GCC Jeopardy

Logarithms

100

Write in logarithmic form: 

(1/10)=10^-1

log₁₀(1/10)=-1

200

Find the value: 

log₇49=

2

300

Use the exponent and log rules to find the value of x:

4^x=8

3/2

400

Use the exponent and log rules to find the value of x.

3log_a4 = log_ax

64

500

Use the change of base formula to write log₃2 with a base of 7. 

log₇2 / log₇3

Exponents and Radicals

100

(2/3)⁴=

16/81

200

Write as a radical:

4^2/3=

∛16

300

Find the value:

(a^x+3)^x-3=

a^x2-9

400

Write with positive exponents:

(-8a⁶b^-12)^-2/3=

b⁸ / 4a⁴

500

Simplify:

√3 / (1−√3)

(√3 + 3) / -2

Quadratic polynomials/equations/inequalities

100

Factor completely:

-4xy + 10x² =

2x (-2y + 5x)

200

Solve by factoring completely:

6x² = x + 2

x= -1/2 and x=2/3

300

Solve, and graph on a number line:

2x² + x - 1 > 0

x < -1 or x > 1/2

400

Solve, and graph on a number line:

x² + 2x < 0

-2 < x < 0

500

Factor completely:

x⁴ + 3x² - 4 = 

(x² + 4) (x + 1) (x - 1)

Rational Expressions

100

Find the sum or difference as indicated (reduce if possible):

[(b - a) / (b + a)] - [(a - b) / (b + a)]  

(2b - 2a) / (b+a)

200

Find the sum or difference:

( 3/x ) - ( 2/a ) = 

( 3a - 2x ) / (ax)

300

Complete:

(x + 3) / (x + 2) = (?) / [(x - 1) (x + 2)]

x² + 2x - 3

400

Find the sum or difference:

[ x / (x - 2)] - [ 4 / (x² - 4)] = 

( x² + 2x - 4) / ( x² - 4)

500

Multiply, reduce if possible:

[ 3(x + 4) / 5y] * [ 5y³ / (x² - 16) ] = 

3y² / (x-4)

Mystery

100

Write in scientific notation: 

93,000,000 = 

9.3 x 10⁷

200

Graph:

y= (x + 1)²

See Desmos graph!

300

x and y are numbers, and two x's equals three y's. 

Find the ratio of x to y. 

3/2

400

Write the answer in the form a + bi:

(3 + 2i) / (3 - 2i) = 

( 5/13 ) + (12i/13)

500

After a rectangular piece of knitted fabric shrinks in length one cm and stretches in width 2 cm, it is a square. If the area of the rectangle was 40 cm², what is the area of the square?

49 cm²