Final Review Jeopardy

Radicals/Exponents

100

^{What is the product rule for exponents?}

a^x _* a^y=a^x+y

200

What is the root, index, and radicand of the following radical expression?

cbroot(8)

root=2

index=3

radicand=8

300

Solve the following expression.

(2²)³

64

400

Solve the following radical using the product rule.

root(8) * root(2)

root(16)=4

500

What is the quotient rule for radicals?

root(a/b)=root(a)/root(b)

Transformations/Graphing

100

What shift is being done?

y=x²+4

Vertical shift up 4

200

Is this a vertical or horizontal shift?

y=(x+3)²

Horizontal shift 3 units to left

300

Reflection over the x or y axis?

y=-|x|

x-axis

400

Is this a compression or stretch?

y=-2x²+3

Stretch by factor of 2

500

How many transformations are applied to the function?

y=-.5(x-12)³+6

4
reflection over the x-axis, compression by a factor of 1/2, horizontal shift 12 units to the right, and a vertical shift of 6 units up

Factoring

100

Factor:

6x²+23x+15

(6x+5)(x+3)

200

Factor:

x²-6x+9

(x-3)(x-3)
or
(x-3)²

300

Complete the square:

x²+6x+8=0

x=-2
x=-4

Steps:
x²+6x=-8
x²+6x+9=-8+9
(x+3)²=1
x+3=+/- 1

400

Factor by grouping:

x³-2x²+5x-10

(x-2)(x²+5)

500

Factor:

4x⁴+12x³+6x²+18x

2x[(x+3)(2x²+3)]

Circles

100

What is the standard form equation of a circle?

(x-h)²+(y-k)²=r²

200

Find the center of the circle:

(x+1)²+(y-7)²=16

(-1,7)

300

What is the radius of the following circle?

(x-256)²+y²=81

r=9

400

Graph this circle:

x²+(y-10)²=25

center: (0,10)
r=5

500

The third planet from the sun

What is Earth?

Logarithms

100

Solve the following logarithm:

log₅25

2

200

What is the log of 1?

0

300

Expand the following logarithmic expression.

log₂(x/x²)

log₂x-2log₂x

400

Convert the following logarithm to exponential form and solve.

log₆36=x

6^x=36

x=2

500

log₂₅₆0=x

x=1