Quiz Measures and Promotes Learning in Math

                              By Victor E. Odarve

Although much of the math classroom activity such as lectures and board works is aimed at helping students acquire and store knowledge, a quiz measures learning as well as to promote it. Quiz, as a measuring educational tool, enables the teacher to gage how far the students learn the course topic and if ready for the next course to be taken up. In addition, a quiz also promotes stronger learning as students have improved retention of the topic and store it more securely in the memory. Quiz, therefore, as a part of a classroom routine, is yardstick on how far are our students learn as well as sort of mechanism in promoting stronger learning.

Engineering Math Quiz

Engineering Math Quiz

Although quiz puts the students under pressure, it allows the teacher to measure their progress in a particular topic, locking in learning along the way, and redirecting effort to areas of weakness where more work and review are needed to achieve proficiency. It also yields hints for the teachers who the weaker and stronger students are – who requires extra attention and who needs more of a challenge. In math, it can change the calculus in time table that is, allowing the

University Campus

University Campus

teacher a flexible time for discussion. Without it, teachers cannot evaluate whether the educational goals and standards of the lessons are being met.

In addition to as a measuring tool, quiz promotes stronger learning by encouraging students to practice their valuable skill of retrieving and using the stored knowledge. Several studies reveal that much of what we learn is quickly forgotten, but there is an improved retention of knowledge after taking a quiz.

Studies further show that quiz serves students best when they are incorporated into the regular classroom classes. This takes into account, among other matters, the students to overcome anxiety when getting up for and taking government standardized exams or practice long examinations such as close of semester examinations. By putting into practice the accessing or applying the stored knowledge, the students build mastery of the course.

Although this requires an ample time for the teachers to deal out and marking the scripts, quiz measures and encourages effective learning at all grade levels in math. So, the quiz is not just a tool to quantify and measure how effective the teaching method is, but also promotes students learning.

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Engineering Economics Final Exam Review ENG 221

ENG 221 ENGINEERING ECONOMICS FINAL EXAM REVIEW

Study the following problems:

1. An Indomie Plant is estimated to cost N 2 Million and the expected annual revenue is N800,000.00 for 4 years. Salvage value is 10 % of the investment. Annual operation and maintenance costs are N300000.00. Taxes and insurance is 5 % of the first cost per year. If the owner wants his capital investment to earn 25 % before income tax, evaluate if this project is profitable or not. Discuss the result. Evaluate by                   a) Rate of Return Method (ROR)             b) Annual worth method

Classroom Quiz

Classroom Quiz

2. An Enugu Charcoal Stove Company is producing a stove at a cost of N2000.00 per unit. Other fixed cost per year is estimated to be N60,000.00. The company sells the stove at N3000.00 each. Determine the number of stoves to be produced per year to breakeven.

3. To make calculation easier for Economics a student buys a laptop which costs N100,000.00 and has a salvage value of N20000.00 after 5 years. Determine the depreciation charge during the second year using a) straight line b) declining balance c) 150 % declining balance d) double declining balance e) sum of the years digit method.

4. Find the interest and the amount after 200 days of the N2000.00 loaned at 10 % ordinary simple interest.

5. Determine the amount of compounded interest earned for a N 600,000.00

Madonna university sunset

Madonna university sunset

deposited in a bank at a rate of 10 % compounded monthly for 6 years and 6 months.

6. Determine the number of years required for a N20,000.00 will be increased by N 5,000.00 if the interest rate is 14 % compounded semi annually ?

7. A parent deposited N 5000.00 in a bank 30 years ago. Today it is worth N 12,000.00 . Interest is paid semi annually. Determine the interest rate paid on this account.

8. Determine the accumulated amount and present worth of a 10 year annuity paying N 7000.00 at the end of each year with interest at 14% compounded annually?

8. What is the amount to be deposited at the end of every month at interest rate of 10% compounded quarterly so that it becomes N 40641.00 after 4 years?

9. A student deposited n 2000.00 in a bank at 15% annual interest at the end of each year. If the student is now 20 years old, how old the student be when the fund accumulated to N 1 million?

EMT 202 Final Exam Review

As an area of concentration on final exam EMT 202 on July 14, 2014, the following exercises serve as your guide. Final exams are close notes and books affair. Similar exercises will come out.

1. Find the product of matrices M and N.

M = [8 4 0 ; -2 6 -3; 0 -4 2]                where  M is a 3×3 matrix
N = [3 -5; 5 -6; -3 -7]                                            N is a 3 x2 matrix

2. For matrix 3 x 3 matrix A,

A = [ 2    3     4 ; 4     1      6 ; 2      -2      4 ]

Find          a) determinant of matrix
b) cofactor of matrix A
c) cofactor transpose of A
d) inverse of matrix A

3. Solve the values of x, y, and z using            a) Gauss Jordan method            B) Cramer’s rule
C) Gaussian elimination method         d) LU Factorization

2x +2y-4z-4=0
2x+5y+8z -4=0
X+2y+4z-6=0

4. Solve the system of coupled first order DE using matrix method.

f1’(x) = 4 f1(x) +10 f 2 (x)
f2’(x) = 3f1(x) +5 f 2 (x)
where f1(0) = 2                 f2(0) = 3

5. Find the eigenvalues and eigenvectors of a matrix [2           -5; 1           -4].

6. Find the modal and spectral matrices of the matrix A = [ 7          6; 6          2]

7. Find the dot and cross products of vectors a= 5i – 17j +12k and b= – 2i +4j – 6k.

8. Find the image of the line 2y – 3x = 4 under the translation   [1    -2].

9. Find the modal matrix P and diagonal matrix using similarity transformation D = P -1 A P.
Matrix A = [ 2          -5;  1      -4]

 

 

 

 

 

Quiz! Open Notes and Books

                                                                 By Vic Odarve

But just imagine open books and notes! Students are smiling from ear to ear. But do students really get perfect scores? At first, students think they can get it handily, but these are not always the case. At the end only a few get a perfect score. Why? Teachers know best to what extent the degree of difficulty the quiz should be that only a few can get away with perfect score. Teachers know what easy, moderate, and difficult problems are. Mathematics is not a memory course, but largely understanding of the principles and formulas. It is more on understanding of when, how, and why we use the formulas and its applications in the solution. That’s why it works on open notes and textbooks – a method of a student’s assessment. This is the real world for engineering students.

Quiz, Engineering Math, open books and notes

Quiz, Engineering Math, open books and notes

In the end, both teachers and students are challenged and thrilled. If many get perfect score the teachers seem defeated, but if only few, students win the battle. It’s like war, and a war of strategy, a war of nerves… and it’s enjoyable!

What about if in this war the teacher is defeated? He can have his next round. The teacher is the one who controls the war game. It is just like Mr. Putin’s strategy on how to defeat the hapless Ukraine

Madonna university, Elele Campus

Madonna university, Elele Campus

and annex Crimea. It is just like “to give difficult problems or not to give”- that is the question. So at the end, the teachers must have their heads high and always come out the winner.

Generally, quiz or assessment with open books and notes is more difficult than traditional closed exams. On this type of quiz, one or two of the given problems draws higher order thinking. More often students may not find the answers directly. Lecturers may offer open books and notes as an accommodation to help and challenge students to study their lessons.

Experience teaches us that only those students who have recognized masterfully the math concepts, formulas or procedures in a different order and at various levels of difficulty than they are presented in their textbook or in class; proof read the solutions before going out the exam room get away with perfect scores. When lecturers give a quiz in mathematics, one of the problems must be difficult or required extra/ deeper analysis, at least. So who wants to get a perfect score? Only those students who study an extra mile from the classroom discussion can get the perfect score.

These very few students who get away with perfect scores out from difficult mathematical problems of the highest order are a gem to the teacher. They are like our moon, which was born from a planet sized object which rammed the earth 4.5 billion of years ago provides romantic lights at nighttime. These students, like our moon, give delight and color to our classroom atmosphere. Imagine? They get perfect scores. They are showing their level of excellence. This is our real world, student’s university life, and a reality. We are talking of a real environment and not wormholes, which arise from our imagination.

So who wants open notes and book examination? It may happen once in your student’s life… once in a blue moon. Try and enjoy your university life!

Final Exam Review MTH 227 Differential Equations

MTH 227 DIFFERENTIAL EQUATION FINAL EXAM REVIEW – COMPUTER SCIENCE
For the area of concentration on our coming final exam tentatively set on March 13, 2014, please concentrate on the following exercises and problems.  Bring individual calculators.
 Similar problems will come out.
1. A microorganism is growing at the rate equal to 10 % of its population each day. If in the beginning there are 205000 microorganisms, how many organisms are present after
                a)15 days                             b) 10 days
2. Determine the time that the amount invested will double if an annual interest rate is 6.8 % compounded continuously?
3. Determine the accumulated amount of N12000.00 after 10 years if invested at a nominal interest of 14 % is compounded continuously?
4. A student deposited N500, 000.00 at an annual rate of 8.25 % compounded continuously, how long will it take the account to double in value?
5. A university canteen serves a cup of tea at 92C  to a Computer Science student. After 3 minutes, the tea has cooled to 74. If the canteen temperature is 23 C, how many minutes that the student must wait to cool the tea to 50 C?
6. Solve                y” – 12y’ + 36y = 0.
7. Solve                y” – 8y’ + 16 y = 0.
8. Solve                y” + 4y’ + 4y = 0.
MTH 227 STUDENTS
 LECTURER:  DR. VICTOR E. ODARVE, BSME, MEP-ME,MAED,EDD
PHILIPPINES, SOUTHEAST ASIA

Top Five (5) Performers – Strength of Materials-MEC 232

Top Five (5) Performers  MEC 232-Strength of Materials

Second Semester 2014-2015

Below are the top 5 performers of Strength of Materials for the Second Semester 2014-2015 of Madonna University, Elele Campus, River State, Nigeria. Final Exam was given last July 31,2015. Final Score consists of Cumulative Assessment (CA) (30%) and Final exam (70%). There are 230 students in a class in MEC 232.

Reg. Number

CA

Final Exam

Total Score

Top 1

SC/13/309

SC/13/385

27

25

65

67

92

92

Top 2

SC/13/437

25

65

92

 Top 3

SC/13/409

23

65

90

Top 4

SC/13/411

SC/13/500

SC/13/516

27

22

27

60

65

60

87

87

87

 Top 5

SC/13/279

SC/13/533

26

26

60

60

86

86

CONGRATULATIONS. KEEP UP THE GOOD WORKS!

Happy vacation for all!

DR. VICTOR E. ODARVE, BSME, MEP-ME,MAED, EDD, PHILIPPINES, ASIA

Final Exam Engineering Mathematics 1

Final Exam Strength of Materials

EMT 201 Final Exam Review

AREAS OF CONCENTRATION                       EMT 201 FINAL                  ENGINEERING MATHEMATICS 1

FIRST SEMESTER 2013/2014                        

Due to the wide coverage of our course EMT 201, I advise to concentrate on the following exercises. Similar exercises will be coming out in the final exam.

1. A tank contains 234 liters of water. A bitter lemon solution containing 5 kg/liter of sugar enters the tank at the rate of 6 liters/min and runs out at 4 liters/min. The tank has a paddle that keeps stirring to keep the mixture uniform. Find the amount of sugar in the tank after 30 minutes. Solve by ODE method.

2. A student deposited N100000.00 at an annual rate of 8% compounded continuously, how long will it take the amount to double in value? Solve by a) ODE              b) Laplace

3. Solve                the first order linear DE                                a) y’ – 6y =12.                    b) y’ + 5xy = 10x.

4. How much will be left after 500 years for a radioactive elements carbon 14 which has a half life of 5750 years if the initial amount is 50 grams? Solve by ODE and Laplace transform methods.

5. Solve the equation y” +y’ –6y = e 4x by a) undetermined coefficient method b) variation of parameters

6. A university canteen serves a cup of tea at 86C  to an Engineering student. After 2 minutes, the tea has cooled to 72C. If the canteen temperature is 24C, how many minutes that the student must wait to cool the tea to 51CUse Newton’s law of cooling. Solve by ODE method.

7. Solve the initial value DE          y’ – 3y=0,   y (0) =1,   find the value of     y (0.4) using        a) ODE

b) Laplace    c) Power series         D) Euler’s numerical method with N=4.

8. Find the equation of motion of a  4 kg mass suspended to a coiled spring with k = 100 N/m, initially displaced a distance of 1 meter from equilibrium position, and released with zero velocity and subjected to no damping or external forces. Find                a) Equation of motion by ODE and Laplace methods        b) amplitude      c) angular frequency      d) natural frequency           e) Period             f) graph of the curve

Engineering Math 201

Engineering Math 201

     DR. VICTOR E. ODARVE, BSME, MEP-ME, MAED, EDD

       Lecturer, Madonna, University, Nigeria, Africa

      Mayana, Jagna, Bohol, Philippines, Asia

TOP 5 PLACERS – ENGINEERING MATH 2

Below were the top 5 placers in Engineering Mathematics 2 (EMT 202) students for the Second Semester 2012-2013 March batch. The class consisted of 420 students.

TOP 5 PLACERS- ENGINEERING MATHEMATICS 2

EMT 202 (2012-2013 MARCH BATCH)

 

Placers

Registration No.

Cumulative Assessment, CA

Final Exam

(70 marks max)

Total Marks

(100 marks max)

First

EE/11/095

30

68

98

 

PTE/11/027

30

68

98

 

 

 

 

 

Second

PTE/11/144

30

66

96

 

CHE/11/018

30

66

96

 

CVE/T/11/075

30

66

96

 

CVE/11/016

30

66

96

 

EE/11/159

30

66

96

 

EE/11/134

30

66

96

 

EE/11/133

30

66

96

 

EE/11/129

30

66

96

 

EE/11/060

30

66

96

 

CE/11/016

30

66

96

 

 

 

 

 

Third

EE/11/070

28

66

94

 

 

 

 

 

Fourth

CVE/11/022

30

63

93

 

MECH/11/085

30

63

93

 

MECH/11/082

30

63

93

 

CHE/11/047

30

63

93

 

EE/11/138

27

66

93

 

EE/11/032

27

66

93

 

 

 

 

 

Fifth

EE/11/082

25

66

91

 CONGRATULATIONS! KEEP UP THE GOOD WORK!

HAPPY VACATION!

REVIEW FINAL EXAM – EMT 202

REVIEW FOR FINAL EXAM -EMT 202

 There is nothing better than a good preparation for the upcoming final exam on July 1, 2013. Since topics are too wide, you must concentrate on the following areas of concentration as shown in the examples below. Study them thoroughly for similar exercises will come out on the final exam. Workbook/textbook and notes will be your references.

1.      1. Find the inverse matrix of       C= 1        2      4

                                                                             2       1       4

               3        2       2

2.  Solve by Cramer’s rule

2x-y+2z=2

x-2y+z=4

x+y+2z=1

 3.    3.  Solve by Gaussian elimination method

X+2y+z=1

3x-2y-3z=1

X+2y+2z=4

 4.      4.Find the eigenvalues and eigenvectors of matrix

                         A=   2      4

1                               1       2

5.     5. Find matrix P and diagonal matrix D with D = P-1 A P of matrix

A                        A =    3        4

                                      2          1

6.      6. Solve the coupled differential equations:

 F1’(x) = 2 f1(x) – 3 f2(x)

F’2(x) = 4 f1(x) + 3 f2(x)

 7.      7.Find the dot or inner product a.b if a= [6, -3, 5] and b= [ 2, 4, 8 ] T, so that b is a column vector.

8.     8.  Find the cross product of vectors U= (3, 2,1) and V= (1, -2, 2).

9.     9. Transform vector V =[  with transformation T(V) =[ . Graph.

10. 10.  Find the image of the line y-x =4 under the translation. Graph.

MULTIPLICATION OF MATRICES-MS EXCEL

Addition and subtraction of matrices do not offer much difficulty to the student. Basically the operation follows the usual arithmetic operation. But multiplication of matrices is a different matter. It is quite difficult as some rules are to be followed. The difficulty of operation increases as the size of the matrices to be multiplied also increases.

MS Excel becomes a valuable tool in obtaining a solution for matrices multiplication. The program saves time and effort. For purpose of illustration, open the MS Excel and solve the following matrices;

EXAMPLE: Find the product of matrix AB.
If matrix A= 4           2         3
1            1         2
2           1          3
and matrix B =    2         4
1           0

1           2

Find AB.

Solution:
Highlight vacant cells for the product. The product
is a 3×2 size. Then move the cursor to the formula bar and put = sign.
Then at Formula heading, browse for function MMULT. Dialogue box
appears. On array 1, highlight data of matrix A. On array 2, highlight
data of matrix B. Then press F2. Then press Ctrl + Shift + Enter
simultaneously. Answer appears at the space provided for the product, as follows;

13          22
5           8
8           14

Below is a dialogue box as shown in the spreadsheet.

Dialogue box where you enter the matrix data.

Dialogue box where you enter the matrix data.