Mathematics Secondary V - SecV chemistrysciencehip.weebly.com/uploads/4/8/6/3/48637575/... · Mathematics Secondary V Science Option THOSE WHO RECEIVE A COPY OF THIS EXAMINATION HAVE

June 2014

Mathematics Secondary V

Science Option

THOSE WHO RECEIVE A COPY OF THIS EXAMINATION HAVE

UNDERTAKEN TO USE IT ON THE FOLLOWING DATE:

Competency 2

Tuesday JUNE 17, 2014 (a.m.) NOTE: This date was established by the Directors of English Education

Network (DEEN) and the Mathematics and Science and Technology Committee (MaST).

Mathematics 565-506 Science Option

Secondary 5

Math 506 SNMath 506 SN

Competency TwoCompetency Two Uses Mathematical ReasoningUses Mathematical Reasoning

Administration and Marking Guide June 2014

Math Math 565565--506 C2506 C2

PPUBLICATIONUBLICATION 2014

DDESIGN ESIGN TTEAMEAM Kevin Stuckey, Lester B. Pearson School Board Haley Robertson, Lester B. Pearson School Board Meryl Midler, Lester B. Pearson School Board

CCOORDINATIONOORDINATION Franca Redivo, Lester B. Pearson School Board Wendy Davies, BIM, GRICS

VVALIDATIONALIDATION

Vicki Krawczyk, Sir Wilfrid-Laurier School Board Sonya Vanderhoeden-Bracken, Sir Wilfrid-Laurier School Board

LL INGUISTIC INGUISTIC RREVISIONEVISION Kevin O’Donnell, BIM, GRICS

CCOMPUTERIZATIONOMPUTERIZATION Martine Sanscartier, BIM, GRICS

II LLUSTRATIONSLLUSTRATIONS Martine Sanscartier, BIM, GRICS Clipart.com

Math 506SN C2 Administration and Marking Guide

BIM GRICS

TTable of Contentsable of Contents General Information .................................................................................................................... 1

Presentation of the Evaluation Situations ................................................................................... 3

General Procedure for the Evaluation Situations ........................................................................ 6

Marking Procedure ...................................................................................................................... 7

Marking Key................................................................................................................................. 8

Appendices

Rubric for the competency Uses mathematical reasoning ......................................... Appendix A

Overall Assessment for the Evaluation Situation ........................................................ Appendix B

Feedback Questionnaire ..............................................................................................Appendix C [The feedback questionnaire is also available online at www.bimonline.qc.ca]


BIM GRICS Page 1

GGEENERAL NERAL IINFORMATIONNFORMATION SUBJECT

Mathematics

COMPETENCY

Uses mathematical reasoning

SUGGESTED TIME ALLOTMENT

Students have three hours to complete the examination. An additional five minutes may be allotted per hour of the examination.

MATERIALS PROVIDED

For the teacher

Administration and Marking Guide, which outlines the evaluation procedure and the marking key.

For the student

Question Booklet – Sections A and B Student Booklet, in which the students record their answers to the questions in Parts A

and B and indicate the reasoning they used for each of the situations involving applications in Part C.

PERMITTED MATERIALS

Calculator (with or without a graphic display) Geometry instruments (ruler, compass, protractor, set square, graph paper) Handwritten memory aid that the student has created by him/herself in advance.


BIM GRICS Page 2

UNAUTHORIZED MATERIALS1

Calculators with or without graphic display designed mainly to perform mathematical calculations are authorized during official exams. Before the exam starts, data and programs stored in the calculator’s memory must be deleted. Calculators equipped with formal calculation software are not authorized for the exams. These models are allowed under the sole condition that the formal calculation functions are deactivated prior to the exam. Using a calculator containing stored data or programs will be considered as cheating. Computers, tablet computers, electronic organizers and calculators with an alphanumeric keyboard (QWERTY or AZERTY) are not authorized. All calculator peripherals, such as instruction manuals and memory expansion devices, are forbidden. Using memory expansion cards or chips, data or program libraries are strictly forbidden. Communication between calculators is not allowed during the exam. Students cannot share their calculators with their peers.

1. As suggested by the Information Document, Mathematics, secondary 4, MELS, 2013.

This information is also included in the Question Booklet and Student Booklet.


BIM GRICS Page 3

PPRESENTATION ORESENTATION OFF THE THE EEVALUATION VALUATION SS ITUATIONITUATIONSS STRUCTURE This examination is designed to evaluate the competency Uses mathematical reasoning. It was developed and validated by education consultants and teachers. The examination is divided into three parts. Part A consists of multiple-choice questions, Part B of short-answer questions, and Part C of situations involving applications. The following table gives a breakdown of the types of tasks involved as well as the number of marks allotted per question for each part of the examination.

EXAMINATION PART TYPE OF TASK NUMBER MARKS PER

QUESTION TOTAL MARKS

Part A Multiple-choice

questions 6 4 24

Part B Short-answer questions 4 4 16

Part C Situations involving

applications 6 10 60


BIM GRICS Page 4

CONCEPTS AND PROCESSES The concepts and processes listed in the table below represent the knowledge that will be evaluated by the questions in Parts A and B.

Question Field Concepts and Processes

1 Analytic

Geometry

Analyzing situations using analytic geometry • Geometric loci: Analyzes and models situations

using conics - circle, ellipse and hyperbola centered at the origin

2 Algebra Analyzing situations using real functions • Describes the properties of functions • The rational function

3 Geometry Relations, functions and inverses • Performs operations on functions (including

composition)

4 Arithmetic

Manipulates numerical expressions involving logarithms

Solves the following types of equations or inequalities in one variable: logarithms

5 Analytic Geometry

Standard unit circle • Analyzes and uses periodicity and symmetry to

determine the coordinates of points associated with significant angles in the standard unit circle

Part A

6 Algebra Vector in the Cartesian or Euclidian plane • Performs operations on vectors • Scalar product of two vectors

7 Geometry

Metric or trigonometric relations • Proves trigonometric identities by using algebraic

properties, definitions (sine cosine, tangent, cosecant, secant, cotangent), Pythagorean identities, and the properties of periodicity and symmetry

8 Algebra Analyzing situations using real functions • Finds the rule of a function or its inverse • Described the properties of real functions

9 Analytic Geometry

Geometric loci • Analyzes and models situations using conics

- finding the rule (standard form) of a conic

Part B

10 Algebra Analyzing situations using real functions

- finds the rule of the function • Exponential function


BIM GRICS Page 5

The table below outlines the concepts and processes that may be used in each task in Part C.

Title Field Concepts and Processes 11- Dog-

Walking

Arithmetic and Algebra

• Manipulates numerical expressions involving - absolute values

• Solves the following types of equations or an inequalities in one variable :absolute value

• Analyses situations using real functions - absolute value function

12- Piecing it

together!

Algebra

Analyzes situations using real functions - piecewise function - second-degree polynomial function - square root function - rational function - absolute value function

13- Terrific

Tides

Algebra

Analyzing situations using real functions • Sinusoidal function

o o

14- Sailing

through the Storm

Geometry

• Analyzes and models situations using vectors • Performs operations on vectors

- addition and subtraction of vectors - multiplication of a vector by a scalar

15- Treasure

Hunt

Analytic Geometry

Analyzing situations using analytic geometry • Geometric loci: determines the coordinates of points

of intersection between two conics (a parabola and a conic)

16- Animal

Hotel Algebra

Analysing situations using systems of equations or inequalities • Determines and translates a situation algebraically or

graphically using a system of inequalities • Solves a system

- of first degree inequalities in two-variables - involving various functional models - optimizes a situation by taking into account different

constraints and makes decisions with respect to this situation


BIM GRICS Page 6

GGENERAL ENERAL PPROCEDURE FOR THE ROCEDURE FOR THE EEVALUATION VALUATION SS ITUATIONITUATIONSS PREPARATION PHASE The week before the examination Ask the students to prepare a memory aid on one handwritten letter-sized sheet of paper

(8½” x 11”). Both sides of the sheet may be used. A typed or photocopied memory aid is not permitted.

PERFORMANCE PHASE Permitted materials Graph paper Geometry instruments (ruler, compass, protractor, set square) Calculator (with or without a graphic display) Handwritten memory aid The day of the examination Hand out copies of the examination booklets. Ask the students to go through their

documents, familiarizing themselves with all of the information and requirements. Make sure they know where they must write their names, answers, calculations and explanations.

Ask students to read the evaluation criteria used to evaluate the competency.

Describe the basic rules for the evaluation situations:

o Each student works alone.

o Students may use a calculator but are expected to indicate the sequence of operations involved as part of the justification for their solution.

o During the evaluation situation, the teacher may clarify the meaning of general vocabulary related to the context of the task.

Remind students that calculations and justifications will be taken into account when evaluating the competencies. The scorer must give a mark of 0 to students who fail to show their work or whose work does not justify their answer for Part C.

Remind students that in Parts A and B only the final answer will be evaluated.

CONTENT OF THE EXAMINATION

The questions in Parts A and B are intended to evaluate Mastery of Mathematical Concepts and Processes.

The Situations Involving Applications in Part C require the student to explain his/her mathematical reasoning and to organize and apply mathematical concepts and processes in a clearly defined context.


BIM GRICS Page 7

MMAARKINGRKING PPROCEDUREROCEDURE The questions in Parts A and B are graded using the marking key on page 8 of this

document. Each of these questions is worth 4 marks.

The situations involving applications in Part C are graded according to the evaluation criteria for the competency Uses mathematical reasoning. The five levels (A, B, C, D, E) in the rubric found in Appendix A make it possible to evaluate student work according to these criteria.

Examples of appropriate reasoning are given for the different situations. Each student’s reasoning may be different, yet still meet the requirements of the situation involving applications. The scorer must exercise his or her judgment and accept any other appropriate reasoning.

Additional information related to the specific requirements associated with the evaluation criteria is given for each situation involving applications and presented under the heading Marking Guidelines. Two types of information are provided:

• observable elements associated with appropriate reasoning;

• maximum level for different examples of student work; each student’s level could be lower for the criterion in question depending on the other aspects of his/her work.

When evaluating the competency Uses mathematical reasoning, the level achieved for criterion 3 is generally regarded as the maximum possible level for criteria 2, 4 and 5.

The Student Booklet presents a marking scale indicating the weighting to be used for each situation involving applications. Each situation involving applications is marked out of 100. An example of the marking scale is pictured below.

Uses mathematical reasoning

Observable indicators correspond to level

LEVEL A B C D E Cr. 3 40 32 24 16 8 0 Cr. 2 40 32 24 16 8 0

Eval

uatio

n C

riter

ia

Cr. 4 Cr. 5 20 16 12 8 4 0

This marking scale is provided as a suggestion.

The preliminary result in Part C is the sum of the results obtained for the situations involving applications. This result is expressed as a mark out of 600.

The scorer must give a mark of 0 to students who fail to show their work or whose work does not justify their answers in Part C.

The final result on Part C is calculated by dividing the preliminary result by 10 and rounding it off to the nearest unit. This final result is expressed as a mark out of 60.


BIM GRICS Page 8

MMARKING ARKING KKEYEY

PPARTSARTS A A ANDAND BB

Part A Questions 1 to 6 4 marks or 0 marks

1. C 4 0

2. B 4 0

3. A 4 0 4. D 4 0 5. D 4 0

6. C 4 0

Part B Questions 7 to 10 0 to 4 marks

7. sec x 4 0

Accept

8. a) The rule of the inverse of the function is

b) The domain of is

4 2 0

Give 2 marks for the correct rule in part a). Give 2 marks for the domain in part b).

9. The conic in standard form is

4 0

10. The rule of the function is

Give 2 marks for the correct a value. 4 2 0

Give 2 marks for the correct c value.


BIM GRICS Page 9

PPARTART CC

Basic Guidelines The situations involving applications in Part C are graded using a Rubric for Competency Two: Uses Mathematical Reasoning (Appendix A). The five performance levels in this rubric, which are presented as brief descriptions, make it possible to evaluate student work in accordance with the criteria indicated.

Examples of appropriate reasoning are given for each situation involving applications in the examination. The student’s reasoning may be different, yet still meet the requirements of the situations involving applications. The scorer must exercise his/her judgment and accept any other appropriate reasoning.

When students are asked to round off their final answer to a specific place value, do not penalize them if they rounded correctly but did not obtain the exact answer. For example if the answer is 3.2, accept 3.1 or 3.3 as equally valid answers, but do not accept 3.19 or 3.21.

The scorer must give a mark of zero to students who fail to show their work or whose work does not justify their answer.

Criterion 3 The grade obtained for criterion 3 is usually the maximum possible grade that can be obtained for the other criteria. A note specifying cases where this does not apply appears below the marking guidelines table.

Criterion 2 Students who make the same conceptual error more than once within a given line of reasoning are considered to have made just one conceptual error.

Criterion 4 and 5 Assign a grade for criterion 4 or for a combination of criteria 4 and 5 only after analyzing all the work the student has shown.

If students show only calculations with no indication of what they represent, then their work consists of confusing and isolated elements. In this case, assign no more than a grade of D for criterion 4, whether combined with criterion 5 or not.

Students whose work is clear and organized and contains only one minor mistake regarding the rules and conventions of mathematical language should be given the same grade for criterion 4 as they were given for criterion 3.

If students make a statement without indicating the property or definition they used to justify their claim, assign them no more than a grade of B for criterion 5, because their reasoning is incomplete.


BIM GRICS Page 10

11. Dog-Walking Example of an appropriate solution: Find the rule of the absolute value function:

From the question, (0, 1), (3, 6), (6.6, 10) are points on the absolute value function. Note: The coordinate (3, 6) is obtained from 1 client + 5 clients.

Find a:

a = and

when

when


BIM GRICS Page 11

Solve for (h, k) using a system of equations.

The vertex (h, k) is (6, 11).

The equation of the absolute value function is .

Plug in y = 8

7.8 - 4.2 = 3.6 weeks Answer: Paige’s dog-walking business had 8 or more clients for 3.6 weeks.


BIM GRICS Page 12

Marking Guidelines

Observable elements associated with appropriate reasoning

Dog-Walking

Maximum grade that can be assigned for different examples of partially correct work

The student…

B uses appropriate strategies to determine the solution of the inequality, graphically or algebraically, but his/her subsequent reasoning is inappropriate or he/she does not show any other steps in his/her reasoning.

C uses appropriate strategies to determine the rule of the absolute value function, but his/her subsequent reasoning is inappropriate or he/she does not show any other steps in his/her reasoning.

Cr. 3

takes the following into account: • the three points; • the slope; • the vertex; • the inequality.

D uses appropriate strategies to determine a system of equations, but his/her subsequent reasoning is inappropriate or he/she does not show any other steps in his/her reasoning.

B applies all concepts and processes, but makes minor calculation errors.

C applies most of the required concepts and processes, but makes one conceptual or procedural error (e.g. only taking into consideration part of the inequality).

Cr. 2

determines: • the points (0, 1) (3, 6) (6.6, 10);

• the two slopes

• equation 1:

• equation 2:

• vertex (6, 11);

• rule:

• when y = 8, x = 4.2 and x = 7.8; • the number of weeks she had 8 or

more clients (3.6).

D applies some of the required concepts and processes, but makes more than one conceptual or procedural error.

B shows work that is somewhat organized.

C shows work that is somewhat disorganized. Cr. 4 Cr. 5

• shows clear and organized work that justifies his/her results.

D shows work that is disorganized.


BIM GRICS Page 13

12. Piecing it together! Example of an appropriate solution:

Rational Function

⇒

Square Root Function

⇒


BIM GRICS Page 14

Quadratic Function

⇒

(21, 8) is the end of the quadratic functions and the beginning of the Absolute Value Function.

Absolute Value Function

⇒

Answer: Isidore catches Calvin in 25 seconds.


BIM GRICS Page 15

Marking Guidelines


Piecing it together!


The student…

B uses appropriate strategies to determine that the quadratic function ends at (21, 8), but his/her subsequent reasoning is inappropriate or he/she does not show any other steps in his/her reasoning.

C uses appropriate strategies to determine (h2, k2) = (15, -2), but his/her subsequent reasoning is inappropriate or he/she does not show any other steps in his/her reasoning. Cr. 3

takes the following into account: • there are four functions; • the domain of each part of the

piecewise function; • the end point of one part is the

starting point of the following part of the piecewise function.

uses appropriate strategies to determine: • coefficient p and solve for y when

x = 6; • coefficient q and solve for y when

x = 15; • coefficient r and solve for y when

x = 21; • coefficient s and solves for x when

y = 0; • point E.

D uses appropriate strategies to determine p = 16, but his/her subsequent reasoning is inappropriate or he/she does not show any other steps in his/her reasoning.


C applies most of the required concepts and processes, but makes one conceptual or procedural error.

Cr. 2

determines: • the value of p (16); • the coordinates of (h1, k1) = (6, 4); • the value of q (-2); • the coordinates of

(h2, k2) = (15, -2);

• the value of r ;

• the quadratic ends at (21, 8); • the value of s (-4); • the zero of the absolute value

function (25); • Isidore catches Calvin in

25 seconds.







BIM GRICS Page 16

13. Terrific Tides Example of an appropriate solution:

The equation: (see graph below)

Substitute and solve for t

or

Answer: The fisherman can be at sea between two consecutive low tides for 8 hours.


BIM GRICS Page 17

Marking Guidelines


Terrific Tides


The student…

B uses an appropriate strategy to determine the solution of the sinusoidal function with 1 incorrect parameter.

C uses an appropriate strategy to determine the rule of the sinusoidal function, but his/her subsequent reasoning is inappropriate or he/she does not show any other steps in his/her reasoning.

Cr. 3

takes the following into account: • the amplitude is half the difference

in the depths at high tide and low tide;

• the vertical displacement is calculated from the depth at low tide;

• the time from low to high tide is 6 hours;

• the depth of the water varies according to a sinusoidal function;

• the parameters for the sinusoidal function;

• the time when the depth is at 5 m between consecutive low tides.

D uses appropriate strategies to determine some of the parameters of the function, but his/her subsequent reasoning is inappropriate or he/she does not show any other steps in his/her reasoning.


C applies most of the required concepts and processes, but makes one conceptual or procedural error (e.g. uses an inappropriate trigonometric ratio).

Cr. 2

determines: • amplitude (6); • period (12); • vertical displacement (8 m); • phase shift:

o Cosine: 0, o Sine: 3;

• parameter b:

• sinusoidal function:

• the fisherman can be at sea

between two consecutive low tides for 8 hours.







BIM GRICS Page 18

14. Sailing through the Storm Example of an appropriate solution: Components of

= (116 – 62, 269 – 43) = (54, 226)

Linear Combination

can be expressed as a linear combination of vectors p and q. a and b = {a and b represent scalars a(3, 4) + b(–8, 15) = (54, 226) (3a, 4a) + (–8b, 15b) = (54, 226) (3a – 8b, 4a + 15b) = (54, 226)

Value of Scalars a and b

We can therefore deduce the system of equations below and use it to determine the value of scalars a and b.

3a – 8b = 54 12a – 32b = 216 4a + 15b = 226 –12a + 45b = 678 –77b = –462

b = 6 Thus: 3a – 8(6) = 54 3a – 48 = 54 3a = 102 a = 34

Lengths of the captain’s planned route and usual path

Length of sailing path : 34 = 34 = 34 (5) = 170 km

Length of sailing path : 6 = 6 = 6 (17) = 102 km

Length of usual path : = 232.36 km Difference in distances: (170 km + 102 km) – (232.36 km) = 39.64 km

Answer: The difference in the distances between the usual path and the redirected path is

39.64 km.


BIM GRICS Page 19

Marking Guidelines


Sailing through the Storm


The student…

B uses appropriate strategies to determine the value of scalars a and b, but his/her subsequent reasoning is inappropriate or he/she does not show any other steps in his/her reasoning.

C uses appropriate strategies to find the linear combination of vectors p and q, but his/her subsequent reasoning is inappropriate or he/she does not show any other steps in his/her reasoning.

Cr. 3

takes the following into account: • the captain’s planned route

between ports A and B • the sailing paths are defined by

= (3, 4) and = ( 8, 15) recognizes the need for a linear combination uses appropriate strategies to determine: • the length of the usual path • the length of the planned route

using a linear combination of vectors

D uses appropriate strategies to determine the components of or to find the norms of vectors p and q but his/her subsequent reasoning is inappropriate or he/she does not show any other steps in his/her reasoning.


C applies most of the required concepts and processes, but makes one conceptual or procedural error (i.e. makes a mistake in solving the system of equations)

Cr. 2

determines: • the components of

( = (54, 226); • the linear combination of vectors p

and q ((3a – 8b, 4a + 15b) = (54, 226));

• the value of scalars a and b (a = 34 and b = 6)

• the length of the planned route (272 km)

• the length of the usual path (232.36 km)

• the difference in the distances of the paths (39.36 km)







BIM GRICS Page 20

15. Treasure Hunt Example of an appropriate solution:

Find the value of parameter c of the parabola: 2.25 − 2 = 0.25

c = 0.25

Using the definition of a parabola find its rule:

(0, 2)

Fence

F (?, ?)

y = 2.25


BIM GRICS Page 21

Find the point(s) of intersection of the parabola and the ellipse by substitution:

Quadratic formula:

y1 = , y2 =

y1 = −7, y2 = 14

Factoring: (y − 14) (y + 7) = 0 y = 14 and y = −7

Reject y = 14 as it is not on the parabola.

Substitute y = −7 into the ellipse

7x2 + 49 = 112 7x2 = 63

x = ± 3 Reject x = −3, as it is on the wrong side of the vertex. Coordinates of the fountain are (3, −7)

Answer: The exact coordinates of the fountain are (3, −7).


BIM GRICS Page 22

Marking Guidelines


Treasure Hunt


The student…

B uses appropriate strategies to solve the system of equations, but his/her subsequent reasoning is inappropriate or he/she does not show any other steps in his/her reasoning.

C uses appropriate strategies to set up the system of equations, but his/her subsequent reasoning is inappropriate or he/she does not show any other steps in his/her reasoning. Cr. 3

takes the following into account: • the vertex of the parabola; • the distance from the vertex to the

directrix; • the equation of the parabola; uses appropriate strategies to determine: • the values for c of the parabola; • the equation of the parabola; • the solution of the system of

equations; • the two possible y-coordinates; • the correct y-coordinate; • the correct x-coordinate by

plugging the y-coordinate into either ellipse or parabola equation.

D uses appropriate strategies to determine the equation of the parabola, but his/her subsequent reasoning is inappropriate or he/she does not show any other steps in his/her reasoning.


C applies most of the required concepts and processes, but makes one conceptual or procedural error (e.g. choosing y =14 over y = -7)

Cr. 2

determines: • the value for c of the parabola

(0.25); • the equation for the parabola

(x2 = -(y − 2)); • The points of intersection (y = 14,

y = -7) • the correct y-coordinate (-7); • the correct x-coordinate (3); • coordinates of the fountain (3, -7);

D applies some of the required concepts and processes, but makes more than one conceptual or procedural error. (e.g. uses an inappropriate formula for the parabola)






BIM GRICS Page 23

16. Animal Hotel Example of an appropriate solution: Inequalities

A minimum of 7 cats: x ≥ 7 A maximum of 13 dogs: y ≤ 13 More than 17 animals at the hotel: x + y > 17 (or x + y ≥ 18) Five times the number of dogs added to twice the number of cats is at most 81: 2x + 5y ≤ 81 There are at least 27 less than three times the number of dogs than cats: y ≥ 3x − 27

Graphing Inequalities

x

y

Number of Cats and Dogs at the Hotel

Num

ber o

f Dog

s at

the

Hot

el

Number of Cats at the Hotel

C (8, 13) (7, 13) B

A

D

E (11, 6)

(7, 10)

(12, 11) P

R (10, 12)

Q (10, 9)

scanning line


BIM GRICS Page 24

Profit Rule The animal hotel charges $100 a week for a cat and $200 a week for a dog.

Revenue = 100x + 200y

The care for a cat is $12 and the care for a dog is $24.

Cost = 12x + 24y

Profit = Revenue − Cost Profit = 100x + 200y − (12x + 24y) Profit = 100x + 200y − 12x − 24y Profit = 88x + 176y

If using a scanning line, the slope of the scanning line is , or

Determine Profit

Vertices Profit = 88x + 176y

A (7, 10) $2376 B (7, 13) $2904 C (8, 13) $2992 ← maximum

D $3074.82 ← not a possible solution as

vertices are not whole numbers

E (11, 6) $1144

Other points of interest

Vertices Profit = 88x + 176y P (12, 11) $2992 ← maximum Q (10, 9) $2464 R (10, 12) $2992 ← maximum

C(8, 13), P(12, 11), R(10, 12) and are all possible maximums. Answer: The possible combinations for the number of cats and dogs that stayed at

Meowoof this week are (8, 13), (12, 11) and (10, 12).


BIM GRICS Page 25

Marking Guidelines


Animal Hotel


The student…

B uses appropriate strategies to recognize the optimum solution of the vertex of the polygon of constraints, but his/her subsequent reasoning is inappropriate or he/she does not show any other steps in his/her reasoning.

C uses appropriate strategies to determine the polygon of constraints, but his/her subsequent reasoning is inappropriate or he/she does not show any other steps in his/her reasoning. Cr. 3

takes the following into account: • the five constraints; • the vertices of the polygon of

constraints; • the values of x and y must be

whole numbers; • the associated revenue; • the associated costs; • the function to be optimized; uses appropriate strategies to determine: • the five inequalities; • the polygon of constraints; • the profit rule; • the profit at points of interest; • the maximum profit; • all possible combinations that

maximize the profit.

D uses appropriate strategies to determine the inequalities, but his/her subsequent reasoning is inappropriate or he/she does not show any other steps in his/her reasoning.

B applies all concepts and processes, but makes minor calculation errors (e.g. does not list all three solutions).

C applies most of the required concepts and processes, but makes one conceptual or procedural error (e.g. does not graph an inequality correctly, or uses all the vertices of the polygon of constraints even though some are not valid).

Cr. 2

determines: • constraints

x ≥ 7 2x + 5y ≤ 81 y ≤ 13 y ≥ 3x − 27 x + y > 17

• some points of interest; • the profit rule (P = 88x + 176y); • the maximum profit is $2992; • that (8, 13), (10, 12) & (12, 11) will

maximize the profit. D applies some of the required concepts and processes, but makes more than one conceptual or procedural error.





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Mathematics Secondary V - SecV chemistrysciencehip.weebly.com/uploads/4/8/6/3/48637575/... · Mathematics Secondary V Science Option THOSE WHO RECEIVE A COPY OF THIS EXAMINATION HAVE