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| Distance
formula |
rate x
time = distance or rt=d |
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time =
distance/rate or t = d/r |
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rate =
distance/time or r = d/t |
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| Triangle
area |
given lengths
of two sides of a triangle, to maximize the area, make it a right triangle |
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| Third
side of a triangle |
The third
side of a triangle must be between the sum and the difference of the two
other sides. If you have 2 sides of a triangle that are 4 and 11, the third
side must be smaller than 15 (4 + 11) and must be greater than 7 (11-4). |
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| prime
number |
a number
that is only divisible by 1 and itself. The only even prime number is 2. |
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| triangle
midline theorem |
when you
connect the midpoints of two sides of a triangle, it is parallel to the
third side and half as long as that side. |
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| average
(arithmetic mean) problems |
always
find the sum of the numbers that were averaged by multiplying back by the
number of items. |
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| zero |
zero is an integer
zero is an even integer
zero is neither positive nor negative |
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| Angles of a triangle |
the smallest angle of a triangle will always be less than
60
the largest angle will always be greater than 60 |
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| Third
side of a triangle |
The third
side of a triangle must be between the sum and the difference of the two
other sides. If you have 2 sides of a triangle that are 4 and 11, the third
side must be smaller than 15 (4 + 11) and must be greater than 7 (11-4). |
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| 30-60-90
triangles |
the lengths
of the sides are 1, square root of 3 and 3, from smallest to largest |
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| perpendicular bisector of a line segment |
If a line is the perpendicular bisector of a line segment,
every point on the line is the same distance from each endpoint of the line
segment. For example, if line L is the perpendicular bisector of AB, then
every point on line L is the same distance from A as from B. X and Y are
on line L, so AX = BX and AY = BY.
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| Multiplying
fractions between 0 and 1 |
Multiplying
fractions, or raising fractions to powers makes them smaller |
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| Mean,
median and mode |
Mean is
the average, median is the middle number, and mode is the most common number. |
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| Raising
a power to a power |
multiply
the powers |
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| Multiplying
the same number or letter with powers |
add the
powers |
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| Dividing
numbers with powers |
Subtract the bottom power from the top power |
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| per |
any rate with a per in the middle, such as miles per gallon
can be thought of as division, miles/gallon |
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| central angle in a circle |
is proportional to the intercepted arc |
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| vertical angles |
Vertical angles are formed when two lines intersect. Angles
a and c are vertical angles, angles b and d are vertical angles. Vertical
angles are equal, angle a is equal to angle c, and angle b is equal to angle
d. Angles a and b add up to 180. |
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| area of a Right Triangle |
In a right triangle, the legs can be used as the base and
the height when calculating the area. |
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| solving systems of equations |
always try to add the equations first, this works most of
the time in helping solve for the information needed to answer the question. |
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| perpendicular slopes of lines |
Perpendicular slopes multiply together to be -1. If one slope is -3, the perpendicular slope is +1/3. If one slope is 2/5, the perpendicular slope is -5/2. |
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| the number 64 |
64 is a very versatile number, so it is used a lot in the math SAT. It is 2 to the 6th power, 4 to the third power and 8 squared. |
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| creating an absolute value equation from data |
If the height of an object is between 40 and 60, you can turn this into an absolute value equation by:
1. find the middle height - 40 + 60 divided by 2, which equals 50.
2. find the distance between the middle height and the ends -> 60 - 50 = 10.
3. the equation will be | h - 50 | < 10 (for between statements, always use "less than" |
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| Combinations and Permutations |
Permutations -> nPr order matters, so there are more answers, for example how many ways can you arrange 10 books on a shelf. Obviously if order didn't matter, there would only be one way
Combinations -> nCr, order doesn't matter, for example, how many ways can you pick a committee of 3 from 10 people. |
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| exterior angle theorem |
 This concept is on the math SAT all the time |
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| operations on even and odd numbers |
Even X Even = Even
Even X Odd = Even
Odd X Odd = Odd
Even + Even = Even
Even + Odd = Odd
Odd + Odd = Even
These make sense when you think about it, but nobody learns this in math, so you have to think about it. Sometimes the only way to narrow down an anwser to an SAT question is that you know it has to be even or odd. |
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| proportional numbers of things |
If you have twice as many apples as oranges, then the sum of apples + oranges is divisible by 3, because x + 2x = 3x.
If you have four times as many apples as oranges, then the sum is 4x + x = 5x, the sum is divisible by 5 |
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| inversely and Directly proportional numberss |
If a and b are inversely proportional, then they are always equal to the same constant (C) -> a x b = C
If a and b are directly proportional, then they are always equal to the same constant (C)-> a/ b = C |
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| 30-60-90 triangles |
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| 45 - 45 - 90 triangles |
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| Area of an equilateral triangle |
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| slope formula |
change in y over change in x
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| solving with exponents |
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| reflecting points across the X and Y axis |
Reflections across the X axis -> the x values stay the same, the y values change from pos to neg or neg to pos
Reflections across the Y axis -> the y values stay the same, the x values change from pos to neg or neg to pos |
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| quadratic equations |
c is the y intercept
a determines if the parabola opens up or down, positive is up, negative is down
if a is a fraction, the parabola will be wider, if it is a whole number it will be thinner |
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| solving absolute values with inequalities |
| x - 10 | < 15
These must be solved twice, solve once as is:
x - 10 < 15
and then solved a second time, reversing the inequality, and changing the number on the right to a negative number (if the number on the right is negative to start with, there is no solution):
x - 10 > -15
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| sum of three consecutive integers |
If a number is divisible by three, it can be the sum of three consecutive integers:
x + x + 1 + x + 2 = 3x + 3
3x + 3 is the same as 3(x + 1), so if you divide the sum of three consecutive integers by 3, the answer is the middle number. |
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| Getting to a quadratic equation from the roots |
Based on a, b and c in this formula, the sum of the roots of a quadratic equation is equal to -b/a and the product equals c/a. So if you have roots of 4 and 5:
4 + 5 = -b/a, or -9.
4*5= c/a, or 20.
The equation is x^2 - 9x + 20 |
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| f(x) |
is function notation for y, when f(x) is used, think of it as y |
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| Tangent |
Tangent means "touches in one point". A tangent line to a circle touches the circle at one point, and a radius drawn to the point of tangency will be perpendicular to the tangent line. |
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| Directly Proportional numbers |
If X is directly proportional to Y, then they can be multiplied by the same number and will still be proportional. If X = 7 and Y = 10, then is X = 14, Y = 20 (both multiplied by 2) |
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| Similar Triangles |
Similar triangles have all sides in proportion, but the angles are EQUAL. |
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| Combination |
If you have 3 different shirts and 4 different pants, how many combinations of outfits do you have?
Think of this as a tree diagram, like this, then you will see why you just multiply 3 X 4.
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| Proportions |
Direct proportions, set up the two values as fractions:
If two numbers are indirectly proportional, multiply them:
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| Remainders |
Remainders MUST be smaller that the number you are dividing by (the divisor). If you are dividing a number by 6, the largest the remainder can be is 5. |
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| Rectangles |
Rectangles have perpendicular sides, so the slopes of two adjacent sides multiply to be negative one. |
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