Algebra 2 with Trigonometry

Exponents & Logarithms

100

log₄ 64

3

200

Solve 27^2x=9^x-1

x=-1/2

300

Solve log₂ x + log₂ (x-2) = 3

x=4

400

If log_b 10 = 0.93, log_b 3 = 0.44, and log_b 9 = 0.88, what is log_b 27?

1.32

500

Solve 5^x = 4^x-7 and round to 4 decimal places.

x=-43.4880

Trigonometry

100

What is the amplitude of y = 3 sin (8 x)?

3

200

What is the period of y = 3 sin (8x)?

pi/4

300

Solve for x in radians (0 <= x < 2pi):

cos² x - 3cos x + 2 = 0

x=0

400

A triangle has sides 13, 24, and 24. What is the angle across from one of the longer sides to the nearest hundredth of a degree?

74.3 degrees

500

Simplify:

(9 sec x + 3 cos x) / sin x + (3 sin x) / cos x

12 / (sin x cos x)

Probability etc.

100

How many odd three-digit numbers can be formed using the digits 1, 2, 3, 4, 5, and 6? Repeated digits are allowed.

108

200

How many ways can a committee of 3 men and 4 women be appointed from a group of 8 men and 12 women if all members of the committee have equal roles?

27,720

300

Find the sum: 4/3+10/9+25/27+...

8

400

A spinner has 8 sections of equal area with -3, -2, -1, 0, 1, 2, 3, and 4 printed in them. A fair six-sided die has 2, 3, 5, 8, 13, and 21 printed on the faces. Find P(sum<5) if the spinner is spun once and the die is rolled once.

7/24

500

Find the sum from n=2 to infinity of 5(1/2)^n-1

5

Miscellaneous

100

Solve x²-3x-10<0

-2<x<5

200

Solve |4x-6|=4

x=1/2, x=5/2

300

Solve

(x+1)/(x+2) + 2/(x+1) = 1

x=-3

400

Solve the system:

3x+2y+z=19

2x-y+z=4

3x+2y-z=15

(3, 4, 2)

500

P(x)=x³-2x²+x+100 has 3+4i as a zero. What are the other zeros?

3-4i and -4

Cats

100

Are kittens cats?

Yes

200

What is a calico cat?

A cat with a pattern of black, white, and orange coloring.

300

What are Dr. Thurber's cats' names?

Hans, Raven, and Pipit.

400

How many ways can 7 kittens be lined up if 3 are black, 2 are orange, and 2 are white?

210

500

What is Charlie's cat's name?

Simba