Math

How many faces does a cube have?

6. Remembering that a face is a plane region of a geometric body, one can determine that since there are six sides to a cube, there are also six faces.

Complementary Angles

Two angles that add up to 90 degrees

States of matter

solid, liquid, gas, and plasma

Energy

the ability to do work

Mass

the amount of matter in an object or thing

Volume

the amount of space that matter takes up

Homogenous

the components are evenly distributed throughout.

median

the data thats in the middle. list all numbers for greatest to least to greatest to least. Cross out until you reach the middle. Mean-all all the data values and divide by the number f values in that set.

mode

the number shows up most often in a set

Photosynthesis

the process of capturing , storing, and converting solar energy. It is the source of oxygen in the atmosphere.

Meiosis

the process of cells dividing to produce the egg and sperm cells each with half the number of chromosomes as the parent cell so they are ready to restore the normal number os the species upon fertilization.

Work

the product of the force acting in the direction of movement and causing displacement

Dan and Stacy live on a farm where they are no longer allowed to let their cattle roam free. They need to add a fence around their land, which has a rectangular shape like the figure below. How many feet of fence do they need to buy in order to fence in all of their land? 223ft height 467ft width

1,380 ft. This problem deals with finding the perimeter of the rectangle. Since the two short legs of fence have the same length and the two long legs have the same length, we know \(P = 2l + 2w\). This gives us a value of \(2 \cdot 223+ 2 \cdot 467 = 1380 \mathrm{ft}\).

Elements

118 basic kinds of matter. Which are organized into the periodic table. Composed of sub-microscopic components called atoms.

Metric Units

Linear-Millimeters, centimeters, meters, kilometers 2.5 centimeters to 1 inch Kilometer for longer distances (1.5 kilometers to a mile) Mass-Units of weight include grams and kilograms. 28 grams to 1 ounce Volume- Capacity includes milliliters and liters 4liters=1 gallon

Units of measure-Customary Units

Linear-units of length includes inches, feet, yards, and miles Mass-Weight includes ounces, pounds, tons Volume- Capacity includes teaspoons, tablespoons, cups, pints, quarts, and gallons

Reasoning

Logical Reasoning-is closely related to children's language development Deductive Reasoning-moving from an assumption to a conclusion. General to specific Inductive reasoning- examining particular instances to come to some general assumptions. This type of

Magnetism and Gravity

Magnetism-the force of attraction or repulsion between objects that results in positive and negative ionic charges.

Molecules

Two or more atoms bonded together in a chemical bond

Three dimensional figures

Volume of rectangular solid V=l x w x h Volume of a cube-V=s3 Edge-line segment where two faces of a three dimensional figure meet Cube has 6 faces, 12 edges, and 8 vertices Volume if a prism- V=base x height Volume of a cylinder- V=pir2h

Pythagorean Theoram

a2+ b2=c2

Matter

anything that takes up space and has mass. Has physical, thermal, electrical, and chemical properties.

Organisms

depend on one another for survival and are inextricably linked in the ecosystem.

congruent

figures have the same shape and size

Parallelograms

four sided polygon with two pairs of equal and parallel sides.

Atoms

made up of protons, neutrons, and electrons.

heterogenous mixture

means an uneven distribution of the substances in the mixture throughout

Given that the radius of the circle shown is 6 units and that the circle is inscribed in the square, which of the following is the approximate area of the shaded region?

31 square units First, it is helpful to view the shaded area as the area of the square minus the area of the circle. With that in mind, you simply need to find the area of each simple figure, and then subtract one from the other. You know that the radius of the circle is 6 units in length. That tells you that the diameter of the circle is 12 units. Because the circle is inscribed in the square (meaning that the circle fits inside of the square touching in as many places as possible), you see that the sides of the square are each 12 units in length. Knowing that, you compute that the area of the square is 144 square units (12 x 12). Using the formula for finding the area of a circle \((\pi r^{2})\), and using 3.14 for \(\pi\), you get approximately 113 square units. (3.14 x 6 x 6). Then, you subtract 113 (the area of the circle) from 144 (the area of the square) for the answer of 31.

Circles

Center Diameter-of a circle is a straight line segment that goes from one edge of a circle to the other side Radius-of a circle is half of its diameter(from the center to the edge) Chord-is any segment that goes from one point on the erg of a circle to any other point on the edge.

DNA

Chromosomes contain the genetic code

Circuit

Closed circuit-when all metal parts are touching and the electrical charge is able to continue to be transferred through the circuit Open-when there is a break someplace in the flow of electricity through the circuit.

Physical Properties

Color-how matter is reflected or perceived Density-is the mass that is contained in a unit of volume of a given substance Hardness-the resistance or penetration offered by a given substance Conductivity-is the ability of a substance to transmit thermal or electric current.

Heat Transfer

Conduction-process of transferring heat or electricity through a substance. The heat is transferred from one molecule to the next and so on through the substance. Radiation-describes the energy that travels at high speed in empty space in the form of light or through the decay of radioactive elements. Convention-describes the flow of heat through the movement of liquid or gaseous matter from a hot region to a cool region.

Layers of the Earth

Crust-the outer layer Mantle-thickest layer right below the crust Core-inner part of the earth

Mitosis

Describes the process of a cell splitting to create two identical cells.

Cube--Faces, vertices and edges formula

F=V=E+2

Adaptions

Features or charactericts of an organism that best help it survive in its environment

Insects

Have three main parts: head thorax, and abdomen

An isosceles triangle is a polygon with two equal sides. What else does this imply? It has two equal angles.

In any triangle, the sum of the angles must equal 180°. If a triangle has two equal sides, the third side cannot be unique and must be a set length. The lines associated with the equal sides will intersect the third side at the same angle. Therefore, the only answer that can be determined to be true from the information is option (D). (802-004 Geometry and Measurement)

Triangles

Isosceles-two equal sides Scalene-three unequal sides Acute-all three angles are acute right-one of the gales is a right angle Obtuse-one of the angles is obtuse

Energy

Kinetic-object possessing energy because of its ability to move Potential-the energy that an object has as the result of its position or condition Activation-Energy necessary to transfer or covert potential energy into kinetic

Human body systems

Musculoskeletal (cartiledge-soft spongy tissue on the ends of bones. )(Smooth muscle-muscle not attached to bones)(Cardiac muscles-muscle of the heart) nervous (Voluntary movement-caused by nerve impulses sent from the brain through the spinal cord to nerves to connecting skeletal muscles.)(Involuntary-direct response to an outside stimulus/reflexes) , circulatory-heart immune-defend against foreign proteins and infectious diseases., respiratory, digestive/excretory systems.

Fungi

Obtain energy, carbon, and water from dead material. Fungi do not have chlorophyll, so they cannot produce food through photosynthesis.

Order of operations

PEMDAS

Finding the Area

Parallelogram- A=b(base)h(height) Triangle- A=1/2bh Rectangle-A=l x w Square-A=s2 Circle-A= pi r(radius)2

Finding the perimeter

Perimeter of a triangle- P=s1+s2+s3 Perimeter of a rectangle-P=2l+2w Perimeter of a square-P=4s Circumference of a circle-C=2pi r or C=pid

Heat and Light

Photosynthesis-plants capture radiant energy from the Sun and transform into chemical energy in the form of glucose. Kinetic energy is used for movement and to do work, while heat is required element for all warm-blooded animals, like humans.

Ecology Ecosystem components

Producers-green plants that produce oxygen and store chemical energy for consumers Consumer-are animals/herbaviors take chemical energy from plants, carnivores take energy from other animals. Decomposers(fungi and bacteria) are in charge of cleaning the environment by decomposing and freeing dead matter.

Force

The action of moving an object by pulling or pushing it

Use the figure below to answer the question that follows. Which formula can be used to find the area of the triangle? \(A = 2(l \times h)\)

The area of any rectangle is equal to the measure of its length times the measure of its width (or to say it differently, the measure of its base times the measure of its height). A right triangle can be seen as half of a rectangle (sliced diagonally)

What is the formula for the relationship between the number of faces, vertices, and edges of a cube?

The correct answer is F+V=E+2. Recall that the Face (F) of a cube is a plain region of a geometric body, the Edge (E) is a line segment where two faces of a three-dimensional figure meet, and a Vertex (V) is the union of two segments or the point of intersection of two sides of a polygon. Knowing this we can see that for a cube there are 6 faces, 8 vertices, and 12 edges. Substituting these numbers into the appropriate spot in each formula allows us to determine option (D) as the only correct answer. (802-004 Geometry and Measurement)

How many lines of symmetry does the following figure have? Lighting bolt

The correct answer is zero (D). The shape in question does not have any lines of symmetry since any lines created would not produce mirror

Transformation

Translation(slide)-means moving Rotation(turn)-rotates or turns the shape around Reflection(flip)-to reflect an object or to make the figure/appear to be backwards or flipped.