of the graph y = x 4 when it is shifted right by 2 units and stretched horizontally by a factor of 1/2.

16 MOD 5: A SYNTHESIS OF MODELING WITH EQUATIONS & FUNCTIONS 1. Elements of Modeling B. Analyzing a Data Set The table below shows 6 students' overall averages and their averages in their math class. If a linear model is applied to these data, which statement best describes. the correlation coefficient? It is close to 1. It is close to 1. It is close to 0. It is close to Rachel and Marc were given the information shown below about the bacteria growing in a Petri dish in their biology class. Rachel wants to model this information with a linear function. Marc wants to use an exponential function. Which model is the better choice? Explain why you chose this model For which type of function is the quotient of any two consecutive y-values a constant that is not equal to 0 or 1 when x-values are at regular intervals? linear quadratic linear quadratic exponential absolute value For which type of function is the first difference of y-values constant when x-values are at regular intervals? quadratic exponential cubic exponential For which type of function is the second difference of data values constant? linear square root absolute value cubic A function has two different x-values for y = 0. What type of function might it be? absolute value exponential What are the values of A, B, and C in the following data set, assuming that it can be modeled by an exponential function Which of the functions can be used to model the following set of data? f(x) = 3x + 7 f(x) = -(x f(x) = -x 2 + 4x - 5 f(x) = x 2 + 2x + 7

17 MOD 6: REMEDIAL REVIEW 15. Number Theory An online company lets you download songs for $0.99 each after you have paid a $5 membership fee. Which domain would be most appropriate to calculate the cost to download songs? rational numbers greater than zero whole numbers greater than or equal to one integers less than or equal to zero whole numbers less than or equal to one Indicate whether each statement below is true and explain why, using mathematical language. a. All natural numbers are integers. b. All real numbers are irrational. c. All natural numbers are rational numbers Indicate whether each statement below is true or false. I. (a + b) + c = a + (b + c) II. (a b) c = a (b c) III. (ab)c = a(bc) Which equation illustrates the additive inverse property? If x and y are any two whole numbers, which statements always true? xy = yx x y = y x x + 3y = y + 3x If a, b, and c are real numbers, which statement is always true? a b = b a a(b + c) = (a + b) (a + c) a(b c) = (a b)c a 0 = a In the solution of this problem, which property of real numbers justifies statement 5? Which field property is illustrated by the expression sin x(cos x + = sin x cos x + sin x? associative property commutative property inverse property distributive property of multiplication over addition Which equation is an illustration of the additive identity property? x 1 = x x + 0 =x x x= O x = Which equation illustrates the multiplicative inverse property? Which statement is an illustration of the commutative property of real numbers? = (6 + 7) = 5(6) + 5(7) = 5 Closure Identity Commutative Inverse In the set of rational numbers, what is the identity element for multiplication? In the step by step simplification of the expression below, which property is not used? 3(1 + x) 3(x + 3 x x + 3 associative commutative ab = ba a(b + c) = ab + ac a(bc) = (ab)c a + 0 = a distributive identity Which is an illustration of the associative property?