MCE 9th 3rd term

Probabilidad

100

What do you call the set of all possible outcomes of an experiment?

Sample Space

200

Find the probability of throwing a prime number on a 20 sided die

2/5 = 0.4

300

How many two letter codes can be formed using the letters A, B, C, D?  Repeated letters are allowed

4² = 16

400

In how many ways can 4 people be lined up?

4 P 4 = 24

500

In how many ways can a committee of 4 students be formed from a pool of 7 students?

7 C 4 = 35

Exponencial

100

Decide if the following function represents exponential growth or decay:

y = 5(0.3)^x

Exponential Decay

200

Determine the initial value of the function

v = 4.3 (2.01)^t

4.3

300

Solve:

5^7x = 5^3x-2

x= -1/2

400

Solve:

3^2x = (1/9)^x+1

x= -1/2

500

solve

3 = 8(5^x)-4

x = -0.08287

Logarithmic

100

What is the base of this logarithm

ln 8

the base is e

200

Find an equivalent logarithmic expression for

b⁸ = 32

8 = log_b 32

300

solve:

2ln (-x) = ln 9

x = -3

400

solve:

log₃(4x+3) = 3

x = 6

500

solve:

log (x+2) + log (x+1) = log (4x+8)

x = 3

Financial

100

When the compound period is semiannually,  n=?

n = 2

200

Find the amount that results from investing $100 at 4% compounded quarterly after a period of 2 years

FV= 108.29

300

Find the value needed to get $300 after 4 years at 3% compounded daily

PV = $266.077

400

What rate of interest compounded annually is required to double an investment in 3 years

I = 25.992%

500

How long does it take for an investment to triple in value if it is invested at 6% compounded monthly

T = 18.35594 

Wild card

100

Find the roots of 

y = x²-2x

x=0   and   x=2

200

Find the intersection point of the lines

y= x+1

and

y= -x+3

(1,2)

300

According to complex numbers,  What is the value of 

i ⁸?

i ⁸ = 1

400

Given the complex numbers A and B, find A+B

A = 3+5i

B = 2-3i

A+B = 5+2i

500

Find other polar coordinates (r,𝜃) of the point (1 , 90°)

for which  r > 0 and  -360° < 𝜃 < 0°

(1 , -270°)