NES Elementary Education Subtest 2

Divisibility by 8.

If the last three digits form a number divisible by 8, then the number itself is also divisible by 8. For example, 1,120 is divisible by 8 since 120 is divisible by 8.

Divisibility by 4.

If the last two digits form a number divisible by 4, then the number is divisible by 4. For example, 316 is divisible by 4 since 16 is divisible by 4.

Divisibility by 10.

If the number ends in 0, then it is divisible by 10. For example, 670 is divisible by 10 since its last digit is 0.

Divisibility by 6.

If the number is divisible by both 3 and 2, then it is also divisible by 6. For example, 168 is divisible by 6 since it is divisible by 2, and it is divisible by 3.

Divisibility by 3.

If the sum of the digits is divisible by 3, then the number is also. For example, 177 is divisible by 3 since the sum of its digits is 15 (1 + 7 + 7 = 15), and 15 is divisible by 3.

Divisibility by 9.

If the sum of the digits is divisible by 9, then the number itself is also divisible by 9. For example, 369 is divisible by 9 since the sum of its digits is 18 (3 + 6 + 9 = 18), and 18 is divisible by 9.

The Sequence of Squares. The sequence of squares of natural numbers is an important sequence.

12, 22, 32, 42, 52, 62, 72, 82, 92, 102, 112,... or 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121 ...

A negative exponent indicates a reciprocal. For example,

2 (-3rd power) =1 / 2 (3rd power) = 1 / 8

The first power of any number is itself. For example,

2 (to the 1st power) = 2

To multiply like bases with exponents, add the exponents. For example,

2 (to the 3rd) x 2 (to the 5th) = 2 (to the eighth)

Every whole number has a unique opposite or negative whose sum with it is 0. For example,

2 + (-2) = 0

Every nonzero integer has a unique reciprocal whose product with it is one. For example,

2 × 1/2 = 1

It is worthwhile to memorize the first several prime numbers.

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, ...

The ratio or fraction of one integer to a nonzero integer is the product of the first integer with the reciprocal of the second. For example, the ratio of 2 to 3 is

2/3 = 2 × 1/3

Converting a fraction to a percentage. Convert the fraction to a decimal and then convert the decimal to a percentage. For example, 2/5

2/5 = .4 = 40%

Identifying Place Value in Numbers 2045

2045 = (2 x 10 to the 3 power) + (0 x 10 to the 2 power) + (4 x 10 to the 1 power) + 5 x 10 to the 0 power)

The other _____ pairs are called somatic chromosomes because their genes produce proteins for building the body rather than determining gender.

22

Digits to the right of a decimal point correspond to negative powers of ten. For example, 23.405

23.405 = (2 x 10 to the 1 power) + (3 x 10 to the 0 power) + (4 x 10 to the -1 power) + (0 x 10 to the -2 power) + (5 x 10 to the -3 power)

convert 3.208 to a mixed number.

3 + 208/1000

Converting a fraction to a decimal. For example 3/8

3 divided by 8 = 0.375

Converting a percentage to a fraction. Convert the percentage to fraction with a denominator of 100. For example, 65%

65/100

and an area, A, given by

A = πr²

Lever.

A lever has three parts: a fulcrum, an effort arm, and a resistance arm. There are three types, or classes, of levers. In all first class levers, the Fulcrum is between the Effort and Resistance (ex., seesaw). In all second class levers, the Resistance is between Fulcrum and the Effort (ex., wheelbarrow). In all third class levers the Effort is between the Resistance and Fulcrum (ex., baseball bat and tweezers).

Pulley.

A pulley is a chain, belt or rope wrapped around a wheel. The mechanical advantage of a pulley system is approximately equal to the amount of supporting ropes or strands. A rig on a flagpole or a sailing mast are examples of pulleys.

Screw.

A screw, like a wedge, is another form of an inclined plane. A screw is an inclined plane wrapped around a cylinder to form a spiral.

Wedge.

A wedge is an inclined plane which moves. Most wedges (but not all) are combinations of two inclined planes. A knife, axe, razor blade, and teeth are all good examples of wedges. Generally, it can be anything that splits, cuts, or divides another object including air and water.

Wheel and axle.

A wheel and axle is a lever that rotates in a circle around a center point, or fulcrum. The larger wheel (or outside) rotates around the smaller wheel (axle). Bicycle wheels, Ferris wheels and gears are all examples of a wheel and axle. Wheels can also have a solid shaft with the center core as the axle such as a screwdriver or drill bit or the log in a log rolling contest.

Incomplete Metamorphosis

About 12 percent of all insects go through incomplete metamorphosis. These include stinkbugs, earwigs, crickets, grasshoppers, cockroaches, ants, praying mantis, and dragonflies. Incomplete metamorphosis has only three life cycle stages: egg, nymph, and adult. The nymph looks similar to, but is a smaller version of, the adult. The nymph is also wingless. As nymphs grow, they shed their hard exoskeletons, a process called molting. There is no pupal stage during incomplete metamorphosis.

Identity property.

Adding zero to a number does not change it. 2 + 0 = 2

Homeostasis.

All living organisms exhibit homeostasis, or the ability to maintain a state of internal balance. For example, if the environmental temperature increases, the human body begins to perspire, and the cooling effect of evaporation decreases the surface temperature of the skin. Likewise, a disruption in any system will set off a diverse set of control mechanisms that return the organism to a state of internal balance.

Inclined plan.

An inclined plane is a slanted surface used to raise an object. A ramp is an inclined plane. When an object is moved up an inclined plane, less effort is needed than if you were to lift it straight up, but you must move the object over a greater distance.

Newton's Second Law.

Any change in motion involves acceleration, or how much the velocity of an object changes in a certain time. This is where Newton's Second Law applies; it gives us the relationship between force, mass, and acceleration. Using Newton's Second Law, force is expressed by the mathematical equation, F=ma or Force=Mass × Acceleration. The greater the mass of the object being accelerated, the greater the amount of force needed to accelerate the object.

Archaea.

Archaea are microorganisms similar to bacteria in form but genetically so vastly different from everything else on the planet that they deserve their own unique branch on the tree of life. Archaea are often found in extreme environments including acidic conditions, boiling hot springs, deep ocean vents, or polar ice.

Divisibility by 2.

If the last digit is even, then the number is divisible by 2. For example, 158 is divisible by 2 since its last digit is 8.

Incomplete metamorphosis has only three life cycle stages: ____ ____ ____

egg, nymph, and adult.

convert 0.45 to a fraction.

45/100

The chemical formula for photosynthesis is:

6 CO2 + 6 H2O → C6H12O6 + 6 O2 Carbon dioxide + Water + Light energy → Glucose + Oxygen

In total, _____ elements have been observed as of March 2010, and new elements continue to be discovered. Of these, _____ occur naturally; the others are produced in laboratories.

118, 95

We define the zero power of any nonzero number to be 1. For example,

(-3)0 = 1

To exponentiate a power, multiply the exponents. For example,

(2 to the 3rd) to the 5th = 2 to the 15th

The Fibonacci Sequence. The Fibonacci sequence is the sequence

0, 1, 1, 2, 3, 5, 8, 13, 21, 34 ... beginning with 0 and 1 so that each term beginning with the third term is the sum of the two preceding terms.

10 to the 0 power

1

10 to the -2 power

1 / 10 to the 2 power or 1 / 100

not every rational number is an integer. For example, 1/2 is a rational number that is not an integer.

1/2 = 0.5

10 to the 1 power

10

10 to the 2 power x 10 to the 3 power

10 to the 5 power

A circle with radius r has circumference, C, given by

C = 2πr

Genes

Chromosomes are microscopic, threadlike structures that contain the genes that carry hereditary information from one generation to the next. Each chromosome contains many genes. Different organisms may have different numbers of chromosomes. In sexually reproducing organisms, chromosomes occur in pairs—one chromosome of each pair comes from the mother and one from the father. Humans have 23 pairs of chromosomes. One pair, consisting of two X chromosomes (XX) in females or an X and a Y chromosome (XY) in males determines the gender of the offspring. The other 22 pairs are called somatic chromosomes because their genes produce proteins for building the body rather than determining gender. In eukaryote organisms, chromosomes, and their genes are found in the nucleus, which is surrounded by its own membrane. In bacteria, no nucleus is present and the chromosomes are found in the cytoplasm of the cell.

_____ are groups of two or more elements that are bonded together through chemical change.

Compounds

Constants.

Constants are symbols that represent fixed values. In the expression 3x + 7, the constants are 3 and 7.

Egg.

Eggs are laid by the adult female insect. Females lay a lot of eggs so that at least some of them will survive.

Every living thing needs energy that they produce or acquire in order to exist, grow, and reproduce. Some organisms (called autotrophic organisms) are capable of harnessing energy from sunlight and using it to produce glucose, the main source of energy for the organism. Others (called heterotrophic organisms) capture energy by eating plants or other animals.

Energy.

Eukaryotes.

Eukaryotes consist of all organisms with cells that have true nuclei and membrane-bound organelles. Four kingdoms—animals, plants, protists, and fungi—fit into this domain.

Exponentiation

Exponentiation is repeated multiplication. An exponent is often called a power. For example, the third power of 2 is 2³ = 2 × 2 × 2 = 8

Grouping symbols.

Grouping symbols are symbols such as parentheses ( ) and brackets [ ] that indicate the order in which we should interpret the operations and the relations in a mathematical expression.

Heredity

Heredity is defined as the transmission of characteristics carried by the genetic code from one generation to the next. Characteristics may be physical, physiological, or psychological as long as they are carried by the genes. Heredity explains why offspring look like their parents and why dogs always give birth to puppies and never guppies or butterflies. Through heredity, living things inherit traits from their parents.

Divisibility by 5.

If the last digit is a 5 or a 0, then the number is divisible by 5. For example, 1995 is divisible by 5 since its last digit is 5.

Commensalism.

In a commensal relationship, members of different species live together, and one member benefits without seriously affecting the other party. As a rule, the animal that benefits is usually the physically smaller of the two. The commensal organism may depend on its host for food, shelter, support, or transportation. The animal that benefits is known as the commensal, or symbiont, while the nonbenefitting species is known as the host. For example, some flatworms live attached to the gills of the horseshoe crab, obtaining bits of food from the horseshoe crab's meals; the horseshoe crab is apparently unaffected.

Mutualism.

In mutualism, members of two different species benefit by associating together. For example, many plant species require an animal to visit its flowers for pollination. The animal benefits in this relationship by having a source of food (nectar or pollen), while the plant benefits by having its ovules fertilized.

Parasitism.

In parasitic relationships, one species receives a benefit from the relationship to the detriment of the other species. For example, there are parasitic fishes, such as the lamprey, that attach themselves to other fishes and suck their body fluids. Similiarly, tapeworms may attach to the intestines of host humans in their intestines. They constantly take in nutrients and can eventually cause organ and tissue damage.

Modern taxonomy uses genetic analysis and comparison of physical traits to classify organisms according to a hierarchy of taxonomic ranks. These include

Kingdom Phylum Class Order Family Genus Species

Larva.

Larvae hatch from the eggs and bear no resemblance to their adult parents. The larva has only one job—to eat and eat so it can grow quickly. Larvae can grow 100 times their size during this stage. Butterfly and moth larvae are caterpillars, fly larvae are maggots, and beetle larvae are grubs. Eventually, when growth is complete, the larva is transformed into a pupa.

Atoms are neither gained nor lost during a chemical change. This is the _____ ______ _____ _____ _____ ; matter can neither be created nor destroyed in a chemical reaction. In a chemical change, however, a new substance is formed, and there may be accompanying clues that a chemical reaction has taken place, such as light, heat, color change, gas production, odor, or sound.

Law of Conservation of Matter

_____, for example, break down glucose to provide energy to the cell.

Mitochondria

Natural Numbers

N = {1, 2, 3, 4, 5, 6, . . . }

Newton's First Law.

Newton's First Law of Motion states that an object at rest will remain at rest and a body moving with a constant speed in a straight line will maintain its motion unless acted upon by an unbalanced external force. An example of force that opposes the motion of a body is friction.

Newton's Third Law.

Newton's Third Law states that all forces in the universe occur in equal but oppositely directed pairs; for every action, there is an equal and opposite reaction. Rockets and jet planes capitalize on Newton's Third Law. Each discharge hot gases in one direction (an action force so as to produce thrust (a reaction force). In both rocket and jet engines, chemical energy is changed to the energy of motion.

Operators.

Operators are symbols such as +, -, × and / that represent operations such as addition, subtraction, multiplication, and division.

Prokaryotes.

Prokaryotes have neither nuclei nor organelles with membranes. True bacteria fit in this domain.

Relations.

Relations are symbols that compare expressions. Common relations are =, <, >, ≤, and ≥.

Scientists believe that there are over _____ million different kinds of life forms, or species, on Earth.

Scientists believe that there are over 10 million different kinds of life forms, or species, on Earth.

Complete Metamorphosis

See the last four

The Human body has _____ organ systems—circulatory, digestive, endocrine, excretory, immune, integumentary, muscular, nervous, reproductive, respiratory, and skeletal.

The Human body has 11 organ systems—circulatory, digestive, endocrine, excretory, immune, integumentary, muscular, nervous, reproductive, respiratory, and skeletal.

Distributive property.

The product of a number with a sum equals the sum of the products of the number with each term of the sum. 2 × (3 + 5) = (2 × 3) + (2 × 5)

Pupa.

The pupa stage is usually considered a resting stage, although much activity is going on within a sealed chrysalis or cocoon. Special cells that were present in the larva are now growing rapidly and will become the legs, wings, eyes and other parts of the adult insect. After the reorganization is complete, the pupa splits to reveal the mature adult with functional wings. This stage can last a few weeks, a month, or even several years.

The system currently used by taxonomists is called the _____ taxonomic system, in honor of Swedish biologist Carolus Linnaeus (1707-1778), one of the founders of the modern system of biological classification.

The system currently used by taxonomists is called the Linnaean taxonomic system, in honor of Swedish biologist Carolus Linnaeus (1707-1778), one of the founders of the modern system of biological classification.

Divisibility Tests

To find the prime factorization of a number, it is helpful to know a few tests for divisibility.

Variables.

Variables are symbols that stand for changing values. Most often we use letters of the alphabet for variables. In the expression 3x + 7, the letter x is a variable. The value of the expression depends on the specific number we substitute for x. For example, if we substitute 2 for x, the value of the expression is 3(2) + 7 = 13.

Whole natural numbers together with zero.

W = {0, 1, 2, 3, 4, 5, 6, . . . }

Associative property.

When adding three or more numbers, the sum is the same regardless of the way in which the numbers are grouped. 2 + (3 + 5) = (2 + 3) + 5

Commutative property.

When adding two numbers, the sum is the same regardless of the order in which the numbers are added. 2 + 3 = 3 + 2

The set of integers consists of the whole numbers and their opposites.

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

autotrophic organisms)

are capable of harnessing energy from sunlight and using it to produce glucose, the main source of energy for the organism.

Compound machines

are two or more simple machines working together. A wheelbarrow is an example of a complex machine that uses a lever and a wheel and axle. Machines of all types make work easier by changing the size or direction of an applied force.

heterotrophic organisms)

capture energy by eating plants or other animals.

Chlorophyll, which is contained within a cell organelle called the ______, captures the light from the Sun;

chloroplast

There are three basic properties of addition:

commutativity, associativity and identity.

There are three basic properties of multiplication:

commutativity, associativity and identity.

A natural number is _____ if it is greater than 1 and not prime.

composite

Humans have four basic types of tissues:

connective, epithelial, muscle, and nerve.

A fundamental concept of mathematics is that the set of real numbers is in one-to-one correspondence with the set of points on a line. That is, each real number corresponds to exactly one point on a line, and each point on a line corresponds to exactly one real number, called the _____ of the point

coordinate

The diameter of circle, d, is twice the radius. That is,

d = 2r

Visible light, or the light energy we see, is only one small portion of a family of waves called _____ _____ _____. If you listen to the radio, watch television, have your teeth x-rayed, talk on a cell phone, or use a microwave oven, you are making use of different types of electromagnetic radiation. Electromagnetic waves are generated by accelerating electric charges. For example, if an electric charge oscillates back and forth, it will radiate energy in the form of an electromagnetic wave. The quickness, or frequency at which charges oscillate, determines the type of electromagnetic radiation produced.

electromagnetic (EM) radiation

A _____ f is a set of ordered pairs that pairs each element x of one set, called the domain (input) of the function, with a unique element f(x) of another set, called the range (output) of the function.

function

epithelium

membranous tissue covering internal organs and other internal surfaces of the body

epithelial

of or belonging to the epithelium

Animal and plant cells contain smaller structures, called _____, which are specialized to fulfill specific functions within the cell. Mitochondria, for example, break down glucose to provide energy to the cell. Bacterial cells lack most of these organelles.

organelles

At the present time, scientists believe that the most fundamental particle of matter is the _____.

quark

A simple food chain might look like this:

sun → grass → grasshopper → toad → snake → hawk → bacteria of decay

The plants discussed in this section are vascular plants; they have a system of tubes (_____ _____ _____) that are used to transport nutrients and water.

xylem and phloem