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Mu Alpha Theta

This tutoring session provides an overview of the Math section of the SAT, including specific topics, tips, and strategies for solving linear equations, literal equations, absolute value equations, interpreting linear equalities, graph analysis, systems of equations, scatterplots, and data distribution.

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Mu Alpha Theta

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  1. Mu Alpha Theta SAT TUTORING SESSION 1

  2. WHAT IS THE MATH SECTION OF THE SAT? • Second of two sections of SAT • 2 Main Sections: • Non-Calculator Section: 25 minutes (15 multiple choice questions, 5 grid-in questions) • Calculator Section: 55 minutes (30 multiple choice questions, 8 grid-in questions) • Specific Topics: • Heart of Algebra: 19 Questions • Problem Solving and Data Analysis: 17 Questions • Passport to Advanced Math: 16 Questions • Additional Topics in Math: 6 Questions

  3. TOPICS COVERED TODAY (DAY 1) • Heart of Algebra • Solving literal equations • Linear Equations • Inequalities • Functions • Graphs • Systems of Equations • Data Analysis

  4. DAY 2 TOPICS • Polynomials • Radicals and Exponents • Geometry • Trig • Complex Numbers • Graphing from Data Tables • Quadratics • Word Problems

  5. LINEAR EQUATIONS AND INEQUALITIES You’re just gonna be solving for x (or whatever variable they choose) Solve Using Reverse PEMDAS to get all the x values on one side and then without a coefficient. For linear inequalities, when you multiply or divide by a negative number, you flip the inequality

  6. CALCULATOR

  7. SOLUTION Isolate x by subtracting 3x and adding three on both sides -2≥ x or x ≤ -2 Check each answer choice. -1 isn’t less than or equal to -2, so the answer is A.

  8. LITERAL EQUATIONS Literal Equations: One that is defined only by variables with few numbers. Tips and Tricks: Use algebra to isolate the variable, and use reverse PEMDAS. *Remember: even though the problem looks complex, you are just rearranging the equation • Reverse distribute, or factor out! • Ex: 3x + 5cx = y, solve for x • x(3+5c) = y, (Factor) • x = y / (3+5c), (Divide to get x by itself)

  9. NO CALCULATOR

  10. SOLUTION Although complicated looking, this problem honestly isn’t that bad. Noticing that P is on the outside, and P is what you’re trying to find, you can divide by the huge fraction on both sides, which will give you choice B after some solving. Remember: dividing by a fraction is the same as multiplying __________by the reciprocal.

  11. ABSOLUTE VALUE Absolute Value • Isolate the Absolute Value • Split into 2 equations • Ex: |x+2| = 3 becomes • x+2 = 3 and • x+2 = -3. • Solve both

  12. CALCULATOR

  13. SOLUTION Subtract 1 from both sides to isolate the absolute value term. Notice that an absolute value equation will never equal -1, so there is no such value of n, and the answer will be D.

  14. INTERPRETING LINEAR EQUALITIES The SAT will include a couple of these types of questions. Don’t get confused by the word problem, they are just asking for what a coefficient or variable represents in the equation. Just read the question carefully.

  15. SOLUTION In the problem, it’s stated that n = the number of landscapers and h = the number of hours. Since 12 is multiplied by both (12nh) it means that 12 dollars is how much per landscaper per hour. (Answer A)

  16. GRAPHS These appear mostly on the calculator section, and you usually don’t need a calculator. Things to know: • X/Y intercepts • Vertex of a parabola • Finding slope of a best fit line • Increasing/Decreasing • Minimum/Maximum • Getting an equation from a line

  17. SYSTEMS OF EQUATIONS VERY common on no-calc section Approach: Solve for one variable, plug in the expression to the other equation to find the other and then plug back in to solve for the other one. ALWAYS plug your results back into both equations to check. Calculator Trick for calculator section

  18. NO CALCULATOR

  19. SOLUTION Solve the bottom equation for x, x = 2y+19 Plug your result of x into the top equation: 3(2y+19) + 4y = -23 Distribute & combine like terms: 10y + 57 = -23, or 10y = -80 Solve for y: y = -8 Plug back in to find x: x = 2(-8) + 19, X = 3

  20. SCATTERPLOTS Look at overall trends, outliers are usually not important: are the majority of the points increasing? Decreasing? etc Go through each and every answer choice and note whether it makes sense in the graph. If specific points are given, mark them on the graph

  21. SOLUTION The graph is generally decreasing Which answers list this as a possibility? B and C However, B says it is ONLY decreasing while C says it increases a little first, then decreases. So C is the correct answer

  22. DATA DISTRIBUTION Mean: Average (changes when an outlier is added/deleted) Median: Center of Data (changes depending on whether or not there are multiple data points with the same value) Mode: Most common data point (unlikely to change) Range: Difference between least and greatest values (only changes if outliers are added or deleted) Standard Deviation: Amount of variation (there will likely be one question about this...once you understand it it is an easy one to get right) The word problem will ask which of these will change, just remember the defs!

  23. SOLUTION Go through each answer choice • Mean: May be impacted because an outlier is being deleted • Median: Unlikely to change because the current median is 12 and there are multiple data points for 12. • Range: Definitely Impacted...without the maximum of 24, the new maximum is 16. This is a significant drop. So this is most likely the correct answer. • Confirm that it is NOT D by solving for mean with old and new values to check, however because the range drops so much, C is a safe answer if low on time.

  24. ANALYZING TABLES Probability: number of ways for event to occur divided by total possible outcomes First understand the table Circle/annotate the parts of the table relevant to the problem Then use the circled parts to answer the question *The SAT will try to trick you by including irrelevant data. Make sure you know what parts of the table to use.

  25. SOLUTION First note that the question only pertains to people who have remembered at least 1 dream, so the none category is useless to us. We are asked for people who remembered AT LEAST 1 dream from the Y group out of all people who remembered at least 1 dream. Therefore, we add up the 1-4 in Group Y and the 5+ in Group Y and divide by the total of 1-4 and the total of 5+, which comes out to 79/164, or choice C

  26. EXTRA PRACTICE Here are some more problems that go over the topics we covered today. Try some of them and come to morning math lab Monday through Thursday and ask a tutor about them if you have any questions.

  27. THANKS FOR COMING!!! We hope you felt better about some of the concepts covered today, and we hope to see you next time, Tuesday, October 1st, or Thursday, October 3rd.

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