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Maloco National High School Final Examination in Basic Calculus

This document appears to be a final exam in basic calculus given to students at Maloco National High School in Ibajay West, Aklan, Philippines. The exam has four sections testing students' abilities to: 1) match functions with their derivatives; 2) determine antiderivatives; 3) integrate using substitution; and 4) prove trigonometric identities. The exam was given in March 2018 to an unspecified section.

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Ean Fagar
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220 views3 pages

Maloco National High School Final Examination in Basic Calculus

This document appears to be a final exam in basic calculus given to students at Maloco National High School in Ibajay West, Aklan, Philippines. The exam has four sections testing students' abilities to: 1) match functions with their derivatives; 2) determine antiderivatives; 3) integrate using substitution; and 4) prove trigonometric identities. The exam was given in March 2018 to an unspecified section.

Uploaded by

Ean Fagar
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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Department of Education

Region VI - Western Visayas


Division of Aklan
District of Ibajay West
MALOCO NATIONAL HIGH SCHOOL SCORE: _____

Final Examination in Basic Calculus

NAME: ______________________________________ SECTION: _________ DATE: March __, 2018

I. Match the functions in column A with its corresponding derivatives in column B. Write only the letter of your
answer.
Column A Column B
f  x   3x  5x  2
2
f '  x   2x  6
1. _____ a.
3 f '  x   6x 3  6x  2
f  x   x 4  3x 2  2x b.
2. _____ 2
f  x   2x 3  3x 2  x  3 f '  x   15x 2  1
3. _____ c.
1 2 f '  x   6x 2  6x  1
f  x   5x 3  x d.
4. _____ 2
f  x   x  3 
2
f '  x   6x  5
5. _____ e.

II. Determine the following antiderivatives.


1
x dx
3

1.
3.
 x dx
5

3 
  3x    4 x  3x 3  1d x
4
3
x dx
2. 4. 

III. Integrate the following by substitution.

  x  3
5
dx
1.
 3x  x 
4
2 3
1 d x
2.
4.  sin x  c o s xd x
 x  2x 
5
2 3
3 dx
3.

IV. Prove the following trigonometric identities.

se c x ta n x 3. c sc 2 x ta n 2 x  1  ta n 2 x
 1
1. c osx c ot x

1 ta n 2 x sin 2 x  ta n 2 x  sin 2 x
se c x  ta n x sin x  4.
2. se c x

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