math review 2-5

13. What is a Pythagorean Theorem?

13. What is a Pythagorean Theorem? The theorem that the sum of the squares of the lengths of the sides of a right triangle is equal to the square of the length of the hypotenuse

2. Find the volume of a sphere with a radius of 9 m.

2. Find the volume of a sphere with a radius of 9 m. Volume of sphere = 4/3 * pi * r cube r = radius of the sphere V= 4/3 * 3.14 * (9m * 9 m * 9 m) V= 3,052.08 m cube

4. Find the volume of a cylinder that is 5m high with a radius of 2m.

4. Find the volume of a cylinder that is 5m high with a radius of 2m. Volume of cylinder = pi * r squared * height (h) V = 3.14 * (2m * 2 m) * 5m V= 62.8 m cube

5. Find the volume of a cone, with a height of 7 inches and a base with a radius of

5. Find the volume of a cone, with a height of 7 inches and a base with a radius of 3 inches. Volume = 1/3 * pi * r squared * height (h) V= 1/3 * 3.14 * 3 in. * 3 in. * 7 in. V= 65.94 inches cube

6. Find the volume of a pyramid with a square base 4 cm by 4 cm and a height of 12 cm.

6. Find the volume of a pyramid with a square base 4 cm by 4 cm and a height of 12 cm. Volume = 1/3 * base * height V= 1/3 * b * h b= 4cm * 4 cm b= 16 cm squared V= 1/3 * 4 cm squared * 12 cm V= 16 cm cube

B) Composite numbers:

B) Composite numbers: whole numbers that have three or more whole number factors. Ex.: 6 is a composite number, because it has four different factors, 1, 2, 3, and 6.

Binomial

Binomial: an expression with two terms Ex: 2ab-cd

Coefficients

Coefficients: the numbers that precede the variable to give the quantity.

Monomial

Monomial: an expression with one term.

Polynomials

Polynomials: an expression with more than one term

1. Find the volume of a box

The length is 6 cm; width is 4 cm; height 7 cm. Volume = length * width * height Volume is measured in cubic units. V= 6cm * 4cm * 7cm V= 168 cm cube

Trinomial

Trinomial: an expression with three terms Ex: x+3y-1

Variable

Variable: a letter that stands for a number in an algebraic expression.

3. Find the volume of a hemisphere with a radius of 20 cm

Volume of hemisphere = 2/3 * pi * r cube V= 2/3 * 3.14 * (20cm * 20 cm* 20 cm) V= 16,746.66 cm cube

Dividing by a Decimal:

When dividing by a decimal you can multiply the dividend and the divisor by the smallest number that will make the two whole numbers. Example: 8.307 / 0.13 = the divisor has 2 decimal places so multiple both sides by 100. This will create a problem of whole numbers = 8307. / 13 = 63.9. After, make sure to multiple the answer by the divisor to check your answer.

A) Prime numbers

all whole numbers greater than 1 which have only two different whole number factors, 1 and the number itself. Ex. 5 is a prime number, because it has only two different factors, 1 and 5.