Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Structure (mathematical logic) wikipedia , lookup
Quartic function wikipedia , lookup
Fundamental theorem of algebra wikipedia , lookup
Cubic function wikipedia , lookup
System of linear equations wikipedia , lookup
Median graph wikipedia , lookup
Elementary algebra wikipedia , lookup
History of algebra wikipedia , lookup
Quadratic equation wikipedia , lookup
Drop That Bubble!!! Guess the missing then drop that bubble! © 2006 Doug Clarke Algebra I To take the square root, you need how Many to pull out? Two To take the cube root, you need how Many to pull out? Three X to the third times x to the sixth Add the exponents X to the 9th When raising a power to a power ___ the exponents. Multiply the exponents A negative exponent means to place That part of the answer where? In the bottom (denom.) When dividing polynomials, ____ the exponents. Subtract Any term raised to the zero Power = ? One To find perimeter … Add all sides To add polynomials … Combine like terms To subtract polynomials … 1. Change subtraction to addition 2. 2.Change 2nd polynomial to its opposite Area = ? Length x width A = lw (2x + 3)(x – 2) 2 x squared – x - 6 When factoring, look for the ____ first. GCF Sum, Difference Product, Quotient Mean to ____. + - X divide X squared -2x-24 divided by X+4 X-6 A rectangle has a width of 2x + 3 and An area of 2x squared – 5x -12. What is the length? X-4 Plus, more than, increased by, Additional, sum are ____ indicators Addition Times, twice, of, product, per are ____ indicators. Multiplication Less, less than, fewer than, Decreased by, difference are ____ indicators. Subtraction Which subtraction word indicators Switch the order? Less than Quotient, share equally, separate into Equal groups are ___ indicators. Division To solve equations in the calculator: Y1 Y2 Y1=left side Y2=right side Zoom 6, 2nd calc 5 enter 3 times The opposite of squaring is to _______ Take the square root. Two things side by side with no sign in Middle is what operation? Multiplication A line that has a positive slope Looks like… Rises up and to the right A line that has a negative slope Looks like…. Falls to the right A horizontal line has what slope? Zero A vertical line has what slope? Undefined Slope given two points M= M=y–y/x-x Slope of (3,0) & (3,2) Undefined No slope Slope is what direction over What direction? Rise / Run Parallel lines have what type Of slopes? Same slope Perpendicular lines have ___ ____ slopes? Opposite Reciprocal slopes The product of the slopes of Two perpendicular lines is Always ___. -1 X intercept Where the graph crosses or Touches the x axis. Y intercept Where the graph crosses or Touches the y axis. Slope Intercept Form Equation Y = mx + b Standard Form Plain number by itself X term is positive No fractions or decimals Calc steps for graphing, slope int form Equation, predictions: Stat/enter X #’s into L1,Y #’s into L2 stat => calc,4, enter twice Y=vars 5=>EQ enter 2nd graph to predict Point Slope Form Equation Y – Y1 = m ( X – X1) The equation of a horizontal Line… Y= The equation of a vertical line … X= Systems of Equations: Two intersecting lines: One solution Consistent Independent system Systems of Equations: Parallel lines: No solution Inconsistent system System of Equations: Only one line: (The two lines coincide) Infinitely Many Solutions Consistent Dependent system Inequality signs: Greater than Less than Not equal to > < < > have what type of Circles when graphing? Open circles Greater than or equal to, Less than or equal to have what Type of circles when graphing? Closed circles When does the inequality sign Reverse? If you multiply or divide BOTH Sides by a Negative. Solve inequalities so that the letter Is on the ___ side. Left Three ( =) Three inequalities Two insides are the same: What property? Transitive Property Two variable inequalities: What type of line? Greater than or Less than? Broken line Two variable inequalities: Greater than or equal to Less than or equal to have what Type of line? Solid To graph equations and inequalities In the calculator, Solve for ___ first. Y= To put > or < in the calculator, Go where? Left of Y1 And left of Y2. When solving inequalities by graphing, Where are the solutions? The region with the darker shading Is the solution. ___, ___, ___, ___ are all where The graph crosses or touches the X axis. Real roots, zeros, x intercepts, Solutions. How many real solutions does a Quadratic have if it touches the X axis once? One real solution How many real solutions does a Quadratic have if it touches the X axis twice? Two real solutions How many real solutions does a Quadratic have if it does not touch the X axis? No real solutions The solutions to solving Quadratic Equations using a table are Y or f(x) = ____ ? When Y = 0 F(x) = 0 Property Justification: -3(2x+5) = 9 Given -6x -15 = 9 ____ -6x=24 ____ X = -4____ Distributive Addition Property of equality Division Property of Equality How do you tell if a relation is A function? If the x coordinates repeat => No If the x coordinates are all different => Yes Is y = -5 a function? Yes Is x = 3 a function? No How do you tell if a graph is a Function? Use the vertical line test. Touches once => Yes Touches more than once => No What is a linear function? When graphed, it is a straight line. Graph x = y squared. Is it a function? Solve for y first and graph. No, it is not a function. Write an equation to represent the Function: f(x) is 3 less than 4 times the Square of x. F(x) = 4x - 3 What is an arithmetic sequence? Adding the same number to get The next number. The number being added each Time in an arithmetic sequence is The ___. Common difference How do you find the Common Difference? D = a2 – a1 (second term – first term) A(n) = a1 + (n – 1) d Identify each term. A (n) = last term A1 = first term N = # of terms D = # being added -2,3,8,13,… Write a formula for finding the nth term Find the 15th term in the sequence. A(n) = 5n – 7 A (15) = 68 What is the domain of a relation? Domain is the x coordinates. What is the range of a relation? The range is the y coordinates. Which is the dependent variable Domain or Range? Range. The y answer depends on the Value of x. Describe the domain and range for function(-4,4)(-3,5)(-1,0)(1,-1)(5,3) (Connected) Domain => -4<x<5 (or equal to) Range => -1<y<5 (or equal to) Describe the domain and range for F(x) = 4x -4. Domain: all real numbers Range : all real numbers Describe the domain and range For f(x) = 3. Domain : all real numbers Range: f(x) = 3 or y = 3 To describe the domain of a graph, Stretch which way? Left and right to see how wide it is. To describe the range, stretch which Way? Up and down to see how tall it is. In direct variation, y is directly proportional to x. Write the formula or equation, Y = kx How does a direct variation graph Look? It goes DIRECTLY to and or through The origin. For a direct variation graph, what is The constant of proportionality? Y intercept? K = slope Y intercept = (0,0) Write the formula for inverse variation. Y = k/x Direct variation proportion: x1 over x2 = y1 over y2 (proportion) Inverse Variation Proportion: X1 over x2 = y2 over y1 To solve proportions … Cross multiply and divide. How do you find the: Mean: Mean Abs. Dev. Stat/enter Key #’s into L1 2nd 0 (down to Mean, 2nd L1) M.A.D. => Stat=>Calc enter twice Variance = ???? Variance = standard deviation Squared. Z – score = Z – score = # - mean/ st. dev Box-&-Whisker Plots: identify: lower Extreme, LQ,whisker,median,UQ, Upper extreme Draw a bow-&-whisker plot Range = IQ Range = Range = highest # - smallest # IQ = UQ - LQ To graph quadratics: Stat/enter #’s into L1 & L2 Y = clear & unhighlight 2nd y= Enter/On Zoom 9 to graph,stat,calc,5enter 3 times, 2nd graph to predict Factor 4x squared -2x-2. 2 (2x squared – x – 1) 2 ( 2x+1)(x-1) Which property? 10a + -10a = 0 10a + 0 = 10a A+10= 10+a Inverse for addition Identity of addition Commutative of addition Which property? 9x + (3x + 8) = (9x+3x) + 8 8(3x-2) = 24x - 16 Associative of addition Distributive