Final Exam Review Jeopardy!

Polynomials

100

Integrate ∫(3x²)dx

What is x³+C

200

Integrate and simplify ∫(4x⁵-4x)dx

What is (2/3)x^6 - 2x²+C

300

Integrate ∫x*sqrt(x)dx

What is (2/5)x^5/2 +C

400

Find f(x) if f`(x) = x³-3 and f(2) = 1

What is f(x)=(1/4)x⁴-3x+3

500

Integrate ∫(6x⁵+4x³)(5x⁶+5x⁴)³ dx

What is (1/20)(5x⁶+5x⁴)⁴ + C

Mixed Exponentials and Trig

100

Integrate ∫cos(3x-pi) dx

what is (1/3)sin(3x-pi)+C

200

Integrate ∫[ sin³x cosx]dx

What is (1/4)(sinx)^4+C

300

Find f(x) if f'(x) = 8e^4x and f(0) = 5

What is f(x) = 2e^4x + 3

400

Integrate ∫ sin²(4x) dx

What is (x/2)-(1/16)sin(8x)+C

500

∫ x²e^x  dx 

what is e^x(x² -2x+2)+ C

Definite Integrals

100

evaluate ∫ (x²+3x) dx on [1, 3]

What is 62/3

200

evaluate ∫cos(x/2)dx on [0,pi]

What is 2

300

evaluate ∫(secx)^2dx on [-pi/4,pi/4]

What is 2

400

evaluate  ∫ xe^{-2x^2} dx on [1,2]

What is 0.0337

500

evaluate ∫ sin²(x/2) dx on [0, pi/6]

what is pi/12 - 1/4

Geometric Vectors

100

The quadrant bearing N23⁰E as a true bearing

and the true bearing 262⁰ as a quadrant bearing

what is 023⁰ and what is S82⁰W  

200

Express the vector FD in terms of u and v

(see additional image)

What is 2u-v

300

Charlie walks 70 meters due west. Once he reaches the fountain, he turns down a street at a
bearing of S 33◦W, and walks another 80 meters to Mac’s house.

How far does charlie end up from his starting position, and at what bearing?

What is 131.9m at a bearing of S59.4W

400

A painting that weighs 90N hangs in the middle of a single wire, so that the angle separating the two halves of the wire is 100◦, and so that the two halves of the wire have the same length. What is the tension in each wire?

What is 70N

500

A projectile is launched into the air with a velocity of 50 m/s such that the horizontal component of the velocity has double the magnitude of the vertical component of the velocity

Find the angle between the horizontal and the projectile, and the magnitude of the horizontal and vertical components of the velocity

What is 26.6⁰

 v _h = 44.7 m/s

v_v = 22.35 m/s

Cartesian Vectors

100

For the vectors  u = [2, −2, 3],  and  v = [−2, −2, 1]

Find u * v

What is 3

200

For the vectors  u = [2, −2, 3],  and  v = [−2, −2, 1]

Find the angle between them.

What is 18.5⁰

300

For the vectors  u = [2, −2, 3],  and  v = [−2, −2, 1]

Find a unit vector that is orthogonal to both of them

What is [1/3, -2/3, -2/3]

400

Find the values of k so that u = [k, −3k, 2] and  

v = [k², k, 2] are perpendicular.

What is k = -1 and k = 2

500

Find the area of the triangle ABC with vertices

 A(3, 2, −1), B(−3, 1, 2), C(4, 1, 1)

What is 15.85 sq units