Free Printable Algebra 2

1.

Select ALL that is true and applicable to this unit circle trigonometric illustration.
(Use only the unit circle diagram provided in this question).

a)

A. The sine of $-45^o$ is $\frac{\sqrt{2}}{2}$ .

b)

B. The sine of $30^o$ is $\frac{1}{2}$ .

c)

C. The cosine of $-45^o$ is $\frac{\sqrt{2}}{2}.$

d)

D. The cosine of $30^o$ is $\frac{\sqrt{3}}{2}.$

e)

E. $\sin^2\left(30^o\right)+\cos^2\left(30^o\right)=1.$

2.

Select ALL that is true, and applicable to this unit circle trigonometric - ratio illustration diagram.

a)

A. According to this diagram, $\sin120^o=\cos30^o.$

b)

B. According to this diagram, $\cos120^o=-\frac{1}{2}.$

c)

C. According to this diagram, $\sin120^o=\frac{\sqrt{3}}{2}.$

d)

D. According to this diagram, $\cos480^o=-\frac{1}{2}.$

e)

E. According to this diagram, $\sin840^o=\frac{\sqrt{3}}{2}.$

3.

Determine the arc length that subtends the central angle of

135^o,

shown in this diagram. Leave your answer in terms of

\pi.

a)

A. $10\pi.$

b)

B. $10.5\pi$

c)

C. $9.8\pi$

d)

D. $11\pi$

4.

Determine $the\ amplitude,$ , $period,$ and the equation of $the\ midline$ respectively of the cosine function to which this section of the graph has been extracted..

a)

A. Amplitude =1, period $360^o,$ and misline equation is $y=0.$

b)

B. Amplitude = 1, period = $180^o.$ and the equation of its midline is $y=2.$

c)

C. Amplitude = 2, period = $300^o.$

d)

D. None of these is correct.

5.

This table of values is known to model a relationship that is represented by the general equation $y=ax+b,$ where $a$ and $b,$ are constants. Determine the numerical values for $a$ and $b$ and write the equation completely.

a)

A. a = 4, b =2 , and $y=4x+2.$

b)

B. a = 2, b = 4 hence, $y=2x+4.$

c)

C. a = 2, b = 14, and $y=2x+14.$

d)

D. a = 0, and b = 4, so $y=b.$

6.

A Group of Epidemiologists investigating a cholera bacteria culture have established that the microbes reproduce exponentially according to the following exponential model,
$N\left(t\right)=N_0e^{1.386t}.$ where, $N\ is\ the\ number\ of\ bacteria\ present\ after\ t\ hours,$ $N_0\ is\ the\ number\ of\ bacteria\ present\ at\ the\ start\ \left(t=0\right).$ If these disease experts started their study with 25 bacteria, in the context of this question, how many bacteria will be present in the culture after 3.5 hours?

a)

A. 3,180 bacteria.

b)

B. 3,197 bacteria.

c)

C. 4000 bacteria.

d)

D. 3,365 bacteria.

7.

Cosmic rays streaming from outer space into our Earth's atmosphere, collide violently with air molecules striping them of their neutrons. Some of our atmospheric nitrogen in turn, capture some of these free neutrons thus transforming themselves into radioactive carbon-14, which becomes assimilated into plant tissue by way of the life-sustaining process of photosynthesis:
$6^{\cdot}CO_2+6H_2O\ \ --->^{\cdot}C_6H_{12}O_6+6H_2O.$ When animals feed on plant tissues and plant products, the radioactive carbon becomes incorporated into animal soft tissues such as muscles and hard tissue such as animal bones and teeth.
Once an animal dies, its present and irreplaceable level of radioactive carbon begins to decrease due to carbon-14 radioactive decay according to the following established exponential model:
$A\left(t\right)=A_0e^{-0.000124t}.$ Where $A\$ is the amount of radioactive carbon remaining in the sample material $t$ years after the death of the plant or animal tissue, $A_0,$ is the amount of radioactive carbon present at the time of death of the organism.

If 650 milligrams of carbon-14 are known to be present in the bones of a human skull today, at the time of the person's death. How many milligrams will be present in the skull bone sample 35,000 years from today?

a)

A. 10.38 milligrams.

b)

B. 9.65 milligrams.

c)

C. 8.47 milligrams.

d)

D. 21.09 milligrams.

8.

Given the following logarithmic equation
$\log_4\left(x+3\right)=2.$ Determine the value of $x.$

a)

A. 13.

b)

B. 12.

c)

C. 14.

d)

D. 15.

9.

What is the numerical value of
$\log_42+\log_432$ ?

a)

A. 1

b)

B. 2

c)

C. 3

d)

D. 4

10.

Select ALL expressions that are mathematically equivalent to the following logarithmic expression.
$\log_264$

a)

A. $\log_24^3.$

b)

B. $3\log_24$

c)

C. $\log_22^6.$

d)

D. $6\log_22$

e)

E. $\log_28^2\ or\ 2\log_28.$

Algebra 2

Total questions: 10

Worksheet time: 19mins

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