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PA Core Review
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Key Concepts:
Terms in this set (131)
Rational Numbers
Numbers that either terminate or repeat
Natural Numbers
Any positive number that is not a decimal or fraction
Whole Number
Any positive number that is not a decimal or fraction, including zero
Integers
Any positive or negative number that is not a decimal or fraction
Real Number
Any number possible
Irrational Numbers
Numbers that do not terminate or repeat. Keep on going, and going, and going
Pi
Always Irrational
The square root of a non-perfect square
Always Irrational
Perfect Squares
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144,
The square root of a number is always...
+ -
Fractions to Decimals
All the numbers after the decimal, you put in the numerator. The denominator is the place value of the last digit.
If my decimal repeats
Subtract 1 from the denominator
Area of a Rectangle
length x width
Area of a square
A=s²
Radical Sign
The sign we use to create square and cubed roots
Perfect Cubes
1, 8, 27, 64, 125, 216, 343, 512, 729, 1000
A cubed root cannot be...
Negative
Put a cubed root on the calculator by...
3 2nd ^
In order to combine exponents
The bases must be the same
When combining exponents my base...
stays the same
When I multiply my bases together
you add the exponents
When I divide the bases together
you subtract the exonents
If there is an exponent outside of parenthesis
you multiply the exponents
If I have a negative exponent
take the base and exponent and switch numerator/denominator thus making exponent positive
If my exponent is 0
my answer is 1
If I do not have an exponent
assume it is 1
scientific notation
used with really big and really small numbers
How scientific notation looks
1 x 10^n
The number in front of the decimal must be...
between 1 - 9
If you have a positive exponent
move the decimal to the right
If you have negative exponent
move the decimal to the left
If you move the decimal and there is no number...
you put a zero
The exponent tells you
how many times to move the decimal
If the number in standard notation is greater than 1...
your exponent is positive
If the number in standard notation is less than 1...
your exponent is negative
If a scientific notation problem says how many times larger, greater, bigger, etc. you...
DIVIDE
To divide in scientific notation
you divide the front numbers and subtract the exponents
To multiply in scientific notation
you multiply the front numbers and add the exponents
EE on my calculators means...
x10
To add and subtract in scientific notation...
you put both numbers into standard form, solve, put back into scientific
slope-intercept form
y = mx + b
What is another for slope
proportional relationship, constant rate of change, unit rate
Slope tells us
how much the variable changes
In word problems, if you see per/each
that is your slope
In an equation, slope is the...
m, always before the x
On a graph, to find the slope...
rise over run
On a chart, to find the slope...
change in y over change in x
If the line on the graph goes up...
the slope is positive
If the line on the graph goes down...
the slope is negative
Any two points on a straight line...
have the same slope
Your y-intercept is your...
initial fee/starting point
On an equation, your y-intercept is
b, at the end
On a graph, your y-intercept...
is where the line crosses the y-axis
On a chart, your y-intercept
is your y-coordinate when your x = 0
A line on a graph that crosses above the origin will have...
a positive y-intercept
A line on a graph that crosses below the origin...
has a negative y-intercept
To solve for you x-intercept...
put a 0 in for y and solve for x
To solve for your y-intercept
put a 0 in for your x and solve for y
Point Slope Formula
y-y₁=m(x-x₁)
Proportional Relationship
Must be straight and cross through the origin
x = a number
one real solution
0 = 0
infinite real solutions. numbers and variables are the same
0 = a number
no real solutions. variables are the same, numbers are different
Solve for a variable
- Draw a wall
- Distribute
- Combine like terms
- Variables on the left, numbers on the right
o Switch sides, switch signs
- Combine like terms
- Divide by the number next to the variable (coefficient) or multiply by the reciprocal
System of equations graphically
where the two lines intersect
If both lines on system of equations are parallel you have
no real solutions
If both lines on system of equations are the same you have
infinite solutions
System of equation algebraically
Put both into y=mx+b form
mx + b = mx + b
Solve for x
Put x back into the problem to solve for y
Ordered Pairs
(x,y)
Graphing is like
Surfing
Coordinate Planes
Have 4 quadrants
4 quadrants make
a C Shape
To graph an equation in slope-intercept form
Graph the y-intercept, and apply the slope
Positive slope
Up and to the right
Negative slope
Down and to the right
Similar
Same shape, different size
Congruent
Same shape, same size
Hypotenuse
The side across from the right angle on a right triangle. Always the biggest.
Coordinate Planes
Have 4 quadrants
4 quadrants make
make a C shape
Everything is a
RELATION
To be a function
the domain cannot repeat
Other words for x are
domain and input
Other words for y are
Range and output
To be a function on a graph, the line must pass
the vertical line test
The vertical line test
A test used to determine whether a relation is a function by checking if a vertical line touches 2 or more points on the graph of a relation
u and n are
functions
c and backwards c are
NOT functions
To be a linear equation your x cannot be
squared or in the denominator
A nonlinear association does not have a
constant rate of change
The 4 transformations are
Reflection, Translation, Rotation, Dilation
These 3 transformations are congruent
Reflection, Rotation, Translation
This transformation is similar
Dilation
Reflection means
flip
If you reflect over the y-axis
change the sign of the x
If you reflect over the x-axis
change the sign of the y
If you reflect over the origin
change the sign of the x and y coordinates
Rotation means
turn
90° means turn
one time
180° means turn
twice
270° means turn
three times or once in the opposite direction
A 180° rotation is the same as
a reflection over the origin
Clockwise you turn to the
right
Counter-clockwise you turn to the
left
90° clockwise rotation
(y, -x)
90° counter clockwise rotation
(-y, x)
Translation means
slide
Dilation means
larger or tinier
On dilation, you ________________ the coordinates by the scale factor
multiply
If your scale factor is more than 1...
the shape gets bigger
If you scale factor is less than 1...
the shape gets smaller
When you see a right triangle, you think...
PYTHAGOREAN THEOREM
If you have both of your legs
SAS: Square, Add, Square Root
If you have only one leg
SSS: Square, Subtract, Square Root
To find out if a triangle is a right triangle...
SAS the two smaller values and see if it equals the larger value. If yes, it's a right triangle. If no, It's not a right triangle.
To find the distance between two points on a graph...
SAS the slope values. The distance will always be your hypotenuse.
If you split a rectangle with a diagonal, you create
a right triangle
To find the perimeter of an object...
add all the sides together
Volume Problems
USE YOUR REFERENCE SHEET
In a volume problem, if pi is in your answer...
do not use it in the formula
Outlier
A data point by itself
Cluster
A group of data points close together
Positive Correlation
Goes up
Negative Correlation
Goes down
No Correlation
Skittles
Line of Best Fit
A line through the middle of the data points. You can determine the slope and y-intercept.
Columns go
up and down
Rows go
left to right
Relative Frequency
Divide the inside number by the total.
Two categories on a two way table go
in the inside
One category on a two way table goes
on the outside
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