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Our education staff publish regular articles, tips and tutorials to help students with their homeworkMon, 02 May 2016 00:19:30 +0000en-UShourly1https://wordpress.org/?v=4.4.2Science Review of Seeds
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Sun, 01 May 2016 17:03:07 +0000http://schooltutoring.com/help/?p=8933Overview
In many types of seeds, the hard casing of the seed is surrounded by flesh called a fruit. Many fruits are attractive to animals, providing food, so the seeds are dispersed that way. Others are dispersed by wind and water. Some seeds are dormant until the conditions are right for plants to grow, while others sprout rapidly. Seeds then germinate and grow into plants.

Fruits

The developing seed of a flowering plant (angiosperm) is contained within a tough seed coat. The seed coat contains the embryo and its food supply. The ovary wall thickens to form a fruit that encloses the hard seeds. Some fruits are fleshy and sweet, such as grapes, berries, and cherries, while others are tough, such as bean pods. Since a fruit is any seed enclosed within an embryo wall, vegetables such as corn, beans, and tomatoes are also fruits, even though they do not taste sweet.

Seed Dispersal

The fruit does not nourish the seedling as it grows, as the food supply is within the seed itself. Some fruits attract birds and mammals as food sources. The seeds pass through the digestive tract and are dispersed that way. Other seeds, such as those of ash and maple trees, are encased in structures that float on the air. The aerodynamic wings that surround a maple seed are actually a fruit. Coconuts are light enough to float on water for long enough to be carried to distant islands.

Seed Dormancy

Some seeds, such as beans, sprout very quickly if they have enough water and warmth. Other types of seeds enter a period of dormancy, where the embryo within them is still alive but will not sprout until the conditions are right. They will not grow until the soil temperature and moisture is right to support the developing seedlings. For example, many plants that grow in temperate regions do not sprout until the spring.

Seed Germination

During germination, the early growth stage of a plant, seeds absorb water. The tough seed coat swells and cracks open beneath the soil. The root grows from the seed and eventually the growing plant breaks through the surface of the soil.

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Sat, 30 Apr 2016 19:47:24 +0000http://schooltutoring.com/help/?p=8928Overview
Bubbles are usually formed when a globule of gas is suspended in a liquid. Some common examples include the bubbles of carbon dioxide found in carbonated drinks, water vapor in boiling water, and soap bubbles.

Carbonated Water

Bubbles form when very small air pockets are trapped in liquids. For example, supersaturated carbon dioxide is introduced under pressure into either plain water or water with flavors added to form carbonated soft drinks. It is weakly acidic. Although carbonation is a natural part of the fermentation process in making sparkling wines, champagne, and beer, artificial carbonated water was not produced until the mid-1700s. By the 1800s, flavorings were added.

Boiling

When a liquid, such as water, is heated to its boiling point, small bubbles of water vapor begin to form and then break at its surface. At first, bubbles of water vapor form slowly, then increase rapidly, as more water is heated. At the boiling point of a liquid, its vapor pressure is equal to the pressure of the gas above it.

Soap Bubbles

Soap bubbles consist of a very thin film of soapy water that surround a sphere of air. The soap itself reduces the surface tension of the water, so that the soap bubbles can form. When plain water flows out of a tap, bubbles form, but the surface tension of the plain water is high enough that those bubbles burst immediately. Soap bubbles are iridescent because light reflects off the surface of the thin film itself, as the bubble itself is clear. Although soap bubbles will pop if their surface ruptures, they can last longer if glycerin is added to the bubble solution.

Foam

Foams contain series of multiple gas bubbles connected by thin surface layers, such as foams of soap bubbles or foaming liquid. The bubbles contained in the foam are not all the same size and clump together. The foaming effect can also occur if there are impurities in the liquid, such as if milk is added to boiling water. Fire retardants are usually foams.
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Sun, 24 Apr 2016 05:03:51 +0000http://schooltutoring.com/help/?p=8924Overview
Factoring polynomial expressions is similar to factoring special polynomials. The difference is that both elements do not have to be perfect squares. It is the reverse of multiplying two binomials by using FOIL.

Factoring Trinomials

Trinomials of the form x^{2} +bx +c, when c>0 have certain aspects in common. The coefficient of the squared term is 1, so the only form to factor is the variable itself, in this case x times x. The constant c is a positive value. If the constant c is a positive number, but not a perfect square, it may have a variety of factors.

Using FOIL in Reverse

In order to multiply two binomials, FOIL is used, for the first term, the outer terms, the inner terms, and the last terms. It is also useful when factoring trinomials, only it is used to unravel the trinomial. In these examples, the first term, x^{2}, can be factored as x ·x. The factorization will have the form of (x + ___) (x + ____), so that first term is already known in these examples.

The Constant Term

The constant term c has a fixed numeric value, so that the last terms in each binomial will be factors of c. Suppose the binomial is x^{2} +7x +12. The constant 12 has a number of factors, as 12 ·1 is 12, 6·2 is 12, and 3·4 is also 12. The constant 12 also has negative factors, as -12·-1 is 12, ·-6·-2 is 12, and -3·-4 is also 12.

The Middle Terms

Since there are usually a number of factors for the constant, there has to be a way to narrow them down and choose the correct one. Recall that the inner terms and the outer terms are added, while the last terms are multiplied. In order for a pair of factors to work, they must be added so that their sum is the coefficient of the middle term of the trinomial. In this example, the coefficient of the middle term is 7. The first pair of factors, 12 +1, equals 13; the second pair, 6 +2, equals 8; and the third pair, 3 +4, equals 7. By substitution, x^{2} +7x + 12 factors as (x +3) (x +4).

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Sat, 23 Apr 2016 23:30:14 +0000http://schooltutoring.com/help/?p=8920Overview
Factoring polynomials in general is the reverse process of multiplying them, and then finding common factors. However, some polynomials follow special patterns, such as the difference of two squares and trinomial squares, leading to shortcut methods of factoring.

Recognizing the Difference of Two Squares

In order for a polynomial to be the difference of two squares, there must be two terms in the polynomial (a binomial), both terms in the binomial must be perfect squares, and there must be a minus sign between them. For example, the binomial x^{2} -16 has two terms in the binomial, there is a minus sign between them, and both x^{2} and 16 are perfect squares, as the square root of x^{2} is x, and the square root of 16 is 4. Suppose the polynomial were x^{4} +81. Although it is a binomial, and both x^{4} and 81 are perfect squares, there is a plus sign between them, so it doesn’t satisfy all the conditions. Suppose the polynomial was 4x^{2} – 10. The monomial 4x^{2} is a perfect square (2x), the expression is a binomial, and there is a minus sign between them. However, 10 is not a perfect square, so it is not the difference of two squares. Suppose the expression is -9x^{2} +25. It can be turned around, using the commutative property, so that the expression becomes 25-9x^{2}. It is a binomial, the minus sign is between the two terms, and both 25 and 9x^{2} are perfect squares, as the square root of 25 is 5 and the square root of 9x^{2} is 3x.

Factoring the Difference of Two Squares

Recall from the discussion of special products of polynomials that the product of (x +y) (x-y) equals x^{2} – y^{2} because xy and –xy cancel each other out. Therefore, a binomial such as x^{2} –y^{2} can be factored so that it follows the pattern (x +y) (x-y). For example, the binomial 16x^{2} – 81 follows the pattern of the difference of two squares, and can be factored as (4x +9)(4x-9) because the square root of 16x^{2} is 4x and the square root of 81 is 9.

Recognizing Trinomial Squares

Trinomial squares also follow special conditions. Recall from the discussion of special products of polynomials that (x +y) ^{2} is always a trinomial in the form of x^{2} +2xy +y^{2}. Similarly, (x-y) ^{2} is always a trinomial in the form x^{2} -2xy + y^{2}. Therefore, a trinomial is a trinomial square if two of the terms are perfect squares, there are no minus signs before either of them, and the other term is twice the product of the first two. For example, x^{2} +6x +9 fits the pattern because both x^{2 }and 9 are perfect squares. The square root of x^{2} is x, the square root of 9 is 3, and 3x + 3x is 6x.

Factoring Trinomial Squares

After recognizing a trinomial square, it is a short step to factoring it. For example, since both x^{2} and 9 are perfect squares, the square root of x^{2} is x and the square root of 9 is 3. To check, multiply (x + 3) (x + 3) using FOIL, for x^{2} + 3x +3x = 9, or x^{2} + 6x +9.

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Sun, 17 Apr 2016 22:00:41 +0000http://schooltutoring.com/help/?p=8915Overview
Capitalization of particular words in English sentences follows a few basic rules. However, it is easy to overlook capitalization when proofreading, since most of the time capitalization errors will not be caught by the spell-checker in the computer program.

First Word of a Sentence

The first word of a sentence is always capitalized. Therefore, the first word of the next sentence is capitalized. This is true even if the sentence is not complete, although the writer usually will make that sentence complete, or combine the phrase with another sentence during the editing phase of the document. Also, capitalize the first word of a complete sentence within quotation marks. Do not capitalize words when the quotation is indirect or continues within the same sentence.

Proper Nouns

Proper nouns, such as names of people and places, are capitalized, such as Mary, John, Montana (the state), Canada (the country), Antarctica (the continent), Mars (the planet), Betelgeuse (the star), and so on. If more than one proper name is used, capitalize the words within the name, such as Mary Jones, Golden Gate Bridge, New Horizons, San Francisco, and New York City. Adjectives derived from proper nouns, such as Russian dressing, the English language, and the Martian landscape, should also be capitalized. However, notice that the second word in the phrase is not capitalized as that word is not part of the name. There are many salad dressings, many languages, and many landscapes, for example. Whether the word the is capitalized depends upon whether or not it is part of the proper noun, such as The Dalles, The Bellingham Herald, or The Hague. If it is not part of the proper noun, it is left without capitals.

Titles of Books

Principal words within titles are capitalized, such as the first word, nouns, pronouns, adjectives, adverbs, and verbs. Titles include titles of books, pictures, plays, movies, TV shows, musical compositions, and other documents. For example, one of my favorite children’s books is A Wrinkle inTime by Madeleine L’Engle. The movie Gone with the Wind is a classic. We watched Game of Thrones on TV.

Common Errors

When addressing a family member, the word is capitalized. Mother, may I go out for a swim? However, when referring to a family member, the word is not capitalized. My mother always attended my concerts. Similarly, I went to visit Aunt Lucille in Alaska, with her name specified. However, I went to visit my aunt in Alaska, as her name isn’t specified.

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English Review of Prepositions
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Sat, 16 Apr 2016 18:18:33 +0000http://schooltutoring.com/help/?p=8911Overview
A preposition is a part of speech that connects a noun or pronoun with a relationship in space, location, or time. Some prepositions such as of, for, to, in, or, and on are the most common words in the English language. When a preposition is used to describe the relationship, the noun becomes its object.

Relationships in Space and Location

One of the ways that prepositions are used are to show relationships in space and location. For example, in the sentence She works at the store, at shows the relationship between the subject of the sentence and the location where she works. Similarly, The books are on the table, on shows the relationship between the books and the table. If he walked to the desk, the preposition to shows the direction where the subject walked.

Relationships in Time

Prepositions also show relationships in time. In the sentence, The class begins at 8:00, at shows the relationship between the class and when it begins. However, in the sentence, The math class is in the morning, the time is not specific, so the preposition in is used to show a relationship in time. The sentence The meeting is on Tuesday at 3:00, shows two time relationships on for the day of the meeting and at for the specific time.

Commonly Confused Prepositions

Some prepositions are often confused. For example, the preposition among refers to more than two, while the preposition between refers to two. The balloons were divided among team members, but the balloons were divided between the two of them. The preposition beside refers to at the side of, while the preposition besides refers to in addition to, so that I walk beside the river, but What class are you taking besides English? If someone walks in a garden, they are walking within the garden, but if they walk into a garden, they are walking from outside into the entrance.

Unnecessary Prepositions

Sometimes extra prepositions are used in a sentence, but they are unnecessary and add nothing to the meaning of the sentence. They can be cut. In the sentence, She met up with her friend at the mall, she already met her friend, so the prepositions up and with can be deleted. In the sentence, Where did they go to? the preposition to is unnecessary and can be deleted.

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Sun, 10 Apr 2016 23:02:30 +0000http://schooltutoring.com/help/?p=8907Overview
The alkaline earth metals are the next column in the periodic table from the alkaline metals. They include beryllium (Be), magnesium (Mg), calcium (Ca), strontium (Sr), barium (Ba), and radium (Ra). They have two electrons in their outermost shell, which they give up in chemical reactions.

Beryllium (Be)

Beryllium (atomic number 4) is a brittle metallic substance that is usually found in other compounds and minerals. The mineral that contains beryllium, beryl, was known since ancient times, as the gemstones emerald and aquamarine. When used in alloys, beryllium makes other metals stronger, such as aluminum and copper. It is often used in the aerospace industry. However, beryllium dust is highly toxic to the lungs, causing a disease similar to chronic pneumonia.

Magnesium (Mg) and Calcium (Ca)

Magnesium (atomic number 12) is also reactive, especially with oxygen. It is almost never found naturally as pure magnesium, but can be produced artificially. It is an essential element to both plants and animals, as magnesium ions are used by many different enzymes. Magnesium is often alloyed with aluminum to produce strong, lightweight metals for aerospace, automotive, and electronics. Calcium (atomic number 20) is very abundant, in compounds such as calcium carbonate (natural limestone) and chalk. It is essential to life, especially in the development and maintenance of bones and teeth.

Strontium (Sr) and Barium (Ba)

Strontium (atomic number 38) is reactive with oxygen, especially in water. It is found naturally in compounds and minerals, but its radioactive isotope strontium 90 is found in fallout. Barium (atomic number 56) is so reactive with the oxygen in air that it is usually stored under oil, similar to the alkali metals. It is found in minerals such as barite, or barium sulfate (BaSO4).

Radium (Ra)

Radium (atomic number 88) is radioactive in all isotopes. The isotope with the longest half-life is about 1600 years. However, radium is a naturally-occurring product of uranium decay, so it is usually found in conjunction with uranium. It is famous as a radioactive element because of the experiments in the late 19th century and early 20th century by Marie and Pierre Curie. Radium paint was once used on watch hands to make them glow in the dark, but it was abandoned for safer alternatives. Marie Curie herself died from the effects of her experiments with radium.

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Science Review of Alkali Metals
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Sun, 10 Apr 2016 03:14:52 +0000http://schooltutoring.com/help/?p=8901Overview
The alkali metals are in Group 1 of the periodic table. They include the elements lithium (Li), sodium (Na), potassium (K), rubidium (Rb), cesium (Cs), and francium (Fr). These highly reactive elements form compounds easily and explosively. They all have one electron in their outermost shell, giving it up to form ionic compounds.

Lithium (Li)

Lithium is the lightest metal, with atomic number 3. It is so soft that it can be cut with a knife, although it is so reactive that it quickly oxidizes. It reacts with water to form lithium hydroxide (LiOH) in solution and free hydrogen. It is also very flammable, and is usually stored in petroleum jelly. Since lithium is so reactive, it is almost always found in various compounds. Lithium is used in batteries (including lithium-ion batteries), in ceramics and glass, in industrial lubricants, and as a catalyst in fusion reactions.

Sodium (Na) and Potassium (K)

Sodium (atomic number 11) and potassium (atomic number 19) are both fairly common elements. Both are even more reactive than lithium, and are also flammable. When sodium comes in contact with water, it produces flammable hydrogen and caustic sodium hydroxide. Therefore, it is usually stored in mineral oil. One of the most common compounds of sodium is table salt (NaCl), which is also an essential nutrient, necessary to plant and animal life. Potassium, its heavier cousin, is also essential to cell functioning. It forms similar chemical compounds to sodium. Potassium compounds are used in fertilizer, food, various dyes, and in potash.

Rubidium (Rb) and Cesium (Cs)

Rubidium (atomic number 37), like the other alkali metals, is highly reactive, flammable, and only occurs naturally in compounds. It is used in atomic clocks and laser cooling. One isotope of rubidium has specialized medical applications, such as PET scans. Particular types of tumors contain more rubidium than normal tissue, so they can be detected and destroyed. Cesium or caesium (atomic number 55) is liquid at about 83 degrees F., although it is not found as pure metal naturally. If cesium comes in contact with water, it explodes, and is so flammable in air that it can catch fire spontaneously. However, atomic clocks that use cesium are so accurate that they lose less than a second in 1.4 million years.

Francium (Fr)

Francium (atomic number 87) is radioactive, with a half-life of about 22 minutes. It is extremely rare because of its short half-life, and occurs naturally as a product of the decay of the element actinium. When francium was discovered in the laboratory, it was first mistaken for more common elements, but careful study by scientist Marguerite Perey showed it was a new element. Although she first isolated it in 1939, it has been synthesized by scientists since 1996 by bombarding a tiny gold target with beams of oxygen atoms emitted by a linear accelerator.
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Sun, 03 Apr 2016 20:47:10 +0000http://schooltutoring.com/help/?p=8896Overview
In order to factor polynomials, common factors must be found for every monomial in the expression. It is the reverse process of multiplying polynomials.

Factoring Monomials

When factoring a number, find all factors that have the product of that number. For example, 30 has the factors 1, 30, 3, 10, 2, 15, 5, and 6. The number 36 has the factors 1, 36, 2, 18, 6, and 6. Similarly, when factoring a monomial, find all factors that have the product of that number. For example, 20x^{2} has the factors 20, x^{2}, 4x, 5x, 20x, x, 2x, 10x and many others.

Negative Factors

Since multiplying a negative number by a negative number results in a positive number, each factor also has corresponding negative numbers as factors, so that 20x^{2} also has negative factors -20x, -x, -4x, -5x, and so on. It is very important to watch the signs of the expression when factoring, and remember the negative factors.

Polynomial Expressions

Polynomial expressions may be binomials such as 3x^{2} +12, trinomials such as 4x^{3} +8z +12q^{2}, or polynomials such as 12m^{4}n^{4} +3m^{3}n^{2} +6m^{2}n^{2}. In order for a polynomial expression to be factored, each element of that expression must have the same factor in common. For example, 3x^{2} and 12 both have a common factor of 3, because 3·x^{2} is 3x^{2} and 3·4 is 12. Suppose the expression were 4x^{3} -3y +5. None of the monomials in that expression have a common factor.

Factoring Polynomials

In order to factor a polynomial, find the common factor of each of the terms in that polynomial. Then factor out that term. The polynomial 4x^{3} +8z +12q^{2} has common factors for the coefficients but not for the variables, so that it can be factored out as 2(2x^{3}) + 2(4z) + 2(6q^{2}) or 2(2x^{3} +4z +6q^{2}). The polynomial 3x^{4} -8x^{2}y -5x^{2} has common factors for the variables but not for the coefficients, so that it can be factored as x^{2}(3x^{2}) +x^{2}(-8y) +x^{2}(-5) or x^{2}(3x^{2}-8y-5). The polynomial 12m^{4}n^{4} +3m^{3}n^{2} +6m^{2}n^{2} has common factors in both the variables and the coefficients, so that 3m^{2}n^{2 }(4m^{2}n^{2}) + 3m^{2}n^{2} (m) + 3m^{2}n^{2 }(2), or 3m^{2}n^{2 }(4m^{2}n^{2} +m +2). Use the common factor for each term that has the greatest power as well as the largest coefficient.

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Sun, 03 Apr 2016 01:45:15 +0000http://schooltutoring.com/help/?p=8892Overview
Multiplying two polynomials is similar to multiplying a polynomial by a monomial, or multiplying a binomial by another binomial. It uses the same principle of multiplying each term by every other term.

Multiplying a Polynomial by a Monomial

Remember when multiplying a polynomial by a monomial to multiply each term of the binomial by using the distributive property. Then like terms can be combined. For example, 4x^{2}(-2x^{3} + 5x^{2} + 10) means the same thing as (4x^{2}) (-2x^{3}) + (4x^{2}) (5x^{2}) + (4x^{2}) (10) or -8x^{5} + 20x^{4} + 40x^{2}. Notice that multiplying each term uses the rules of multiplying numerical coefficients, such as 4·-2 equals -8, 4·5 equals 20, and 4·10 equals 40. Multiplying each term also uses the rule of multiplying exponents.

Special Products of Binomials

When multiplying binomials, each term of one binomial must be also multiplied by each term of the other binomial. The distributive property is also used and like terms can be combined. For special binomials, shortcuts can speed the process. For example, any binomial (A + B) ^{2} equals A^{2} + 2AB + B^{2}, and any binomial (A-B) ^{2} equals A^{2}– 2AB + B^{2}. Similarly, (A + B) (A-B), also known as the sum and difference of two binomials, always equals A^{2} – B^{2}.

Using FOIL

Any two binomials, whether they are special products or not can be multiplied by using the acronym FOIL, as a mnemonic to ensure all terms in one binomial are being multiplied by all terms in the other binomial. Using FOIL, the first terms are multiplied, the outer terms, the inner terms, and the last terms. Then like terms are combined. For example, when multiplying (x +5)(x +6), the first terms are x·x, or x^{2}. The outer terms are 6·x, or 6x, and the inner terms are 5·x, or 5x. Then, 5x and 6x are like terms and can be added, as 11x. Finally the last terms, 5·6, or 30 can be combined. The entire equation is (x +5) (x +6) equals x^{2} +11x +30.

Multiplying Polynomials

Multiplying polynomials is similar to multiplying monomials and binomials, except that every term in one polynomial is multiplied by every other term in the other polynomial. Suppose the equation is (x^{2} + 2x +3) (4x +5). Start by multiplying x^{2} by 4x, or 4x^{3}, then x^{2} by 5 or 5x^{2}. Next, 2x by 4x or 8x^{2}. Next 3 by 4x gives 12x and 3 times 5 is 15. That leaves 4x^{3} + 5x^{2} + 8x^{2} + 12x + 15. Finally, combine like terms, since 5x^{2} +8x^{2} equals 13x^{2}, so that the equation in simplest terms is 4x^{3} + 13x^{2} + 12x +15.

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