Algebra 1 SOL Review 1 - Finding MAD and Variance 1) Find the - PowerPoint PPT Presentation

Algebra 1 SOL Review

1 - Finding MAD and Variance 1) Find the mean of the data 2) Create the new data set (x is the existing data element) by calculating: For MAD, use 𝑦 − 𝜈 a) For variance, use 𝑦 − 𝜈 2 b) 3) Find the mean of the new data set – this is either MAD or variance 4) Find standard deviation by taking the square root of the variance

2 - Direct and Inverse Variation 1) First find k (It’s the same for all the data elements! And it tells what kind of variation you have!) 𝑧 a) For direct variation, use 𝑦 For inverse variation, use 𝑦𝑧 b) 2) Write the equation Direct is 𝑧 = 𝑙𝑦 a) 𝑙 Inverse is 𝑧 = b) 𝑦 3) Find the missing value if required

3 - Graphing Quadratics 1) Graph on the calculator (make sure the equation is in y=, f(x)=, or =0 format) Domain for all quadratics is all real numbers ℝ 2) 3) Range is: Up - ℝ ≥ 𝑧𝑑𝑝𝑝𝑠𝑒𝑗𝑜𝑏𝑢𝑓 𝑥ℎ𝑓𝑠𝑓 𝑗𝑢 𝑢𝑣𝑠𝑜𝑡 a) Down - ℝ ≤ 𝑧𝑑𝑝𝑝𝑠𝑒𝑗𝑜𝑏𝑢𝑓 𝑥ℎ𝑓𝑠𝑓 𝑗𝑢 𝑢𝑣𝑠𝑜𝑡 b) 4) Zeroes, roots, solutions, x-intercepts is where the parabola (graph) crosses/touches the x-axis

4 - Writing Equations of Lines 1) Find the slope (m) a) If not given, use two point and the formula 2) Find the y-intercept (b) If not given, use one point and the slope, plug into 𝑧 = 𝑛𝑦 + 𝑐 a) and solve for b Write the equation in 𝑧 = 𝑛𝑦 + 𝑐 format 3) 4) Vertical lines are always x=the x-coordinate where it crosses the x-axis (m=undefined) 5) Horizontal lines are always y=the y-coordinate where it crosses the y-axis (m=0)

5 - Factoring and Solving Quadratics 1) There are 3 types of factoring: Rainbow factoring – use when the format is 𝑏𝑦 2 + 𝑐𝑦 + 𝑑 a) Difference of squares – use when the format is 𝑦 2 − 𝑧 2 b) c) GCF – use when there is a GCF between all the terms – can be used with Rainbow and Difference of Squares 2) Factor to either two binomials or a monomial and binomial (GCF only)

5 - Factoring and Solving Quadratics Continued 3) To solve, set each binomial or monomial equal to zero and solve for the variable. 4) The answers are known as the roots, solutions, zeroes, or x- intercepts.

6 - Regression (Line or Curve of Best Fit) 1) Enter the data into L1 and L2 using Stat-Edit on the calculator. 2) Find the equation using Stat-Calc and: a) Line – use 4 (LinReg) b) Curve – use 5 (QuadReg) 3) Record the equation (round all decimals to 2 decimal places) 4) Use equation to make predictions for a given x value.

7A - Systems of Equations 1) Three possible solutions a) One point – lines intersect b) No solution – parallel lines c) Infinite solutions – same line 2) Use graphing to solve if both equations are in slope-intercept form or one line is either vertical or horizontal 3) Use substitution to solve if one equation is solved for one variable 4) Use elimination if you can easily eliminate one variable quickly

7B - Systems of Inequalities 1) Put each inequality into slope-intercept form. 2) Graph on a coordinate plane. 3) Use (0,0) or another point to find where to shade. (Substitute into the slope-intercept form of each inequality.) 4) Solution is where the shading overlaps. Remember <, > graphs as a dashed line, ≤, ≥ graphs as a 5) solid line.

8A - Graphing Linear Equations 1) Put the equation into slope-intercept form. 2) Plot the y-intercept (0,b) 3) Use the slope to graph a second point. 4) Draw the line. 5) Remember about horizontal and vertical lines.

8B - Graphing Linear Inequalities 1) Put the inequality into slope-intercept form. 2) Plot the y-intercept (0,b) 3) Use the slope to graph a second point. 4) Draw the line. 5) Use (0,0) or another point to find where to shade. (Substitute into the slope-intercept form of the inequality.) Remember <, > graphs as a dashed line, ≤, ≥ graphs as a 6) solid line.

9 – Box and Whisker Plots 1) Put the data in numerical order 2) Find the five number summary a) Lower Extreme (lowest number) b) Lower Quartile (median of lower half of data) c) Median (middle number) d) Upper Quartile (median of upper half of data) e) Upper Extreme (highest number) 3) Draw the plot above a number line a) Box is from lower quartile to upper quartile b) Whiskers are from lower extreme to lower quartile and upper quartile to upper extreme c) Line at the median

10A – Order of Operations 1) PEMDAS a) Parentheses – really all grouping symbols b) Exponents c) Multiplication and Division left to right d) Addition and Subtraction left to right 2) Don’t forget to simplify all answers – especially fractions and radicals

10B - Properties 1) Use foldable or cheat sheet for properties. 2) Don’t confuse commutative, reflexive, and symmetric!

11A – Solving One Variable Equations 1) Remember – goal is to get variable by itself 2) Distribute if necessary 3) Get rid of the fraction if necessary 4) Get rid of addition and subtraction using opposite operation 5) Get rid of multiplication and division using opposite operation 6) Remember – fraction answers must be in simplest form

11B – Solving One Variable Inequalities 1) Remember – goal is to get variable by itself 2) Follow steps for solving one variable equations 3) Remember to have the variable of the left and switch the inequality sign if you multiply or divide both sides by a negative number 4) Graph the solution on a number line Use open circle for <, > a) Use closed circle for ≤, ≥ b)

12 - Slope 𝑧 2 −𝑧 1 𝑠𝑗𝑡𝑓 Memorize the slope formula 𝑛 = 𝑦 2 −𝑦 1 = 1) 𝑠𝑣𝑜 2) If given the graph, count! 3) If given points, use formula. If given the equation in 𝑧 = 𝑛𝑦 + 𝑐 , slope is m. 4) 5) Perpendicular lines – multiply the slopes – answer should be -1. 6) Parallel lines have the same slope. 7) Vertical lines have an undefined slope. 8) Horizontal lines have a slope of zero.