Study Guide Fall and Spring Updated 1. Order of Operations a. PEMDAS 2. Translating into Algebra a. Examples: 5 times the sum of x and 3 3. Classifying Real Numbers a. Rational, Irrational, Whole, Integer, Natural. 4. Polynomials a. Add and Subtract b. Multiply (There are three methods we learned) c. Factor a GCF d. Factor (Guess and Check or AC) e. Special Cases f. Naming (First and Last) g. Perimeter and Area (Word problems. Shaded Region) 5. Exponents a. What is an exponent a short cut for? b. Properties of exponents (We had a handout on these) i. What does an exponent of 0 mean? ii. What does a negative exponent mean? iii. When do you add exponents? iv. When do you multiply exponents? v. When do you leave the exponents alone? c. Rational Exponents !
i. Fractions as the exponent. Simplify: (𝑛! )! !
6. Radicals : a. How do you simplify the radical b. What does the number outside the radican mean? How does it help simplify? !
c. Simplifying 24 or 81𝑣 ! ℎ! 7. Going from Rational to Radical and Radical to Rational a. What does it mean to be the !
? !
b. What does it mean to be raised to the power? !
8. Coordinate Plane a. Can you tell me the coordinates of a point on the coordinate plane? b. Can you graph the coordinate (-­‐3, 2) c. What can you tell me about the coordinates in each quadrant? d. What are the coordinates of the y-­‐int? x-­‐int? 9. Graphs and Functions a. What does a quadratic function look like? Linear? Exponential? b. What is a relation? What is a function? c. What is the vertical line test and how does it help? d. What is the domain? Range? How do you list them? e. Function notation: f(x) i. Can you tell me the range of a function given the domain? 10. Lines a. Parallel Lines, Perpendicular Lines, Same Lines i. Identify their slopes. How do you know two lines are parallel, perpendicular, the same line? ii. Find the equation of a line parallel, perpendicular, or same as a given equation or. 11. Linear Functions/ Inequalities a. What is the standard form of a linear function? b. Slope i. Find using a graph, table, or two points ii. What is the slope of a vertical line? a horizontal line? c. Y-­‐int d. Write the function rule given: i. Table ii. Two points iii. Graph e. How do you know if a function is linear? f. How does your NEXT-­‐NOW rule look with a linear function (think of slope and y-­‐int) g. How do you find the linear regression model? (line of best fit) Hint: Calculator’ h. Graph a linear function i. Given a function rule ii. Given slope and y-­‐int i. Solve for x i. One-­‐Step, Two-­‐Step, Multi-­‐Step Equations and Inequalities ii. Graph equations or in equalities on the coordinate plane or the number line. iii. Word Problems involving equations and inequalities 12. Systems of Equations and Inequalities a. Graphing a system on the coordinate plane i. Knowing the solution to a system of equations is: 1. Intersecting Lines: Coordinate Point 2. Parallel Lines: No Solution 3. Same Line: Infinitely many solutions ii. Knowing the solution to a system of inequalities is the overlapping shaded region b. Word Problems where you have to set up the system or equations or inequalities and solve i. Identify the two variables. Be able to solve for either or both and explain what that solution means. c. Solving systems by graphing, elimination, and/or substitution. Be able to use elimination or substitution if you don’t have a calculator (Sometimes one method is preferable over another). d. Linear Programming i. Graphing multiple equations and/or inequalities and being able to find the solution (One of the vertices of the bounded figure). ii. The money part comes at the end iii. Set up your multiple equations given a word problem by identifying the variables first. iv. Explain your solution 13. Exponential Functions a. What is standard form of an exponential function? b. What does your NEXT-­‐NOW rule look like? (Think of your initial amount and rate) c. How do you know a function is exponential? d. Know your translations. i. Vertical Translation: y = b · ax ± c 1. If it’s + c then the graph moves up c units 2. If it’s – c then the graph moves down c units ii. Horizontal Translation: y = b · ax ± c 1. If it’s + c then it moves left c units 2. If it’s – c then it moves right c units 14. Quadratic Functions a. What is the standard from of a quadratic function? b. What is the shape of a quadratic function? c. What does a negative a value do to the graph? (The coefficient of x2) d. What does the general form look like when we are talking about throwing an object or shooting it out of a cannon? e. What does the general form look like when we are talking about dropping something? f. What does the constant term mean in the situations mentioned in d and e. g. What does the linear term mean in the situations mentioned in d and e? (The term with a t) h. What does the -­‐16t2 represent? i. How do you calculate a maximum? (Remember your calculator steps) j. What do you know about an object when it hits the ground? (The height is 0) k. If I give you a function, can you list everything you know about it? l. What are all of the things that a does to the graph? m. What does c do to the graph? n. How do you find income? o. How do you find profit? p. Factor to solve (when does it hit the ground, what is the max charge to still make profit) You don’t necessarily need a calculator to solve these‼ i. To solve you need to set each of your factors to 0. If this is a real world problem, make sure your answer makes sense. Can you have negative money or negative people? 15. Geometry: a. Find the perimeter of: i. Any figure (They could be any sided bounded figure) b. Find the area of: i. Circle (in terms of pi and decimal) ii. Rectangle iii. Square iv. Parallelogram v. Triangle c. Find the circumference of: i. Circle ( in terms of pi and decimal) d. Volume: i. Prism 1. Rectangular, Triangular, ii. Cylinder iii. Cone iv. Pyramids e. Real World Problems i. Finding area, volume, perimeter given real world problems f. Coordinate Geometry i. Be able to use the distance and midpoint formula in coordinate geometry to find the perimeter of a figure. ii. Be able to use the distance and midpoint formula given 2 points, given a line on the coordinate plane. iii. Be able to identify a quadrilateral given 4 coordinate points (distance formula, midpoint formula, slopes) iv. Find the area or perimeter of a figure on the coordinate plane v. Find the area of the shaded region? g. Points, Lines, Planes i. Are points collinear, coplanar? ii. Where do two lines intersect? A line and a plane? A line lying on the plane? Two planes intersect? h. Segments and Angles i. Given a segment, what is the length of the segment? Length of parts of the segment? ii. Given an angle, what is the measure of the angle? What is the measure of the parts of the angle? iii. Types of angles: Acute, Right, Obtuse i. Parallel Lines and Transversals i. What do you know about angles given two parallel lines and a transversal? j. Quadrilaterals i. Properties of: 1. Kite 2. Trapezoid a. Isosceles Trapezoid 3. Parallelogram 4. Rectangle 5. Rhombus 6. Square 16. Statistics i. Data Points ii. Histograms and Dot Plots iii. Box Plots 1. Skewed 2. Center 3. Mean, Median, Range (Spread) iv. 5 number Summary 1. Min, Q1, Q2(median), Q3, Max v. Two-­‐Way Frequency Tables 1. Identify joint frequency, marginal frequency, relative frequency (%) 2. Set up a two-­‐way frequency table vi. Standard Deviation 1. On your calculator. 2. The average distance from mean vii. Scatter Plots 1. Draw on graph paper and find on calculator 2. Correlation a. Positive, Negative, Weak, Strong b. Correlation coefficient : r (Closest it is to 1, stronger it is) 3. Models a. Which model fits the data best? b. Residual Plot (How do I know I picked the model that fits the best)?