Answers to Grammar Practice Test 1

Below are the answers and the explanations to the Grammar and Correct Usage Practice Test 1. The incorrect word or phrase in the sentence is highlighted red, while the correct word or phrase is highlighted green.

1. The inventor stood to except the award.

Correct Sentence: The inventor stood to accept the award.
Explanation: Accept means “to receive”, except means “to exclude.”

2. Between the three of us, I think I am the slowest runner.

Correct Sentence: Among the three of us, I think I am the slowest runner.
Explanation: Among is used to refer to 3 or more members of the group, while between is used to refer to two member of the group. Continue Reading

Grammar and Correct Usage Practice Test 1

One of the types of test in the Philippine Civil Service Examinations both Professional and Subprofessional is about grammar and correct usage. In the actual examinations, sentences are divided into phrases and numbered 1 through 5. You will be asked to identify the number of the phrase with incorrect grammar or usage.

In the practice test below, the sentences are shorter than the actual examinations, but the important thing is you should be able to identify the error. We will have compound and complex sentences in later practice tests.

Instructions Identify the word/phrase that makes the sentence incorrect if there are any. If no error is found, write NE. Continue Reading

A Teaser on Answering Number Series Questions

First of all, I would like to point out the term series in the “Number Series” questions in the Civil Service Examinations is a bit incorrect. Technically, the list of numbers in the examinations is actually called a sequence.  A series is a sequence of sums — well, I will not go into details since it is not included in the examinations.  You can  click the link though if you want to know about it.

Second, this is quite a premature discussion since I have only written a few posts about integers. I planned to write about this later, but I thought that a teaser would be nice. In this post, I will show you that it is a must to master all the topics in mathematics because they are all connected. We will not discuss the strategies on how to answer the sequence problems here; I will have a separate post about them later. Don’t stop reading though because you are going to miss half of your life if you do (kidding). Continue Reading

Practice Test on Multiplying Integers

In the previous post, we have learned the rules in multiplying integers.  Below is a 10-item practice test on multiplying integers. Note that in multiplication, we can use the x and () symbols in multiplying two numbers. This means that 3 x 4 is the same as 3 (4) and (3)(4). We will use both symbols in the practice test below to familiarize yourselves with them.  Any of the two symbols can be used in the Civil Service exams.

Practice Test on Multiplying Integers

1. -4 x -8

2. 3 x -7

3. -12 x -7

4.  -8 x -1 x -4 Continue Reading

How to Multiply Signed Numbers

In the two previous post in Mathematics, we have discussed how to add and subtract signed numbers. In this post, we are going to learn how to multiply signed numbers particularly integers. Signed means positive and negative.

Positive Integer x Positive Integer

Clearly, the product is positive. We had been multiplying positive integers since Grade school and we all know that the product is positive.

Positive Integer x Negative Integer

When you multiply, notice that you are actually adding repeated. When we say 2 x 3, we are actually saying twice three or 2 groups of 3 or 3 + 3. When we say, thrice 11, we are saying 11 + 11 + 11. With this in mind, 3 x – 5 = -5 + -5 + -5. Since we are adding integers which are negative, the sum is also negative or -15. This means that 3 x -5 = -15. If we generalize this, we can say that the product of a positive integer and a negative integer is negative. Continue Reading

Solutions to Subtracting Integers Practice Test

Blow are the solutions to the Civil Service Exam subtracting integers practice test.  As I have mentioned before, you do not have to memorize the rules of subtraction. All you have to do is convert it to addition. We can do this by converting a subtraction of integers problem  to addition of integers by changing the signs: minus “-: to plus negative “+ (-“  and minus negative “– –” or “– (-” to plus “+“. Observe how the subtraction problems are converted into addition problems in the solutions below. If you have any questions, please use the comment box below.

 1. 12 23 = 12 + (-23) = -11

2. -21 – (-4) = -21 + 4 = -17

3. 17 – (-36) = 17 + 36 = 53

4. -18 13 = -18 + (-13) =-31

5. 22 35 = 22 + (-35) = -13

6. -34 – (-21) = -34 + 21 = – 13

7. 29 – (-6) = 29 + 6 = 35

8. 98 – 14 = 84 (no need to change signs, this is ordinary subtraction since the minuend is larger than the subtrahend).

9. -87 53 = -87 + (-53) = -140

10. 63 92 = 63 + (-92) = -29

In the next post, we are going to discuss about multiplication and division of integers.

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.