Unit 1 - Real numbers, radicals, exponents, scientific notation

The real number below that is irrational is:

• 5,1212121212....

A faucet fills a tank in 6 hours, and a drain empties the same tank in 10 hours. If both are open at the same time, how long will it take to fill the tank?

• 15 hours

• 7,5 hours

• 10 hours

• 15/4 hours

A cube has a volume of 2000 cm³. The cube's surface is painted. What is the total painted area in simplest radical form?

A cylinder has a height h that is twice the radius r. If its volume is 432π cm³, what is the total surface area (including top and bottom)?

Evaluate the following statements regarding set theory:

I. The set of real numbers is nothing more than the intersection of rational and irrational numbers.

II. {1,3,5,7,11} belongs to the set of natural numbers.

III. The square root of 5 is an irrational number.

IV. Non-positive integers belong to the set of natural numbers.

• I and IV

• II and IV

• II and III

• III and IV

The distance from Earth to the Sun is approximately 1.5 × 10⁸ km. A spacecraft travels at 3 × 10⁴ km/h. About how many hours would it take for the spacecraft to reach the Sun?

A certain gas molecule has a mass of 4.5 × 10⁻²⁵ g. If there are 2 × 10²³ molecules in a sample, what is the total mass of the sample in grams?

A photon has an energy of 6.63 × 10⁻³⁴ J. If a laser emits 5 × 10²⁰ photons per second, how much total energy is emitted in one hour?