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Flashcards in SAT Lvl 2 Deck (29):
1

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

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

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

2/3 * 3/k = -1.
Solve through.
k = -2

5

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?

Vertical axis: x^2 = 4py
Horizontal axis: y^2 = 4px

10

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

(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

(x-h)^2 = 4p(y-k)
switch x and y for vertical/horizontal

12

Focus of a hyperbola?

(+/- 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?

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

Descartes Rule of Sings:

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

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)

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

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

If f(x) = log 3 ( sqrt(x) ) + 3, and g(x) is the inverse of f(x), what is g(2)?

1/9
replace f(x) with y. Swap