SAT Lvl 2

Question 1

Multiplicative inverse of the complex number a -bi

3 - i ?

Answer 1

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

Question 2

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

Answer 2

Determinant is negative

k^2 -423

Question 3

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

(4,0) and (0,2)

Answer 3

Find midpoint.
Find line perpendicular through midpoint.

midpoint (2,1)
y = 2x - 3

Question 4

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

Answer 4

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

Question 5

Formula for the distance between a point and a line?

point: (x,y)
line: ax+by +c = 0

Answer 5

ax + by + c |
_______________
sqrt(a^2 + b^2)

Question 6

Ellipses: what is c? equation for c?

Answer 6

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

Question 7

Ellipses: what is c? equation for c?

Answer 7

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

Question 8

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

Answer 8

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

Question 9

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

Answer 9

Vertical axis: x^2 = 4py

Horizontal axis: y^2 = 4px

Question 10

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

Answer 10

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

switch x and y for vertical/horizontal

Question 11

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

Answer 11

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

switch x and y for vertical/horizontal

Question 12

Focus of a hyperbola?

Answer 12

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

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

Question 13

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

Answer 13

1. plug in -x instead of x

2. see if f(-x) = f(x)&raquo_space; even or = -f(x)&raquo_space; odd

Question 14

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

Answer 14

1. plug in -x instead of x

2. see if f(-x) = f(x)&raquo_space; even or = -f(x)&raquo_space; odd

Question 15

Descartes Rule of Sings:

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

Answer 15

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.

Question 16

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

Answer 16

slant: 2x
Vertical: 0

Question 17

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

Answer 17

Direct Substitution: -6

Question 18

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

Answer 18

Direct Substitution: -6

Question 19

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

Answer 19

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

Question 20

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

Answer 20

Do Difference of Squares on bottom and top.
Simplify
Yields 8 as end result

Question 21

Formula for permutation

Answer 21

Collection of n
Selecting r
n!/(n-r)!

Question 22

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

Answer 22

10 choose 5 * 6 choose 3 = 5040

Question 23

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

Answer 23

Sum and product of roots
» sin + cos = -k/3
» sincos = -1/3
(sin + cos)^2 = 1+ 2sincos = k^2/9

Solve through.

Question 24

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

Answer 24

Sum and product of roots
» sin + cos = -k/3
» sincos = -1/3
(sin + cos)^2 = 1+ 2sincos = k^2/9

Solve through.

Question 25

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

Answer 25

4 sinx *cosx = 2sin2x

Amp = 2
p = 2pi/2 = pi

Question 26

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

Answer 26

4 sinx *cosx = 2sin2x

Amp = 2
p = 2pi/2 = pi

Question 27

tan(2a)=?

Answer 27

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

Question 28

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

What to remember?

Answer 28

sort of( x^2) is |x|

Question 29

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

Answer 29

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