PRE-CAL JEOPARDY Andrea S. and Joyce M.

Sequences & Series

100

Is the following sequence geometric or arithmetic?

2, 4, 6, 8,...

Arithmetic

200

Find the a₁₀₁ term for:

3, 8, 13, 18, 23, 28,... 

503

300

Find the a₇ term for the following geometric sequence: 

3, 6, 12, 24, 48

192

400

Find an equation for the n^th partial sum of S_n

100+75+50+... 

S_n=-25n²+225/2

500

Find an equation for the n^th partial sum of S_n and find S₃

4(b)^n-1

4+4b+4b²

Exponential Equations

100

Solve 

10^1-x=10⁴

x=3

200

Solve

3^{x^2-3x}=81

x=1, 4

300

Solve

4^x+1=1/64

x=-4

400

8^x-2= square root of 8

x=5/2

500

2^x=-4

No solution

Log Equations

100

log₃(x)=log₃(14)

x=14

200

log₁₀(x²-30)=log₁₀(x)

x=6

300

2log₁₀(x)=log₁₀(4)+log₁₀(x-1)

x=2

400

log₂(x)=4.5

x=22.63

500

log₁₀(7x+2)+log₁₀(9)=log₁₀(2x)

No solution

Rt. Angle Trigonometry/Law of Cosine and Sine

100

A four-meter-long ladder leans against a building. If the ladder makes an angle of 60° with the ground, how far up the wall does the ladder reach? How far from the wall is the base of the ladder?

The ladder reaches at 3.46 meters.

The base of the ladder is 2 meters.

200

A five-meter-long ladder leans against a wall, with the top of the ladder being four meters above the ground. What is the approximate angle that the ladder makes with the ground?

About 53 degrees

300

Two sides of a triangle are 8 units and 12 units long. The angle opposite the 8 unit long side is 35 degrees. What is the angle opposite the side that is 12 units long?

About 59.4 degrees

400

A triangle has sides measuring 3 units and 4 units, with an included angle of 57 degrees. What is the length of the side opposite the 57 degrees angle?

3.5 units

500

Find the measure of C

a=29

c=24

B=101

C=36.322 degrees

Trigonometry Proofs and Equations

100

What is the first step to verify this equation:

cot(x)/csc(x)=cos(x)

Converting cotangent and cosecant into their alternative expressions.

200

Solve

2cos(theta)+1=0

theta= 4pi/3 or 2pi/3

300

Simplify

cos²(x)-1/sin²(x)

tan²(x)

400

tan(x)+cot(x)/cot(x)

1

500

tan(x)/tan(x)+cot(x)

sec²+1