## Addition of Fractions Exercises – Set 1

Find the sum of the following.

1. 1/8 + 2/8 + 3/8
2. 2/5 + 1/4
3. 5/8 + 7/12
4. 1/15 + 3/5 + 1/3
5. 4 + 3/5
6. 2 1/3 + 1/2
7. 3 3/4 + 7/10
8. 6 1/5 + 2 7/15 + 1/3
9. 3 + 7 1/8 + 4/5
10. 9 1/2 + 11/3

1. 3/4

2. 13/20
LCD: 20
8/20 + 5/20 = 13/20

3. 1 1/6
LCD: 24
15/24 + 14/24 = 29/24 = 1 5/24

4. 1
LCD: 15
1/15 + 9/15 + 5/15 = 15/15 = 1

5. 4 3/5
4 3/5

6. 2 5/6
LCD: 6
2 2/6 + 3/6 = 2 5/6

7. 4 9/20
LCD: 20
3 15/20 + 14/20
= 3 29/20 = 4 9/20

8. 9
LCD: 15
6 3/15 + 2 7/15 + 5/15
= 8 15/15 = 9

9. 10 37/40
LCD: 40
3 + 7 5/40 + 32/40
= 10 37/40

10. 13 1/6
LCD: 6
9 3/6 + 22/6
= 9 25/6 or 13 1/6

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## Patterns, Sequences, and Series Exercises Set 1

Consider the patterns below and find the next term for each.

1.) 5, 12, 19, 26, 33, ___

2.) 8, 9, 11, 14, 18, 23, ___

3.) 3, 9, 21, 45, 93, ___

4.) W2, T3, Q5, N7, K11, ___

5.) 8/27, 4/9, 2/3, 1, ____

6.) 28, 14, 12, 6, 4, 2, ____

7.) 4, 7, 11, 18, 29, ____

8.) 4, 9, 16, 25, 36, ____

9.) 2.5, 1.25, 0.625, .3125, ____

10.) 1, -8, 27, -64, ____

More reviewers!

1. PCSR English Page – reviewers abour English grammar, vocabulary, correct usage, analogy, etc.
2. PCSR Math Page – reviewers about basic math including fractions, decimals, integers, percent, etc.
3. PCSR Word Problems Page – reviewers about word problems such as age number problems, motion problems, work problems, etc.

## PCSR Civil Service Exam Review Guide 10

After learning how to solve number problems, let’s learn how to solve age problems. Watch the videos below and read the articles. Then, we will have exercise later.

PART I: MATH

A. Videos (These videos are in Taglish and the links point to Youtube).

B. Articles

C. Exercises

Part II ENGLISH

A. Vocabulary

Civil Service Exam Vocabulary Review 9

For those who are searching the Review Guides 1 to 9, you can find them here.

## Solving Equations Exercises Set 1A Answers

Below are the answers to Solving Equations Exercises Set 1A.

Part I

1. $x + 2 = 10$
$x = 10 - 2$
$x = 8$

2. $x - 7 = -14$
$x = -14 + 7$
$x = -7$

3. $4x = 20$
$x = \frac{20}{4}$
$x = 5$

4. $-3x = 18$
$x = \frac{18}{-3}$
$x = -6$

5. $\frac {x}{4} = 20$
$x = 20(4)$
$x = 80$

6. $\frac {x}{9} = -10$
$x = -10(9)$
$x = -90$

7. $2x + 1 = 15$
$2x = 15 - 1$
$2x = 14$
$x = \frac {14}{2}$
$x = 7$

8. $4x - 7 = 13$
$4x = 13 + 7$
$4x = 20$
$x = \frac {20}{4}$
$x = 5$

9. $-6x + 2 = -14$
$-6x = -14 - 2$
$-6x = -16$
$x = \frac {-16}{-6}$
$x = \frac {8}{3}$ or $2 \frac {2}{3}$

10. $3x - 1 = 8$
$3x = 8 + 1$
$3x = 9$
$x = \frac {9}{3}$
$x = 3$

Part II

1. $9 - x = 17$
$-x = 17 - 9$
$-x = 12$
$x = \frac {12}{(-1)}$
$x = -12$

2. $4x - 7 = -15$
$4x = -15 + 7$
$4x = -8$
$x = \frac {-8}{4}$
$x = -2$

3. $7x + 36 = 4x$
$7x - 4x = -36$
$3x = -36$
$x = \frac {-36}{3}$
$x = -12$

4. $-2x - 11 = -x$
$-2x + x = 11$
$-x = 11$
$x = \frac {11}{-1}$
$x = -11$

5. $7x = 5x - 6$
$7x - 5x = -6$
$2x = -6$
$x = \frac {-6}{2}$
$x = -3$

6. $2x - 5 = x + 4$
$2x -x = 4 + 5$
$x = 9$

7. $9x + 6 = 7x - 8$
$9x - 7x = -8 - 6$
$2x = -14$
$x = \frac {-14}{2}$
$x = -7$

8. $9 - x = 2 + 6x$
$-x - 6x = 2 - 9$
$-7x = -7$
$x = \frac {-7}{-7}$
$x = 1$

9. $\frac {x}{2} = x + 7$
$x = 2(x + 7)$
$x = 2x + 14$
$x - 2x = 14$
$-x = 14$
$x = \frac {14}{-1}$
$x = -14$

10. $-\frac {1}{4}x = 3x - 12$
$-x = 4(3x - 12)$
$-x = 12x - 48$
$-x - 12x = - 48$
$-13x = -48$
$x = \frac {-48}{-13}$
$x = \frac {48}{13}$ or $3 \frac {9}{13}$

Part III

1. $2(x - 5) = -8$
$2x - 10 = -8$
$2x = -8 + 10$
$2x = 2$
$x = 1$

2. $6(2x - 1) = -8 + x$
$12x - 6 = -8 + x$
$12x - x = -8 + 6$
$11x = -2$
$x = \frac {-2}{11}$

3. $3(4 - 3x) = 3x$
$12 - 9x = 3x$
$-9x - 3x = -12$
$-12x = -12$
$x = 1$

4. $5(x- 7) - 2 = x - 1$
$5x - 35 - 2 = x - 1$
$5x - 37 = x - 1$
$5x - x = -1 + 37$
$4x = 36$
$x = \frac {36}{4}$
$x = 9$

5. $4(x - 1) = 3(x + 1)$
$4x - 4 = 3x + 3$
$4x - 3x = 3 + 4$
$x = 7$

6. $7(4 - 2x) = x - 2$
$28 - 14x = x - 2$
$-14x - x = -2 - 28$
$-15x = -30$
$x = \frac {-30}{-15}$
$x = 2$

7. $4 - 6(x - 7) = -x - 4$
$4 - 6x + 42 = -x - 4$
$-6x + 48 = -x - 4$
$-6x + x = -4 - 48$
$-5x = -52$
$x = \frac {-52}{-5}$
$x = \frac {52}{5}$ or $10 \frac {2}{5}$

8. $\frac {-x}{4} = x + 10$
$-x = 4(x + 10)$
$-x = 4x + 40$
$-x - 4x = 40$
$-5x = 40$
$x = \frac {40}{-5}$
$x = -8$

9. $3x + \frac {1}{2} = 12$
To eliminate the fractions, we multiply both sides by 2.

$2(3x + \frac {1}{2}) = 2(12)$
$6x + 1 = 24$
$6x = 24 - 1$
$6x = 23$
$x = \frac {23}{6} or 3 \frac {5}{23}$

10. $\frac {3x}{5} = 4x - 8$
$3x = 5(4x - 8)$
$3x = 20x - 40$
$3x - 20x = -40$
$-17x = -40$
$x = \frac {-40}{-17}$
$x = \frac {40}{17}$ or $x = 2 \frac {6}{17}$

We will have more exercises soon.

## PEMDAS Exercises Set 1 Answers

Below are the answers to PEMDAS Exercises Set 1.

Part I

1. $5 + 3 - 2$
$= 8 - 2$
$= 6$

2. $9 - 6 + 4$
$= 3 + 4$
$= 7$

Note: Be careful! A lot of people make mistakes in number 2. If no other operation is between addition and subtraction, you operate from left to right. Here, we must subtract first before we add.

3. $7 + 4 \times 3$
$= 7 + 12$
$= 19$

4. $6 \times (-2) + 3$
$= -12 + 3$
$= -9$

5. $2 \times (-9 + 4)$
$= 2 \times (-5)$
$= -10$

6. $60 \div (-6 + 2)$
$= 60 \div (-4)$
$= -15$

7. $(-3 - 11) \times (-7)$
$= (-14) \times (-7)$
$= 98$

8. $12 \div 3 \times 5$
$= 4 \times 5$
$= 20$

Note: Be careful! Just like in number 2, if no other operation is between multiplication and division, you operate from left to right. Here, we must divide first before we multiply.

9. $4 \times (-1 - 6)$
$= 4 \times (-7)$
$= -28$

10. $-5 + (13 - 7) \div 3$
$= -5 + (6) \div 3$
$= -5 + 2$
$= -3$

Part II
1. $4 \times (-3 - 5)$
$= 4 \times (-8)$
$= -32$

2. $-2 \times (3 + 6)$
$= -2 \times (9)$
$= -18$

3. $(9 - 13) \div (-1)$
$= (-4) \div (-1)$
$= 4$

4. $(4 + 6)^2 - 7$
$= (10)^2 - 7$
$= (100) - 7$
$= 93$

5. $(-4)^2 \times (-2)^3$
$= (16) \times (-8)$
$= -128$

6. $-3 - 7 \times 2$
$= -3 - 14$
$= -17$

7. $= 3 - (-2) + 8$
$= 3 + 2 + 8$
$= 13$

8. $-12 - 8 \div 4$
$= -12 - 2$
$= -14$

9. $9 - (-4^2) \times (-2)$
$= 9 - (-16) \times (-2)$
$= 9 - 32$
$= -23$

Note the difference: $latex -4^2 = -16$ and $(-4)^2 = 16$.

10. $10 \div (-2) - (-3 \times 4)$
$= 10 \div (-2) - (-3 \times 4)$
$= (-5) - (-12)$
$= -5 + 12$
$= 7$

Part III
1. $3 - (-2) \times 5$
$= 3 - (-10)$
$= 3 + 10$
$= 13$

2. $-4 \times 3 + 6 \times 2$
$= -12 + 12$
$= 0$

3. $16 \div (-2) + 12 \div 4$
$= -8 + 3$
$= -5$

4. $36 \div (-13 + 4)$
$= 36 \div (-9)$
$= -4$

5. $18 \div (-3)^2 + (-4)$
$= 18 \div (9) + (-4)$
$= 2 + (-4)$
$= -2$

6. $4 \times (-2) + (-3^2)$
$= 4 \times (-2) + (-9)$
$(-8) + (-9)$
$= -17$

Note: Be careful! Please note that $-3^2 = -9$ and  $(-3)^2 = 9$.

7. $3 \times [-4 - (12 - 5)]$
$= 3 \times [-4 - (7)]$
$= 3 \times [-11]$
$= -33$

8. $(-3)^2 + 2^3 \div (-4)$
$= 9 + 8 \div (-4)$
$= 9 + (-2)$
$= 7$

9. $9 - (-4^2) \times (-2)$
$= 9 - 16 \times (-2)$
$= 9 - (32)$
$= -23$

Note: Again, $-4^2) = -16$, not $16$.

10. $-2 \times (-3 \times 2)^2 - (-2)^2$
$= -2 \times (-6)^2 - (4)$
$= -2 \times (36) - (4)$
$= -72 - (4)$
$= -76$

## PCSR Civil Service Exam Review Guide 2

PCSR 2017 CIVIL SERVICE EXAM REVIEW GUIDE 2
Updated: April 25, 2017

PART I: MATHEMATICS

Videos

More videos

Articles

PART II: ENGLISH

A. Vocabulary

Civil Service Exam Vocabulary Review Part 2
Tip: Try to memorize the words and use it in your own words.

B. Grammar

Simple Tenses
Lesson 1: The Simple Present Tense
Lesson 2: The Simple Past Tense
Lesson 3: The Simple Future Tense
Quiz: Simple Tenses Summary and Quiz

PART III: TIPS AND TRICKS

8 Tips on How to Pass the Civil Service Examination Next Time

Enjoy!

## Week 11 Review: Practice Exercises and Problems

After learning about work problems, let’s solve the following exercises. Solutions and answers will be posted soon.

Week 11 Review: Practice Exercises and Problems

1.) Aria can do a job in 7 days. What part of the job is finished after she worked for 3 days?

2.) Katya can do a job in 5 days. Marie can do the same job in 6 days. If they both worked for 1 day, what part of the job is finished?

3.) Ramon can paint a house in 6 days. Ralph can do the same job in 10 days. If they both worked for 2 days, what part of the job is done?

4.) One hose can fill a pool in 3 hours and a smaller hose can fill the same pool in 4 hours. How long will it take the two hoses to fill the entire pool?

5.) Marco can dig a ditch in 5 hours and he and Jimmy can do it in 2 hours. How long would it take Jimmy to dig the same ditch alone?

6.) Maria can paint a fence in 6 days and Leonora can do the same job in 7 days. They start to paint it together, but after two days, Leonora left, and Maria finishes the job alone. How many days will it take Leonora to finish the job?

7.) An inlet pipe can fill a pool in 4 hours. An outlet pipe can fill the same pool in 6 hours. One day, the pool was empty. The owner opened the inlet pipe but forgot to close the outlet pipe. How long will it take to fill the pool?

## Week 10 Review: Answers and Solutions

After learning how to solve motion problems, let’s answer some exercises and problems. In the solutions, we let d = distance, r = rate, and t = time.

Exercises

1.)   A car travels and average speed of 75 kph. If it traveled for 3.5 hours, what is the total distance traveled?

d = rt
d = (75 kph)(3.5 hrs) =
d = 262.5 km

2.) A bus traveled 4 hours from City A to City B which is 450 kilometers apart. What is its average speed?

d = rt
450 km = (4 hrs)(r)
r = (450 kph)/(4 hrs)
r = 112.5 km

Problem

1.) Two cars left City A at 8:00 am going to City B using the same route. Car 1 traveled at the average speed of 60 kph while Car 2 traveled at an average speed of 50kph. At what time were the two cars 25 kilometers apart?

Let x = time traveled by the two cars
60x – 50x = 25
10x = 25
x = 25/10
x = 2.5 hours

2.5 hours = 2hours and 30 mins
2 hours and 30 minutes after 8:00 am is 10:30 am.

2.) The road distance from Sapiro City to Lireo City is 195 km. Car 1 left Sapiro City going to Lireo City at an average speed of 70kph. Car 2 left City Lireo City going to Sapiro City at an average speed of 60 kph. If both cars left the two cities at the same time and use the same road, after how many hours will the two cars meet?

Car 1
Rate = 70kph
Time = x
Distance = 70x

Car 2
Rate = 60kph
Time = x
Distance = 60x

Total distance = 195kph

70x + 60x = 195
130x = 195
x = 195/130

x = 1.5hrs

3.) A red car left Vigan at 9:00 AM and traveled to Manila at an average speed of 45 kph. After one hour, a white car left the same place for Manila using the same route at an average speed of 60 kph. At what time will the white car overtake the red car?

RED CAR
Rate = 45kph
Time = x+1
Distance = 45(x+1)

WHITE CAR
Rage = 60kph
Time = x
Distance = 60x

60x = 45(x+1)
60x = 45x+45
60x – 45x = 45
15x = 45
x = 45/15
x = 3hours

3 hours after 10:00am is 1:00 p.m.

Note: We add 3 hours to 10:00 am because the second car left at 10:00 am.

4.) Two cars started from the same point, at 12nn, traveling to opposite directions at 50 and 60 kph, respectively. What is the distance between them at exactly 3:30 PM?

CAR 1
Rate = 50kph
Time = 3.5 hrs
Distance = (50 kph)(3.5 hrs) = 175

CAR 2
Rate = 60kph
Time = 3.5 hrs
Distance = (60 kph)( 3.5 hrs) = 210

What is the distance between them at exactly 3:30 PM?
175 km + 210 km = 385 km

5.) Two cars from the same point traveling to opposite directions at 75 and 85 kph, respectively. After how many hours will they be 240 kilometers apart?

75x + 85x = 240
160x = 240
240/160 = x
x = 1.5 hours

6.) A blue car leaves City A for City B at exactly 8:00 AM traveling at average speed of 55 kph. A gray car leaves City B for City A at the same time traveling at an average speed of 45 kph. The distance between the two cities is 75 kilometers.

If the two cars use the same route, what time will they pass each other?

let x be the time
d = r x t

sum of the distance traveled by 2 cars is equal to 75km
so

55x + 45x = 75
100x = 75
x = 75/100 or 0.75 hours
0.75 hours (45 mins)

They will pass each other 45 mins after 8:00am so the answer is 8:45 am.