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Math Course - Divisibility Rules

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Refresher Course in Mathematics - Number Theory</div>
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<b>Divisibility Rules</b><br />
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<b>Divisibility by</b></div>
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<b>Rule</b></div>
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<b><i>2</i></b></div>
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If the number is an even number</div>
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<b><i>3</i></b></div>
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If the sum of all individual digits in the number is divisible by 3</div>
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<b><i>4</i></b></div>
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If the last two digits of the number is divisible by 4</div>
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<b><i>5</i></b></div>
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If the last digit of the number is 0 or 5</div>
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<b><i>6</i></b></div>
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If the number is even and is divisible by 3</div>
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<b><i>7</i></b></div>
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Double the last digit. Subtract the doubled last digit from the number without the last digit. If the difference is a multiple of 7, then it is divisible by 7.</div>
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<b><i>8</i></b></div>
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If the last three digits of the number is divisible by 8</div>
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<b><i>9</i></b></div>
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If the sum of the individual digits in the number is divisible by 9</div>
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<b><i>10</i></b></div>
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If the last digit of the number is 0</div>
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<b><i>11</i></b></div>
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If after subtracting and adding the digits successively the result is divisible by 11</div>
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<b>Examples</b><br />
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1) 124 is divisible by 2 since the last digit 4 is divisible by 2.<br />
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2) 258 is divisible by 3 since the sum of the digits is 15 (2+5+8=15), and 15 is divisible by 3.<br />
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3) 516 is divisible by 4 since 16 is divisible by 4.<br />
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4) 395 is divisible by 5 since the last digit is 5.<br />
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5) 258 is divisible by 6 since it is divisible by 2 AND it is divisible by 3.<br />
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6) 1,603 is divisible by 7, since 160-3(2)=154, 15-4(2)=7, and 7 is divisible by 7.<br />
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7) 8,120 is divisible by 8 since 120 is divisible by 8.<br />
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8) 549 is divisible by 9 since the sum of the digits is 18 (5+4+9=18), and 18 is divisible by 9.<br />
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9) 3,770 is divisible by 10 since the last digit is 0.<br />
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10) 9,284 is divisible by 11 since the alternating sum of the digits is 11 (9-2+8-4)<br />
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<b>Practice Test - Give it  a try!</b><br />
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1. The number 477 is divisible by each of the following numbers EXCEPT: 3, 6, 9<br />
A. 3<br />
B. 9<br />
<b>C. 6</b><br />
D. None of the above.<br />
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2. The number 348 is divisible by each of the following numbers EXCEPT: 2, 3, 4, 5, 6<br />
A. 6<br />
<b>B. 5</b><br />
C. 4<br />
D. None of the above.<br />
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3. If a number is divisible by 9, then it is also divisible by which number?<br />
A. 2<br />
B. 6<br />
<b>C. 3</b><br />
D. None of the above.<br />
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4. Which number is divisible by 8?<br />
<b>A. 23,624</b><br />
B. 39,126<br />
C. 120,458<br />
D. None of the above.<br />
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5. Which number is divisible by 6?<br />
A. 213<br />
<b>B. 468</b><br />
C. 621<br />
D. None of the above.<br />
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Math Course - Divisibility Rules

Refresher Course in Mathematics - Number Theory Divisibility Rules Divisibility by Rule 2 If the number is an e...

Math Course - Properties of Number

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Refresher Course in Mathematics - Properties of Number</div>
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<b>Number Properties</b><br />
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<b>Property</b></div>
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<b>Definition</b></div>
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<b>Examples</b></div>
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<b><i>Closure
  Property</i></b></div>
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§ When we add or multiply any element in a set of numbers, the sum or product is a unique real number which belongs to that same set.</div>
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<i>14  + 25 + 44 + 52 = 135</i></div>
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<i>23 x 14 x 10 = 3 220</i></div>
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<b><i>Commutative Property</i></b></div>
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§ states that changing the position of the addends or the factors does not affect the sum or the product</div>
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<i>33 + 10 = 10 + 33</i></div>
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<i>18 x 9 = 9 x 18</i></div>
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<b><i>Associative Property</i></b></div>
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§ states that changing the grouping of addends in a sum or the grouping of factors in a product does not change the resulting sum or product</div>
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<i>(5 + 6) + 7 = 5 + (6 + 7)</i></div>
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<br /></div>
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<i>2 x (4 x 6) = (2 x 4) x 6</i></div>
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<b><i>Identity Property</i></b></div>
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<i>Addition</i></div>
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§ The sum of any number and zero is the same number.</div>
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§ 0 is the identity.</div>
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<i>512 + 0 = 512</i></div>
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<i>Multiplication</i></div>
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§ The product of any number and one is the same number.</div>
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§ 1 is the identity</div>
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<i>512 x 1 = 512</i></div>
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<b><i>Distributive Property of Multiplication over Addition / Subtraction</i></b></div>
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§ states that multiplication distributes over addition and subtraction</div>
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<i>7(9 + 12) = 7(9) + 7(12)</i></div>
</td>
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</tbody></table>
<br />

Math Course - Properties of Number

Refresher Course in Mathematics - Properties of Number Number Properties Property Definition Examples Closu...

Math Course - Analytic Geometry

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Refresher Course in Mathematics - Analytic Geometry</div>
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I. The Cartesian Plane<br />
<br />
II. The Straight Line<br />
A. Distance Between Two Points<br />
B. Slope of a Line<br />
C. Equation of the Line<br />
D. Different forms of the Equation of the Line<br />
E. Parallel and Perpendicular Lines<br />
F. Segment Division<br />
G. Distance of a Point from a Line<br />
<br />
III. Conic Section<br />
A. The Circle<br />
B. The Parabola<br />
C. The Ellipse<br />
D. The Hyperbola<br />
<br />
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Math Course - Analytic Geometry

Refresher Course in Mathematics - Analytic Geometry I. The Cartesian Plane II. The Straight Line A. Distance Between Two Points B. ...

English Course - The Function of Verb Tenses

English Course - The Function of Verb Tenses

The Function of Verb Tenses The Simple Present Tense The simple present is used to describe an action, an event, or condition that ...

English Course - 20 Rules of Subject Verb Agreement in Standard English

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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhhCdafWhMvO9hbM_4UCHuOGxQrdwBSf3omgqqAgMHaJ7F_1gKYLlQezZM8JHW9uovRioNDZYJFNtYg5PQ9FEE5GiXHAoSOmA2oQ6yz8LtG2VvNW-7tWbae-Wh1jsloPVTT6mBs-gPzoBCg/s1600/gramar.jpg" imageanchor="1" style=""><img alt="20 Rules of Subject Verb Agreement in Standard English" border="0" height="144" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhhCdafWhMvO9hbM_4UCHuOGxQrdwBSf3omgqqAgMHaJ7F_1gKYLlQezZM8JHW9uovRioNDZYJFNtYg5PQ9FEE5GiXHAoSOmA2oQ6yz8LtG2VvNW-7tWbae-Wh1jsloPVTT6mBs-gPzoBCg/s280/gramar.jpg" title="20 Rules of Subject Verb Agreement in Standard English" width="280" /></a></div>
<br />
<div style="text-align: justify;">
Grammar is not as static a science as is typically assumed, but there are 20 rules of subject verb agreement that attempt to objectify part of the English language form. Most of the concepts of subject verb agreement are straightforward, yet some aspects of singular and plural usage in English grammar are more complicated.</div>
<div>
<br /></div>
<b></b><br />
<div style="text-align: center;">
<b><b>What are the Rules?</b></b></div>
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<b>
</b>
1. <u>Subjects and verbs must agree in number</u>. This is the cornerstone rule that forms the background of the concept.<br />
<div>
<ul>
<li>The <i>baby cries</i> when he is angry.</li>
<li>The <i>babies cry</i> when they are angry.</li>
</ul>
2. Don’t get confused by the <u>words that come between the subject and verb; they do not affect</u> agreement.</div>
<div>
<div>
<ul>
<li>The dog, <i>who is chewing on my jeans</i>, is usually very good.</li>
<li>The flowers, <i>which thrives in our backyard</i>, are very appealing to the eyes</li>
</ul>
3. Prepositional phrases between the subject and verb usually do not affect agreement.</div>
<div>
<ul>
<li>The colors <i>of the rainbow</i> are beautiful.</li>
<li>One <i>of the universities</i> in Pampanga is implementing a new academic calendar.</li>
</ul>
4. When sentences start with “<u>there</u>” or “<u>here</u>,” the subject will always be placed after the verb, so care needs to be taken to identify it correctly.</div>
<div>
<ul>
<li><i>There</i> is a problem with the billing information.</li>
<li><i>Here</i> are the documents you requested.</li>
</ul>
5. Subjects don't always come before verbs in questions. Make sure you accurately identify the subject before deciding on the proper verb form to use.</div>
<div>
<ul>
<li>Does <i>Horsy</i> usually <i>eat grass</i>?</li>
<li>Where <i>are</i> the <i>pieces</i> of this puzzle?</li>
</ul>
6. If two subjects are joined by <u>and</u>, they typically require a plural verb form.<br />
<ul>
<li>The president <i>and</i> the vice president <i>are</i> from different political parties.</li>
<li>My father <i>and</i> I will <i>go</i> to fishing today.</li>
</ul>
7. The verb is singular if the two subjects separated by <i>and</i> refer to the same person or thing.</div>
<div>
<ul>
<li><i>Red beans and rice</i> is my mom's favorite dish.</li>
<li><i>Bread and cheese</i> has been my favorite snack</li>
</ul>
8. If one of the words <i>each, every, or no</i> comes before the subject, the verb is singular.</div>
<div>
<ul>
<li>No <i>smoking or drinking is</i> allowed.</li>
<li>Every <i>man and woman is</i> required to check in.</li>
</ul>
9. If the subjects are both singular and are connected by the words <i>or, nor, neither/nor, either/or</i>, and <i>not only/but also</i> the verb is singular.</div>
<div>
<ul>
<li><i>Miguel or Christian is</i> to blame for the accident.</li>
<li><i>Neither Melissa nor Cathy</i> was present yesterday.</li>
</ul>
10. The only time when the object of the preposition factors into the decision of plural or singular verb forms is when noun and pronoun subjects like some, half, none, more, all, etc. are followed by a prepositional phrase. In these sentences, the object of the preposition determines the form of the verb.</div>
<div>
<ul>
<li>All of the <i>chicken</i> is gone.</li>
<li>All of the <i>chickens</i> are gone.</li>
</ul>
11. The singular verb form is usually used for units of measurement or time.</div>
<div>
<ul>
<li>Four <i>quarts of oil was</i> required to get the car running.</li>
<li>Two thirds <i>of the members</i> of the congress believes that president is responsible for the incident.</li>
</ul>
12. If the subjects are both plural and are connected by the words <i>or, nor, neither/nor, either/or</i>, and <i>not only/but also</i>, the verb is plural.</div>
<div>
<ul>
<li><i>Dogs and cats are</i> both available at the pound.</li>
<li><i>The president and the former PNP chief are</i> both responsible for the misencounter.</li>
</ul>
13. If one subject is singular and one plural and the words are connected by the words <i>or, nor, neither/nor, either/or</i>, and <i>not only/but also</i>, you use the verb form of the subject that is nearest the verb.</div>
<div>
<ul>
<li>Either the <i>bears</i> or the <i>lion has</i> escaped from the zoo.</li>
<li>Neither the <i>lion</i> nor the <i>bears have</i> escaped from the zoo.</li>
</ul>
14. <u>Indefinite pronouns</u> typically take singular verbs.  *</div>
<div>
<ul>
<li><i>Everybody wants</i> to be loved.</li>
<li><i>Nobody has</i> qualified for the special promotion.</li>
</ul>
15. * Except for the pronouns (few, many, several, both, all, some) that always take the plural form.</div>
<div>
<ul>
<li><i>Few were</i> left alive after the flood.</li>
<li><i>Many still harbor</i> doubts about true intention of China.</li>
</ul>
16. <u>If two infinitives</u> are separated by <u>and</u> they take the plural form of the verb.</div>
<div>
<ul>
<li><i>To walk and to chew gum require</i> great skill.</li>
<li><i>To sketch and to paint are</i> his professional work.</li>
</ul>
17. <u>When gerunds are used as the subject</u> of a sentence, <u>they take the singular verb form</u> of the verb; but, when they are linked by and, they take the plural form.</div>
<div>
<ul>
<li><i>Standing</i> in the water <i>was</i> a bad idea.</li>
<li><i>Swimming</i> in the ocean and <i>playing drums are</i> my hobbies.</li>
</ul>
18. <u>Collective nouns</u> like herd, senate, class, crowd, etc. usually take a singular verb form.</div>
<div>
<ul>
<li>The school <i>faculty</i> is to join a national workshop next week.</li>
<li>The <i>herd</i> is stampeding.</li>
</ul>
19. Titles of books, movies, novels, etc. are treated as singular and take a singular verb.</div>
<div>
<ul>
<li><i>The Burbs is</i> a movie starring Tom Hanks.</li>
<li><i>The Lord of the Rings is</i> my favorite movie.</li>
</ul>
20. Final Rule – Remember, only the subject affects the verb!</div>
</div>
<div>
<br /></div>
<div>
<br /></div>
<div>
<b>Practice Test - Give it a try!</b></div>
<div>
<br /></div>
<div>
<div>
1. Either the physicians in this hospital or the chief administrator ____ (is, are) going to have to make a decision. </div>
<div>
<br /></div>
<div>
2. ____ (Is, Are) my boss or my sisters in the union going to win this grievance? </div>
<div>
<br /></div>
<div>
3. Some of the votes ____ (seem, seems) to have been miscounted. </div>
<div>
<br /></div>
<div>
4. The tornadoes that tear through this county every spring ____ (is, are) more than just a nuisance. </div>
<div>
<br /></div>
<div>
5. Everyone selected to serve on this jury ____ (has, have) to be willing to give up a lot of time. </div>
<div>
<br /></div>
<div>
6. Luke Miguel, together with his teammates, ____ (present, presents) a formidable opponent on the basketball court. </div>
<div>
<br /></div>
<div>
7. He seems to forget that there ____ (is, are) things to be done before he can graduate. </div>
<div>
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<div>
8. There ____ (has, have) to be some people left in that town after yesterday's flood. </div>
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<div>
9. Some of the grain ____ (appear, appears) to be contaminated. </div>
<div>
<br /></div>
<div>
10. Three-quarters of the students ____ (is, are) against the tuition hike. </div>
</div>
<div>
<br /></div>

English Course - 20 Rules of Subject Verb Agreement in Standard English

Grammar is not as static a science as is typically assumed, but there are 20 rules of subject verb agreement that attempt to objectify p...

English Course - Uses of Prepositions (In, On, and At)

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<div>
<b>Prepositions "In," "On," and "At"</b></div>
<div>
<br /></div>
<div>
A preposition is a word that links a noun, pronoun, or noun phrase to some other part of the sentence.</div>
<div>
<br /></div>
<div>
<div style="text-align: justify;">
Prepositions can be tricky for learners of English and is one of the most confusing lessons in grammar. There is no definite rule or formula for choosing a preposition.<span style="background-color: white; font-family: verdana; font-size: 14px; line-height: 20px;"> </span>Oftentimes, common examples of it, such as <i>in, on</i> and <i>at</i> are used inappropriately. To avoid misuse, consider the following pointers:</div>
<br />
Here are a few common prepositions and examples.<br />
<br />
<b>In</b></div>
<div>
<br /></div>
<div>
Used for unspecific times during a day, month, season, year:</div>
<div>
<div>
<ul>
<li>She always cooks breakfast in the morning.</li>
<li>The Earth is closer to the sun in summer and farther from the sun in winter.</li>
<li>The new academic calendar will start in August.</li>
</ul>
Used to indicate a location or name of a place:</div>
</div>
<div>
<ul>
<li>I am currently in an airport.</li>
<li>My hometown is Legazpi, which is in Albay.</li>
</ul>
</div>
<div>
<div>
Used to indicate a shape, color, or size:</div>
<div>
<ul>
<li>The remaining jackets are mostly in medium and large sizes.</li>
<li>The students stood in a circle and held a silent protest.</li>
<li>This pair of shoes comes in five different colors.</li>
</ul>
</div>
<div>
Used to express while doing something:</div>
<div>
<ul>
<li>In preparing for the final report, we revised the tone three times.</li>
<li>A catch phrase needs to be impressive in marketing a product.</li>
</ul>
</div>
<div>
Used to indicate a belief, opinion, interest, or feeling:</div>
<div>
<ul>
<li>I believe in the afterlife but not in reincarnation.</li>
<li>We are not interested in political affairs.</li>
</ul>
</div>
</div>
<div>
<b>On</b></div>
<div>
<br /></div>
<div>
<div>
Used to express a surface of something:</div>
<div>
<ul>
<li>I left a message on the table.</li>
<li>The geometry book is on my desk.</li>
</ul>
</div>
<div>
Used to specify days and dates:</div>
<div>
<ul>
<li>The garbage truck comes on Thursdays.</li>
<li>I was born on the 14th day of September in 1994.</li>
</ul>
</div>
<div>
Used to indicate a device or machine, such as a phone or computer:</div>
<div>
<ul>
<li>She is on the phone right now.</li>
<li>My brother has been on the computer since this morning.</li>
<li>My favorite anime show will be on TV tonight.</li>
</ul>
</div>
<div>
Used to indicate a part of the body:</div>
<div>
<ul>
<li>A lizard fell on my head.</li>
<li>I kissed her on her cheek.</li>
<li>I wear a ring on my finger.</li>
</ul>
</div>
<div>
Used to indicate the state of something:</div>
<div>
<ul>
<li>Everything in this store is on sale.</li>
<li>The building is on fire.</li>
</ul>
</div>
</div>
<div>
<div>
<b>At</b></div>
<div>
<br /></div>
<div>
Used to point out specific time:</div>
<div>
<ul>
<li>I will meet you at nine o'clock in the morning.</li>
<li>The bus will arrive here at 4:45 p.m.</li>
</ul>
</div>
<div>
Used to indicate a place:</div>
<div>
<ul>
<li>There is a party at the club house.</li>
<li>Hundreds of people are at the park.</li>
<li>We watched a basketball game at the Philippine stadium.</li>
</ul>
</div>
<div>
Used to indicate a contact information:</div>
<div>
<ul>
<li>Please email me at nosupport@infinithink.com.</li>
<li>If anything happens, call me at 1234-567-890.</li>
</ul>
</div>
<div>
Used to indicate an activity:</div>
<div>
<ul>
<li>He laughed at my singing.</li>
<li>I am good at drawing a portrait.</li>
</ul>
</div>
</div>
<div>
Used to indicate an event (a group activity):<br />
<ul>
<li>I met Mary Jane at a party.</li>
<li>Zayn Malik will not be at the concert in Manila.</li>
</ul>
<i>Prepositions of Place</i>. When to use <i>in</i> and <i>at</i> to indicate a place? As stated above, there is no definite rule for choosing a preposition, depending on the situation, both may be interchangeably used.<br />
<br />
<i>Stating your own location:</i><br />
Example 1: "I fell asleep <b>in</b> the library today as I haven't been sleeping so well lately."<br />
Example 2: "I fell asleep <b>at</b> the library today as I haven't been sleeping so well lately."<br />
<br />
In the examples, both convey the same meaning, so they are equally acceptable.<br />
<br />
<i>Stating a person's location:</i></div>
<div>
If the person asking a question <u>is not</u> in the location, then use "at".<br />
If the person asking the question <u>is in</u> the location, then use "in".</div>
<div>
<br /></div>
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Example 1: "Is Luke <b>in</b> the office now?", asked Miguel. (the speaker is in the office)<br />
Example 2: "Is Luke <b>at</b> the office now?", asked Miguel. (the speaker is on the phone and not in the office)</div>
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<b>Sample Practice Test! Have some practice.</b></div>
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Fill in the sentences with its appropriate preposition. (Hover the cursor on the dark box to reveal the answer.)<br />
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1. Men from different fields  gathered __ a party last night.<br />
<em class="postspoiler">Answer: at</em><br />
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2. __ the wall is a masterpiece crafted by a world renowned artist.<br />
<em class="postspoiler">Answer: On</em><br />
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3. "I am __ the meeting room waiting for you.", said Luke to his secretary on the phone.<br />
<em class="postspoiler">Answer: in</em><br />
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4. "Trigonometry class will be held __ Mondays.", announced the professor to his class.<br />
<em class="postspoiler">Answer: on</em><br />
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5. The campers have to ride __ the bus, otherwise they will be left staying in the campsite until next morning.<br />
<em class="postspoiler">Answer: on</em><br />
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6. Time flies! Next week, I will be __ Seoul for vacation.<br />
<em class="postspoiler">Answer: in</em><br />
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7. __ the door stands a very pale old woman, asking for a water to drink.<br />
<em class="postspoiler">Answer: At</em><br />
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8. My sister seems to be interested __ Psychology more than Literature.<br />
<em class="postspoiler">Answer: in</em><br />
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9. You can always see him reading alone __ the library.<br />
<em class="postspoiler">Answer: at</em><br />
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10. Look for the missing map __ the left of this apartment.<br />
<em class="postspoiler">Answer: on</em><br />
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English Course - Uses of Prepositions (In, On, and At)

Prepositions "In," "On," and "At" A preposition is a word that links a noun, pronoun, or noun phrase...