Basic Trigonometry
Spicier Trigonometry
Exponentials and Logarithms
Polynomials
Miscellaneous
100
What does SOHCAHTOA stand for?
Sine is opposite/hypotenuse, cosine is adjacent/hypotenuse, and tangent is opposite/adjacent
100
Convert the following radian angle to degrees:
(3pi)/4
135°
100
Simplify the following expression:
3u^4v^5*7u^2v^3
21u^6v^8
100
Describe what the degree of a polynomial is.
It corresponds to the highest value exponent. In general, it tells you the number of roots you are looking for.
100
Find x. Round to the nearest tenth and provide units.
7.7 cm
200
Find the missing side length. Round to the nearest tenth.
8.1
200
Convert the following angle measured in degrees to radians:
210°
(7pi)/6
200
Solve for x in the following equation:
log_2x=6
64
200
Find the roots of the following function:
f(x)=(x-4)(x-3)(x+2)
-2, 3, and 4
200
State the initial value, the growth/decay factor, and whether the graph is growing or decaying for the function given below:
f(x)=3(1/2)^x
Initial value: 3
Growth/decay factor: 1/2
Decaying
300
Find the measure of the indicated angle. Round to the nearest tenth.
48.2°
300
Determine the reference angle for 225°
45°
300
Cam invests $8,634 in a savings account with a fixed annual interest rate of 2.67% compounded continuously. What will the balance be after 6 years?
$10,134.12
300
Divide the following polynomials. Write any remainder as a fraction.
(p^3-10p^2+20p+26)-:(p-5)
p^2-5p-5+1/(p-5)
300
A basket contains 4 apples and 8 tangerines. You randomly select one piece of fruit and eat it. Then you select another piece of fruit and eat it. Determine the probability that the first piece of fruit is an apple and the second is a tangerine.
(4/12)(8/11) or 0.2424
400
A blimp hovers 400 feet above a stadium. A fan is standing outside the stadium. To directly view the blimp, the fan looks up at an angle of 7 degrees. Approximately how far from the stadium is the fan standing?
3258 feet
400
Write the equation of a cosine curve that has been transformed in the following ways:
- moved up 2
- amplitude stretched 4
- frequency change of 3
y=4cos(3x)+2
400
Solve for x in the following equation. Round your answer to the nearest tenth.
log(x+4)+log3=2
29.3
400
Write the equation of the third degree polynomial whose roots are -6, 2, and 3, and whose graph passes through the point (0, 4).
y=1/9(x+6)(x-3)(x-2)
400
Write the exponential regression equation for the table below. Round your answers to the nearest hundredth.
y=180.38*0.95^x
500
The slope of a ramp is 1/11. What is the angle of elevation of the ramp? Round to the nearest hundredth.
5.19°
Use inverse tangent!
500
Determine the EXACT value of the following trig expression without using a calculator:
sin(240)
-sqrt3/2
500
Solve for x in the following equation:
-6log_3(x-3)=-24
x=84
500
Find the roots of the function given below. You must do so algebraically in order to receive the points.
f(x)=x^3-6x^2-4x+24
-2, 2, and 6
500
The population of New York State in millions of people since 2003 can be modeled with the function given below. When will/did the population reach 15 million?
y=10.78e^(0.02304t
2017