Post Test Review

Complex Numbers

100

The standard form of a complex number

a+bi

200

Find the value of i³⁵

-i

300

Subtract the following expressions:

(2+i) - (-i+4) - (3i-4)

-i+2

400

Multiply the following expression:

(6i+2)(-3i+6)

30+30i

500

Perform the series of operations:

(2-3i)(i³+2) - 2(4i+2)

-3-16i

Functions

100

Evaluate the function:

f(x) = 2x + 1, when x = -2

-3

200

Add the following functions:

f(x) = x²+x-3, g(x) = 2x³+x²+1

2x³+2x²+x-2

300

What is the range of the function in interval notation:

f(x) = (x-2)²-1

[-1, infinity)

400

Compose the functions and evaluate them: 

(f o g) (1)

f(x) = x+5, g(x) = x²+x-1

6

500

Compose the functions and evaluate: 

(g o f) (2x)

f(x) = -x, g(x) = x²+x-1

4x²-2x-1

Matrices

100

What are the dimensions of the matrix with 8 columns and 3 rows?

3x8

200

Given the dimensions of the matrices. Which multiplications are defined? You can choose more than one.

a) 2x3 to 2x3                  d) 4x2 to 2x5

b) 3x2 to 3x2                  e) 1x2 to 2x8

c) 8x10 to 8x11

d and e only

300

How many elements would the product of a 2x4 matrix and a 4x8 matrix would be?

16

400

Identify the following elements:
(-2A - 2B)₂₁ and (-2A - 2B)₂₂

-28 and 32

500

Find the element: AB₂₃

24

Natural Log Equations

100

What is the value of 'e' in the nearest hundredths?

2.72

200

Find the value of x in the nearest hundredths:

e^2x+3 = 14

1.2

300

Solve for x in the nearest hundredths:

ln 3x + ln 10x = 3

0.82

400

A culture of bacteria doubles every 4 hours. Initially, there were 100 of the bacteria, After several hours, a scientist observed that it had grown six times its size, how many hours have passed for the bacteria to grow to that size?

24 hours

500

An investor deposits $4000 in a bank that pays at a rate of 1.5% monthly in 5 years. How much money will the depositor yield at that given time?

(Round up to the next whole number)

$4312

More Logs

100

Change the expression: 4² = 16, into its logarithmic form.

log₄16 = 4

200

Expand the following log:

log₄x²y³z⁴

2log₄x+3log₄y+4log₄z

300

Simplify the following log function:

log₂32 + log₂16 - log₂2

8

400

Condense the following log:

1/2(4logx+6logy-16logz-2logw)

log(x²y³)/(wz⁸)

500

If a $100 deposit is made at a bank that pays 12% per year, compounded semi-annually, determine how long it will take for the investment to reach $4000.

Use the formula: A = P(1+r/n)^t, where A is the accumulated amount, P is the initial amount, r is the rate, n is the conversion period, and t is time.

Round up your answer to the next whole number.

64 years