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## Review Exercises

Exercise (PageIndex{1}) Introduction to Factoring

Determine the missing factor.

1. (12x^{3}−24x^{2}+4x=4x( ? ))
2. (10y^{4}−35y^{3}−5y^{2}=5y^{2}( ? ))
3. (−18a^{5}+9a^{4}−27a^{3}=−9a^{3}( ? ))
4. (−21x^{2}y+7xy^{2}−49xy=−7xy( ? ))

1. ((3x^{2}−6x+1))

3. ((2a^{2}−a+3))

Exercise (PageIndex{2}) Introduction to Factoring

Factor out the GCF.

1. (22x^{2}+11x)
2. (15y^{4}−5y^{3})
3. (18a^{3}−12a^{2}+30a)
4. (12a^{5}+20a^{3}−4a)
5. (9x^{3}y^{2}−18x^{2}y^{2}+27xy^{2})
6. (16a^{5}b^{5}c−8a^{3}b^{6}+24a^{3}b^{2}c)

1. (11x(2x+1))

3. (6a(3a^{2}−2a+5))

5. (9xy2(x^{2}−2x+3))

Exercise (PageIndex{3}) Introduction to Factoring

Factor by grouping.

1. (x^{2}+2x−5x−10 )
2. (2x^{2}−2x−3x+3 )
3. (x^{3}+5x^{2}−3x−15 )
4. (x^{3}−6x^{2}+x−6 )
5. (x^{3}−x^{2}y−2x+2y )
6. (a^{2}b^{2}−2a^{3}+6ab−3b^{3})

1. ((x+2)(x−5))

3. ((x+5)(x^{2}−3))

5. ((x−y)(x^{2}−2))

Exercise (PageIndex{4}) Factoring Trinomials of the Form (x^{2}+bx+c)

Are the following factored correctly? Check by multiplying.

1. (x^{2}+5x+6=(x+6)(x−1) )
2. (x^{2}+3x−10=(x+5)(x−2) )
3. (x^{2}+6x+9=(x+3)^{2} )
4. (x^{2}−6x−9=(x−3)(x+3))

1. No

3. Yes

Exercise (PageIndex{5}) Factoring Trinomials of the Form (x^{2}+bx+c)

Factor.

1. (x^{2}−13x−14 )
2. (x^{2}+13x+12 )
3. (y^{2}+10y+25 )
4. (y^{2}−20y+100 )
5. (a^{2}−8a−48 )
6. (b^{2}−18b+45 )
7. (x^{2}+2x+24 )
8. (x^{2}−10x−16 )
9. (a^{2}+ab−2b^{2} )
10. (a^{2}b^{2}+5ab−50)

1. ((x−14)(x+1))

3. ((y+5)^{2})

5. ((a−12)(a+4))

7. Prime

9. ((a−b)(a+2b))

Exercise (PageIndex{6}) Factoring Trinomials of the Form (ax^{2}+bx+c)

Factor.

1. (5x^{2}−27x−18 )
2. (3x^{2}−14x+8 )
3. (4x^{2}−28x+49 )
4. (9x^{2}+48x+64 )
5. (6x^{2}−29x−9 )
6. (8x^{2}+6x+9 )
7. (60x^{2}−65x+15 )
8. (16x^{2}−40x+16 )
9. (6x^{3}−10x^{2}y+4xy^{2})
10. (10x^{3}y−82x^{2}y^{2}+16xy^{3})
11. (−y^{2}+9y+36 )
12. (−a^{2}−7a+98 )
13. (16+142x−18x^{2} )
14. (45−132x−60x^{2})

1. ((5x+3)(x−6) )

3. ((2x−7)^{2})

5. Prime

7. (5(3x−1)(4x−3) )

9. (2x(3x−2y)(x−y) )

11. (−1(y−12)(y+3) )

13. (−2(9x+1)(x−8))

Exercise (PageIndex{7}) Factoring Special Binomials

Factor completely.

1. (x^{2}−81)
2. (25x^{2}−36)
3. (4x^{2}−49)
4. (81x^{2}−1)
5. (x^{2}−64y^{2})
6. (100x^{2}y^{2}−1)
7. (16x^{4}−y^{4})
8. (x^{4}−81y^{4})
9. (8x^{3}−125)
10. (27+y^{3})
11. (54x^{4}y−2xy^{4})
12. (3x^{4}y^{2}+24xy^{5})
13. (64x^{6}−y^{6})
14. (x^{6}+1)

1. ((x+9)(x−9))

3. ((2x+7)(2x−7))

5. ((x+8y)(x−8y))

7. ((4x^{2}+y^{2})(2x+y)(2x−y))

9. ((2x−5)(4x^{2}+10x+25))

11. (2xy(3x−y)(9x^{2}+3xy+y^{2}))

13. ((2x+y)(4x^{2}−2xy+y^{2})(2x−y)(4x^{2}+2xy+y^{2}))

Exercise (PageIndex{8}) General Guidelines for Factoring Polynomials

Factor completely.

1. (8x^{3}−4x^{2}+20x)
2. (50a^{4}b^{4}c+5a^{3}b^{5}c^{2})
3. (x^{3}−12x^{2}−x+12)
4. (a^{3}−2a^{2}−3ab+6b)
5. (−y^{2}−15y+16)
6. (x^{2}−18x+72)
7. (144x^{2}−25)
8. (3x^{4}−48)
9. (20x^{2}−41x−9)
10. (24x^{2}+14x−20)
11. (a^{4}b−343ab^{4})
12. (32x^{7}y^{2}+4xy^{8})

1. (4x(2x^{2}−x+5))

3. ((x−12)(x+1)(x−1))

5. (−1(y+16)(y−1))

7. ((12x+5)(12x−5))

9. ((4x−9)(5x+1))

11. (ab(a−7b)(a^{2}+7ab+49b^{2}))

Exercise (PageIndex{9}) Solving Equations by Factoring

Solve.

1. ((x−9)(x+10)=0 )
2. (−3x(x+8)=0 )
3. (6(x+1)(x−1)=0 )
4. ((x−12)(x+4)(2x−1)=0 )
5. (x^{2}+5x−50=0 )
6. (3x^{2}−13x+4=0 )
7. (3x^{2}−12=0 )
8. (16x^{2}−9=0 )
9. ((x−2)(x+6)=20 )
10. (2(x−2)(x+3)=7x−9 )
11. (52x^{2}−203x=0 )
12. (23x^{2}−512x+124=0)

1. (9, −10)

3. (−1, 1)

5. (−10, 5)

7. (±2)

9. (−8, 4)

11. (0, frac{8}{3})

Exercise (PageIndex{10}) Solving Equations by Factoring

Find a quadratic equation with integer coefficients, given the following solutions.

1. (−7, 6)
2. (0, −10)
3. (−frac{1}{9}, frac{1}{2})
4. (± frac{3}{2})

1. (x^{2}+x−42=0)

3. (18x^{2}−7x−1=0)

Exercise (PageIndex{11}) Applications Involving Quadratic Equations

Set up an algebraic equation and then solve the following.

1. An integer is (4) less than twice another. If the product of the two integers is (96), then find the integers.
2. The sum of the squares of two consecutive positive even integers is (52). Find the integers.
3. A (20)-foot ladder leaning against a wall reaches a height that is (4) feet more than the distance from the wall to the base of the ladder. How high does the ladder reach?
4. The height of an object dropped from the top of a (196)-foot building is given by (h(t)=−16t^{2}+196), where (t) represents the number of seconds after the object has been released. How long will it take the object to hit the ground?
5. The length of a rectangle is (1) centimeter less than three times the width. If the area is (70) square centimeters, then find the dimensions of the rectangle.
6. The base of a triangle is (4) centimeters more than twice the height. If the area of the triangle is (80) square centimeters, then find the measure of the base.

1. {(8, 12)} or {(−6, −16)}

3. (16) feet

5. Length: (14) centimeters; width: (5) centimeters

## Sample Exam

Exercise (PageIndex{12})

1. Determine the GCF of the terms (25a^{2}b^{2}c, 50ab^{4}), and (35a^{3}b^{3}c^{2}).
2. Determine the missing factor: (24x^{2}y^{3}−16x^{3}y^{2}+8x^{2}y=8x^{2}y( ? )).

1. (5ab^{2})

Exercise (PageIndex{13})

Factor.

1. (12x^{5}−15x^{4}+3x^{2})
2. (x^{3}−4x^{2}−2x+8)
3. (x^{2}−7x+12)
4. (9x^{2}−12x+4)
5. (x^{2}−81)
6. (x^{3}+27y^{3})

1. (3x^{2}(4x^{3}−5x^{2}+1))

3. ((x−4)(x−3) )

5. ((x+9)(x−9))

Exercise (PageIndex{14})

Factor completely.

1. (x^{3}+2x^{2}−4x−8)
2. (x^{4}−1)
3. (−6x^{3}+20x^{2}−6x)
4. (x^{6}−1)

1. ((x+2)^{2}(x−2))

3. (−2x(3x−1)(x−3))

Exercise (PageIndex{15})

Solve.

1. ((2x+1)(x−7)=0 )
2. (3x(4x−3)(x+1)=0 )
3. (x^{2}−64=0 )
4. (x^{2}+4x−12=0 )
5. (23x^{2}+89x−16=0 )
6. ((x−5)(x−3)=−1 )
7. (3x(x+3)=14x+2 )
8. ((3x+1)(3x+2)=9x+3)

1. (−frac{1}{2}, 7 )

3. (±8 )

5. (−frac{3}{2}, frac{1}{6})

7. (−frac{1}{3}, 2)

Exercise (PageIndex{16})

For each problem, set up an algebraic equation and then solve.

1. An integer is (4) less than twice another. If the product of the two integers is (70), then find the integers.
2. The sum of the squares of two consecutive positive odd integers is (130). Find the integers.
3. The length of a rectangle is (4) feet more than twice its width. If the area is (160) square feet, then find the dimensions of the rectangle.
4. The height of a triangle is (6) centimeters less than four times the length of its base. If the area measures (27) square centimeters, then what is the height of the triangle?
5. The height of a projectile launched upward at a speed of (64) feet/second from a height of (36) feet is given by the function (h(t)=−16t^{2}+64t+36). How long will it take the projectile to hit the ground?

1. {(7, 10)} or {(−14, −5)}

3. Width: (8) feet; length: (20) feet

5. (4frac{1}{2}) sec

## 6.E: Review Exercises and Sample Exam

Midterm Exam Study Questions

1. Describe the "Great English Canine Shift" in detail and explain its significance in terms of lexico-semantic change.

2. Use the word "sister" to exemplify polysemy in terms of central, peripheral, metaphorical, and extended meanings.

3. Discuss and exemplify the role of homeostasis (structural pressure or structural equilibrium) in language change and comparative historical linguistics.

4. Give a brief outline of significant dates, events, influences, and language contact in the history of the English language.

5. Explain and exemplify the four categories of contiguity and similarity in sense and form (Ullmann). McMahon

6. Explain and exemplify the linguistic approaches of the Neogrammarians, Structuralists, and early Generativists as they relate to language change.

7. Explain the significance of automorphism as subtype of iconicity (McMahon).

8. Explain the role of analogy in historical linguistics and language change.

9. Explain the importance of writing in historical linguistics. Why is it important that Sanskrit, Latin, and Greek were written languages? Would we have been able to make the same advances in philology if they were not?

10. Explain five of the following terms and give an example of each: lenition, rhotacism, cluster reduction, apocope, syncope, haplology, metathesis, epenthesis, prothesis, assimilation, dissimilation.

11. Use the spelling of the following words to explain sound changes that have occurred in the history of English: lamb, sing, night, rough, stone, mate, tune, Christmas .

12. What is the comparative method?

13. Discuss the major sub-groups of the Indo-European family of languages.

14. Discuss the difference between genetic relationships and cultural contact in languages.

15.Explain the factor responsible for the following unpredictable changes from Standard English in Papua New Guinea English:

lingua francalingo franco

16.In the past there have been theories that the Polynesians originated in South America or from the islands off the coast of British Columbia. Why do many scholars disregard such theories? What do you think?

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## Mathematics Practice Questions 1 1. C: The equation, x-0.10x-0.15(x-0.10x)=306, may be used to solve the problem. Solving for x gives 0.90x – 0.15x + 0.015x = 306, where x = 400. Thus, the original price was $400. 2. B: The equation may be solved by first distributing the y across the expression, x – 1, on the left side of the equation. Doing so gives: xyy = Z. Adding y to both sides of the equation gives: xy = Z + y. Finally, division of both sides of the equation by y gives: x=(Z+y)/y or x=Z/y+1. 3. B: This problem illustrates the distributive property of multiplication over addition. The factor being distributed may not change. 4. D: The measure of the third angle of the triangle is equal to 180°-(15° + 85°), or 80°. 5. C: Since there are 32 ounces in 2 pounds (16 ounces = 1 pound), the following proportion may be written: 5/140=32/x . Solving for x gives x = 896. Thus, there are 896 grams in 2 pounds of meat. 6. E: The largest number of children taking swimming lessons, in one year, was 500, in 1995. 7. C: The only decrease in number of children taking swimming lessons was from 1992 to 1993, with a decrease of 200 children. 8. B: The average may be written as (200+250+400+200+300+500)/6, which is approximately 308. 9. A: Movement of the decimal point two places to the left gives 0.0593. 10. C: The following proportion may be used to solve the problem: 1/20=6.2/x. Solving for x gives x = 124, so there are actually 124 miles between the two towns. 11. A: The correct graph should show a line segment between 1 and 4, including the points, 1 and 4. 12. D: The volume of the tin is 972 in”. The volume of each piece of fudge is 27 in”. 972 ÷ 27 = 36. 13. B: The following system of equations may be used to solve the problem: (s=2b@sb=15). Substituting 2b for s, in the second equation, gives: 2bb = 15, where b = 15. The younger brother is 15 years old. 14. C: Multiplying the numerator and denominator of the given fraction by 5 gives the fraction, 25/30, which is equivalent. 15. B: Converting feet to yards, the dimensions may be rewritten as 4 yards by 6 2/3 yards. Thus, the area of the floor is 26 2/3 yd’. Multiplication of this area by the cost per square yard gives the expression, 26 2/3?8.91, which equals 237.6. Thus, the cost is$237.60.

16. C: The following equation may be solved for x: 6000=1/2 x. Solving for x gives x = 12,000. Thus, the amount of prize money distributed equaled $12,000. 17. D: The distance may be determined by writing and solving the following equation for c: 50 2 +120 2 =c 2 . c = 130, thus the distance is 130 feet. 18. D: The average rate for the round trip is the total distance traveled divided by the total travel time. Distance traveled=2x. Travel time=x/10+x/8=4x/40+5x/40=9x/40. Average Rate=2xx9x/40=(2xx40)/9x=80/9 = approximately 8.9 mph. 19. E: The length is equal to 216 inches. The width is equal to 36 inches. So, the length may be covered by 18 12-inch stones, while the width may be covered by 3 12-inch stones. A total of 42 stones is needed for one layer, and 84 stones need for two layers. Multiplication of 84 by$2.32 gives 194.88. Thus, the total cost is $194.88. 20. E: The equation may be solved for x by first subtracting 6x from both sides of the equation. Doing so gives -3x = -15, where x = 5. Substituting 5 for x into the second expression gives 5 + 8, which equals 13. 21. B: There are 1,000 milliliters in 1 liter. 22. D: The problem may be modeled with the equation, 6.50 = 5.00 + 0.50x, where x represents the number of passengers. Solving for x gives x = 3. Thus, there were 3 passengers, plus 1 driver, for a total of 4 people in the vehicle. 23. C: This problem may be represented as 1/9 . 9, which equals 1. 24. D: Taking out 3 of each color will ensure that he has 1 of each color. Thus, he needs to take out 9 marbles, in all. 25. E: 0.20% = 0.002, and 1/500=0.002. 26. D: The increase from term to term is twice the increase from the previous two terms. Thus, the increase from 19 to the missing term will be 20, or twice the increase of 10. Thus, the missing term is equal to 19 + 20, or 39. 27. C: The solution may be modeled by the expression, 0.25(2490). Thus, her budget allowed$622.50 for housing in April of 2001.

28. E: The average may be represented as (0.10(2578)+0.10(2432)+0.10(2668)+0.10(2490)+0.10(2622)+0.10(2555))/6, which simplifies as (257.80+243.20+266.80+249.00+262.20+255.50)/6, or 255.75. The average budget amount for clothing in the first six months of 2001 was $255.75. 29. A: The amount she saved may be represented by the expression, 0.25(2622) – 0.20(2622), which equals 131.10. Thus, she saved$131.10.

30. B: The problem may be modeled with the equation, 1/40+1/30+1/24=1/t. Solving for t gives t = 10. Thus, working together, they can type the same document in 10 minutes.

31. D: The fraction, 3/5, equals 0.6, which is less than 2/3.

32. C: The ratio may be written as 6/14, which reduces to 3/7.

33. B: The amount of money she made may be represented by the expression, 90 + 0.12x, where x represents the amount of sales. Substituting 3000 for x gives 90 + 0.12(3000), which equals 450. So, she made $450 this week. 34. A: First, the perimeter measurement may be converted to feet. Multiplying 25 1/3 yards by 3 gives an equivalent measurement of 76 feet. Thus, the following equation may be written: 76 = 2(22) + 2w, which simplifies to 76 = 44 + 2w, where w = 16. The width of the house is 16 ft. 35. A: The problem may be modeled with the expression, 15,000 + 0.15(15,000), which equals 17,250. Thus, he sold the boat for$17,250.

36. A: 3/2000=0.0015, which is equivalent to 0.15%.

37. D: Moving the decimal point 4 places to the right gives 63,340.

38. C: Solving the given equation for x gives x = -1. Substitution of -1 for x, in the second equation, gives -1 + 1 = 0.

39. A: The interior angle measures of a triangle sum to 180°. Thus, the measure of the third angle is equal to the difference of 180° and 120°, or 60°.

40. B: Cups is an appropriate measure of capacity for sugar.

## Lactation Exam Practice The Health e-Learning Lactation Exam Practice is released twice a year. For students sitting the April IBLCE Exam, enroll in the Lactation Practice Exam released in February. For students sitting the September IBLCE Exam, enroll in the Lactation Practice Exam released in July (multilingual). The Lactation Practice Exam is not available outside of our enrollment dates.

IBLCE modified the exam dates for 2021 so LP English starts early February in 2021

The Lactation Exam Practice provides IBLCE Exam candidates practice in multiple-choice assessments on a range of questions, based on the IBLCE Exam content outline. Practice your exam-taking skills on these questions. You'll learn techniques to ensure you answer the questions accurately, giving you lots of practice with photograph-related questions. This will help you to identify topic areas where you need more study. 100% of participant evaluations in 2020 indicated they were able to identify areas they needed to study more as a result of doing Lactation Exam Practice.

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Access to over 300 multiple-choice questions on which to practice. The first 4 exams (200+ questions) align closely with the number of questions on each subject you'll find in the IBLCE content outline in preparation for the exam. Exams E & F (100+ questions) are on topics most students have more difficulty with. A significant number of questions are based on full-color photographs. The questions are divided into exams of 50 questions each for easy time management. All the questions have feedback, many with evidence-based research references - a great learning aid! The question range has been created according to the content outline topics to be examined, as published by the IBLCE. All the questions are automatically graded - your results are available immediately after you complete each of your practice exams. You have unlimited attempts to do each Practice Exam.

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To be eligible to receive the designated CERPs for the Lactation Practice Exam YOU MUST complete all 6 exam practices, review the feedback to each question, and actively participate in the discussion forum.

To receive the CERPs Certificate you are required to

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The aim of Lactation Exam Practice is to give the candidate of the IBLCE exam, practice in multiple-choice exam techniques using question-style the same or very similar to that of the IBLCE exam.
A secondary aim is to give the candidate a feeling for the subject topics which they may need to study more thoroughly.
And finally, the LPEX PLUS provides a venue for exam candidates from around the world to gather, give one another support, and share friendship during a special time in their lives.

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• Be able to examine a multiple-choice question carefully and thoroughly with a view to discerning the exact intention of the question.
• Identify areas of the IBLCE Exam Blueprint which may require additional study to feel fully prepared.
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• This program is facilitated by an experienced International Board Certified Lactation Consultant who has extensive experience in clinical practice and education.
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• The program accepts enrollments from February 1st (English only) and July 1st (Multilingual) each year.
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## Free Citizenship Sample Questions for the US Naturalization Civics Test

Our sample exams for the Citizenship Test require no registration, and include scoring and answer explanations. Citizenship practice tests are an effective way to study for your test and prepare for your final examination. Our free citizenship practice sample tests provide you with an opportunity to assess how well you are prepared for the actual Citizenship Test, and then concentrate on the areas you need to work on.

After you submit answers to the naturalization test practice questions, a test score will be presented. In addition, you will be given rationales for all of the questions to help you understand any questions you may have gotten wrong. In the actual civics portion of the Citizenship Test, you will be asked up to 20 questions out of a possible list of 128 questions. You will need to answer at least 12 of the questions correctly.

On the Test-Guide.com citizenship practice tests, you will be presented with around 20 multiple-choice questions. Each correct answer on our exams is worth 10 points. If you score a 120 or better on our exams, then you have a "passing" grade. although you should strive to get all of our questions correct so that you are fully prepared for your final, official exam.

Preparing for the naturalization test by using free online citizenship practice tests is a truly effective way to study, as you get to learn the rationales behind all of the questions and their correct answers so that you can better understand what is expected of you in the final test. The more Citizenship Test questions that you practice, the better able you are to do well on the actual test.

The official Citizenship Exam has questions on American government, American history, and integrated civics. The questions are pulled from the following specific topics:

• Principles of American Democracy
• System of Government
• Rights and Responsibilities
• Colonial Period and Independence
• 1800s
• Recent American History and Other Important Historical Information
• Geography
• Symbols
• Holidays

## Testing the Plan

When you hear the word “testing,” you probably think about a pass/fail evaluation. You may find that there are parts of your preparedness program that will not work in practice. Consider a recovery strategy that requires relocating to another facility and configuring equipment at that facility. Can equipment at the alternate facility be configured in time to meet the planned recovery time objective? Can alarm systems be heard and understood throughout the building to warn all employees to take protective action? Can members of emergency response or business continuity teams be alerted to respond in the middle of the night? Testing is necessary to determine whether or not the various parts of the preparedness program will work.

## Full English Sample Tests

Thithutienganh provides full free English sample tests for you to practice. You will step by step familiarize yourself with the test formats and sample questions before taking a real test. All the tests were designed according to the standard formats of official tests.

Level A sample tests: provide you questions that were formatted and followed a standard test for English beginner. If you have just started learning English. This test is suitable for you to check your English ability. Especially grammar and reading sections.

Level B sample tests: If you have just completed an English course for pre-intermediate learner, this test is for you. You can check what you have learned from the textbook.

## Cloze Exercises

The MELAB and ECPE tests have cloze exercises. You can find a free cloze test below.

After you have finished the cloze exercises, you should take the reading comprehension test and do the vocabulary and grammar exercises.

##### Close Exercise

Instructions: Read the cloze passage below and place the appropriate word in the gap from the choices provided below the passage.

Running for the office of the President of the United States is exceptionally arduous and should not be undertaken by the (1) hearted. The candidates must first compete in the local primary elections. During the primary campaign, the candidate endeavors to (2) the votes of his or her constituents. Any new candidates are the opponents (3) the incumbent, the President currently in office who is running for re-election. The candidates refrain from actions that might create animosity (4) them and the public.

Rather, they attempt to appease their constituency by using promotional gimmicks and ambiguous equivocation, as well as (5) decorous protocol. The public is indeed curious about, if not (6) of, the candidate’s professional life, in addition to his or her personal life, which will be under (7) scrutiny during the campaign. Since his or her private life becomes public domain, the candidate may (8) to disclose any controversial behavior in his or her past before the press digs it up. (9) history has shown us, even a prominent politician can be revealed as a phony. A politician exhibiting scandalous behavior might even be subjected (10) censure from his political colleagues.

1) a. faint b. meek c. mild d. weak

2) a. extract b. gain c. exist d. drop

4) a. by b. beside c. between d. to

5) a. observance b. observing c. appeal d. appellation

6) a. adventurous b. dangerous c. querulous d. suspicious

7) a. near b. care c. close d. front

8) a. to fit b. see fit c. look fit d. be fit

9) a. Contrary b. Despite c. As d. Where

10) a. by b. under c. to d. with

The voters must also (11) the political platform of the candidate. The platform includes the core issues (12) the candidate promises to resolve during his or her term in office. Typical campaign promises include establishing (13) to reduce bureaucratic red tape. The candidate (14) the primary election will be nominated by his or her particular political party to run (15) the final election.