TAKS REVIEW. Mitochondria TAKS REVIEW Mitochondria = ENERGY.
Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter-...
-
Upload
leona-james -
Category
Documents
-
view
215 -
download
0
Transcript of Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter-...
![Page 1: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/1.jpg)
Math TAKS Review
![Page 2: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/2.jpg)
Formula Charts
![Page 3: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/3.jpg)
![Page 4: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/4.jpg)
![Page 5: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/5.jpg)
Graphing Quadrants
III
III IV
The Quadrants on a Graph go Counter-Clockwise
![Page 6: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/6.jpg)
Plotting Points on the Coordinate Plane
Remember in ordered pairs, x comes before y.
(x, y) First go left or right to plot x, then up or
down to plot y.
![Page 7: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/7.jpg)
Parent FunctionsA Parent Function is the original graph of a
function before it has been changed in any way.Linear Function Quadratic Function
y=x y=x2
![Page 8: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/8.jpg)
Determining Functions
When given ordered pairs, table values, mappings, or graphs, the x-value cannot be repeated. In other words, the input value cannot have more than one output value.
(3,4)
![Page 9: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/9.jpg)
X and Y Terminology The following words are used during the
test but have the same meaning as x and y values.
( x-value , y-value ) (independent, dependent) ( domain , range ) ( input , output )
![Page 10: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/10.jpg)
Interpreting Information Drawing conclusions to given scenarios Note: Dummy variables, terminology (per,
more than, less than, etc…
![Page 11: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/11.jpg)
Systems and Solutions (X , Y) In order for a value to be a solution to an
equation or a system of equations then it implies that it is in fact a true statement. When graphing, the solution is the intersection point.
You will have to write equations for systems. Remember that ordered pairs represent x and
y values whereas set notation represent simply all x-values (domain).
![Page 12: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/12.jpg)
y = mx + b Be able to identify the slope (also known as rate of
change = m) and the y-intercept (b). It is essential to understand what these values
represent in any given equation. M = rate of change → this implies for each
change in the x-value, there is a corresponding change in the y-value.
M= y2-y1 ∕ x2-x1
![Page 13: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/13.jpg)
Parallel Lines vs. Perpendicular Lines
![Page 14: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/14.jpg)
If two lines are parallel then they have the same slope . This implies they never cross one another therefore have no point of intersection (no solution).
If two lines are If two lines are perpendicular then they have perpendicular then they have opposite reciprocal slopes . This opposite reciprocal slopes . This implies the two lines have implies the two lines have exactly one point of intersection exactly one point of intersection and the intersection forms 90 and the intersection forms 90 degree angles (one solution).degree angles (one solution).
Y= 1/3x+2.5
Y=1/3x-2
Y=3/4x
y=-4/3x
![Page 15: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/15.jpg)
Midpoint and Distance Formulas Note key words. Midpoint implies CENTER or MIDDLE
position. Distance implies LENGTH between two
places or positions
![Page 16: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/16.jpg)
Positive Correlation As you move from left
to right the data plots move up.
0
1
2
3
4
5
6
0 5 10
PositiveCorrelation
![Page 17: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/17.jpg)
Negative Correlation As you move from left
to right the data plots move down.
0
1
2
3
4
5
6
0 5 10
NegativeCorrelation
![Page 18: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/18.jpg)
No Correlation As you move from left
to right the data plots show no pattern.
0
1
2
3
4
5
6
0 5 10
NoCorrelation
![Page 19: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/19.jpg)
Undefined Correlation As you move from left
to right the plots represent a vertical or horizontal pattern.
0
2
4
6
0 5
X = 3
X = 3
X = 3
X = 3
X = 3
0
1
2
3
Y = 2
![Page 20: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/20.jpg)
Effects of Change and Comparison of Quadratic Equations Parabolas can be
graphed in the calculator to determine change
The larger the a value the narrower the graph.
The smaller the a value the wider the graph
y=x2
![Page 21: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/21.jpg)
Roots A root to an equation
simply implies where the function crosses the x-axis on a graph.
Also known as x- intercepts, solutions and zeros.
![Page 22: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/22.jpg)
The answer is usually given in set notation form. It is very important to read these types of questions very carefully because the question could ask either how many solutions or roots the equation has or to determine what in fact the actual solution or root is (its specific point on the x-axis).
Do not get confused when given two values in a { } answer and assume that it represents the same thing as (x , y). Remember that only ordered pairs represent these values while { } represent all the roots of the given equation.
![Page 23: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/23.jpg)
Pythagorean Theorem This formula is used when
given two sides of a right triangle and solving for the third side (remember the side representing c is always the hypotenuse). Usually there will be more steps to solving the given question when using this theorem than simply solving for the unknown sides. It is imperative to read the question thoroughly
A
B
C
A2+B2=C2
![Page 24: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/24.jpg)
Special Right Triangles These types of triangles are used when
given only one side and one angle of a right triangle.
45-45-90 30-60-90
X
X√3
2X
![Page 25: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/25.jpg)
Arc or Sector Lengths and Arc or Sector Areas
These questions are asked when given circle graphs and a triangle is inscribed inside the circle. The information needed to solve these types of questions is the angle measurement and radius. These formulas must be memorized.
Arc or Sector Length: Always use circumference)
(angle degree ∕ 360)(2πr) Arc or Sector Area: (Always use area)
(angle degree ∕ 360)πr2
![Page 26: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/26.jpg)
Probability The answer can be represented as a percent or fraction. The
formula used to find the probability of an event occurring is found by . Remember that probability always implies multiplication (if given more than one scenario, you should multiply the choices together). Remember the marble or spinning wheel examples.
Theoretical: getting heads if flipping a coin Experimental: doing the process ( taking marbles out of the
jar)
FAVORABLEOUTCOME ∕ TOTALCHOICES
![Page 27: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/27.jpg)
Combinations The total combinations you can have when
given a certain scenario. You always multiply the different number of choices given with the total number of combinations in each distinct choice.
![Page 28: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/28.jpg)
Angle Terminology Complimentary- add to equal 90 degrees Supplementary- add to equal 180 degrees Interior Angles- sum of inside angles equal
(n-2)180, where n represents the # of sides.
Vertical Angles- directly across from each other and are congruent.
![Page 29: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/29.jpg)
Perimeter vs. Area vs. Volume The formulas for each are given in the formula charts
but it is essential to understand when to use the formulas. Perimeter: the distance around a given object or
figure (ex. fence): P=2l+2w Area: the amount of material needed to cover an
object or figure (ex. wrapping a present) A=LW Surface Area: the area of a 3-deminsional figure (remember
the SA of a rectangular prism is the area of each side including the top and bottom added together.
Volume: the amount needed to fill an object or figure
up (water in swimming pool) V=L x W x H
![Page 30: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/30.jpg)
Geometric Nets and Figures Flat views of figures Front, side, and top views of figures Sides, edges, and vertices
![Page 31: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/31.jpg)
Scale Factor and Dilations The word scale factor implies the number of
times an object increased or decreased in size compared to its original status.
The word dilation implies the actual act of increasing or decreasing an object.
![Page 32: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/32.jpg)
Similarity The symbol that is used to imply similarity is ~ . If two
objects are compared with this symbol or simply implied that they are in fact similar then this means they are proportional to one another and should be set up as ratios that are equal to one another which gives us a proportion. Let the unknown value represent x and cross multiply to solve.
Note… the actual word similar might not be used in the problem so if two items are compared to one another then they are in fact similar (remember the flag pole and shadow example).
![Page 33: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/33.jpg)
Congruent Figures Shapes that are identical in every way. Congruent triangles are referred to as
equilateral triangles. This implies all sides and all angles are the
same.
![Page 34: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/34.jpg)
Finding Unknown Values When given information and asked to find
percent or exact number, you should use the following formula: PART ∕ WHOLE= % ∕ 100
This formula is to be memorized and is extremely useful when asked to find three different types of information.
An extremely similar formula can be used to change the value of a given percent to an actual angle degree measure (key word is central angle).
X ∕ 360 = % ∕ 100
![Page 35: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/35.jpg)
Inequalities An inequality is an equation that divides the coordinate
plane into shaded areas. To determine which region is being represented
(shaded) we must first solve the inequality for y and then graph the line. Remember when solving an inequality and division by a negative value occurs, the inequality symbol < or > must flip directions.
Less than < and < represent the shaded region to be shaded below
Greater than > and > represent the shaded region to be shaded above the given line.
Note…if the inequality is < or > then a dotted line implies and < and > imply solid lines.
![Page 36: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/36.jpg)
Mean, Median, Mode, and Range It is imperative to know and understand the
definitions of these terms. Mean: implies the average value Median: implies the middle value when they
are placed in ascending order Mode: implies the most given value Range: the difference between the highest
and lowest values
![Page 37: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/37.jpg)
Tessellation, Rotation, Reflection, and Translation
You should know what each term implies. Tessellation: placing an object side by side in
different arrangements without developing any gaps.
Rotation: Taking a figure and simply rotating it around while keeping an end point centered.
Reflection: A mirror image. Translation: Simply sliding a figure from it original
status but not picking it up or changing its direction.
![Page 38: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/38.jpg)
Exponents When solving problems with exponents it is incorrect to have
a negative exponent value in the final answer. In order to change the value of the negative exponent to a
positive value, you simply move the base of the negative to either to top (numerator) or to the bottom (denominator) depending on its original location.
All whole numbers are multiplied or divided depending on the question being asked just as if they were regular values without exponents.
When multiplying exponents simply combine all the same bases and add the exponents and when dividing exponents you are to subtract the exponents of the same base. Note….the overall answer can in fact have a negative value (the whole number) but NOT negative exponents.
![Page 39: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/39.jpg)
Fractals Writing equations from given patterns The use of dummy variables Plug the equations into the calculator and
test the picture or table
![Page 40: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/40.jpg)
Things to Remember Parent Functions: Linear and Quadratic Domain and Range Open Circles: Strictly < or > Closed Circles: Strictly < or > Inequalities: dotted and solid lines,
shading above and below Independent and Dependent Variables
![Page 41: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/41.jpg)
Solutions Roots Probability Special Right Triangles (45-45-90 and 30-60-90) Pythagorean Theorem Midpoint Formula (when is it used, may ask for
center) Distance Formula (when is it used may ask for
length) Similarity means Proportional ( symbol is ~)
![Page 42: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/42.jpg)
B* ( area of base of object) Surface Area of a rectangular prism Arc Area and Arc Length Mean, Median, Mode, and Range Translation, Tessellation, Reflection, and
Rotation Scale Factor Dilation Exponents (how to eliminate negative
exponents)
![Page 43: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/43.jpg)
Perimeter Area Volume Surface Area Parallel Lines: same slope Perpendicular Lines: negative reciprocal
slopes
![Page 44: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/44.jpg)
Y = mx + b (rate of change and x & y intercepts) X intercept: let y = 0 and solve, must graph Y intercept: let x = 0 and solve, the b value Complementary angles: 2 angles that =90 Supplementary angles: 2 angles that = 180 Equilateral Triangle: all 3 sides and angles are
equal Isosceles Triangle: 2 equal sides and angles Scalene Triangle: no equal sides Acute angle: an angle less than 90 degrees Obtuse angle: angle greater than 90 but less than
180 degrees
![Page 45: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/45.jpg)
Sample Problems
![Page 46: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/46.jpg)
Parent Functions
![Page 47: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/47.jpg)
![Page 48: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/48.jpg)
Domain and RangeRemember Open and Closed
Circles
![Page 49: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/49.jpg)
![Page 50: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/50.jpg)
Reading GraphsBe sure you know what you are
comparing
![Page 51: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/51.jpg)
![Page 52: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/52.jpg)
Rate of ChangeUsing the formula to determine future outcome…follow pattern
![Page 53: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/53.jpg)
![Page 54: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/54.jpg)
Solution to a SystemThe intersection point of two lines
(x,y)
![Page 55: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/55.jpg)
![Page 56: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/56.jpg)
![Page 57: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/57.jpg)
X- InterceptGraph equation or plug value (x,y)
into equation
![Page 58: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/58.jpg)
![Page 59: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/59.jpg)
Slope Solve equation…. y = mx + b
Also determined by
rise / run
![Page 60: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/60.jpg)
![Page 61: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/61.jpg)
![Page 62: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/62.jpg)
Points on a linePlug into calculator and go to
table…
![Page 63: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/63.jpg)
![Page 64: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/64.jpg)
Mid PointMight have to work backwards.
The answer is always an ordered pair.
(x, y)
![Page 65: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/65.jpg)
![Page 66: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/66.jpg)
Parallel and Perpendicular Lines
Parallel lines- same slope
Perpendicular lines- opposite reciprocal slopes
![Page 67: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/67.jpg)
![Page 68: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/68.jpg)
Alterations to graphs
Test the given choices in the calculator
![Page 69: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/69.jpg)
![Page 70: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/70.jpg)
RootsAlso known as x- intercepts and
zeros
![Page 71: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/71.jpg)
![Page 72: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/72.jpg)
![Page 73: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/73.jpg)
Pythagorean Theorem
Used when given two sides and determining a third
![Page 74: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/74.jpg)
![Page 75: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/75.jpg)
Special Right Triangles
Used when given one side and one angle.
45-45-90
30-60-90
![Page 76: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/76.jpg)
![Page 77: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/77.jpg)
Arc Area and Arc Length
Memorize formulas…use area and circumference of a circle
![Page 78: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/78.jpg)
![Page 79: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/79.jpg)
ProbabilityFavorable Outcome / Total Choices
Multiply scenarios together
![Page 80: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/80.jpg)
![Page 81: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/81.jpg)
Angle TerminologyComplementary and Supplementary
![Page 82: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/82.jpg)
![Page 83: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/83.jpg)
ApothemDistance from center to outside
length
![Page 84: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/84.jpg)
![Page 85: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/85.jpg)
Geometric FormulasAdd or Subtract values
![Page 86: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/86.jpg)
![Page 87: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/87.jpg)
Edges, Vertices, and Sides
![Page 88: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/88.jpg)
![Page 89: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/89.jpg)
Changes and alterations to
geometric shapes
![Page 90: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/90.jpg)
![Page 91: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/91.jpg)
RatiosComparisons
![Page 92: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/92.jpg)
![Page 93: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/93.jpg)
InequalitiesShading above and below
Solid and dotted lines
![Page 94: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/94.jpg)
![Page 95: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/95.jpg)
ExponentsMultiplying…add exponents
Dividing…subtract exponents
![Page 96: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/96.jpg)
![Page 97: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/97.jpg)
Fractals…the nth stage
Plug given equations into calculator
![Page 98: Math TAKS Review Formula Charts Graphing Quadrants III III IV The Quadrants on a Graph go Counter- Clockwise.](https://reader035.fdocuments.in/reader035/viewer/2022062520/56649e6a5503460f94b687e8/html5/thumbnails/98.jpg)