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ALEKS > Notes > Flashcards

Notes Flashcards

1
Q

Union symbol + word

A

U + or

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2
Q

Intersection symbol + word

A

∩ + and

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3
Q

Equation of a circle & center point.

A

(x - h)^2 + (y - k)^2 = r^2, center at (h,k)

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4
Q

Quadratic formula standard form + vertex

A

f(x) = a(x - h)^2 + k, vertex: (h,k)

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5
Q

Slant Asymptote: how to find & how to know if there is one

A
  • Find through polynomial long division (not including remainder)
  • Present when degree of numerator leading coefficient is greater than degree of denominator leading coefficient
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6
Q

Horizontal Asymptote: how to find & how to know if there is one

A
  • Look at degree of leading coefficient in numerator (n) and denominator (m).
  • Asymptote at y=0 if m > n
  • Asymptote = leading coefficient of n divided by leading coefficient of m if m = n

n < m (slant asymptote)

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7
Q

Vertical Asymptote: how to find

A

-Present at x = ? when x causes denominator to equal 0.

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8
Q

Distance Formula

A

distance = rate * time

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9
Q

Vertex: how to find without standard quadratic formula

A

x-coord: -b/2a, y-coord: plug in x

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10
Q

Exponential Growth Formulas (2)

A

y = Initial(1 + rate)^time

y = Initial * e^(rate*time)

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11
Q

Exponential Decay Formulas (2)

A

y = Initial(1 - rate)^time

y = Initial * e^(-rate*time)

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12
Q

Point Slope Form

A

y - y1 = m(x - x1)

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13
Q

Direct Variation

A

y = kx

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14
Q

Indirect Variation

A

y = k/x

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15
Q

Distance Formula (between two points on a plane)

A

distance = √( (x2 - x1)^2 + (y2 -y1)^2 )

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16
Q

Rectangular Prism: Volume + SA

A
  • Volume: lwh

- SA: 2lw + 2wh + 2lh

17
Q

Cube: Volume + SA

A
  • Volume: a^3

- SA: 6a^2

18
Q

Cone: Volume + SA

A
  • Volume: 1/3πr^2*h

- SA: πrs + πr^2 (s = slant)

19
Q

Cylinder: Volume + SA

A
  • Volume: πr^2*h

- SA: 2πr^2 + 2πrh

20
Q

Sphere: Volume + SA

A
  • Volume: 4/3πr^3

- SA: 4πr^2

21
Q

Circle: Area + Circumference

A
  • Area: πr^2

- Circumference: 2πr

22
Q

Radians - > Degrees

Degrees - > Radians

A
  • Multiply by 180/π

- Multiply by π/180

23
Q

Quadratic Formula

A

x = ( -b ±√(b^2 - 4ac) )/2a

24
Q

Rectangle: Area + Perimeter

A
  • Area: l*w

- Perimeter: 2l + 2w

25
Q

Triangle: Area + Perimeter

A
  • Area: 1/2b*h

- Perimeter: a + b + c

26
Q

6 Trig Functions

A
  • Sinx = O/H
  • Cosx = A/H
  • Tanx = O/A or Sinx/Cosx
  • Cscx = 1/Sinx or H/O
  • Secx = 1/Cosx or H/A
  • Cotx = 1/Tanx or A/O or Cosx/Sinx
27
Q

Pythagorean Thereom

A

H^2 = A^2 + O^2

28
Q

What are inverse ratios/arcratios used for?

A

To find angles using sides

29
Q

Magic Hex + Functions

A
  • Quotient Identities: Target identity = Next Identity/Identity After (Clockwise or Counter-clockwise) (Ex. Tanx = Sinx/Cosx)
  • Product Identities: Identity Between Two Identities = The Two Multiplied + Identity Multiplied by Identity Directly Across = 1. (Ex. Tanx*Cosx = Sinx)
  • Reciprocal Identities: Target identity = 1/Identity Across (Go Through 1) (Ex. Sinx = 1/Cscx)
  • Pythagorean Identities: Clockwise In Upside Down Triangles Squared. Target + Next = Next (Ex. Tan^2(x)+ 1 = Sec^2(x).
  • Angle Bonus: Left to Right Only: Target(x) = Next(90-x) (Ex. Sec(40) = Csc(90 - 40) = Csc(50)
30
Q

Sin^2θ vs. Sinθ^2

A

Sin squared vs. Theta squared

31
Q

Law of Sines

A

a/SinA = b/SinB = c/SinC

32
Q

Law of Cosines

A

c^2 = a^2 + b^2 - 2ab*CosC

33
Q

Arc: Definition + Length Formula + Theta Formula

A
  • Arc = s, 2 points intersect on a circle make major (3 points) & minor arcs. Minor = Arc AB, Major = Arc ACB
  • Length Formula: s = rθ
  • Theta Formula: θ = s/r
34
Q

Trig Not on Unit Circle (Where x^2 + y^2 ≠ 1): Radius Formula, 6 Functions, Terminal Side

A
  • Radius Formula: r^2 = x^2 + y^2 OR r = √(x^2 + y^2)
  • Terminal Side: ( x, y )
  • 6 Functions:
  • Sinx = y/r
  • Cosx = x/r
  • Tanx = y/x, x ≠ 0
  • Cscx = r/y, y ≠ 0
  • Secx = r/x, x ≠ 0
  • Cotx = x/y, y ≠ 0
35
Q

Loga(x) = s in Exponential Form

A

a^s = x

36
Q

a^s = x in Logarithmic Form

A

Loga(x) = s

37
Q

Logarithm Properties (3)

A
  • Logarithm of a Product: Loga(MN) = Loga(M) + Loga(N)
  • Logarithm of a Quotient: Loga(M/N) = Loga(M) - Loga(N)
  • Logarithm of a Power: Loga(M)^p = pLoga(M)
38
Q

Change of Base Formula

A

Loga(b) = Logc(b)/Logc(a), where C is any number (with few exceptions)

ALEKS (1 decks)

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