Sample 201-206-VA Introduction to Applied Math Assessments

EVALUATION OF ASSESSMENT TOOLS USED TO MEASURE ACHIEVEMENT OF IET COURSE COMPETENCIES

Please attach copies of all assessment tools used in this section of the course

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Teacher Name: Julie Plante

Course Number:201-206-VA Section Number: All Ponderation: 2-2-2 Semester:H2012

Competency code and statement: 0435 To solve mathematical problems in industrial electronics.

Elements of the Competency

(Objectives)

Performance Criteria

(Standards)

Assessment Tools

Relevance of Assessment Tool

1.

Analyze the elements of an

industrial electronics

problem.

1.1 Accurate interpretation of information

Exam #1.

Exam #2

Pertinent. Question 1, 4, 7

Pertinent, Question 5,6

1.2 Proper determination of operations to

be performed

Exam #1

Exam #2

Pertinent. Question 1, 4, 5, 7

Pertinent, Question 2, 5,6

1.3 Accurate interpretation of units of

measurement

Exam #1

Exam #2

Pertinent. Question 1, 4

Pertinent, Question 2, 5,6

1.4

1.5

1.6

2.

Solve linear equations with

two variables.

Proper use of analytical, iterative and graphic

problem-solving methods

Test # 2

Test #3

Pertinent, question 3, 4, 6

Pertinent, question1,2, 3,9

Algebraic manipulations in conformity with

rules

Test # 2

Test #3

Pertinent, question 3, 4, 6

Pertinent, question1,2, 3,9

Accurate calculations

Test # 2

Test #3

Pertinent, question 3, 4, 6

Pertinent, question1,2, 3,9

3. Trigonometry : Not

in 206 but in 305.

4.

Calculate the values of

exponential and

logarithmic functions.

Proper graphic representation of functions

Test #3 Pertinent, question 5

Proper use of calculation methods

Test #3 Pertinent, question 4, 6, 8

Algebraic manipulations in conformity with

rules

Test #3 Pertinent, question 4, 5, 6, 8

Accurate calculations

Test #3 Pertinent, question 4, 5, 6, 8

5 Vectors : in 305.

Competency code and statement: 0435 CTND

Elements of the Competency

(Objectives)

Performance Criteria

(Standards)

Assessment Tools

Relevance of Assessment Tool

6. Complex numbers :

in 305

7. Calculate sine and

temporal functions : in

305

8. Present the results and

explain the problem-

solving approach.

Appropriate use of terminology and

conventions

Test #1

Test #3

Somewhat Pertinent,

question 1, 4

Somewhat Pertinent,

question 3

Assessment of plausibility of results

Test #1

Test #3

Somewhat Pertinent,

question 1,4

Somewhat Pertinent,

question 3

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201-206-VA Exam # 1 - Introduction to Applied Mathematics

Your Name : _______________________________________

1 ) [ 6 pts ] The distance between the college and its fiber optic internet provider is 748.35 km, measured in an

experiment done by physicists. It takes light 0.00391 seconds to travel this distance, again measured by a Vanier

Physics teacher.

A ) Re-write the distance and time in Scientific Notation.

B ) Use milliseconds units to re-write the time the light takes.

C ) What is the speed of light traveling the fiber optic cable following these experiments?

2 ) [ 9 pts ] Solve for x, if possible. If there are no x such that the equation is true, say “no solution”.

A ) (x2+3)

2 = 64.

x =

B ) √

√

x =

C )

x =

3 ) [ 5 pts ] The polynomial 2x2 – 9x – 5 is the product of ( x+c ) and 2x+1, c being a constant real number. Find

c by dividing the polynomial 2x2 – 9x – 5 by ( 2x+1) .

c =

4 ) [ 10 pts ] A ) A Hyundai Sonata Hybrid 2011 in 2011 cost $7 000 more than the Sonata 2005 in 2005. Both

together new would cost $53 000. What is the price of each?

Cost of 2005 Model : Cost of 2011 Model :

B ) The sum of three electric currents that come together at a point in a circuit is zero. If the second current is

twice the first and the third current is 9.2 milliamps more than the first, what are the currents?

i1= i2= i3=

5 ) [ 5 pts ] A circle is encircling a square. Express the Area of the square AS(r) and area of the circle AC(r) in

function of the radius r. Find the area of one semi-circle AL(r) left out by the square in the circle in function of

r. hint: the diagonal of a square is its side multiplied by √2.

AL(r)

AS (r) =

AC (r) =

AL (r) =

r

6 ) [5 pts ] Find the domain of the function: √

and calculate f(6).

Domain : f(6) =

7 ) [ 5 pts ] You create an open box by cutting out from a rectangular metal sheet four squares of side x out of

the four corners. The original length of the metal sheet is 5 cm shorter than the width. You know that the

perimeter of the original sheet is 38 cm. After folding the box, the perimeter of the bottom is 30 cm. What is

the side x of the four squares? Hint : Set two variables, l and w. Link the two variables together with the

perimeter of the sheet.

x =

x

x

width

length

8 ) [ 15 pts ] Solve the following set of equations by the method of your choice. If no answers exist, just write

“No Solution”.

A ) 0.4 x – 0.5 y = 1.2

0.3 x + 1.2 y = 2

B ) r = -3s – 2

-2r -9s = 2

C ) 2x + y = 4

3x + 3y = 1

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201-206-VA Exam # 2 - Introduction to Applied Mathematics

Your Name : _______________________________________

1 ) [ 25 pts ] Please simplify or factor the following expressions :

A ) ( 6x2 – 7x – 3 ) / ( 4x

2 – 8x + 3 ) =

B )

=

C )

=

D ) a6 – 27 b

6 =

E ) (27x6-8y

12) / (3x

2-2y

4) =

2 ) [ 5 pts ] Solve for the variable C;

; C =

3 ) [ 5 pts ] Compute the determinant of this system and from this determinant, indicate if there will be one

unique solution:

0.2 x1 + 0.5 x2 – 0.4 x3 = -1

1.5 x1 – 2.1 x2 + 4.6 x3 = 2

-0.45 x1 + 2.1 x2 – 4 x3 = 3

Will there be a unique solution? Yes / No.

4 ) [ 10 pts ] Solve this system :

x1 + x2 + 2 x3 = 9

2 x1 + 4 x2 - 3 x3 = 1

3 x1 + 6 x2 – 5 x3 = 0

5 ) [ 10 pts ] A ) You have been able to reduce the area used on a chip by 168 mm2 out of a chip that was 21mm

by 25mm. You have done that by reducing the width and the length of the used area by the same amount, x.

What is the size of the new smaller chip?

5 B ) You estimate that the cost of producing x units of this new chip is $ C = 0.1 x2 + 0.8 x + 7. That is, to

produce 5 units, for example, would cost you 0.1(25)+0.8(5)+7 = $13.50.

How many units can you do for $50?

6 ) [ 10 pts ] Solve this system derived from the electric diagram in milliAmps.

i1+ i2 = 30

i2 + i3 = 35

i3 + 15 = 60

i1 + 15 = 55

i1 = i2 = i3 =

7 ) [5 pts ] Solve for x : 3√(x-2) - √(x+1) = 0

x =

21 mm

25 mm

x

x

30

i1

55

15

i2

35

60

i3

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201-206-VA Exam # 3 - Introduction to Applied Mathematics

Your Name : _______________________________________

1 ) [ 9 pts ] You have to solve an electrical circuit using Kirchhoff's law giving you 3 equations involving 3

unknowns: i1, i2 and i3. You use MatLab to solve your 3 by 3 system… Write in each blank which one of the

words would fill-in the blanks of this paragraph. Yes, only one answer is correct for each blank line, a word can

be used more than once, and there are more words than blanks.

You should first type in the matrix ____________ the constants ( the right-side of the ‘=’ in Ax=C ) using

_______ to indicate the end of __________. Based on the ___________ of the matrix, you will know if either

the system has a unique solution when the ________ equals ____________or it is a case where it has none or

infinity of solutions. In the latter case you need to enter the matrix ________ the constants. Then, to know if

your system has no solution or rather an infinite amount of solutions, you use the _____________ function of

MatLab with this new matrix. If you see a row with all 0 coefficients equal to __________, then you have no

solutions, otherwise, you have an infinity of solutions!

a) with b) without c) brackets d) semi-colon ; e) parentheses f) rows g) columns h) determinant

i) reduced row echelon form j) inverse k) 1 l) not 0 m) 0

2 ) [ 9 pts ] Given the following constraints :

x ≥ 0 ; y ≥ 0

3x + 2y ≤ 20 ;

x - 2y ≥ 0 ;

Find the x and y which maximize the function 2 x + 5 y. You should use the graph paper available. Draw your

constraints; identify the possible zone and the coordinates of corners.

X : __________________________ Y : ________________________

3 ) [ 12 pts ] You need to prepare for your exams in two big courses : Math and Electrical Technology. For

each hour of reading you do, it adds 25 points to your mark in Math and adds 10 points to your mark in

Electrical Technology. For each hour of homework you do, it adds 10 points to your Math mark and it adds 15

points to your Technology course. How many hours, minimally, do you have to do readings and do homework

to pass those two courses, that is: to have 60 in both courses? You should use again the back of the graph paper

available. Draw your constraints; identify the possible zone and the coordinates of corners

# hours of reading : __________________ # hours of homework : ______________________

4 ) [ 12 pts ] Solve by finding the value of x:

A ) ( )

x = _____________

B ) 2 ln ( x ) – 1 = 7

x = _____________

C ) x = log4(1024) - log2(128)

x = _____________

D ) ln ( e2x

) + log10( 1000x ) = - 5

x = _____________

E ) calculate log4 ( 11 ) = x

x = _____________

F ) ln ( 3e -7) = x

x = _____________

5 ) [10 pts ] Identify each graph with a function :

1. ln ( x-2 )

2. ln ( -x )

3. – ln ( x )

4. 2 + ln ( x )

5. ln ( 2 – x )

A _________ B _________ C _________ D _________ E __________

6 ) [ 3 pts ] Using logarithmic rules, simplify to have A, B and C:

( √

) ( ) ( ) ( )

A = __________________ B = __________________ C = ___________________

7 ) [ 12 pts ] Solve the following inequalities by providing the interval(s) solving them.

A ) | 4 -x | ≤ 5

B ) 2 | x-3 | ≤ 14

C )

√

D ) 0 ≤ x2 – 2x - 3

8 ) [ 6 pts ] A ) Uranium -235 has a half-life of 700,000,000 years. Find the decay constant k in grams/year for

the model N = Ce-kt

. Write your answer using the scientific notation.

B ) If you store 500 grams of Uranium-235and your family ( of course, the Addams family! ) keeps it for

200,000,000 years, how many grams do your grand(many times) children have of Uranium-235 after these 200

millions of years?

9 ) [ 7 marks ] After using MatLab with a system of 3 equations and 3 unknowns x,y,z, you have the following

information:

A ) matrix A =

The determinant of A = ____________________

B ) Including the constant vector C =

to have AX=C, we have the reduced-row-echelon form of the system

as :

1.0000 0 -1.4000 -0.8000

0 1.0000 -0.2000 0.6000

0 0 0 0

State if this system has NO solution, one solution or an infinity of solution by encircling your answer.

If it has one or several solutions, state one.

Good luck!