Math Review

Law of sins and cosine

100

What is the law of sines?

a/sin(alpha)=b/sin(beta)=c/sin(gamma)

200

For a triangle with angles 80, 60, and 40. A length 1 m on the side opposite to angle 40 find the length of another side

1.34 m and 1.53

300

If the length of one side of a triangle is 1 m, another is 2m, and the angle between these two sides is 25, what is the length of the 3rd side?

1.17 m

400

If the length of one side of the triangle is 2 meters and the other 2.7 meters, we don't know the angle between these two sides, but the other two angles are 45 and 81. What is the length of the third side?

2.11 m

500

A pole tilts toward the sun at an 8 degree angle from the vertical, and it casts a 22-foot shadow. The angle of elevation from the tip of the shadow to the top of the pole is 43 degrees. How tall is the pole?

23.84 feet

Differential Calculus

100

What is the derivative of x³+2x+cos(x)

3x²+2-sin(x)

200

f(x) =  81x² - 42x - 8 what is its vertex

y=-13.4

x=0.25

300

What is the derivative of ln(x)/e^x

e^-x/x- e^-x ln(x)

400

What is the derivative of cos(x²)?

-2 x sin(x²)

500

What is the derivative of cos(ln³(x))

-(3 log²(x) sin(log³(x)))/x

Integral Calculus

100

integral sin(ax) dx=?

-1/a cos(ax)+C

200

∫₁^x  1/t dt

What is the natural logarithm?

300

∫₀³ 1/√(9-x²) dx

tan^-1(x/√(9 - x²))+C

pi divided by 6

400

∫e^x cosx dx

½ (e^x sinx+e^x cosx) +C

500

integral cos(ln(x)) dx

1/2 x (cos(ln(x)) + sin(ln(x)))