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Name ___________________________________________________ Period ____________ Date ________________Intermediate IITerm 3 Final Review9.1 and 9.2: Scatter Plots and Lines of Best Fit:Things to remember:How to Find a line of best fit and write an equation for it:step 1: Draw a line that most closely splits the data points (this only works if it is a linear relationship).step 2: Using YOUR drawn line, find the slope (riserun) and the y-intercept (where it crosses the y-axis). step 3: Using the slope (m) and your y-intercept (b) from step 2, plug those values into the equation y=mx+b.Sample problems:1. The scatter plot below represents the relationship between the cost (y-axis) and the amount of memory of an MP3 player (x-axis).a. Interpret the scatter plot (positive, negative, no correlation; linear or non-linear; clusters; outliers). b. Give an equation for a line of best fit.c. Make a conjecture about how much a 10 gig MP3 player would cost.2. The scatter plot below represents the correlation between the number of cans of caffeinated soda a person drinks (y-axis) to the number of hours of good sleep they get the same night (x-axis).a. Interpret the scatter plot (positive, negative, no correlation; linear or non-linear; clusters; outliers). b. Give an equation for the line of best fit.c. Make a conjecture about how much sleep a person who drinks 6.5 sodas would get.4.7 (Linear and Nonlinear Functions)Things to remember:* In order for a function to be LINEAR, there must be a CONSTANT RATE OF CHANGE (slope; change in y-valueschange in x-values )* If the table shows an INCONSISTENT rate of change, that function is NOT LINEAR!Sample Problems: Tell if the function is linear or non-linear. If it IS linear, state the constant rate of change (slope). 1.2.3.4.5. If you were to compare the side length of a square (x) to its area (y), would this relationship be linear or nonlinear? Make an input/output table to investigate.4.9 (Qualitative Graphs)Things to remember:* Pay attention to the x- and y-axes and their labels. Describe what the graph is SHOWING, not what you think is happening. * Describe or draw each part of the drawing/story and don’t leave anything out!Sample problems:Describe in words what the graph is showing:1.2.3.4.Draw a graph for the given explanation:5. A child climbing up a ladder, then sliding down a slide. (Use distance from ground for y-axis; time for x-axis.)6. The change in water level of a pool from May to September. (Use water level for y-axis; time for x-axis.)7. A child jumping on a trampoline. (Use distance from ground for y-axis; time for x-axis.)8. A car speeding down the freeway; gets pulled over and ticketed; pulls back onto the freeway. (Use speed for y-axis; time for x-axis.)4.8 (Graphing Quadratic Functions)Things to remember:Rules of the game:* Greatest power is 2* “U” shaped* Opens UP if the number in front of the x2 is ___________________ * the lowest point is called the ______________________* Opens DOWN if the number in front of the x2 is _____________________ * the highest point is called the ________________* The number in front of the x2 makes the graph: * SKINNIER if ___________________ * WIDER if ____________________* The constant (plain old number after the x2) makes the graph: * MOVE UP if _______________________ * MOVE DOWN if _________________________If you can’t remember the rules, go back to what you know: an input/output table.xquadratic f(x)y-2-1012Sample problems:Graph the following quadratic equations: 1. y= -x2+42. y=12x2-2 3. y=4x2Write an equation for the following quadratic graphs:3.7 (Solving Systems by Graphing)Things to remember:Step 1: Put the equations in slope-intercept form (y=mx+b)Step 2: Graph the equations using the slope and y-interceptStep 3: The solution is where the two lines cross (x,y)Also, remember: If the lines cross, then there is ONE SOLUTION. If the lines are parallel, then there is NO SOLUTION. If both equations are the same line then there are INFINTIELY MANY SOLUTIONS.3.7 GraphingLevel 1:y=2x+1y=1+2x-825517399000Level 2:y=xy=3020101900Level 3:3y=2x+153x-y=41399716573500Level 4:Joanne bought 2 more apples than Jake. If Joanne and Jake bought 10 altogether, write and solve a system of equations by graphing to represent the situation.336578135034003.8 (Solving Systems Using Substitution)Things to remember:y=x+23x+7y=54Solve one equation for one of the variables. (in our example, y=x+2)Substitute into other equation. (in our example, substitute "x+2" for the “y” in the TEAM equation so the team equation becomes 3x+7x+2=54)Solve for other variable. (in our example, 3x+7x+14=54; 10x+14=54; 10x=40; therefore, x=4)Plug back into first equation. (in our example, y=x+2, so y=4+2)Solve for the first variable if needed. (in our example, y=6)** If you get rid of the variable(s), but you get a true statement (2=2 or 0=0), then there are INFINITELY MANY SOLUTIONS. **If you get rid of the variable(s), but you get a false statement (2=-2 or 0=6), then there is NO SOLUTION.3.8 SubstitutionLevel 1:y=14x+3y=23Level 2: x=y-12x+y=-11Level 3: 2x+y=-13y=-6x-3Level 4: A loaf of bread and a box of cereal cost $5.00. Three loaves of bread and two boxes of cereal cost $12.00. Write and solve a system of equations to find how much one loaf of bread costs and how much one box of cereal costs?3.9 (Solving Systems Using Elimination)Things to remember:Multiply one (or both) of the equations in order to create opposite coefficients. (2 and -2 are opposites, 5 and -5 are opposites)Add the two equations together.Solve for the remaining variable.Plug the solution back into one of the original equations.Solve for the other variable.** If you get rid of the variable but you get a true statement (2=2 or 0=0), then there are INFINITELY MANY SOLUTIONS. ** If you get rid of the variable but you get a false statement (2=-2 or 0=6), then there is NO SOLUTION.3.9 EliminationLevel 1:2x+3y=13-2x+5y=27Level 2:4x+3y=32x+-2y=-16Level 3:4x+2y=-105x+3y=-11Level 4:A dozen eggs and one jug of orange juice costs $6.00. Three dozen eggs and 6 jugs of orange juice costs $30.00. How much does one dozen eggs cost and how much does one jug of orange juice cost?9.3 Two-way Tables: To fill in a two-way table, first find the information that is given, then fill in any remaining information.The Venn diagram below compares the Timberline track students who purchased TMS track attire last year. -38735000Complete the two-way table below.HatsNo HatsTotalSweatsNo SweatsTotal-62230141605*The Venn diagram gives you the track students who purchased just hats, sweats and hats, just sweats, and neither. You have to add to determine the totals.00*The Venn diagram gives you the track students who purchased just hats, sweats and hats, just sweats, and neither. You have to add to determine the totals.Relative Frequency: subtotaltotal (written as a decimal, but used as a percent)2166647520702154555118938What are rows? Side to side199136023826001904337242400Columns? Up and downStep 1. Find the totals.Step 2. Find the relative frequency (in decimal form) by row or column.Step 3. Interpret the results (what do they mean).Complete the frequency table then find the relative frequencies by column, round to the nearest hundredth.? ?BushesNo BushesTotalTrees20;48;?No Trees5;12;?Total???What does this tell you about the people who planted bushes in their backyard? (Use relative frequency as a percent when talking about what it means.)9.4 (Descriptive Statistics)Mean: Add them up and divide.Median: Put them in order. Find the middle.Mode: Most occurring #.Range: Biggest # minus smallest #.Five Number Summary:Minimum: Smallest #Q1: 25% of dataMedian: Put them in order. Find the middle.Q3: 75% of dataMaximum: Biggest #Box-plot: Make sure that the number line has a scale (i.e. counts by 5s)Conclusion: Is the first 50% more spread out than the last 50%? Closer together? The same?Sample problem:The ages in months of babies when they got their first tooth are 6, 7, 9, 7, 4, 10, 12, 6, and 5. What is the mean, median, mode, and range age of these children when they got their first tooth?Mean:_____________Median:_____________Mode:_____________Range:_____________The number of patients that a dentist saw on different days throughout the month of December was 15, 4, 17, 25, 3, 13, 5, 15, 9, and 15. What is the Five-Number Summary?Minimum:__________Q1:__________Median:_________Q3:__________Maximum:________Draw a box-whisker plot for question 1 above (babies and age for first tooth).63514033500What is a conclusion that can be drawn from the box plot? ................
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