INTEGRAL BEE

ALGEBRA

100

solve for 'x'

3x-7=11

x=6

200

factor completely:

x² - 9

(x-3)(x+3)

300

solve:

2x² - 8x = 0

2x (x - 4) = 0

x = 0,4

400

simplify:

x² - 16 / x - 4

x + 4

500

solve the system:

2x + y = 7

x - y = 1

x = 8/3  , y =5/3

TRIG

100

evaluate:

sin(π /2)

= 1

200

solve :

sin x = 0    on 0 < x < 2π 

x = 0, pi, 2pi

300

simplify:

1 + tan²x

=sec²x

400

simplify:

1-cos²(X) / 1 + cos(X)

use identity..

1- cos² (X) = sin²(x) --> sin²(X) / 1+cos(x)

cancel..

=1-cos(x)

500

solve for 'x' on 0 < x < 2π 

2sin²(x) - 3sin(x) + 1 = 0

factor..

(2sinx-1)(sinx-1) = 0

solve..

sinx = 1/2       or   sinx=1

unit circle ..

x = pi/6, 5pi/6, pi/2

PRECALC

100

find the slope between points

(2,3) and (5,9)

m = 2

200

evaluate:

f (x) = x² + 3x

find f(2)

= 10

300

solve:

x² - 5x + 6 = 0

= (x - 2)(x - 3)

x = 2,3

400

find inverse of:

f (x) = 3x+1

f^-1(X)= x-1 / 3

500

solve : 

2^x = 16 

= 4

CALC 1

100

d/dx (x³)

= 3x²

200

d/dx (sin(x))

= cos(x)

300

∫ x² dx

= x³ / 3  + c

400

∫ cos(X) dx

= sin(x) + c

500

evaluate :

∫²₀   x dx

= 2

CALC 2

100

∫ e^x dx

= e^x + c

200

∫  1/x dx

= ln|x| + c

300

∫  sin(X) dx

= - cos(X) + c

400

evaluate:

∫ ₀^π  sin(X) dx

= 2

500

evaluate:

∫  xe^x dx

integration by parts

= xe^x - e^x + c