Pre-Calculus Ch. 1-8 Review

General Functions

100

Find the equation of a line passing through (4, 5) and (-1, 8) in slope-intercept form.

y= 37/5 - 3/5 x

200

Find the distance between (0.4, 0.7) and (2.1, 4.9).

4.531 units

300

f(x) = 3x + 4

g(x) = x² - x +2

Find g(f(x)) in standard form.

9x² +21x +14

400

Find the inverse of f(x) = x³ +8

f^-1(x) = (x-8)^1/3

500

What is Balaji's favorite formula in math?

The slope formula.

Polynomial/Rational Functions

100

Factor x² - 6x + 5

(x-5)(x-1)

200

Divide using synthetic division:

(2x⁴ - 5x² - 3) / (x - 2)

2x³ + 4x² + 3x + 6 + 9/(x-2)

300

Write in standard a + bi form:

5/(2+i)

2 - i

400

Determine the equation of the horizontal asymptote of f(x) = (2x² - 5x - 12)/(x² - 16)

y = 2

500

What is the title and subtitle of Balaji's Viewboard?

Balaji's Board

Awesome Math

Exponential/Logarithmic Functions

100

Convert to logarithmic form:

25 = 5²

log₅(25)=2

200

Expand:

log (7x²/yz³)

2log(x) - log(y) - 3log(z) + log(7)

300

Convert to logarithmic form:

y=ae^kt

ln(y)=ln(a) + kt

or

log(y)=log(a) + (kt)log(e)

400

Solve for x in exact form:

18 + 4ln(x) = 7

x = 1/e^11/4

500

How many siblings does Balaji have?

4

Trigonometry

100

Convert 5pi/4 radians to degrees

225 degrees

200

Convert 130 degrees to radians.

2.269 radians

or 

13/18 pi radians

300

Find exact value of 

tan(arccos(3/5))

4/3

400

Find all solutions to tan²(x)+tan(x)=0

x=n(pi)

x=(pi)/4 +n(pi)

500

When Balaji learned SOHCAHTOA, he learned this phrase to remember it with...

Some Old Hen Caught Another Hen Taking Oats Away

Future Topics

100

Determine the common ratio of the geometric sequence:

-1/3, 1/9, -1/27, 1/81, ...

-1/3

200

Find a formula for the arithmetic sequence

7, 11, 15, 19, ...

a_n = 4n + 3

300

Expand (a+b)⁴

a⁴ + 4a³b + 6a²b² + 4ab³ + b⁴

400

Find the dot product of the vectors 

<0, 3, -2> dot <4, -2, 3>

-12

500

What is Balaji's first name?

Pete