Civil Service Practice Test on Subtracting Integers

Three days ago, we have learned how to subtract positive and negative integers or signed numbers. In this post, I am going to give you a practice test on subtracting integers. For convenience, I have colored the negative signs blue instead of raising them to an exponent.

1. 12 – 23

2. 21 -(4)

3. 17 – (36)

4. 18 – 13

5. 22 – 35

6. 34 -( 21)

7. 29 -( 6)

8. 98 – 14

9.  87 – 53

10. 63 – 92

Click here to see the solutions and answers to the practice test given above.

The Scope of the Civil Service Examinations

The scope of the Civil Service examinations in the Philippines, both Professional and Subprofessional, are mainly  English and Mathematics proficiency. They comprise  about 80%  of the examination. Some of the questionnaires in grammar, correct usage, and paragraph organizations are in Filipino.  The remaining 20% are General Information questions, clerical operations in the Subprofessional examination and logical reasoning in the Professional examination.

Below are the scope of the Civil Service Examinations.

Professional Level

In mainly English and a small percentage in Filipino: vocabulary, grammar and correct usage, paragraph organization, reading comprehension, analogy, logical reasoning, and numerical reasoning.

Subprofessional Level

In mainly English and a small percentage in Filipino: vocabulary, grammar and correct usage, paragraph organization, reading comprehension, spelling, clerical operations, and numerical reasoning.

Both Professional and Subprofessional exams also include General Information on the following topics: Code of Conduct  and Ethical Standards for Public Officials and Employees (Republic Act 6713), Peace and Human Rights Issues and Concepts, and Environment Management and Protection.

For more information visit the Official Civil Service Commission website of the Philippines.

 

5 Effective Ways to Improve Your Vocabulary

English Proficiency makes up about 50% of the Philippine Civil Service Examinations both Professional and Subprofessional. Vocabulary test items such as word meaning and analogy are included in these exams. For a higher probability of passing, it is important that you have a wide vocabulary when taking these examinations. In this post, I am going to give you some tips on how to improve your vocabulary in English based on personal experience. I think these tips will not only improve your vocabulary, but also will improve your command of the English language in general. One thing to remember though: a wide vocabulary does not just develop overnight. It takes time.

1. Read, Read, and Read

Reading is one of the best ways to improve your vocabulary and you should do this everyday. In reading, you do not only meet new words, you see how they are used in sentences. Try reading an article or two a day and you will see your progress in a few months.

Dictionary

via Wikiepdia

Reading novels will introduce you to conversational English and reading news will introduce you to technical English. If you are observant with sentence structure, reading will also introduce you to correct grammar and usage. In effect, if you have not learned grammar formally, you’ll have an idea if a sentence is constructed correctly or not.

2. Play Word Games

Playing word games especially Scrabble against a computer will surely introduce you to new words. If you own a gadget, download a word game app and play against a computer. Download also a dictionary app so that you can look up the new words that you have learned.

In playing word games, you will not just enjoy, you will also learn.

3. Watch English Movies

Watching English movies can also help improve vocabulary. If you are not native English speaker (I assume that this is also read in other countries), I recommend that you watch movies with subtitles.  In so doing, you will most likely meet new words that are used in daily conversations especially in movies with modern settings. Be warned though that in order to make the movies more realistic, some dialogues may be grammatically incorrect. This is because it happens in reality.

4. Take Notes

Whether reading, playing word games, or watching movies, you might also want to take note of the new words that you encounter. Look up their meaning in a dictionary and use them in sentences. After writing a sentence using the new words, you might also want to look at online dictionaries. Most online dictionaries nowadays (such as TheFreeDictionary.com) have sample sentences on how to use words.

5. Write, Write, and Write

Writing a blog or a journal can also help improve your vocabulary. In writing your thoughts, you search for appropriate words to use. This will also help you better remember those words.

After all I said, you are probably asking the following questions in your mind.

How about memorizing?
What if I randomly look up a word at a dictionary and memorize them?

Well, picking some words and memorizing their meaning will help you a little. This strategy based on personal experience is not effective. Most word meanings that are memorized without context are easily forgotten.

How to Subtract Positive and Negative Integers

This is the continuation of the series of Civil Service review in mathematics particularly on operations of integers. In this post, we are going to discuss the most complicated operation on integers. I have taught people of all ages about this topic and it seems that for many, this is the most difficult among the four operations. In this post, we are going to learn how to subtract positive and negative integers or signed numbers. Note that in subtracting integers, there are only  four forms. If a and b are positive, the subtraction are of the following forms.

Case 1: positive minus positive (ab)
Case 2: negative minus positive (ab)
Case 3: positive minus negative (ab)
Case 4: negative minus negative (ab)

How to Subtract Positive and Negative Integers

What most people don’t know that ab is the same as ab, or subtracting a number is the same as adding its negative. That means that you only have to memorize the steps in addition of integers. Given a subtraction sentence, you then transform it  into addition. Here are a few examples.

Case 1 Exampe 1: 5 – 8

Subtracting is the same as adding its negative, so 5 – 8 = 5 + 8. Note that 5 + 8 is already addition and 5 + 8 = 3.

Case 2 Example: 10 – 4

The expression 10 – 4 is the same as 10 + 4 = 14.

Remember also that if you see two consecutive – signs or a minus and a negative sign, you can transform it to +. That is, -(a) = + a and -(a) + a. In most exam, the negative signs are not usually superscript, so you will likely -(-a).

Case 3 Example: 5 – 6

The above expression might be written in 5- -6 or 5-(-6). In any case, two negative signs, a minus and a negative sign can be transformed into a plus sign so, 5 (6) = 5 + 6 = 11. Notice that the last equation is also an addition sentence.

Case 4 Example: 8 – 6

The expression 8 – 6 = 8 + 6 = 2.

Observe that the four forms are already completed in the examles. From the strategy above, we only remember two strategies: (1) transform any subtraction sentence to addition sentence and (2) replace two consecutive negatives or a minus and a negative with + sign.

 

Solutions to Practice Exercises on Addition of Integers

We have learned how to add integers and in the previous post, I have given you practice exercises that you can use to evaluate your understanding of the topic. Below is the complete solutions to the practice exercises on adding integers. Share to me how many did you get right.

Solutions to Practice Exercises on Addition of Integers

1. 28 + 12 = 40.

2. 14 + 11 = 25

3. 24 + 15 = 9

Solution: We pair 15 and 15  to get 0. We have 9  left. So, the correct answer is 9.

4. –16 + 31 = 15

We pair 16  and 16 to get 0. We are left with positive 15.
5. 23 + 46 + 15 = 54

We add the two positive numbers first: 23 + 46 = 69. Next, we add 69 and 15. We get 15 from 69 and pair it with 15 resulting to 0, so we have 54 left.

6. 45 + 12 + 16 = 17

We add the negative numbers first: 12 + 16 = 28. We add the result to 45. We get 28 from 45 and pair it with  28 to get 0 leaving 17.

7. 12 +15 + 62 =  89

Explanation: They are negative, so we just added them. Of course negative added to negative is always negative.

8. 22 +  36 + 36 = 22

Explanation: 36 + 36 = 0, so we are left with 22.

9. 12 + 18 + 12 + 18 = 0

Explanation: 12 and 12 and 18 and 18 = 0.

10. 31 + 55 + 41 +  32 + 10 = 3

Explanation: Adding the positive integers, we have 31 + 55  = 86. Adding the negative integers, we have  41 +  32 + 10 =83. Now, 86 + 83 = 3

April 2013 Civil Service Exam Top 10 and Results

Below are the lists of the national top 10 of  the 2013 Civil Service Exam. The paper-and-pencil test was held nationwide on April 14, 2013.  To view the official complete list of passers, please go to the official website of Civil Service Commission.

Professional National Topnotchers 

1. Maravilla, Jan Angelique B – 86.21
2. Villaraza, Kristine C – 86.07
2. Baello, Joseph Alejandro M – 86.07
3. Mina, Rhinebert Kyle A – 85.95
3. Canoza, Bianca May O  – 85.95
4. Maravilla, Jan Abigail B – 85.94
5. Gapuz, Hazel Bernadette B – 85.93
6. Ganzon, Mina Angeles L  – 85.91
7. Guillen, Neil Daniel B – 85.75
8. Querubin, Emmanuel S – 85.7
8. Villar, Irene Marie F – 85.7
9. Palabay, Francis A – 85.67
10. Asur, Jodel LL – 85.63

SubProfessional Topnotchers

1. Gaite, Danielle JOanna C – 87.63
2. Ysulat, Andrea Claire C – 87.4
3. Tolentino, Ericko Paolo S – 87.35
4. Torres, Rosette Joy DF – 86.77
5. Quindoza, Mara Patricia D – 87.62
6. Durian, Noreen Rose A – 86.65
7. Briones, Glenn Ray B – 86.47
8. Marquez, Cielo Mae D – 86.39
9. Flores, Maria Kimmy I – 86.29
10. Villanueva, Acer M – 86.24

Source: Civil Service Commision

Practice Exercises on Addition of Integers

In the previous post, we have learned about adding positive and negative integers particularly on how to add integers with different signs. In this post, I am going to give you 10 exercises on adding integers. I will give the answers below for you to be able to check if your answers are correct. Also, I am going to omit the + sign before the positive integers because this is not usually shown in the exam. This means that 3 will automatically mean +3 unless a – sign precedes it.

Exercises on Addition of Integers

  1. 28 + 12
  2. 14 + 11
  3. 24 + 15
  4. 16 + 31
  5. 23 + 46 + 15
  6. 45 + 12 + 16
  7.  12 + 15 + 62
  8. 22 +  36 + 36
  9. 12 + 18 + 12 + 18
  10. 31 + 55 + 41 + 32 + 10

See if your answers and solutions are correct.

How to Add Positive and Negative Integers

One of the topics in basic mathematics  that will likely be included in the the Philippine Civil Service Exam both professional and subprofessional are operations on integers. Although a few Civil Service test items may be given from this topic,  it is important that you master it because a lot of calculation in other topics will need knowledge of integers and its operations (addition, subtraction, multiplication, division). For example, solving some word problems in mathematics and solving equations will need knowledge on operations of integers.

Integers are whole numbers that are either positive or negative. Examples of integers are -5, 6, 0, and 10. If we place this on the number line, negative integers are the integers that are below 0 (left of 0), while the positive integers are the integers above 0 (right of 0).

integers

Adding Integers that Are Both Positive

When you add integers that are both positive, it is just like adding whole numbers. Below are the examples.

Example 1: +2 + +4 = +6

Example 2: +9 + +41 + +6 + = +56

Example 3: +120 + +13 + +12 + = +145

Although we have created a small + before the number to indicate that it is positive, in reality, only negative numbers have signs. This means that +2 + +4 = +6 is just written as 2 + 4 = 6.

Adding Integers that Are Both Negative

Adding number that are both negative is just the same as adding numbers that are both positive. The only difference is that if you add two negative numbers, the result is negative.

Example 1: 5 + 8 = 13

Example 2: 10 + 18 + 32 + = 60

Example 3: 220 + 11 + 16 + = 247

How to Add Positive and Negative Integers

Before adding, you should always remember that +1 and 1 cancel out each other, or +1 + 1 is 0. So the strategy is to pair the positive and negative numbers and take out what’s left.

Example 1:  What is +13 + 8?

Solution:

We pair 8 positives and 8 negatives to cancel out. Then what’s left is of +13 is +5. In equation form, we have

 +138 = ++ +8 + 8+5 + (+88) = +5 + (0) = +5

Example 2: What is +17 + 20?

Solution:

We pair 17 negatives and 17 positives. What’s left of 20 is 3. In equation form, we have

+1720 = +17 + (173) =  (+17 + 17) + 3 = 0 + 33

Example 3: What is +16 + +37 + 20 + 3 +9 ?

In answering questions with multiple addends, combine all the positives and the negatives then add.

That is +16 + +37 = +53 and  20 + 3 +9 = 32.

So, the final equation is +53  + 32. We pair 32 positives and 32 negatives leaving 21 positives.

In equation form, we have

+53  + 32 = +21  +3232+21  + (+3232) = +21 + 0 = +21

By now, you will have realized, that adding integers is pretty easy. If you have questions, please fill out the comment box below.

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