Transcript X , Y - Fort Bend ISD

Math TAKS Review
Formula Charts
Graphing Quadrants
II
III
I
The
Quadrants
on a Graph
go CounterClockwise
IV
Plotting Points on the Coordinate
Plane
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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.
Parent Functions
A Parent Function is the original graph of a
function before it has been changed in any way.
Linear Function
y=x
Quadratic Function
y=x2
Determining Functions
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When given
ordered pairs, table
values, mappings,
or graphs, the xvalue cannot be
repeated. In other
words, the input
value cannot have
more than one
output value.
(3,4)
X and Y Terminology
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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 )
Interpreting Information
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Drawing conclusions to given scenarios
Note: Dummy variables, terminology (per,
more than, less than, etc…
Systems and Solutions (X , Y)
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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).
y = mx + b
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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
Parallel Lines vs.
Perpendicular Lines
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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).
y=-4/3x
Y=1/3x-2
If two lines are
perpendicular then they have
opposite reciprocal slopes . This
implies the two lines have
exactly one point of intersection
and the intersection forms 90
degree angles (one solution).

Y=3/4x
Y= 1/3x+2.5
Midpoint and Distance Formulas
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Note key words.
Midpoint implies CENTER or MIDDLE
position.
Distance implies LENGTH between two
places or positions
Positive Correlation
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As you move from left
to right the data plots
move up.
6
5
4
Positive
Correlation
3
2
1
0
0
5
10
Negative Correlation
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As you move from left
to right the data plots
move down.
6
5
4
Negative
Correlation
3
2
1
0
0
5
10
No Correlation

As you move from left
to right the data plots
show no pattern.
6
5
4
No
Correlation
3
2
1
0
0
5
10
Undefined Correlation
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As you move from left
to right the plots
represent a vertical or
horizontal pattern.
6
4
2
0
0
5
X=3
X=3
X=3
X=3
X=3
3
2
Y=2
1
0
Effects of Change and Comparison of
Quadratic Equations
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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
Roots
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A root to an equation
simply implies where
the function crosses
the x-axis on a graph.
Also known as xintercepts, solutions
and zeros.
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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.
Pythagorean Theorem
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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
A2+B2=C2
C
A
B
Special Right Triangles
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These types of triangles are used when given
only one side and one angle of a right triangle.
30-60-90
45-45-90
X
2X
X√3
Arc or Sector Lengths and Arc or
Sector Areas
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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)
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Arc or Sector Area:
(Always use area)
(angle degree ∕ 360)πr2
Probability
The answer can be represented as a percent or fraction. The
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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
Combinations
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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.
Angle Terminology
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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.
Perimeter vs. Area vs. Volume
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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
Geometric Nets and Figures
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Flat views of figures
Front, side, and top views of figures
Sides, edges, and vertices
Scale Factor and Dilations
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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.
Similarity
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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).
Congruent Figures
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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.
Finding Unknown Values
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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
Inequalities
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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.
Mean, Median, Mode, and Range
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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
Tessellation, Rotation, Reflection,
and Translation
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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.
Exponents
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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.
Fractals
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Writing equations from given patterns
The use of dummy variables
Plug the equations into the calculator and
test the picture or table
Things to Remember
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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
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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 ~)
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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)
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Perimeter
Area
Volume
Surface Area
Parallel Lines: same slope
Perpendicular Lines: negative reciprocal
slopes
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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
Sample Problems
Parent Functions
Domain and Range
Remember Open and Closed Circles
Reading Graphs
Be sure you know what you are
comparing
Rate of Change
Using the formula to determine
future outcome…follow pattern
Solution to a System
The intersection point of two lines
(x,y)
X- Intercept
Graph equation or plug value (x,y)
into equation
Slope
Solve equation…. y = mx + b
Also determined by
rise / run
Points on a line
Plug into calculator and go to table…
Mid Point
Might have to work backwards.
The answer is always an ordered pair.
(x, y)
Parallel and
Perpendicular Lines
Parallel lines- same slope
Perpendicular lines- opposite
reciprocal slopes
Alterations to
graphs
Test the given choices in the
calculator
Roots
Also known as x- intercepts and
zeros
Pythagorean
Theorem
Used when given two sides and
determining a third
Special Right
Triangles
Used when given one side and one angle.
45-45-90
30-60-90
Arc Area and Arc
Length
Memorize formulas…use area and
circumference of a circle
Probability
Favorable Outcome / Total Choices
Multiply scenarios together
Angle Terminology
Complementary and Supplementary
Apothem
Distance from center to outside
length
Geometric Formulas
Add or Subtract values
Edges, Vertices, and
Sides
Changes and
alterations to
geometric shapes
Ratios
Comparisons
Inequalities
Shading above and below
Solid and dotted lines
Exponents
Multiplying…add exponents
Dividing…subtract exponents
Fractals…the nth
stage
Plug given equations into calculator