Liam Final Project Pre-Calc

Unit 8: Vectors and Parametric Equations

100

Express the vector V = 2i - 3j in component form.

The component form of the vector V is (2, -3).

200

Given two points A(2, 3) and B(5, 7), find the vector AB.

The vector AB is (5 - 2)i + (7 - 3)j = 3i + 4j.

300

Given vectors u = 3i + 2j and v = -2i + 5j, find the sum u + v

i + 7j

400

Find the direction angle of the vector <-6, 8>

126.870

500

Find the magnitude of the vector <-6, 8>

10

Unit 9:Polar Coordinates and Complex Numbers

100

Find 9u-3v given u=3i+4j and v=-2i+8j

33i+12j

200

Simplify (4+4i)(5-3i)

32+8i

300

Find the rectangular form of the polar equation r=4/(1-cos x)

y2-8x=16

400

Convert the rectangular coordinates (3, 4) to polar coordinates.

5, arctan(4/3)

500

Convert the point with polar coordinates (4, π/3) into rectangular coordinates

(2, 2√3)

Unit 11:Exponential and Logarithmic Functions

100

What is 2^3

8

200

What is the value of log(100)

2

300

What is the value of log(2) in base 4?

1/2

400

What value of x satisfies the equation log2(3x+4)=3

x=4/3

500

 log2(x − 2) + log2(x + 1) = 2

x=3

Unit 12:Sequences and Series

100

Find the next 3 terms in the sequence

1, 3, 6, 10, 15

21, 28, 36

200

Determine whether the sequence converges or diverges. If it converges, give the limit.

2, -4, 8, -16, ...

Diverges

300

Determine whether the sequence converges or diverges. If it converges give the limit

12, 4, 4/3, 4/9, ...

Converges 18

400

Find the 10th term in the sequence

-15/n

-3/2

500

Sum the first 7 terms of A/A+1

1479/280

Unit 13:Combinatorics and Probability

100

What is the probability of getting heads in a coin toss?

50%

200

Solve C(7,4)

35

300

Solve P(6,5)

720

400

What is the probability of pulling 2 red marbles out of a bag containing 3 red marbles, 8 green marbles, and 5 clear marbles without replacement?

1/40

500

How many ways can 13 CDs be arranged on a counter?

13! or 6227020800