Pre-Calc Quarter 3 Review

Log Equations

100

−10 + log₃(n + 3) = −10

n = -2

200

log (4k − 5) = log (2k − 1)

k = 2

300

log₉(−11x + 2) = log₉(x² + 30)

x = -7, -4

500

Determine all real values of x such that log₁₀2x+log₁₀(x-5) = 2

10

Circles

100

Identify the center and radius of this circle.

(x − 2)² + (y + 1)² = 16

C: (2, -1), R: 4

200

Identify the center and radius of this circle.

9 = 2y − y² − 6x − x²

C: (-3, 1), R: 1

300

Identify the center and radius of this circle.

16 + x² + y² − 8x − 6y = 0

C: (4, 3), R: 3

500

Determine the distance between the vertex of the graph of y=-3x²-12x-4 and the center of a circle x²+y²-6x+8y-50=0

13

Inverse Trig Functions

100

Evaluate: Arc sin (1)

90 degrees

200

Evaluate: cos[Arc sin 1/2]

square root 3 over 2

300

Evaluate: cos[Arc tan (-1)]

Square root 2 over 2

500

Let k be the number of solutions for θ, 0≤θ<360, when 12tan²θ-8=10

k = 4

Permutations

100

There are 10 finalists in a figure skating competition. How many ways can gold, silver, and bronze medals be awarded?

720 ways

200

A contractor wants to plant six oak trees, nine maple trees, and five poplar trees along the subdivision street. The trees are to be spaced evenly apart. In how many distinguishable ways can they be planted?

78,960 distinguishable ways

300

How many distinguishable permutations are there for the word: SLEEPLESS?

30,240 distinguishable permutations

BONUS

1000

A shepherd has five distinct sheep. Each sheep wears a name tag consisting of the five letters: S, H, E, E, and P. Determine the total number of distinct ways possible if you both rearrange the order of the five sheep and, for each sheep, rearrange the letters on its individual name tag.

93,312,000,000 ways