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01:640:135 Quiz: 01:640:135 Quiz: Pre-Calculus Cheat Sheet.docx


Department
Mathematics
Course Code
01:640:135
Professor
Noone
Study Guide
Quiz

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Pre-Calculus Review
Slope Form:
Slopes Of Lines : (rise/run): m=
x2¿x1
y2¿y1
¿
¿
Slope Intercept Form: y = mx + b
Point Slope Form: (y -
y1
) = m
¿
(x –
x1
)
Distance Formula: d =
x
y
(¿¿2x1)2+(¿¿2y1)2
¿
¿
Midpoint Formula: (
x1+x2
2,
y1+y2
2,
)
Other Important Equations:
Pythagorean Theroem:
a2+b2=c2
Hypotenuse Equation:
c
=
Difference Quotient:
f
(
x
)
=f
(
x+h
)
f(x)
h
Example:
f
(
x
)
=2x2+x
Plug the function into the equation…
f
(
x
)
=
[
2
(
x+h
)
2+(x+h)
]
[2x2+x]
h
Intervals

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Closed Intervals: [c,d] means c x d≤ ≤
Open Intervals: (c,d) means c < x < d
Infinite Intervals:
[b, ) means x b∞ ≥
(b, ) means x > b
(- ,b] means x b∞ ≤
(- ,b) means x< b
Factoring:
Basic Trinomials:
(a x2+b+c)=¿
(dx+e)(fx+g)
(dx
¿
fx) = a
x2
(dx
¿
g) + (fx
¿
e) = b
(e
¿
g) = c
Examples:
(x2+4x32)=¿
(x - 4)(x+8)
(1x
¿
1x) =
x2
(x
¿
-4) + (x
¿
8) = -4x + 8x = 4x
(-4
¿
8) = 32
(15 x2+14x8)=¿
(5x + 2)(3x+4)
(5x
¿
3x) =
15 x2
(5x
¿
4) + (3x
¿
2) = 20x + 6x = 14x
(2
¿
4) = 8
Difference of Two Squares:
x
¿
¿
¿
y2¿
= (
x
y¿(
x+
y)
Example:
x
(¿¿216)=(x4)(x+4)
¿
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