Flashcards in SAT Lvl 2 Deck (29):

1

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Multiplicative inverse of the complex number a -bi

3 - i ?

###
1 == j* (a -bi) where j is the multiplicative inverse

1. j == 1/(a-bi)

2. Multiply by the conjugate above and below

(3 + i )/ 10

2

## If a quadratic equation 2x^2 - kx + 3 = 0 have imaginary roots, what is the value of k?

###
Determinant is negative

k^2 -4*2*3

3

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What is the equation of the line which is equidistant from two points (x1, y1) and (x2 , y2)?

(4,0) and (0,2)

###
Find midpoint.

Find line perpendicular through midpoint.

midpoint (2,1)

y = 2x - 3

4

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If the two lines 2x - 3y + 2 = 0 and 3x - ky -1 = 0 are perpendicular, k =?

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2/3 * 3/k = -1.

Solve through.

k = -2

5

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Formula for the distance between a point and a line?

point: (x,y)

line: ax+by +c = 0

###
| ax + by + c |

_______________

sqrt(a^2 + b^2)

6

## Ellipses: what is c? equation for c?

### C is the length from the center to the focus, c^2 = a^2 - b^2

7

## Ellipses: what is c? equation for c?

### C is the length from the center to the focus, c^2 = a^2 - b^2

8

## Tangent line y = mx + b to ellipse x^2/a^2+ y ^2/b^2 = 1?

### Substitute. Put linear equation as x = (y-b)/m

9

## Standard for of equation of a parabola with vertex at the origin is?

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Vertical axis: x^2 = 4py

Horizontal axis: y^2 = 4px

10

## Standard equations of a parabola with vertex at (h,k) are

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(x-h)^2 = 4p(y-k)

switch x and y for vertical/horizontal

11

## Standard equations of a parabola with vertex at (h,k) are

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(x-h)^2 = 4p(y-k)

switch x and y for vertical/horizontal

12

## Focus of a hyperbola?

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(+/- c, 0): c^2 = a^2 + b^2

asymptotes are +/- b/a if horizontal, a/b if vertical

13

## How can you find out if a function is even or odd?

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1.plug in -x instead of x

2. see if f(-x) = f(x) >> even or = -f(x) >> odd

14

## How can you find out if a function is even or odd?

###
1.plug in -x instead of x

2. see if f(-x) = f(x) >> even or = -f(x) >> odd

15

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Descartes Rule of Sings:

Find the possible real zeros of f(x) = 4x^3 - 6x^2 + 3x - 3

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Check the number of variations in sign of f(x):

>> 3 variations in sign.

Check the number of variations in sign of f(-x)

No variations in sign.

Conclusion: 3 positive zeroes or 1 positive real zero and no negative zero.

16

## All asymptotes of 2x^2+1/x ?

###
slant: 2x

Vertical: 0

17

## limit as x goes to -1 of x^2 + x - 6) / (x+2)

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Direct Substitution: -6

18

## limit as x goes to -1 of (x^2 + x - 6) / (x+2)

###
Direct Substitution: -6

19

## limit as x goes to -1 of (x^2 + x - 6) / (x-2)

### Simplify and cancel above and below terms of (x-2): leaves x+3 == 5

20

## limit as x goes to -1 of (x^2 + 2x - 3) / (sqrt(x) -1)

###
Do Difference of Squares on bottom and top.

Simplify

Yields 8 as end result

21

## Formula for permutation

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Collection of n

Selecting r

n!/(n-r)!

22

## There are 6 boys and 5 girls in a club. How many ways can you select 2 boys and 3 girls?

### 10 choose 5 * 6 choose 3 = 5040

23

## If the roots of the equation 3x^2 + kx - 1 = 0 are sin and cos, what is the positive value of k?

###
Sum and product of roots

>> sin + cos = -k/3

>> sincos = -1/3

(sin + cos)^2 = 1+ 2sincos = k^2/9

Solve through.

24

## If the roots of the equation 3x^2 + kx - 1 = 0 are sin and cos, what is the positive value of k?

###
Sum and product of roots

>> sin + cos = -k/3

>> sincos = -1/3

(sin + cos)^2 = 1+ 2sincos = k^2/9

Solve through.

25

## Period and Amplitude of y = 4sin x * cos x - 1

###
4 sinx *cosx = 2sin2x

Amp = 2

p = 2pi/2 = pi

26

## Period and Amplitude of y = 4sin x * cos x - 1

###
4 sinx *cosx = 2sin2x

Amp = 2

p = 2pi/2 = pi

27

## tan(2a)=?

### 2*tan(a)/1-tan^2(a)

28

##
x + sqrt(1-sqrt(3))^2 = 3

What to remember?

### sort of( x^2) is |x|

29