UNIT 1: Lesson 1 Solving for a Variable

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1 AMS I Final Exam Review Packet Name: UNIT 1: Lesson 1 Solving for a Variable To solve for equations you need to use inverse operations. List the inverse operation(s) you could use while solving Addition: Subtraction: Multiplication: Division: Square: Square root: Examples. Solve for x. The DECA club is selling t-shirts for a fundraiser. The equation for the profit in dollars, P, in terms of the number of t-shirts they sold, t, is P = 5t ( t). Use the equation to find the number of t-shirts they must sell to make a $400 profit. How many t-shirts must they sell to breakeven? 1

2 UNIT 1: Lesson 2 Linear Functions **Linear Function Vocabaulary and Formulas to remember.** An independent variable is a variable whose value determines the valus of other variables. A dependent varaible is a variable whose value is determined by evaluating expressions using independent variables. Helpful hint: in almost every case a measure of time is independent because no matter what time continues to pass on no matter what you are doing. Time is independent but how you spend your time is dependent on what you are doing. Write the formula for slope when given two points: change in y change in x = Y intercept: where a straight line crosses the y axis of a graph; the b in y=mx+b Point Slope Form: equation of a line requiring the slope and any point on the line Slope Intercept form: equation of a line requiring the slope and the y intercept Standard form: equation that can be used to describe all possible lines **NO decimals or fractions**

3 Write the equation in point-slope form. Slope of 2 and goes through ordered pair (3, -4) Rate of Change: the speed at which a variable changes over a specific period of time. Generally related as a ratio (function) between a change in one variable relative to a change in a corresponding variable.

4 Now think about a linear equation. Most linear equations are functions. That means for every value of x, there is a only one corresponding value of y. When you assign a value to the independent variable of x, you can compute the value of the dependent variable of y. C = (n -8) ; n=independent variable and C= dependent variable A graph represents a function when it can pass the A linear function has a constant or. Sketch two graphs that are linear functions and two graphs that are not linear functions. Linear Functions Non Linear functions Identify if the following situations are linear functions and give an explanation. YES or NO: X Y YES or NO: X Y

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7 UNIT 2: REGRESSION AND CORRELATION There are 4 types of outliers. Explain each of them below: An outlier for the x values only An outlier for the y values only An outlier for both x and y values Only an outlier when the x values and y values are considered jointly Correlation is ranked between 1 and -1 with the strongest correlation being closest to 1. We can rank the data as either strong or weak and positive or negative depending on the points on the graph.

8 e. How would you explain the correlation between the number of newspapers and the time it takes to deliver them? The following is the chart from January 7, Songs This week Last week Difference Squared difference Love Yourself 1 3 Hello 2 1 Sorry 3 2 Stitches 4 5 Stressed Out 5 6 Hotline Bling 6 4 What Do You Mean 7 7 Adventure of a 8 9 Lifetime Same Old Love 9 8 Ex s & Oh s Sum= 0 Sum= Spearman s Rank Correlation Formula r s=

9 a) Make a scatterplot of the data to predict how closely related the songs are between weeks. b) Predict whether the value of Spearman s Correlation r s will be closer to 1, 0, or -1. Use the scatterplot to help you explain your answer. c) Calculate the value of r s. Show your work.

10 Unit 3: Systems of Equations We have used three different methods to solve equations: Graphing, Substitution, and Elimination. How do you decide on a method to use in any particular problem? GRAPH: Use when both equations are in slope-intercept form (y=mx+b) SUBSTITUTION: Use when at least one equation is solved for x or y. ELIMINATION: Use when both are in Standard form (Ax + By = C) -4x + 8y = -20 3x 2y = 11 3x + 2y = 18 x = 1 + y

11 Be able to determine when there will be certain numbers of solutions. One Solution: No Solutions: Infinitely Many Solutions: Solve the following systems using any method you choose. y = x { y = 3 x 4x + 2y = 7 { x 0.5y = 10 y = 5 + 6x { 2y + 12x = 10