MATHEMATICS DEPARTMENT

JUNE 2001

EXAMINATION

COURSE: Grade 9 Academic Mathematics	NAME:

COURSE CODE:	MPM1D	TEACHERS:	M. Abi-Zeid

J. Battye

DATE:	Tuesday, June 19, 2001	R. Bergamin

K. Dion

TIME:	9:00 a.m. to 10:30 a.m.	J. Watson

No. of Pages in Exam:	11

OUTSIDE MATERIALS NEEDED:

Non-programmable non-graphing calculator, straight edge, eraser, pencil, pen.

INSTRUCTIONS

1.	After this covering page, there are 10 pages to this examination. Please be sure that you have a complete paper before you begin the examination.

2.	Write a complete solution for each question in the space provided on the examination paper.

3.	You should expect to give more than a simple answer for each question. Your teacher will look to see how much relevant mathematics you have been able to show for each question posed.

4.	You may ask for help only to clarify instructions. You may not ask how to do a particular question.

FOR DEPARTMENTAL USE

Part A	/ 21	Knowledge	/25
Part B	/ 29	Thinking, Inquiry, Problem Solving	/21
Part C	/ 24	Communication	level
Part D	/ 6	Application	/34

FINAL MARK

TOTAL EXAM SCORE	%

PART A:	NUMBER SENSE and ALGEBRA

[Questions 1, 2 & 3 will be assessed for Knowledge, K]

1.	Simplify.

(a)	(b)

(c)	(d)

2.	Evaluate, without using a calculator.

(a)	(b)

3.	Simplify by collecting like terms, then factor.

(a)

(b)	Evaluate the simplified expression found in part (a) when .

K:	/12

[Questions 4 & 5 will be assessed for TIPS, and Communication, C]

4.	(a)	Make up one question using laws of exponents, where your answer is equal to 1. Your question must have a minimum of 2 steps.

(b)	Show the answer by solving your own question.

5.	At Compumart, a computer is regularly priced at $1299.00. It is on sale for 20% off the regular price. At Nextshop, the same computer is regularly priced at $1549.00. It is on sale for 30% off the regular price. Explain why Mr. Watson should buy his computer at Compumart.

TIPS:	/5

C: level

[Question 6 will be assessed for Knowledge, K]

6.	Nina was asked to solve the following equation: . Because she was in a hurry, she made some mistakes. Identify her mistakes by circling them, and provide a correct solution.

Wrong Solution	Correct Solution

K:	/4

PART B:	RELATIONSHIPS

[Question 1 will be assessed for Knowledge, K]

1.	Using the graph to the right, fill in the blanks.

(a)	A quadrant with no point in it is .

(b)	The x-intercept of line segment CD is .

(c)	The distance between A and B is units.

(d)	The slope of line segment CD is .

K:	/4
[Questions 2 & 3 will be assessed for TIPS]

2.	Students are allowed into the school at 8:00 AM. Classes start at 9:00 AM. There are 15-min breaks that begin at 10:30 AM and 2:30 PM. Lunch is from 12:00 to 1:00 PM. School is dismissed at 4:00 PM. Students must leave the building by 5:00 PM. Students are allowed to use the pop machine in the school cafeteria before and after school and during their breaks and lunch hour. The machine is filled twice a day, at 7:00 AM and 2:00 PM. Sketch a graph of the number of cans in the machine versus time on a hot Monday in June.

[Exact number of cans is not important.]

3.	(a)	Based on the following graphing calculator screen and table of values, is this a linear or non-linear relation? Explain your reasoning.

x	?
1	3
2	6
3	11
4	18
5	27
6	38

(b)	State the equation for this relation. (This would be the heading for the second column in the table of values.) Justify your answer.

(i)	y = x

(ii)	y = x2 + 2

(iii)	y = 2x

(iv)	y = x + 2

(v)	y = x3 +2

TIPS:	/7

[Question 4 will be assessed for Application, A, and Communication, C]

4.	For the tree planting, all of the students in Environmental Studies brought along water because the day was warm and the work quite strenuous. One student had a sealed plastic bottle filled with water. A leak opened in the bottle and the water drained out.

Time

(sec.)	Height of water in bottle

(cm)
0	24
10	22
20	19
30	16
40	14
50	12
60	8
70	6
80	4

(a)	What type of relation or correlation is shown? Explain.

(b)	Is the line of best fit that is shown a good one? Explain.

(c)	Determine two points on the line of best fit.

(d)	What is the slope of the line of best fit? What does it mean in this context?

(e)	Determine the equation of the line of best fit.

(f)	What would be the exact height of water after 1 minute? Show your work.

(g)	What would be the approximate height of water after 4 seconds? Explain your method.

(h)	When will the water bottle be completely empty? Justify your answer.

(i)	What is the y-intercept of the line of best fit? Explain its significance in this context.

A:	/18

C:	Level

PART C:	ANALYTIC GEOMETRY

[Questions 1 & 2 will be assessed for Knowledge, K, and Communication, C]

1.	Today, Miss Abi-Zeid is showing her grade 9 math class some magic tricks. To test her out, one of her students, Cullan, says to her: "I'm thinking of a number. If you subtract 6 from the number and divide the result by 3, you get 15. What number am I thinking of?' Miss Abi-Zeid giggles, and confidently says: "Well, the answer is 51. That was really easy!!!".

Show how she got this answer by creating an equation to model the problem, and then solving it.

2.	Determine the equation of the line with x-intercept 4 and y-intercept −8.

K:	/5

C:	Level

[Questions 3 & 4 will be assessed for TIPS, and Communication, C]

3.	An air traffic controller is plotting the course of two jets scheduled to land in about 15 minutes. Let x represent the time in minutes, and let y represent the altitude in metres. One aircraft is following a path defined by the equation and the other by the equation . Should the controller alter the paths of either aircraft?

4.	Ms. Dion needs to rent a car for the weekend. This screen shot of a TI83+ calculator shows the number of kilometres driven of a car rental in L1, the cost in $ to rent from Avis in L2, and the cost in $ to rent from Budget in L3. The car is identical from the two rental companies.

Four statements follow. For each one, accept it as true or reject it as false, and justify your choice.

Statement	True or False	Justification
(a)	Using the data, Budget charges customers 30¢ per kilometre driven.

(b)	If she rents a car from Avis, she will pay a fixed rate of $20 and 18¢ per kilometre.

(c)	Using the data, it is always cheaper to rent from Budget.

(d)	If she drives 120 km with the rental car, both companies will charge the same amount of money.

[Question 5 will be assessed for Application, A, and Communication, C]

5.	Ryan listens to music all the time. He usually downloads songs from two websites: Kazaa and Napster. The total costs for the music downloads are listed in the chart below.

Price per song	Price of Software
Kazaa	50¢	Free
Napster	20% less than Kazaa	$5.00

(a)	Complete the chart.

Number of songs downloaded	Total Cost at Kazaa	Total Cost at Napster
10	$5.00	$9.00
20
30
40
50
60
70

(b)	Graph both relations on the grid provided.

(c)	Write an equation for the total costs at Kazaa and at Napster.

Kazaa:

Napster:

(d)	At what point does the cost of downloading songs from Kazaa equal the cost of downloading songs at Napster? Explain how you determined the answer.

(e)	Ryan earned $63.00. He decided to download some new songs from Napster. How many songs can he download using as much of his $63.00 as possible? Show your work.

A:	/10

C:	Level

PART D:	MEASUREMENT & GEOMETRY

[Questions selected will be assessed for Application, A, and Communication, C]

THIS SECTION IS WORTH 6 POINTS. ANSWER ANY 2 OR 3 QUESTIONS OF YOUR CHOICE. THE TOTAL MARKS FOR THE QUESTIONS ANSWERED MUST EQUAL 6 POINTS!

1.	Sam is an excellent basketball player. Whenever she throws the ball, she scores. Using the graph below, determine the maximum height reached by the ball and the time when this height is reached. Show your work.

2.	Line 1 and Line 2 are not parallel. Explain how you know this.

Line 1

Line 2

3.	Mr. Battye assigned to his class the following question.

"If a basketball has a volume of 2618 cm3, find the radius of the ball."

Adrien's answer was 28.9 cm.

Explain why Adrien's answer is incorrect. What did he do wrong?

4.	An inflated balloon has a radius of 12 cm. When the radius increases by 25% and more air is added, then the volume of the balloon will also increase by 25%. Is this true? Justify your reasoning.

5.	Given the following diagram, solve for the values of x, y, z, and w.

A:	/6

C:	Level

Please hand in the entire examination paper.

The Mathematics Department

FORMULA SHEET