Algebra II/Trig Honors Final Exam Review

Exponential and Logarithmic Functions

100

This is the base of the common logarithm.

What is 10?

200

In order to solve an equation with a variable in the exponent, you must do this.

What is take the log of both sides of the equation?

300

When log 2 + 3 log x - log y is condensed it becomes this.

What is 2x³/y?

400

Double Jeopardy:

When 4^2x+3 = 64^3x-5 is solved for x, the solution is this.

What is 18/7?

500

When log(4x³y²)/z⁵ is expanded, it becomes this.

What is log 4 + 3 log x +2 log y - 5 log z?

Rational Equations and Functions

100

These are the vertical and horizontal asymptotes of the function y = (4-3x)/(2x-1).

What is x = 1/2 and y = -3/2?

200

This is the sum of (3x+4)/(x²-25) and 2/(x+5).

What is (5x-6)/(x²-25)?

300

This is the difference of (4x-5)/(x²-36) and 3/(x+6).

What is (x+13)/(x²-36)?

400

When -3/(x-2) = 1 - (12/(x²-4)) is solved for x, the solution is this.

What is -5?

500

When the complex fraction (3/(x+1)-4/x)/(4/(x+1)+3/x) is simplified, it simplifies to this.

What is (-x-4)/(7x+3)?

Trigonometric Ratios and Functions

100

In a right triangle, if a side with length 11 is across from a 60 degree angle, then the length of the hypotenuse is this.

What is 22 √ 3  /3?

200

-130 degrees converted to radians is this.

What is -13π/18?

300

The tan (-5π/4) is this.

What is - √ 2  /2?

400

If tan x = -5/12 in the second quadrant, then sin x is equal to this.

What is 5/13?

500

What is the arc length of a sector with a radius of 4 cm and a central angle of 80 degrees?

What is 16π/9 cm?

Systems of Equations

100

Define a system of equations

What is two or more equations that are simultaneously true?

200

Sketch the graphs of a system of equations that has 1 solution.

What is two (or more) lines that intersect at 1 point.

300

Find all solutions of the system of equations: x+y=3, 2y-6= -2x How many solutions are there?

What is y = 3-x (infinitely many)?

400

How many solutions does the system 6x+y = 7 and 3x+0.5y = 4 have? Explain how you know.

What is none? Since the second equation's left side is the match of the first up to a factor of 2, but the right side isn't.

500

Emily, Poliana and Brian have a doughnut party. Together, Emily and Poliana ate 7 doughnuts, while Poliana and Brian ate 14 doughnuts, and Emily and Brian had 13 doughnuts together. How many doughnuts did the 3 kids eat altogether?

What is 17?

Random

100

The amplitude and period of y = -3sin(x)

What is amplitude is 3 and period is 2pi?

200

Double Jeopardy:

In an m by n matrix, m is the number of ____ and n is the number of _____.

What is row and column?

300

The exact value of the sine of 330 degrees is this.

What is -1/2?

400

Is x=2 a function? What about y = 2? Explain.

What is no and yes? (First one fails the vertical line test while the second does not.)

500

The range of the graph of f(x) = 2^x+3 -1 is this.

What is y > -1?