Algebra II & Trigonometry H Final Exam

Sequences & Series

100

Find the recursive formula of the series 3, 15, 75, ...

a_n = 5a_n-1

a₁ = 3

200

Find the common ratio of a geometric series with the given terms a₂=2 and a₄=8

2

300

Calculate the sum of the first nine terms of a series with the rule 3n+5

180

400

Find the 52nd term of the sequence algebraically:

-22, -122, -222, ...

-5122

500

Find the explicit formula of the arithmetic series given the terms a₁₅=(62/3) and a₃₅=(152/3)

a_n = (-11/6) + (3n/2)

Expressions

100

Simplify:

ln(e^x) + 10^log6

x+6

200

(2x²+19x+24) / (4x²+24x-64)

(2x+3)/(4(x-2))

300

(x⁴+4x³-64x-256) / (x+4)

f(x)=(x+4)(x-4)(x²+4x+16)

400

Simplify:

√(20e^8x)

2e^4x√5

500

(6x)/(x²-5x+4) + 1/(x²-4x+3)

(6x²-17x-4)/((x-3)(x-1)(x-4))

Equations & Inequalities

100

Solve for x:

(1/5)^3x-2=√(25^x)

x=1/2

200

Solve for x:

0<-2x²-16x-30

-5<x<-3

300

Solve for the exact value(s) of n:

8×10^7n-7+10=13

n=(log(3/8)+7)/7

400

Solve:

log₃(-3v-10) = log₃(-5v-4)

{ }

500

Find the exact value(s) of x: 5^2x=4^2x-1

x= -log4/(2log5-2log4)

Trig

100

Write a function for a sine wave with a period (2pi/3) that passes through the points ((pi/6), 2) and ((pi/2), -2).

y=2sin3x

200

Find the other five trigonometric functions of x. 

secx=(7/3), (3pi/2)<x<(2pi)

sinx=(-2(√10)/7) cosx=(3/7) tanx=(-2(√10)/3) cscx=(-7(√10)/20) cotx=(-3(√10)/20)

300

Simplify:

(2sec²x-2tan²x)/(tan(-x)cos(-x))

-2cscx

400

Solve the equation for x over the interval 0°<x<360°:

tan²x-1=0

x=45°, 135°, 225°, 315°

500

Solve for x over the interval 0°<x<360°:

2cosx-3secx=-5

x=60°, 300°

Miscellaneous

100

Describe the end behavior of the function 

f(x)=3x²-x⁵-1

f(x)→+∞ as x→-∞

f(x)→-∞ as x→+∞

200

Describe the transformation of the function in relation to its parent function.

f(x) = ³√(-3x) +1

Reflection over the y-axis

Horizontal shrink by 1/3

Translation 1 unit up

300

Expand:

log₄(c√(ab))

log₄c + (log₄a)/2 + (log₄b)/2

400

You deposit money in an account that pays 6.75% interest compounded continuously. To the nearest year, how long will it take your money to double?

10 years

500

Write a polynomial function of least degree with the integral coefficients that has the given zeroes: 1+2√(2), 2-3i

y=x⁴-6x³+14x²+2x-91