The 3 in 3^2 is what?

The 2 in 3^2 is what?

Is the square of a whole number.

Of a given number is a number which square is the given number.

When 2 is used as an exponent, the base is _____.

When 3 is used as an exponent, the base is _____.

The symbol √ is used to indicate the positive square root and is known as the _____.

The combination of the radical sign with the number is called a _____.

The number under the radical sign is known as the _____.

11^2

12^2

13^2

14^2

15^2

16^2

17^2

18^2

19^2

20^2

X^2 = 169

√1600 = X

√484 = X

√81/625

The cube root of a positive number “n” is a positive number, and the cube root of a negative number “n” is a negative number.

8

27

64

125

216

343

512

729

1 000

Between which two consecutive integers does each number lie?

a. √20

Between which two consecutive integers does each number lie?

. √250

Between which two consecutive integers does each number lie?

c. √27

Between which two consecutive integers does each number lie?

d. √2

Approximate 30 to the tenths place.

If √a = b, then a = b, b and a/b = b.

Approximate 50 to the tenths place.

If √a = b, then a = b, b and a/b = b.

Is a real number that cannot be expressed as a quotient of two integers. The first _____ discovered was √2

π

is the distance for the tip of the little finger to the tip of the thumb of the outstretched hand.

is the distance across the base of the four fingers that form the palm.

is the thickness or width of the index finger.

is the length of a foot.

is the distance from the tip of the middle finger of the outstretched hand to the front of the elbow.

is the distance of one full step.

Queen Elizabeth I changed the measure of the mile from 5 000 feet to 5 280 feet. Her reason for doing this was because a furlong equaled to 220 yards (660 feet), and if 1 mile equaled to 5 280 feet, then a mile would equal to 8 furlongs. Thus, a partial list of English measurements was released in 1500 CE, which includes the following:

1 foot

1 yard

1 pace

1 furlong

1 mile

1 league

Is about 39.37 inches long—a little longer than a yard.

The metric unit used for determining mass (weight) is called a

is the metric unit used for determining volume.

1 inch

1 foot

1 yard

1 mile

1 foot

1 yard

1 mile

Perimeter of a Rectangle

Perimeter of a Equilateral Triangle

Perimeter of a Square

Perimeter of a Regular Pentagon

distance around a circle.

ΠD or 2ΠR

A = (l) (w)

A = (b) (h)

A = 1/2(h)(b1 + b2)

A = Πr^2

A = 1/2(b)(h)

A = (length of side)^2

A = (b)(h)

is any flat surface.

is a line segment where two faces meet.

is a point where several planes meet in a point.

A _____ is a polyhedron with two identical parallel faces called bases. A _____ has two bases which are congruent polygonal regions lying in parallel planes. It can be named according to the shape of its bases. A triangular _____ has 5 faces, 9 edges, and 6 vertices The five faces are the two triangular bases and the other three (lateral faces) are rectangular faces. In a right _____, the lateral faces and lateral edges are perpendicular to the base. The lateral faces of a right _____ are rectangles.

A _____ is a solid where base is a polygonal region. The altitude of the

_____ is a segment from its vertex perpendicular to the plane containing the line.

A rectangular _____ is a _____ that has the

following properties:

• its base is a regular polygon

• its lateral faces are congruent isosceles triangles

• its altitude meets the base at its center

The altitude of each lateral face of a regular

_____ is called the slant height of the _____.

The lateral area of a _____ is the sum of the

areas of its lateral faces.

A _____ is a solid that has many properties in common with a prism. A circular _____ has two bases, which are congruent circular regions lying in a parallel plane. The axis is the line segment joining the centers of the two circles. An altitude is a segment perpendicular to the plane of each base, with the endpoints in the planes of the bases. When the axis is also an altitude, the _____ is a right circular _____. From this point on, when the word “_____” is used, we will mean “ right circular _____”.

The _____ of a space figure is the sum of the areas of all the faces.

SA = 6a^2

SA = 2lw + 2hw + 2hl

L = (h)(p)

SA = L + 2B

L = 1/2(L)(P)

S = L + B

L = 2ΠRH

S = L + 2B + 2ΠRH + 2ΠR^2

Amount of liquid it can hold.

Can hold one cubic centimeter of water has a capacity of one milliliter.

Defined as the volume of a cubic decimeter. In other words, a _____ is the capacity of a cube that is 1 decimeter long, 1 decimeter wide, and 1 decimeter high. The water in the _____ container will fit exactly into the box with a 10 cm length, 10 cm width, and 10 cm height. One _____, 1 cubic decimeter, and 1 000 cubic centimeters represent the same volume.

1 000 liters

100 liters

10 liters

1 liter

0.1 liter

0.01 liter

0.001 liter

1 cup (c)

1 pint (pt)

1 quart (qt)

1 gallon (gal)

about 200 gallons

about 7.48 gallons

about 1 gallon

Is a measure of the earth’s gravitational pull.

Is the measure of the amount of matter that objects are made of.

number of non overlapping cubic units contained in its interior.

Volume of a Cube

Volume of a Rectangular Prism (or Cuboid)

The volume of a cylinder is equal to its base area times its height.

Volume of a Cylinder

Volume of a Pyramid

Find the volume of the following figures.

Find the volume of the following figures.

Find the volume of the following figures.

A cylindrical solid has a base of radius 15 cm and an altitude of 22 cm. Find the volume of the cylindrical solid.

Find the volume of the pyramid.

Find the volume of the pyramid.

A cylindrical container has a volume of 750 cu. cm. A rectangular pyramid with a base area of 20 sq. cm, and a height of 15 cm is placed inside it. Find the volume of the space outside the rectangular pyramid.

A cylindrical container has a volume of 750 cu. cm. A rectangular pyramid with a base area of 20 sq. cm, and a height of 15 cm is placed inside it. Find the volume of the space outside the rectangular pyramid.

may be thought of as a well-defined collection of objects. These objects are called elements or members of the _____.

{1, 2, 3, 4, 5,…}

{..., -3, -2, -1, 0, 1, 2, 3, ...}

Which of the following sets are well-defined?

A set of all factors of 18

A set of friendly students in your class

A set of senior citizens

Which of the following sets are well-defined?

a collection of all integers more than -2 but less than 5

a collection of all rivers in Region 1

a group of popular volleyball players

We use _____ such as A, B, C, D, and E to denote sets. Example: You could name the set of continents as set C.

We use _____ such as a, b, c, d, and e to denote the elements of a set. It is also a common practice to list the elements of a set in braces { } and separate them by commas. Example: Set A = {5, 10, 15, 20}

The symbol _____ is read as “is an element of.”

A set with no element is an empty set or null set. The symbol for an empty set is _____ or { }.

Assume that T is the set of Tropical fruits, which of the following is true?

1. pineapple ∈ T

Assume that T is the set of Tropical fruits, which of the following is true?

2. coconut ∉ T

Assume that T is the set of Tropical fruits, which of the following is true?

3. papaya ∈ T

Assume that T is the set of Tropical fruits, which of the following is true?

4. apple ∈ T

Assume that T is the set of Tropical fruits, which of the following is true?

5. avocado ∈ T

 It is a method of describing a set in words. We can describe the sets named in number 1 as follows: • Set A is the set of letters in the word “Philippines” • Set B is the set of positive multiples of 5. • Set C is the set of a natural Earth satellite.

It is a method of describing a set by listing each element of the set inside the symbol { }. The elements of sets A, B, and C are listed below. Note: We do not repeat an element while representing a set. A={p,h,i,l,n,e,s} B={5,10,15,…} C={moon}

 It is a method that lists the rules that determine whether an object is an

element of the set rather than the actual elements.

 This method uses this general form in which a set can be written as

A = 𝒙|𝒙 𝒊𝒔 𝑷 which is read as “set A is the set of all x’s such that x satisfies P.”

EXAMPLE:

A= 𝑥|𝑥 𝑖𝑠 𝑎 𝑙𝑒𝑡𝑡𝑒𝑟 𝑖𝑛 𝑡ℎ𝑒 𝑤𝑜𝑟𝑑 "𝑃ℎ𝑖𝑙𝑖𝑝𝑝𝑖𝑛𝑒𝑠"

B= 𝑥|𝑥 𝑖𝑠 𝑎 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑒 𝑜𝑓 5

C= 𝑥|𝑥 𝑖𝑠 𝑎 𝑛𝑎𝑡𝑢𝑟𝑎𝑙 𝑠𝑎𝑡𝑒𝑙𝑖𝑡𝑒 𝑜𝑓 𝐸𝑎𝑟𝑡ℎ

The _____ of a set A, denoted by n(A), is the number of elements in the set.

Two sets that contain exactly the same number of elements are called _____.

Two sets that contain exactly the same elements are said to be _____.

Set A is a _____ of set B, written as A ⊆ B, if and only if every element in A is also an element in B.

Set A is a _____ of set B, written as A ⊂ B, if there is at least one element in B not contained in A.

The _____ of sets A and B, written as A ∩ B, is a set of elements that are members of both A and B

The _____ of sets A and B, written as A∪B = {x|x ∈ A or x ∈ B}, is the set of elements that are members of A, members of B, or members of both A and B.

The _____ of sets A and B, written as A – B, is a set of elements in A that are not in B.

The _____, denoted by U, is the set of all possible elements of any set used in the problem. The _____ can be changed from problem to problem, depending on the nature of the set being discussed.

The _____ of a set A, written as A’, Is the set of all the elements in the universal set (U) that are not in set A.

defined as the union of both rational and irrational numbers. They can be both positive or negative and are denoted by the symbol ℝ.

These numbers are used for counting.

These numbers are formed by adding 0 to the set of natural numbers.

They are formed by adding the negatives of the natural numbers to the sets of the whole numbers.

The set of _____ is the set of all numbers that can be expressed in the form 𝑎 𝑏 , where a and b are integers, b  0. The decimal representation of a _____ either terminates or repeats.

The set of _____ is the set of numbers that decimal representations are neither terminating nor repeating. These numbers cannot be expressed as quotient of integers.

1. All rational numbers are integers.

2. Some irrational numbers are integers.

3. All integers are whole numbers

4. Natural numbers are also whole numbers.

5. All irrational numbers are real numbers.

The numbers on the right of 0 are _____

The numbers on the left of 0 are _____

The sum of a + b is a real number.

The product of a • b is a real number.

Two real numbers can be added in any order.

Two real numbers can be multiplied in any order.

a + (b + c) = (a + b) + c

a • (b • c) = (a • b) • c

a ● (b + c) = a ● b + a ● c

Any number added to the identity element 0 will remain unchanged. 0 is the identity element for addition. a + 0 = a and 0 + a = a

Any number multiplied by the identity element 1 will remain unchanged. 1 is the identity element for addition. a • 1 = a and 1 • a = a