zilongwang/ReadingBank huggingface dataset:
A postal clerk sold 75 stamps for $4.80. Some were 5-cent stamps and some were 8-cent stamps. How many of each kind did he sell? Mr. Perkins cashed a $185 in his bank. He receives $1 bills, $5 bills and $10 bills. In this order, the numbers of the three types of bills he received were three consecutive integers. How many of each type of bill did he receive? In Paul’s bank there is $2.60 in pennies, nickels and dimes. In all there are 45 coins. If there are twice as many nickels as pennies, find out how many of each kind there are. Beth paid a bill of $2.70 with quarters, and pennies. She had five less quarters than dimes and four less quarters than pennies. How many coins of each kind did she use to pay the bill?
+4x y Hence draw the graph of . (a) Copy and complete the table below for the graph of for values of x from –3 to 3. x –3 –2 –1 0 1 2 3 x2 –2x y Hence draw the graph of . (a) Copy and complete the table below for the graph of for values of x from –4 to 3. x –4 –3 –2 –1 0 1 2 3 x2 +3x y Hence draw the graph of . (a) Copy and complete the table below for the graph of for values of x from –4 to 3. x –4 –3 –2 –1 0 1 2 3 x2 –3x y draw the graph of . (a) Copy and complete the table below for the graph of for x from –4 to 3. x –4 –3 –2 –1 0 1 2 3 x2 +2x –3 y
(a) Draw the graph of for values of x between –3 and 5 On the same set of axes draw the graph of solve the set of simultaneous equations and (a) Draw the of for values of x between –5 and 3 On the same set of axes draw the straight line with equation solve the set of simultaneous equations and (a) Draw the graph of for values of x between –4 and 4 On the same set of axes draw the straight line with equation solve the set of simultaneous equations and Algebra (11) Simultaneous equations I Exercise 1 Solve each of the following sets of simultaneous equations. Remember to show your working. Exercise 2 Solve each of the following sets of simultaneous equations. Remember to show your working
Algebra (16) Substituting into formulae If find a when If find m when Given work out t when Given what is the value of a when and ? If what is the value of x when and ? If work out the value of y given . If what is the value of y when ? Given work out the value of d when . If what is the value of q when ? If find the value of g when . If work out the value of m when and . Given what is the valuw of y when , and ? Given find v when , and . Evaluate when and . If work out V when and . Given work out S for and . If work out h for . Given work out the value of m when .
Chapter 5: Linear Functions 5.1 Rate of Change and Slope 5.2 Direct Variation 5.3 Slope-Intercept Form 5.4 Slope Form 5.5 Standard Form 5.6 Parallel and Perpendicular Lines 5.7 Scatter Plots and Trend Lines Chapter 6: Systems of Equations and Inequalities 6.1 Solving Systems by Graphing 6.2 Solving Systems Using Substitution 6.3 Solving Systems Using Elimination 9.3-9.5 (Dolciani) Problem Solving with Systems 6.5 Linear Inequalities State Standards A1.3.3e A1.4.1a A1.4.1b A1.4.1c A1.4.2a A1.4.2b A1.4.2c A1.4.2d A1.4.2e A1.4.2f A1.4.3a A1.4.3b A1.4.3c A1.4.3d A1.4.3e A1.4.3f A1.4.4a A1.4.4b A1.4.4c A1.4.4d A1.4.5a A1.4.5b A1.4.5c A1.4.5d A1.4.6a A1.5.1a Slope Forms of Linear Equations Scatter Plots Solving Systems of Equations Graphically Solving Systems of Equations Algebraically Problem Solving with Systems of Equations Linear Inequalities Systems of Linear Inequalities ●Find rates of change from tables. ●Find ●Write and graph an equation of a direct variation. ●Write linear equations using slope intercept form. linear equations in slope intercept form. ●Write and graph linear equations using point slope form. ●Graph linear equations using intercepts. ●Write linear equations in standard form. ●Determine whether lines are parallel, perpendicular or neither. ●Write equations of parallel lines and perpendicular lines. an equation of a trend line and of a line of best fit. ●Use a trend line and a line of best fit to make predictions. ●Solve systems of equations by graphing. ●Analyze special systems. ●Solve systems of equations using substitution. Textbook assignments Worksheet assignments Section Quizzes Quizzes Tests Oral responses Observations Textbook: Dolciani “The Classic” Algebra 2000 edition Textbook Prentice-Hall Algebra 1 Foundation Series 2011 Edition Textbook (Larson) Algebra 1 Concepts and Skills 2010 Edition On Core Mathematics Activity Generator Power Point Presentations USA Test Prep
Bainbridge (A3) Function Characteristics 11-13 questions File Name & Description State Strand Item Specification Ch2 A Relations and Functions A1.3.A Determine whether a relationship is a function and identify the domain, range, roots, and independent and dependent variables. Ch2 B Domain, finding roots A1.3.A Determine whether a relationship is a function and identify the domain, range, roots, and independent and dependent variables. Ch2 C Functions defined piecewise In the notes it says, step functions will be described verbally or graphically not symbolically Ch2 D Independent, dependent variables A1.3.A Determine whether a relationship is a function and identify the domain, range, roots, and independent and dependent variables. Ch2 E Multiple representations (symbolic, graph, table, words) A1.3.B Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations. Ch2 F Make Connections (Linear & Exponential) A1.3.B Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations. Ch2 G Make Connections (Quadratic & Absolute Value) A1.3.B Represent a function with a symbolic expression, as a graph, in a table, and using words, and make connections among these representations. Ch2 H Function notation ( Find f(x) at x = a) A1.3.C Evaluate f(x) at x=a Ch2 I Function notation (Solve for x if f(x)=b) for x in the equation f(x)=b Ch2 B is not written yet Ch2 C is not written yet. Ch2 D is not written yet. APPENDIX Chapter 2: Characteristics and behaviors of linear and non-linear functions (continued) File Name & Description State Strand Item Specification Ch2 J Select and justify functions (to model and solve problems) A.1.1.A Select and justify functions and equations to model and solve problems Ch2 K Solve problems (that can be modeled with exponential functions) A.1.1.E Solve problems that can be represented by exponential functions and equations Ch2 L Sketch the graph (exponential) A.1.7.A Sketch the graph for an exponential function of the form y=ab^x where n is an integer. Answer questions that arise in situations that arise in situations modeled by exponential functions.
Question 22 What is the of the parabola given by the equation y = x2 − 2x − 3? Question 23 Which point is the vertex for the graph f(x) = |x| + ? Question 24 Graph y = |x2| − 2x − 8? Question 25 What is the value of f(x) = 81x when x = 1 2 ? Question 26 Find the inverse of y = 3x – 2 Question 27 What is the value of log 26 rounded to the nearest hundredth? Question 28 one represents the equation log8 25 = 2 in exponential form? Question 29
Question 28 Which one represents the equation log8 25 = 2 in exponential form? Answer : 82 =25 Question 29 Determine whether the parabola y = −x2 + 18x + 2 opens up, down, left, or right. Answer: Look at the coefficient of the x squared. If it is positive then opens up. If it is negative, then opens down. This has a -1 in front of x squared so it opens down. Question 30 What is the vertex of the parabola given by y = x2 − 20x + 5? First find -b 2(a) this is the x part of the vertex = - -20 2(5) = 2 now you have the x so plug that into equation for y. y = 22 – 20(2) + 5 = 4- 40 +5 = -31 so the vertex is (2, -31) Question 31 If f(x) = x2 − 2x + 9 and g(x) = 8 − x, what is (f o g)(−7)? Answer : First find g(-7) g(x) = 8 – x g(-7)= 8- - 7 g(-7)= 15 Now plug this into f(x) f(x) = x2 − 2x + 9 f(x)= 152 - 2(15) +9 f(g(x)) = 225 -30 + 9
Properties Commutative Property 3+5=5+3 3*5=5*3 (change order) Associative property (3+4) +5 = 3+ (4+5) same for multiplication (grouping) Identity Property a*1= a a+0=a (What you start with is what you end with) Distributive Property 3(a+8) = 3a+24 Multiplicative Property of Zero x*0=0 Reflexive property IF ab=4 THEN ab=4 (the same on both sides) Symmetry property IF xy=6 THEN 6=xy (flipped ---Has to have the if then) Transitive If x+2=y and y=6 then x+2=6 (three items) Function Families: Linear (/ ),Quadratic (U), Absolute value (V), Rational (2 curves) , exponential , Logarithmic Polynomial Odd degree Even degree Square root Interval of Increasing or decreasing Use only the X values and look at the graph to decide where it is increasing or decreasing End behavior= What direction the graph going at the ends. f(x) ___ as x _____ Use +∞ or -∞ for the blanks or numbers for Roots, Logs, Expos Parent Functions- Horizontal if the number is changing the x “Golden Rule” Vertical shift is the number that is not with the x Absolute equations- 2bars 2 equations! Look out for bars equaling a negative number That’s a {no solution} Variations Direct Variation-Where the line goes through the origin. Also uses y=kx, where k is the constant (slope) Indirect/Inverse Variation- (division) Joint Variation- y=kxz (Needs two or more items) Polynomials Standard form ax2+bx+c=0 highest degree 1st Degree of polynomial is the largest exponent. FACTOR—Check for GCF first (could be # or variable or both) Sign rules for factoring ___ + ___ + ____ Difference of Perfect Squares x2-4 (prefect square) - (perfect square) Perfect trinomials ( + )2 signs are the same, either + or – Difference of = “alternate signs” Quadratics ax2+bx+c=0 **Must show for zero **Can factor or y= key
What I want students to know, do and understand? Concept(s) Relationship, generalization (predicting), representation, connection, cause and effect, change, system Big Idea Curricular Competencies Content Linear relations can be represented in many connected ways to identify regularities and make generalizations. REASONING AND ANALYZING Use reasoning and logic to explore, analyze, and apply mathematical ideas Demonstrate and apply mental math strategies Use tools/technology to explore and create patterns and relationships, and test conjectures Model mathematics in contextualized experiences UNDERSTANDING AND SOLVING Develop, demonstrate and apply mathematical understanding through play, inquiry and problem solving Visualize to explore mathematical concepts COMMUNICATING AND REPRESENTING Use mathematical vocabulary and language to contribute to mathematical discussions Explain and justify mathematical ideas and decisions Communicate mathematical thinking in many ways CONNECTING AND REFLECTING Reflect on mathematical thinking Connect mathematical concepts to each and other areas of personal interest Incorporate First Peoples worldviews and perspectives Discrete linear relations, using expressions, tables and graphs Two step equations with number coefficients, constants and solutions Multiplication and division facts to 100 Operations with integers (addition, subtraction, multiplication, division, order of operations) How will I know my students have it? Summative Assessment Multiplication and division facts to 100 (extending computational fluency) Algebraic Equations/Expressions Linear Relations On-going, formative assessment; imbed into other units Unit Test Unit Test
Algebra I Syllabus Miss Embry B117 Course Description In Algebra I students will the fundamentals necessary to succeed in any future math. This course covers expressions, equations, inequalities, functions, graphing, systems, exponent rules, polynomials, factoring, quadratics, and radicals. Passing Algebra I will help students earn 2 of 6 math credits towards graduating with a Core 40 diploma. At the end of the year students will also take an End of Course Assessment (ECA) that students will need to take in order to graduate. Supplies Students need to bring their textbook, a notebook, a folder and a pencil to class with them every day. A calculator that does basic operations will be helpful throughout the year. Grading Policy Every quarter students will receive credit for classwork, homework, quizzes, and tests. Quarter grades are calculated by: 20% classwork/homework, 80% quizzes/tests Semester grades are calculated by: 40% first quarter, 40% second quarter, 20% final Although quizzes and tests do make up the majority of a student’s grade this is not an excuse to not complete and turn in homework. Lack of homework usually results in lower quiz and test grades. The grading scale is broken down as seen here and can also be found in your student handbook. Percentage Letter GPA 94-100 A 4.0 90-93 A- 3.7 87-89 B+ 3.3 84-86 B 3.0 80-83 B- 2.7 77-79 C+ 2.3 74-76 C 2.0 70-73 C- 1.7 67-69 D+ 1.3 64-66 D 1.0 60-63 D- 0.7 0-59 F 0
Write an equation in slope-intercept form for a line that passes through the given point and is perpendicular to the given line. 48. y = 4x –7; (5, –1) 49. y = (1/3)x + 5; (4, –2) each system. Show your work. 50. 3y – 2x = 11 51. 4x + 3y = -1 y + 2x = 9 5x + 4y = 1 each inequality by graphing. List two solutions. 52. y +3x 2 53. y – 5x -2 Simplify each expression. Express only positive exponents. 54. a4b–7c0 55. (5a4b2)(-2a3b2)(4a5) 56. 57. (m3 n–5m–1)–3 58. 59.
110. 111. 112. 113. Solve each equation. 114. 115. 116. There are three consecutive integers. The product of the first two is 5 more than 6 times the third. Write the equation that represents this relationship. 117 bought some packages of Oreos and 2 half gallons of chocolate milk for $16.00. If a package of Oreos costs $3.25 and a half gallon of chocolate milk costs $1.50, how many packages of Oreos did she buy?
Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context. For example, compare and contrast quadratic functions in standard, vertex, and intercept forms. Standards for Mathematical Practice Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. Introduction In this task, we create equations (of one to variables) in order to model some realistic phenomena. The structure of this task could, of course, be manipulated to suit the preferences of the teacher. The reasoning for the structure of this task is based on two needs: First, the obvious need to give a narrative structure to the context of the task. Second, and more importantly, while teachers (or students) may question why the task begins with a system of equations utilizing three variables, the task begins here to present (and ask students to evaluate) the types of equations that students will be required to create on their own later. The task covers a number of relationships between variables, including linear, exponential, and quadratic. Materials Pencil Handout Calculator Ted’s Quest for a Tablet Ted has had his eye on a tablet computer for several months, and he’s trying to figure out a way to save enough money so that he can buy one using cash instead of credit. Ted is trying every possible method to build his computer fund – he’s looking for change in the couch, he’s drawn up a savings plan, he’s budgeting in other areas of his life, and so on. But Ted is growing impatient, and he’s afraid that he will resort to using a credit card so that he can get one quickly, but of course that means Ted will have to pay interest on his purchase.
Part III: Polynomial Practice 1. the following portions of a graph of a function defined over the domain [-8,8] F 2. Write the polynomial with the following zeros: , 3. What is the remainder when is divided by ? From this information, give one on the graph (without graphing). If the divisor is , then some students will want to try synthetic division with , which takes too long and leaves too many placeholder errors possible. Students should realize that we can use substitution, which is much quicker here:
3. 4. and D: and D: We’ll revisit inverse functions in a moment. 2. Combining and Compositions I. Basic Combinations and Compositions For 1 – 8 below, use the following information. Give the domain of each. and 1. Find 2. Find 3. Find 4. Find 5. Find 6. Find 7. Find 8. Find No domain – this is a function value II. Function Compositions Sets of Points f={(–2, 3), (–1, 1), (0, 0), (1, –1), (2, –3)} g={(–3, 1), (–1, –2), (0, 2), (2, 2), (3, 1)}
19. 9x2 + 18x + 8 _______________________ 20. 4x2 + 13x + 10 _______________________ Difference of Two Squares 21. x2 – 100 _______________________ 22. 36x2 – 64 _______________________ 23. 25x2 – y8 _______________________
M1 for 20c – 12d – 7c or better or W1 for 13c or – 12d seen as terms in final answer (b) m(m – n) www 1 [3] 12. 2x2 + 3xy or x(2x + 3y) B2 B1 for 3x2 – x2 + 3xy or x(3x – x + 3y) seen. SC1 for answer 2x2 – 3xy o.e. or 2x2 seen in final answer of 2 terms. [2]
Correlation to the 2016 Mathematics Standards of Learning and Curriculum Framework – Algebra I Text/Instructional Material Title: ______________________ Publisher: __________________________________________ Committee Member: _________________________________ Date: ________ NOTE: The rating in the tables below are empty in order for division-level review teams to utilize this form. Section I. Correlation with the Mathematics 2016 SOL and Curriculum Framework Mathematics Standard of Learning Adequate Rating Limited Rating No Evidence Rating A.1 A.2 A.3 A.4 A.5 A.6 A.7 A.8 A.9
Name ___________________ Algebra 1 Module 2 Lesson 10 Relative Frequencies Example 1: Extending the Frequency Table to a Relative Frequency Table Determining the number of students in each cell presents the first step in organizing bivariate categorical data. Another way of analyzing the data in the table is to calculate the relative frequency for each cell. Relative frequencies relate each frequency count to the total number of observations. For each cell in this table, the relative frequency of a cell is found by dividing the frequency of that cell by the total number of responses. Consider the two-way frequency table from the previous lesson. Two-Way Frequency To Fly Freeze Time Invisibility Super Strength Telepathy Total Females 49 60 48 1 70 228 Males 51 71 27 25 48 222 Total 100 131 75 26 118 450 The relative frequency table would be found by dividing each of the above cell values by 450. For example, the relative frequency of females selecting “To Fly” is 49/ 450, or approximately 0.109 to the nearest thousandth. A few of the other relative frequencies to the nearest thousandth are shown in the following relative frequency table: Calculate the remaining relative frequencies in the below. Write each value in the table as a decimal rounded to the nearest thousandth. To Fly Freeze Time Invisibility Super Strength Telepathy Females Males Problem Set Consider the King data from the previous lesson regarding after school activities:
Name ___________________ Algebra 1 Module 2 Lesson 12 Relationships Between Two Numerical Variables A scatter plot is an informative way to display numerical data with two variables. The two numerical variables are denoted by x and y, the scatter plot of the data is a plot of the (x,y) data pairs. Thinking about Linear Relationships Below are three scatter plots. Each one represents a data set with eight observations. The scales on the and axes have been left off these plots on purpose so you will have to think carefully about the relationships. If one of these scatter plots represents the relationship between height and weight for eight adults, which scatter plot do you think it is and why? If one of scatter plots represents the relationship between height and SAT math score for eight high school seniors, which scatter plot do you think it is and why? If one of these scatter plots represents the relationship between the weight of a car and fuel efficiency for eight cars, which scatter plot do you think it is and why? 4. Which of these three scatter plots does not appear to represent a linear relationship? Explain the reasoning behind your choice. Not Every Relationship is Linear When a straight line provides a reasonable summary of the relationship between two numerical variables, we say that the two variables are linearly related or that there is a linear relationship between the two variables. Take a look at the scatter plots below and answer the questions that follow.
107. (Old Standard 4: MA.912.A.4.3) Rewrite the expression below factored completely. 18x2y2 + 36x3y3 − 27x3y 108. Factor out the greatest common monomial factor. Rewrite each expression below factored completely. 109A.x2 − 2x – 120 109B. a2 – 7a + 12 109C. 5x2 – 31x + 6 109D. 2x2 + 7x + 6 109F. 16x2 – 16x + 3 110A. (Old Standard 4: MA.912.A.4.3) Rewrite the expression factored completely. 36x − 100y2x 110B. 2x2 – 18 110C. Which is NOT a factor of x4 – 81? A. x + 3 B. x – 3 C. x2 – 3 D. x2 + 9 E. All are factors 111. (Old Standard 7: MA.912.A.7.2) Marna wants to find the values of x for which the function below will have a value of 10. f(x) = x2 + x − 20 Which of the following shows the correct factorization of this function for f(x) = 10?
161 A taxi ride costs $29.40. The driver charged $3 plus $0.40 per 0.2 mile traveled. How far did the taxi travel on this trip? a. 9.8 miles b. 13.2 Standard: A1.1.B* (Chapter 3, 4) c. 66 miles d. 73.5 Mrs. Morris gave her students this pattern of white tiles. She asked her students to write an equation to represent the number of white tiles, t, for any figure number, n. Which equation represents the number of white tiles in the pattern? a. t = n +2 b. t = n + 4 c. t = 4n + 4 Standard: A1.4.A* (Chapter 3, 4) d. t = 4n + 8 Eddie works the algebra problem 5(3x - 4) = 4x + 29 as shown. Problem 5(3x - 4) = 4x + 29 Step 1 15x – 4 = 4x + 29 Step 2 15x – 4 – 4x = 4x – 4x + 29 Step 3 11x – 4 = 29 Step 4 11x -4 + 4 = 29 + 4 Step 5 11x = 33 Step 6 x = 3 Which statement about Eddie’s work is correct? Eddie’s work is correct; 3 is the correct answer. Eddie made a mistake in step 1. Standard: A1.4.A* (Chapter 3) Eddie made a mistake in step 3. Eddie made a mistake in step 5. 10. The slope of the line shown is . Find the length of d. a. 2 b. 3 c. 4 d. -6 Standard: A1.4.C* (Chapter 3, 4) 11. A club did a study comparing the cost of a sweatshirt with the number of sweatshirts sold. The number of sweatshirts sold at various prices was recorded in the scatter plot below. Which of the following could be an equation of the line showing the general trend of the data? a. Standard: A1.6.D* (Chapter 3, 4)
b. c. d. 12. equation best represents the set of data in the table? x y −3 5 −2 4 1 1 4 −2 2x + y = −1 x + y = 2 Standard: A1.4.B* (Chapter 3, 4) x − y = −2 x − y = −6 13. Which equation most likely represents the line shown on the graph? a) Standard: A1.4.B (Chapter 3, 4) b) c) d) 14. The perimeter of a rectangular field is 244 ft. If its length is 2 feet longer than twice its width, what are the dimensions of the field? a. 40 ft, 82 ft Standard: A1.4.A* (Chapters 3, 4) b. 21 ft, 40 ft c. 20 ft, 42 ft d. 42 ft, 80 ft 15. Mrs. Gumas bought 4 pencils and 3 pens for $5.60. Mr. Houston bought 2 pencils and 3 pens of the same kind for $4.60. What is the price of each pencil and each pen? $0.50 per pencil, $1.20 per pen $0.17 per pencil, $1.64 per pen $1.70 per pencil, $0.20 per pen $0.80 per pencil, $0.80 per pen Standard: A1.4.D* (Chapter 3, 4) 16. A student solved the following inequality as shown. Problem 9 – 5(2x + 1) ≥ -28 Step 1 9 – 10x – 5 ≥ -28 Step 2 4 – 10x ≥ -28 Step 3 4 – 10x ≥ -28 -4 -4
Fig. 4 Vary a or b to form ellipses or a circle. Complex computations can be illustrated with the ‘animate’ command, also. The next example is the computation for the amortization of a fixed loan with level monthly payments. Students may substitute a constant for r based on a rate from their local bank. Let x represent time in years and p the amount of money financed, the value y for the monthly payment can be determined (see fig. 5). The “trace command” can give points on the curve. Fig. 5 The monthly payment for an amortized loan. year algebra students can be introduced to the concepts of slope and y-intercept (see fig. 6) by using animate with: Fig. 6 Discovery of slope and y-intercept concepts. In both curricular content and instruction style, there “should be a renewed effort to focus on exploring patterns, not just learning formulas” (National Research Council, 1989). ‘Animate’ works in 3-D plots as well. One choice might be:
AFDA.7 The focus of this standard is on the interpretation of descriptive statistics, z-scores, probabilities, and their relationship to the normal curve in the context of a data set. Descriptive statistics include measures of center (mean, median, and mode) and dispersion or spread (variance and standard deviation). Variance (σ 2) and standard deviation (σ) measure the spread of data about the mean in a data set. Standard deviation is expressed in the original units of measurement of the data. The greater the value of the standard deviation, the further the data tends to be dispersed from the mean. In order to develop an understanding of standard deviation as a measure of dispersion (spread), students should have experiences analyzing the formulas for and the relationship between variance and standard deviation. The normal distribution curve is the family of symmetrical, bell-shaped curves defined by the mean and the standard deviation of a data set. The arithmetic mean (μ) is located on the line of symmetry of the curve and is approximately equivalent to the median and mode of the data set. The normal curve is a probability distribution and the total area under the curve is 1. The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to Identify the properties of a normal distribution. (a) Describe how the standard deviation and the mean affect the graph of the normal distribution. (a) Given standard deviation and mean, calculate and interpret the z-score for a data point. (b) Compare two sets of normally distributed data a standard normal distribution and z-scores, given mean and standard deviation. (b) Represent probability as area under the curve of a standard normal distribution. (c) Use a graphing utility or a table of Standard Normal Probabilities to determine probabilities associated with areas under the standard normal curve. (c) Use a graphing utility to investigate, represent, and determine relationships between a normally distributed data set and its descriptive statistics. (a, b, c)
Let g(x) = − 7x + 4. Find the following: a. b. g(2) c. g(-1) d. g(0) Let f (x) = 3x2 − 1. Find each of the following: a. f (9) b. f (‐2) c. f (5) d. f (0) Let g(x) = ‐4x2 − 3x − 7. Find the following: a. g(‐4) b. g(‐1) c. g(0) d. g(3) Let f (x) = x2 − 2x. Find each of the following: a. f (-5) b. f (2) c. f (‐8) d. f (1)
Equation Preliminaries Choose two safe prime numbers p and q, form , and determine . Safe prime numbers are of the form , where p is also a prime. Define the function Equation Note: that is usually an exponential . The notation used is a little awkward because only the exponential should be calculated . The division by cannot be accomplished because has no MMI . The numerator should be a multiple of , and the “normal” division should result in an integer with no residue. Choose a generator value such that Equation Note: See section 6.12 regarding choosing values of . The public key is . The private key is λ. Encrypt The plaintext message is . Choose a random number . Calculate the encrypted message Equation Decrypt Plaintext Equation Explanation The Generator g Starting from the Carmichael function Equation 63. Equation If we use binomial expansion of the polynomial, we get where
Algebra 1A/B Syllabus Teacher: Mr. Justin Bonner Email: Room: 4-302 Dear Students and Parents: Welcome to Algebra 1A/B! I am super excited to get started in meeting you and beginning to set the tone for high school mathematics. I have a Mechanical Engineering Degree from the University of South Florida and I was previously a Project Engineer at Johnson Controls Inc. I am passionate about trying to make a positive impact in the community that I have lived in for the majority of my life. The chance to provide transformative, opportunity-expanding, super EXCITING mathematical experience for your child is what motivated me to leave the engineering field. By enrolling at THE Boca High School, your family has made a commitment to high standards and work ethic. I feel the best opportunity to get everything your student can from this class is when I can reinforce the expectations that you have for your child at school. If at any time your student is feeling unmotivated, behind, or frustrated in anyway, please let me know immediately. I am here for your student, and will reflect on my practice to make the most out of the experience for both your student and myself. Thank you for your time! I am looking forward to working together to make this school year amazing! Sincerely, Justin Bonner
114. Emily is selling candy bars for $1.50 each. The function f(x) = 1.5x gives the total amount of money Emily makes after selling x candy bars. Give the domain and range for this function. Domain: ______________Range: ___________ Learning Target: Using Intercepts Find the x- and y-intercepts. 115. 116. 117. –4x + 2y = –16 118. 7x – 4y = 28 x-int: _____ y-int: _____ x-int: _____ y-int: _____ x-int: _____ y-int: _____ x-int: _____ y-int: ____ Graph the equation. Label the points where the line crosses the axes. 119. 5x – 2y = –20 120. –2x – 4y = –8 121. –3x + 4y = 12 x-int: _____ y-int: _____ x-int: _____ y-int: _____ x-int: _____ y-int: _____ Learning Target: Rate of Change and Slope 122. The table shows the average cost per gallon of gasoline. Find the rates of change for each time period. Year 1995 2000 2001 2003 2007 Cost ($) 1.35 1.55 1.20 1.90 2.70 1995-2000: ________ 2000-2001: ________ 2001-2003: ________ 2003-2008: ________ During which time interval did the cost per gallon increase at the greatest rate? Tell whether the slope of the line is positive, negative, zero, or undefined. Then find the slope of each line. 123. 124. 125. positive/negative/zero/undefined positive/negative/zero/undefined positive/negative/zero/undefined
Identity – All Real Solutions 1 5 B –a2 – 4a – 14 4y6 6x2 – 17x – 14 x2 + 14x + 49 m = 3:30 PM -1 10e6 8n2 – 4n + 5 5a(x2 + y2) (5x + 3)(5x – 3) 2x(x + 2)(x + 6) (6x + 7)(x + 3) (7n – 1)2 0, 7, 12r x + 1 - 8:7 9 - 63 and 72 6 kg of $5 nuts and 3kg of $10 nuts 36 minutes 9 X 104 (graph) (graph) x + 2y = -2 y = x + 2 -35; -8 {11, 5, 2, -1, -7} (2, -2) (-1, -2) (3, -5) 26 dimes, 36 nickels Jet – 650 km/hr, wind – 50 km/hr 54 Betty – 15 years old, Don – 36 years old x < -1 -3 < c < 4.5 (graph) u > 6 or u < 4 (graph) 260 4x2 29 -6 - 8 2, -6 5 ± 2
Answer: MAFS.912.S-ID.1.2 Also assesses MAFS.912.S-ID.1.3 Answer: 1-stays the same 2-descreases 3-stays the same 4-decreases MAFS.912.S-ID.2.5 Answers: Line 1 – 13, 23 Line 2 – 31, 20 Line 3 – 48, 35
Describe any patterns you see in the tables Does f(x) mean f “times” x? Explain. Activity 3.3.4 Problem The graph below shows the altitude during a hot air balloon ride with Berkshire Balloons. The altitude of the hot air balloon is a function of time. Hot Air Balloon Find the domain and range of the function graphed above. Domain: Find ƒ(30) and explain what it in the context of the problem. If ƒ(x) = 100, find all values of x and explain what they mean in the context of the problem. When is the balloon at 200 feet? For how long are you flying at an altitude at or above 200 feet? If ƒ(x) = 300, find all values of x. Exit Slip 3.3.1 Problem Timmy gets paid $20.00 to baby-sit plus $5.00 for every room he cleans, r, at his Aunt’s house. His total payment, P, is represented by the equation . Write the equation in function notation. Find P(4). What does P(4) mean in the context of the problem? Find the value of r which satisfies the equation P(r) = 35. What does the solution of the equation P(r) = 35 mean in the context of the problem?
Exit slip 3.3.2 Problem Riot signed up with an online network. The network charges customers $25.00 per month but pays customers $0.02 for every song that they upload from their music collection. Riot’s monthly cost, C, depends on the number of songs that he uploads during the month, s, and is represented by the equation . Write the equation in function notation. Find C(200). What does this mean in the context of the problem? Find the value of s which satisfies the equation C(s) = $12.08. What does the solution of the equation C(s) = $12.08 mean in the context of the problem? How many songs would Riot have to upload in a month in order for his membership to be free? Activity 3.3.4a Problem Ben’s free follows a curved path. It goes up and then comes back down. The height of the ball h (in meters) at time t (in seconds) is given by the equation . Independent variable: Dependent variable: Use function notation to express the function: We can say ___________________________ is a function of __________________________. Complete the table below:
25. Which of the following best describes the data in the table? A. Exponential with a growth factor of 3 B. Linear with a rate of change of 6 C. Quadratic with a second difference of 12 D. none of the above 26. Use the table below to help determine which function has the greatest value as x gets larger and larger. A. has the greatest value as x gets larger and larger. B. has the greatest as x gets larger and larger. C. has the greatest value as x gets larger and larger. D. has the greatest value as x gets larger and larger.
F. G. H. I. J. K. L. M. Alternative Item Answers # Stnd IM Ans 3. alt A.REI.3 -2.00 5. alt A.REI.3 A.REI.1 F, H, I 15/16. alt F.IF.1 F, H, J, K, L 19. alt F.IF.5 G, J 36. alt F.IF.4 G, H, K 48. alt A.REI.5 A.REI.6 +7.00 51. alt A.REI.12 I, M
Algebra 1 Miss Sobanski 2018-2019 Contact Information www.csobanskimath.weebly.com (860) 923-9303 ext 216 Available: Friday 2:10 - 2:30 and by appointment during XC Season (September 3rd to November 15th) Monday to Friday 2:10 - 2:30 (After November 19th) Class Materials Chromebook and Headphones Graphing Calculator (TI-83, TI-83 Plus, TI-84, Plus) Provided in class but may be useful for home 3 Ring Binder Tab Dividers Lined Paper/Graph Paper Pens/Pencils Ruler Math and Focus Areas Patterns and Sequences Features of Functions Linear and Exponential Functions Equations and Inequalities Descriptive Statistics Exponents Quadratic Functions Quadratic Equations will be a total of: 8 Math Units 9 Focus Areas 5 Additional Focus Areas 3 Challenge Grading Policy Students receive grades that are designed to reflect their learning and growth throughout the year. Math Concept Units (70%):
Example 6: (x + 2)(x - 7) = 5 3[(x + 2)(x - 7)] = 3[5] 1(x + 2)(x - 7) = 15 x 2 - 5x - 14 = 15 x 2 - 5x - 29 = 0 a = 1 b = -5 c = -29 Remember, to be a quadratic equation, the integers a, b, and c must have a greatest common factor of 1. Example 7: x 3 - 2x 2 + 1 = 0 is not a quadratic equation because it contains a third-degree term. Example 8: 3x - 11 = 0 is not a quadratic equation because it does not contain a second-degree term. In fact, you may recall that this is a linear equation. Solve Quadratic Equations Graphically The solution of the quadratic equation is the point or points on the graph where y is equal to zero, or the x-intercepts. If the parabola never crosses the x-axis, there is no solution to the equation. Example: The parabola shown is the graph of y = x 2 - 4x + 5. Find the solutions of the quadratic equation 0 = x 2 - 4x + 5. Solution: The solutions are the x-intercepts. The parabola does not cross the x-axis. There are no solutions to the quadratic equation. The solution set of 0 = x 2 - 4x + 5 is Ø.
Objective Level 2 3 Level 4 5 13. Solve systems of linear equations -Limited to 2x2 systems of equations. -Integer coefficients for all equations -Coefficients are integers and solutions limited to integers and common fractions (halves, quarters, etc) -Systems are in same linear format -No limit to solutions for 2x2 systems. -Extend topic to include 3x3 systems. -All solutions to 3x3 systems kept as integers. -Systems given are in mixed linear formats -No limit to coefficients and solutions. -Graphical representation of 2x2 systems Topic extensions: -Solving 3 dimensional systems of linear equations. -Graphical representation of the case of no solution and infinite solutions for 3 dimensional systems. -Specifying the vector solutions of an infinite solution 3x3 system. 14. Solve real world problems using systems of inequalities. -feasible regions limited to 3 with only one being oblique -distinguish between points on boundary lines and those inside the feasible region -Feasible regions limited to 3 oblique lines or 4 lines (at most 2 being oblique) -uniform formats presented Brief diagnostic review of topic formats presented Topic extensions: -Modeling real-world scenarios as linear inequalities (e.g. animal dietary requirements). 15. Use linear programming to real-world problems** Not Taught -Constraints given -No more than 3 constraints -Only one line as oblique -All integer solutions -No constraints given -All integer solutions -no limit to formats of lines -compound inequalities often -feasible regions extended to uncommon quadrilaterals and pentagons -extend to discrete math with lattice points -No constraints given -Non integer solutions likely 16. Describe and perform operations on matrices. Solve systems through Not Taught -Operations limited to 2x2 matrices by hand -Systems of equations limited to a 2x2 systems using inverses - Writing and solving systems of equations of 3x3 system using matrices on graphing utility - Use and application of Cramer’s Rule - Writing and solving systems of equations of 3x3 systems matrices - Use and application of Cramer’s Rule -See the advantages of using matrices to solve systems Topic extensions:
Name____________________________________ Date _________________ Period_____ Complete the using what you know about linear functions and slope-intercept formula. Vocabulary (define the terms) Find the Slope of the Line Find the of the Line Express in Form Express in Form Review y-intercept of a line y = 2x + 1 y = 4x – 5 m = -5 and the y-intercept is 1 m = -2 and a point on the line is (-3,4) Solve 3x + 2 = 5x - 6 x-intercept of a line y + 3x=5 Through (1,3) and (0,4) m = 0 and the is -4 m = - and a point on the line is (2,3) |x – 1| = 3 Linear function 2y – 5x = 1 3x – y = -6 9x +6y = -18 Contains the points (2,3) and (5,4) Evaluate f(x) = -9x + 2 when x = 6 Graphing Practice: Graph each function. Name____________________________________ Date _________________ Period_____ 1. 2y = 4x + 8 2. 2x – 3y = 6 y-
Algebra II Course Outline and Pacing Topic Related Chapter TN Standard Approximate Pacing for split class Chapter 1 Expressions, Equations, and Inequalities A2.A.CED.A.1 A2.A.CED.A.2 5 Chapter 2 Functions, Equations, and Graphs A2.F.BF.B.3 A2.F.IF.B.3 A2.N.Q.A.1 A2.F.IF.A.2 A2.F.BF.A.1 A2.F.LE.B.3 5 Chapter 3 Linear System A2.A.REI.C.5 A2.A.REI.C.4 A2.A.REI.D.6 5 Chapter 12 Matrices ACT 2 Quadratic Functions and Equations Chapter 4 A2.F.IF.A.1 A2.F.BF.B.3 A2.N.CN.A.1 A2.N.CN.B.3 A2.N.CN.A.2 A2.A.REI.B.3 A2.A.REI.B.3a A2.F.IF.B.5 15 days Polynomials and Polynomial Functions Chapter 5 A2.F.BF.B.4 A2.F.BF.B.4a A2.N.RN.A.1 A2.N.RN.A.2 A2.A.REI.A.2 A2.F.IF.B.3b A2.A.APR.C.4 A2.A.SSE.B.2 A2.A.APR.B.3 10 days Total Days 42 End Fall 9-weeks – Give Test Start 1st 9-weeks Spring Semester Review 4-5 10 days Radical Functions and Rational Expressions Chapter 6 A2.F.IF.B.3 A2.F.BF.B.3 A2.F.IF.B.3a A2.A.SSE.A.1 A2.A.SSE.A.1a A2.F.BF.A.1b A2.A.APR.A.1 5-10 days
Student Name: List three things you learned about your new math teacher: 1) 2) 3) How can a test score be improved? When retaking a test, how soon must you do the retake? What must you do to receive credit for answering a homework problem? List the school supplies you need to have at your desk every day? Get your answers from the Class Expectations sections on the other side, Choose and list the five expectations that you think are most helpful so that our classroom is a good learning environment? 1) 2) 3) 4) 5)
properties of the quantity represented by the expression.★ Factor a quadratic expression to reveal the zeros of the function it defines. Complete the square in a quadratic expression to reveal the maximum or minimum of the function it defines. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. A-SSE.4 4. Derive the formula for the sum of a finite geometric series (when the common is not 1), and use the formula to solve problems. For example, calculate mortgage payments.★ A-APR.1 1. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. A-APR.2 2. Know and the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x). A-APR.3 3. Identify of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. In Both In PARCC Only In Appendix A Only A-APR.4 4. polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x2 + y2)2 = (x2 – y2)2 + (2xy)2 can be used to generate Pythagorean triples A-APR.5
The Real Number System – RN Quantities – Q The Complex Number System – CN Vectors and Matrix Quantities – VM High School Algebra – HSA Seeing Structure in Expressions – SSE Arithmetic with Polynomials and Rational Expressions – APR Creating Equations – CED Reasoning with Equations and Inequalities – REI High School Functions – HSF Interpreting Functions – IF Building Functions – BF Linear, Quadratic and Exponential Models – LE Trigonometric Functions – TF High School Geometry – HSG Congruence – CO Similarity, Right Triangles, and Trigonometry – SRT Circles – C Expressing Geometric Properties with Equations – GPE Geometric Measurement and Dimension – GMD Modeling with Geometry – MG High School Statistics and Probability – HSS Interpreting Categorical and Quantitative Data – ID Making Inferences and Justifying Conclusions – IC Conditional Probability and the Rules of Probability – CP Probability to Make Decisions – MD Algebra II Domain Cluster The Real Number System 1. Extend the properties of exponents to rational exponents 2. Use properties of rational and irrational numbers
The information contained in this document provides one way to frame discussions about scope and sequence of the standards leading to the development of local curriculum maps. This document incorporates the priorities assigned to each standard in the PARCC Model Content Frameworks (Major, Supporting, and Additional), which will help guide discussions related to priority, focus, and time allocated for each topic. In the spring of 2013, a committee composed of Arkansas educators categorized each standard based on its cognitive demand or complexity. These categories are defined below. Districts are encouraged to approach the development of a curriculum in a manner that best serves the needs of their students. Frameworks Committee Categorization of Algebra II Standards (indicated in the column to the far right of each standard): Statistics (S) Compare and Analyze (CA) Create and Model (CM) Compute and Solve (CS)
ALGEBRA II – 2018-19 February 27, 2019 Today’s Agenda (Day 112) Homework SAT Stuff #6 Practice Problems Section 8.4 Exercise, p. 558 [#8, 10, 12, 14, 18, 20, 24, 28, 30, 32, 36] Activity Section 8.5 – Variation Functions Direct variation Joint variation Inverse variation Write and solve an inverse variation Combined variation HOMEWORK: Review Ch 8 – Rational Functions and Relations Complete Section 8.5 Exercise, p. 566 [#8-38 evens] Work on Term 3 Project – see msbeland.weebly.com; in PAIRS REMINDERS: Section Exercise 8.5 – Feb. 28 Chapter 8 Test 1 Term 3 Project – March 5
TN Ready Algebra 2 Pacing Guide Unit/Chapter Topic TN Ready Standards Days Honors Algebra 2 Days Regular Algebra 2 First Degree Equations and Inequalities Chapter 1 Expressions, Equations, and Inequalities A2.A.CED.A.1 A2.A.CED.A.2 2.5 5 Chapter 2 Functions, Equations, and Graphs A2.F.BF.B.3 A2.F.IF.B.3 A2.N.Q.A.1 A2.F.IF.A.2 A2.F.BF.A.1 A2.F.LE.B.3 2.5 5 Chapter 3 Linear System A2.A.REI.C.5 A2.A.REI.C.4 A2.A.REI.D.6 2.5 5 Chapter 12 Matrices ACT 1 1 Polynomial and Radical Equations and Inequalities Chapter 4 Quadratic Functions and Equations A2.F.IF.A.1 A2.F.BF.B.3 A2.N.CN.A.1 A2.N.CN.B.3 A2.N.CN.A.2 A2.A.REI.B.3 A2.A.REI.B.3a A2.F.IF.B.5 5.5 7 Chapter 5 Polynomials and Polynomial Functions A2.F.BF.B.4 A2.F.BF.B.4a A2.N.RN.A.1 A2.N.RN.A.2 A2.A.REI.A.2 A2.F.IF.B.3b A2.A.APR.C.4 A2.A.SSE.B.2 A2.A.APR.B.3 5.5 7
Chapter 6 Radical Functions and Rational Exponents A2.F.IF.B.3 A2.F.BF.B.3 A2.F.IF.B.3a A2.A.SSE.A.1 A2.A.SSE.A.1a A2.F.BF.A.1b A2.A.APR.A.1 A2.APR.A.2 A2.A.APR.C.4 A2.A.REI.A.2 5 6.5 TOTAL DAYS 24.5 36.5 MIDTERM ----------- ----------- ----------- ----------- Advanced Functions and Relations Chapter 7 Exponential and Logarithmic Functions A2.F.BF.B.3 A2.S.ID.B.2 A2.F.IF.B.4 A2.F.IF.B.4a A2.F.LE.A.2 A2.F.LE.B.3 A2.F.IF.B.3c 4 5.5 Chapter 8 Rational Functions A2.F.IF.B.3 A2.A.REI.A.2 A2.REI.A.1 4 5.5 Chapter 10 Quadratic Relations and Conic Sections Equation of a circle only center and radius 0.5 0.5 Discrete Mathematics Chapter 9 Sequences and Series A2.F.BF.A.2 A2.F.BF.A.1 A2.ASSE.B.3 A2.ACED.A.2 A2.F.LE.A.1 3.5 5 Chapter 11 Probability and Statistics A2.S.CP.A.1 A2.S.CP.A.2 A2.S.CP.A.3 A2.S.CP.A.4 A2.S.CP.B.5 5.5 7
A2.S.CP.B.6 A2.S.IC.A.2 A2.S.ID.A.1 A2.S.IC.A.1 A2.S.ID.B.2a Trigonometry Chapter 13 Periodic Functions and Trigonometry A2.F.TF.A.1 A2.F.TF.A.1a A2.F.TF.A.1b A2.F.TF.A.2 5 6.5 Chapter 14 Trigonometric Identities and Equations A2.F.TF.B.3 A2.F.TF.B.3a A2.F.TF.B.3b 2.5 2.5 TOTAL DAYS 25 32.5 FINAL EXAM ---------- ---------- ---------- ----------
Beginner 1 Point Novice 2 Points Intermediate 3 Points Expert 4 Points Score Clear Roles Reading/Finding Factors Include Charts and Graphs Participation Visual Appeal for Power Point Visual Appeal for 3 Sided Board Participation with Power Point Scale: 18-20: Expert 15-17: Intermediate 10-14: Novice 6-9: Beginner Grade: Expert: A Intermediate: B Novice: C Beginner: D Final Score:_______ Grade: Group Grading Rubric Individual Grading Rubric Beginner 1 Point Novice 2 Points Intermediate 3 Points Expert 4 Points Score