MATH098 Final Exam Review

Quadratics

100

Vertex for f(x)=-2x² + 6x + 3 

What is (1.5, 7.5)?

200

Axis of symmetry for f(x) = 5x² + 4

What is x = 0?

300

Domain and range for f(x)=x² - 4.

What is (-oo, oo) and [-4,oo)?

400

The point of intersection between f(x)=x² and g(x)=-1/2x. 

What is x=1,4?

500

The x value for the equation 3x² - 12x + 12 = 20.

What is x=(6+2sqrt(15))/3 and (6-2sqrt(15))/3?

Function operation

100

The simplified form of b(x) - a(x) when 

a(x) = 2x² -3x + 5 and b(x) = x² + 4x - 1, 

What is -x² + 7x - 6?

200

The simplified form of c(x+3) when c(x) = 2x - 7.

What is 2x - 1?

300

The simplified form of b(x)*c(x) when b(x) = x² + 4x -1 and c(x) = 2x - 7.

What is 2x³ + x² - 26x - 7?

400

The simplified form of f(4/x²) when f(x) = (x+2)/(x-1).

What is (2x² + 4)/(-x² + 4)?

500

The simplified form of (f(x)-f(4))/(x-4) when f(x) = (x+2)/(x-1).

What is -1/(x-1)?

Logarithm 1

100

The logarithmic form of 3²=9.

What is log₃9=2?

200

The logarithmic form of e^2x = 200

What is ln 200 = 2x?

300

The exact x value of 10^x + 18 = 152.

What is log 134 = x?

400

The approximation to the nearest thousandths of x for 5e^x+2 = 200.

What is 1.689?

500

The approximation to the nearest hundredth of x when g(x) = 50 and g(x) = 10e^x - 5.

What is 1.70?

Logarithm 2

100

log₅1

What is 0?

200

ln e⁹⁹⁹

What is 999?

300

log₈(3x+1)=2

What is 21?

400

The approximation of x for 11+2 ln x = 15 to the thousandths place.

What is 7.389?

500

The exact value of x to 4 + ln(2 - x) = 7.

What is 2+e³?

Application

100

A toy rocket is shot straight into the air.  The function H(t)=-16t² + 128t + 3 gives the height (in feet) of a rocket after t seconds.  It takes the rocket this much time to reach its maximum height.

What is 4 secs?

200

A toy rocket is shot straight into the air.  The function H(t)=-16t² + 128t + 3 gives the height (in feet) of a rocket after t seconds.  It takes the rocket this long to hit the ground.

What is 8.02 secs?

300

Given the function D(t)=e^-0.25t, where D is the amount of drug (in mg) in the person's system, t hours after it was given.  It takes this long for the body to metabolize half the drug.

What is 2.77 hrs?

400

It is defined by M_w = 2/3 log (M₀) - 6, where M₀ is the seismic moment measure in N-m (Newton-meter) and the moment magnitude, M_w is a dimensionless number.  The moment magnitude of an earthquake with a seismic moment of 10¹⁸ N-m.

What is M_w=6?

500

¹It is defined by M_w = 2/3 log (M₀) - 6, where M₀ is the seismic moment measure in N-m (Newton-meter) and the moment magnitude, M_w is a dimensionless number.  The seismic moment of an earthquake with a moment magnitude of 6.4.  (Write your answer in scientific notation.)

What is 3.9811x10¹⁸ N-m?