THE NEW EL SALVADOR COLLEGESEl Salvador City, Misamis Oriental

Final ExaminationMathematics 19 (Theory of Equations)

Name:_______________________________________________Score:_______________Course & Year:_______________________________________Date:________________Test I. Multiple Choice

Read the questions carefully and select your best answer. Write the letter of your best answer on the space provided before each number.ERASURE means wrong in all test areas!

____1. In the ___ century, the theory of equations acquired its status as an independent mathematical discipline.

a. 20th b. 19th c. 18th d. 17th

____2. Abelian Equations was introduced bya. HENRIK ABEL b. LEONHARD EULER c. OPHILE VANDERMONDE d. JOSEPH LOUIS LAGRANGE____3. The first mathematician sought to prove the impossibility of solving the general quintic algebraically.

a. ABEL b. EULER c. RUFFINI d. LAGRANGE____4. He made the comprehensive study of the solution of equations

a. ABEL b. EULER c. RUFFINI d. LAGRANGE____5. The mathematician who introduced the theory of permutations which provided basic notation and terminology

a. ABEL b. CAUCHY c. RUFFINI d. LAGRANGE____6. He introduced the new concept of irreducibility

a. ABEL b. CAUCHY c. RUFFINI d. LAGRANGE____7. He abandoned the permutation theoretic pillar of the unsolvability proof

a. ABEL b. CAUCHY c. RUFFINI d. LAGRANGE____8. He invested large efforts in clarifying, elaborating, and extending GALOIS’ ideas

a. ABEL b. CAUCHY c. LIOUVILLE d. LAGRANGE____9. He put forth a very general theory with the help of which the solvability of any equation could at least in principle be decided.

a. GALOIS b. CAUCHY c. LIOUVILLE d. LAGRANGE____10. The year when ABEL abandoned the permutation theoretic pillar of the unsolvability proof

a. 1828 b. 1829 c. 1830 d. 1831___11. One of the most influential mathematicians in the 18th century

a. Gauss b. Cauchy c. Waring d. Ruffini___12. He recognized patterns which led him to the known solutions of low degree equations.

a. Gauss b. Cauchy c. Waring d. Ruffini___13. Both WARING and ________ believed by 1770 that the theories which they had advanced carried in them the solution of the general equations.

a. Ruffini b. Lagrance c. Euler d. Cauchy___14. He found the implicit assumption that any polynomial equation could be solved by radicals.

a. Gauss b. Cauchy c. Waring d. Ruffini___15. He published his first proof of the impossibility of solving the quintic in 1799.

a. Ruffini b. Lagrance c. Euler d. Cauchy___16. He demonstrated the algebraic unsolvability of the quintic.

a. Abel b. Lagrance c. Ruffini d. Cauchy___17. The writings of RUFFINI were thoroughly inspired by ______’s analysis of the solvability of equations.

a. Abel b. Lagrance c. Ruffini d. Cauchy___18. He set out to classify all such permutations of arguments which left the function (formally) unaltered.

a. Ruffini b. Lagrance c. Euler d. Cauchy___19. One of RUFFINI’s friends and critical readers is

a. Abbati b. Abatti c. Abbot d. Abott___20. The mathematician who severely criticized RUFFINI’s result since it contradicted a general solution is

a. Ruffini b. Lagrance c. Abbati d. Malfatti___21. He gave a fusion argument incorporating the permutation theoretic arguments of RUFFINI’s final proof into the setting of ABEL’s proof.

a. Malfatti b. Lagrance c. Wantzel d. Euler

___22. At least by ____, the validity of RUFFINI’s claim that the general quintic could not be solved by radicals was propounded.

a. 1820 b. 1821 c. 1822 d. 1823___23. In November of ____, CAUCHY handed in a memoir on symmetric functions to the First Class of the Institut de France which was published three years later as two separate papers.

a. 1810 b. 1811 c. 1812 d. 1813___24. With _____ the term “permutation” came to mean an arrangement of indices.

a. Abel b. Lagrance c. Ruffini d. Cauchy

Test II Word BoxLook for the following words inside the word box.Encircle the 1-10 words, Box the 11-20 words and Underline the 21-30 words.Note: Erasure means wrong!

1. Algebraic 11. Solutions 21. Communicate2. Solvability 12. Construct 22. Reduced3. Polynomial 13. Degree 23. Sufficient4. Fundamental 14. Theories 24. Cyclotonic5. Mathematicians 15. Advanced 25. Computational6. Impossibility 16. General 26. Alluding7. Computations 17. Acknowledged 27. Outright8. Practical 18.Quintic 28. Suspicion9. Ambivalent 19. Criticisms 29. Analysis10. Algebraically 20. Assumptions 30. Italian

A L G E B R A I C S I S Y L A N A Q W M W E R TW E R T Y U I O P A S D F G H J M K L A Z O X CC V B N M Q W E R Y T Y U I O P B A S T E U D FC O M M U N I C A T E D S D F G I N S H S T A DD F G H J K L Z X C V B N M Q W V E D E G R E EI M P O S S I B I L I T Y Z X C A V B M N I M QE D A L G E B R A I C A L L Y F L V S A S G A BQ W E R R T Y U I O P A S D F G E H I T E H D TZ X C V B N M A S D F G H J K L N L Z I X T C VQ W E E R T Y U I O Y W E R T S T S D C A S D FV F U N D A M E N T A L S A D N E G C I V B N MN Q W E R T Y U I O P A S D F O G N H A G R T YO A S D F G H L G H J K L Z X I C I V N B N N NI P R A C T I C A L S L D F G T H D J S K A L AC Q W E R B T Y U I O P Z X C U V U D F G I N SI D F G A V B N M Z X C W E R L T L E R T L S EP A S V D F E R D T H H J U K O L L A S D A C BS E L R C O M P U T A T I O N S E A R T Y T I OU O S D F G H J K L A Z X C V B N C I T N I U QS C O N S T R U C T L A I M O N Y L O P X C V BV B N M Q W A C K N O W L E D G E D A S D F G HH J K L Z X C G V B N M Q W E R T Y U I O P A SD F G H J K L X E C T R C Y C L O T O N I C C XQ S U F F I C I E N T S A S D F E R T H Y U I OQ A W S E D R F T R E D U C E D R T G Y H U J IK O L P A Z S X D C F R F V G B H N J M K L A QA D V A N C E D Q A W S A S S U M P T I O N S EC O M P U T A T I O N A L L Y Y U I O J K O L AC R I T I C I S M S X Y T U I O S E I R O E H T

THE NEW EL SALVADOR COLLEGESEl Salvador City, Misamis Oriental

Final ExaminationMathematics 11(Calculus 1)

Name:_______________________________________________Score:_______________

Course & Year:_______________________________________Date:________________Test I. Multiple Choice

Read the questions carefully and select your best answer. Write the letter of your best answer on the space provided before each number.ERASURE means wrong in all test areas!

____ 1. What should be multiplied to (2x-5) to get 4x2-25?a. 2x+5 b. 2x-5 c. 4x2+10x+25 d. 4x2-10x+25

____ 2. What is the area of a square whose side is 4x-1?a. 16x2-1 b. 16x2-8x+1 c. 16x2+8x+1 d. 16x2+4x+1

____3. ____ is a directed line with its points corresponding to real numbers. a. Number line b. Directed line c. Curved line d. Intersected lines

____ 4. If a and b are positive integers, which of the following numbers is the largest?a. ab b. a2+b2 c. (a+b)2 d. (a-b)2

____ 5. If a and b are both negative integers, which of the following numbers is the largest?a. ab b. a2+b2 c. (a+b)2 d. (a-b)2

____6. The number corresponding to a point on the line is called ______.a. Axis b. Coordinates c. Ordinate d. Abscissa

____7. The French mathematician and philosopher who pioneered the concept of Cartesian Coordinate System

a. Archimedes b. Leonhard Euler c. Silvanus Thompson d. Rene Descartes ____ 8. If x2+y2=73 and xy=24, what is (x-y)2?

a. 24 b. 25 c. 48 d. 121____ 9. If (x+y)2=49 and x2+y2=29, what is xy?

a. 2 b. 5 c. 10 d. 20____10. The Cartesian Coordinate System is divided into 4 equal parts called____

a. Axis b. Coordinates c. Plane d. Quadrants ____11. The Cartesian Coordinate System is divided by how many axis?

a. 1 b. 2 c. 3 d. 4 ____ 12. Find the missing term so that 16x4+___+25 forms a perfect square trinomial.

a. 20x b. 20x2 c. 40x d. 40x2

____ 13. Find the missing term so that ___-48m+64 forms a perfect square trinomial.a. 3m2 b. 6m2 c. 9m2 d. 12m2

____14. The x-axis is also called______ a. Abscissa b. Ordinate c. Quadrants d. Line

____15. The point of intersection between x and y axis is called a. point b. vertex c. center d. Origin

____ 16. In 17+N=0, what is N?a. -17 b. 0 c. 1 d. 17

____ 17. /x+3/=0. What is the possible value of x?a. 0 b. -3 c. 1/3 d. 3

____18. Coordinates of Quadrant 1?a. (+,+) b. (+,-) c. (-,+) d. (-,-)

____19. Coordinates of Quadrant 2?a. (+,+) b. (+,-) c. (-,+) d. (-,-)

____ 20. Simplify: -130+(-120) –(-1)13

a. 1 b. -1 c. 0 d. -2____ 21. If m=-2 and n=3, what is the value of -2m2n2+5?

a. 76 b. 62 c. -27 d. -67 ____22. Coordinates of Quadrant 3?

a. (+,+) b. (+,-) c. (-,+) d. (-,-) ____23. Coordinates of Quadrant 4?

a. (+,+) b. (+,-) c. (-,+) d. (-,-) ____24. The symbol for distance formula.

a. A b. B c. C d. D

____25. The midpoint for x – axis in the coordinates (3,9)(5,0).a. 5 b. 4 c. 3 d. 2

____26. The distance between the points (2,5)(2,10)a. 3 b. 5 c. 9 d. 25

____27. The distance between the points (3,9)(-3,1)a. 8 b. 10 c. 64 d. 100

____28. The coordinates (2,-5) is in what quadrant?a. Quadrant 1 b. Quadrant 2 c. Quadrant 3 d. Quadrant 3

____29. The coordinates (-4,-5) is in what quadrant? a. Quadrant 1 b. Quadrant 2 c. Quadrant 3 d. Quadrant 3

____30. The midpoint for y – axis in the coordinates (3,9)(5,5).a. 14 b. 12 c. 10 d. 8

Test II. Solving (Use separate sheet of papers for the solutions)

1. Find the equation of this family of concentric circles centered at (1,1) and whose radii are 1 unit and 2 units respectively. Find this member of the family that passes through (4,1). Sketch the graph.

2. F(x) = 4x3 - 4x2 +4x – 4

a. F(5) =b. F(4) =c. F(3) =d. F(2) =e. F(1) =

3. F(x) = 5x3 -2

a. F(2) =b. F(-2) =c. F(0) =d. F(4) =e. F(3)=

4. F(x) = x4 + x3 - x2 – x + 1

a. F(2) =b. F(-2) =c. F(0) =d. F(4) =e. F(3)=

5. lim x3 - 2x2 + 3x + 4 x→ ½

6. lim x4 - 5x2 + 4x + 2 x→-1

7. lim x 4 - 16 x→-1 x2 - 4

8. lim 12x 2 - x - 1 x→-1 4x +1