Direct, Inverse Variation, Roots

Direct/Inverse Variation

100

Solve the inverse variation formula for k.

What is k = xy

200

If y varies directly as x, and y = 3 when x = 9, find x when y = 5.

What is 15.

300

Y varies inversely as x and y = 2 when x = 8. Find y when x = 32

What is 1/2 ?

400

Y varies directly as x squared and y = 32 when x = 4. Find y when x = 12.

What is 288?

500

x varies inversely as y cubed. x is 16 when y is 5. Find x when y is 2.

What is 250 ?

Exponent Rules

100

Simplify with no negative exponents: x² / x⁴

What is 1 / x²

200

(3ab³)/(9ab³)

What is 1/3

300

(7ab²c⁴)²

What is 49a²b⁴c⁸

400

(9a^-4b²c)^-1/2

What is a² / 3bc^1/2

500

(6ab/3ab²)*b⁰

What is 2/b

Word Problems

100

On a map, distance in km and distance in cm varies directly, and 25 km are represented by 2cm. If two cities are 7cm apart on the map, what is the actual distance between them?

What is 87.5 km

200

The time it takes to fly from Los Angeles to New York varies inversely as the speed of the plane. If the trip takes 6 hours at 900 km/h, how long would it take at 800 km/h?

What is 6.75 hours?

300

Hooke’s law states that the distance d that a spring is stretched by a hanging object varies directly as the mass m of the object. If the distance is 20 cm when the mass is 3 kg, what is the distance when the mass is 8 kg?

What is 160/3 = 53.3 cm

400

The frequency of a vibrating string varies inversely as its length. A string 3 feet long vibrates 175 cycles per second. Find the frequency of a 5 foot string.

What is 105 cycles per second

500

Completely simplify this radical: sqrt(9a²b⁴)

What is 3ab²

Rational Exponents + Radicals

100

Convert to exponent form: sqrt(x)

what is x^1/2

200

Simplify: 8^2/3

What is 4

300

Convert to radical form: (ab)^1/4

What is the fourth root of ab

400

Convert to radical form: x^1/2 * x^1/3 

What is the sixth root of x⁵

500

In planning a trip, the time it takes to make the trip varies inversely with the rate of the car. If I take Route A and average 40 mph, it will take 9.5 hours to complete the trip. If I go by Route B and average 50 mph, how long will the trip take?

What is 7.6 hours

Square Root Functions

100

Solve for all possible values of a: 

sqrt(a-2) = 9

What is 83

200

Find f(5)

f(x) = 3sqrt(2x+6)

What is 12?

300

Consider the parent function y = sqrt(x). Write an equation that translates the equation UP 3.

What is y = sqrt(x) + 3

400

Consider the parent function y = sqrt(x). Write an equation that translates the equation DOWN 3 and RIGHT 5.

What is y = sqrt(x - 5) + 3 ?

500

What is the domain of the function y = -1 sqrt(x - 4) + 2

What is x > 4 ?