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AVRSB Math 10 Examination January 2013

ANNAPOLIS VALLEY REGIONAL SCHOOL BOARD

To Be Completed by Student

To Be Completed by Teacher

School: ___________________________

Student: ___________________________

Adaptations:

Mathematics 10

Examination

January 2013


Instructions for Selected Response Questions

1. There are 20 multiple choice questions for this part of the exam. Each question is worth 1.5 points for a total of 30 points.

2. Consider the four choices for each question, select the best one. Then fill in the bubble that has the letter that you think is the best answer.

3. Remember you may use the formula sheet, calculator reminder sheet, TI-83 or TI-84 calculator, and algebra tiles.

4. You may mark on the diagrams and questions in the booklet, and use any available space as scrap paper.

5. You should spend about 30 minutes on this part of the exam. Remember each question is worth 1.5 points, so do not spend too much time on any one question. You can always come back and try it later when you finish the rest of the exam.

Instructions for Constructed Response Questions

1. There are 13 questions for a total of 63 points.

2. You must show all your work. Part values may be given for any correct work shown.

3. If you use a graphical solution make sure you draw both your graph and the point(s) used to answer the question.

4. You may use the formula sheet/grid paper, calculator reminder sheet, TI-83 or TI-84

graphing calculator, algebra tiles, and ruler.

5. If you use a formula, write the formula, and show all of the substitutions you make before working out your answer using the calculator to find the answer.

6. When needed, your answers to numerical computations should be rounded to at least the

nearest hundredth, such as 123.16 m.

7. When units are presented in a question then your final answers should include the units, where appropriate, such as 16.72 cm.

8. Diagrams are not drawn to scale.

9. For scrap paper, use any available space on the question booklet.


Selected Response Questions

1. Four different crates of apples were packed. The diameters of the apples, in cm, were measured for each crate. The following data was obtained. Which crate holds the apples having the most consistent size? Crate A Crate B Crate C Crate D

A. Crate A B. Crate B C. Crate C D. Crate D

2. The following scatter plot compares calories and sodium content of several brands of hot dogs. The linear regression line has been drawn. The correlation between the calories and the sodium content of these hot dogs would be best described as:

A. Scattered correlation.

B. Negative correlation.

C. Positive correlation.

D. No correlation.

3. The time for a 2 km run for students in grade 10 is known to possess a normal distribution with a mean of 500 seconds and a standard deviation of 60 seconds. Between what times do we expect approximately 95% of the students to run this course?

A. between 440 and 560 seconds B. between 380 and 620 seconds

C. between 320 and 680 seconds D. between 60 and 500 seconds


4. The box and whisker shown below represents the number of hours spent on Facebook in

a week by students who are members of a school club. Which statement do we know is true?

A. More club members spend 10 – 14 hours than spend

21 – 22 hours on Facebook each week. B. This data is normally distributed. C. Half of the club members spend between 14 and 21

hours on Facebook each week. D. 68% of the club members spend between 14 and 21

hours on the internet each week.

5. The Environmental club is selling t-shirts to raise funds to dig a well in a third world country. The supplier charges a fee of $40 for each order and $6 for each t-shirt in the order. Which equation could be solved to determine the number of t-shirts, n, that the environomental club can order if they have $1246 to work with.

A. 40 + 6n = 1246 B. 46n = 1246 C. 6n – 40 = 1246 D. 6 + 40n = 1246

6. Susan is paying her nephew to paint a fence. The cost of the project is represented by the graph shown below.

Which equation describes the cost, C, in terms of the number of hours, h, to paint the fence.

A. C = 8h + 40 B. C = 8h+ 56

C. C = 0.125h + 40 D. C = – 8h + 96

10 14 18 21 22


7. Which of the following sets of data could best be described as linear with a negative

slope?

A. B. C. D.

x 2 3 4 5 x 5 4 3 2 x 2 3 4 5 x 5 4 3 2

y 11 9 7 9 y 11 9 7 5 y 5 6 7 8 y 5 7 9 11

8. Which of the following graphs represents the equation 2� � 3� � 12 ?

A. B.

C. D.

9. What is the solution for the system of linear equations represented by the graph shown to the right:

A. � � 4, � � 3

B. � � 3, � � 4

C. � � 2, � � �1

D. � � �1, � � 2

10. Solving the equation: )3(8)24(5 −=−− xx results in x having a value of:

A. The value of x is �2. B. The value of x is 28 .

C. The value of x is �� . D. The value of x is 2 .


11. Which region is described by: �� 2� � 10� � 4� � 2� � 0 �

A. B.

C. D.

12. If �� 9� � 4 determine the value ��5�. A. 1 B. 45� � 4

C. 45� � 20 D. 41

13. What is the equation of the quadratic shown to the right?

A.�� 3� � �� 1��

B. �� 3� � �� 1�� C. �� 1� � �� 3�� D. �� 1� � �� 3��

14. What are the domain and the range of the graph shown to the right?

A. � � � ; � � 1 B. � � � ; � � 3 C. � � 1 ; � � � D. � � � ; � � 3


15. Factor: 9 � 4��.

A. (3x – 2)(3x + 2) B. ( 2x + 3)(2x – 3)

C. (3x – 2)(3x – 2) D. (3 – 2x)(3 + 2x )

16. Using the following diagram, what is the measure of angle C?

A. 2.99° B. 32.66°

C. 39.87° D. 50.13°

17. The angle of elevation to the top of a flag pole measures 48.2° from a point on the ground 5.4 metres away from its base. What is the height of the flagpole?

A. 3.60 m B. 4.03 m

C. 4.83 m D. 6.04 m

18. The length of the shadow cast by a tree 6.5 m tall is 8.2 m. What is the length of the shadow cast by a tree that is 2.1 m tall?

12.5m

A. 2.65 m B. 3.80 m

C. 5.42 m D. 26.31 m

19. Susan decides to try a new dessert for a childrens’ party. She fills a standard sized ice cream cone with pudding (level to the top of the cone). If the cone is 15 cm high with a diameter of 8 cm at the top. How much pudding will fit in each cone?

A. 60.00 cm3 B. 251.33 cm3

C. 753.98 cm3 D. 1005.31 cm3

20. A square based prism is stretched so all of its dimensions are doubled. How does the volume of the resulting prism compare to that of the original square based prism, V?

A. It is 2V. B. It is 4V. . C. It is 8V. D. Can’t be determined.

B

A C

2.5

3.9


Constructed Response Questions

21. Two factories produce television sets using two different processes. Assume that the life time of these television sets is normally distributed.

• The sets produced by Factory A have a mean life of 86 months with a standard deviation of 8 months.

• The sets produced by Factory B have a mean life of 75 months with a standard deviation of 6 months.

a) Clearly indicate, by shading, on the normal curve shown below the region that

represents the percentage of television sets produced by Factory A that will be expected to last more than 94 months. Determine this percentage. (3 points)

b) The factories promise that they will replace any television sets that last less than 65 months. Which factory, A or B, minimizes the percentage of televisions that they will likely need to replace? Explain your thinking. (3 points)


22. The student enrolment in three different community colleges has been recorded between the

years of 2000 and 2012. Rae has decided to do a linear regression on all three sets of data.

Using the graphing calculator Rae determined the following three r values.

College A: r = 0.576

College B: r = 0.727

College C: r = – 0.895

a) Which model would best be described by a linear model? Explain your reasoning.

(2 points)

b) If you use the model to determine the student enrolment at this community school in 2007

is it interpolation or extrapolation? Explain your choice. (2 points)


23. Ayla conducted a science experiment where she poured different amounts of liquid into a cylinder and then measured the mass of the cylinder and liquid. Here is her data:

Amount of

Liquid

(mL)

Mass of

Cylinder and

Liquid

(g)

10 35

15 50

20 65

a) Plot these points in the space provided. Explain why you chose to join these points. (2 points)

b) When these data points are plotted and joined, i) what is the slope of the resulting line and what does it represent? (include units)

(2.5 points)

ii) what is the y-intercept of the resulting line and what does it represent? (include units) (2.5 points)

c) Using an equation, determine the amount of the liquid, in mL, when the mass of the cylinder and liquid is 68 g. (3 points)


24. The perimeter of the triangle shown below is 30cm.

a) Develop and solve an equation to find the value of x. (3 points)

b) Is this triangle a right triangle? Explain your reasoning. (3 points)

x + 4 3(3+x)

5x+8


25. Two companies charge the following rates for printing a brochure.

• Company A charges $175 for set up and 10 cents per brochure.

• Company B charges $250 for set up and 7 cents per brochure.

Determine the number of brochures which would result in the same cost for both Companies. (4 points)


26. Your school is planning to make hats and scarves to sell at the winter festival as a fundraiser. The textile class divides into two groups – one group can make hats, the other group knows how to make scarves. The graph, shown below, has been constructed with the appropriate constraints.

a) Because the material is being donated by community members, each hat sold makes a profit of $5 and each scarf sold makes a profit of $4. Write the profit equation that could be used to determine the number of each type of item that this company should produce each week in order to maximize their profit. (1 point)

b) Determine the number of hats and scarves that should be produced in order to maximize their weekly profit. (3 points)

# hats produced

# s

carv

es p

rod

uce

d


27. Solve for x using any method. (3 points)

2x2 + x – 3 = 0

28. For the following equation: – 2 (y – 3) = (x + 1)2

a) State the transformation. (2 points)

b) Draw the graph on the grid provided. Clearly label, using coordinates, the vertex and two other points. (3 points)


height

Sloped ceiling

29. A bookcase is built under the sloping ceiling of an attic (as pictured below). The bottom of the bookcase is 350 cm long. The angle that the sloped ceiling makes with the floor is 40°.

If you wish to have a shelf be 30 cm above the bottom of the bookcase, how long will that shelf be? (5 points)

40°

350 cm Bottom of bookcase


30. Ralph walks 10 km at a bearing of 45° and then turns and walks 6 km at a bearing of 135°. Draw a picture illustrating Ralph’s walk. Clearly label the diagram with the given information. Calculate how far Ralph is from where he began his walk. (3 points)


A

B E

C D

31. The area of ∆ACD is double the area of square BCDE.

∆ACD is an isosceles triangle.If the side length of the square is 12 cm, determine the perimeter of ∆ACD. (5 points)

Diagram not to scale


Height of silo

32. The silo shown below is made up of a cylinder topped by a half sphere. The diameter of the silo is 3m and it has a total volume of 91.89 m3.

Determine the height of the silo. (5 points)

The volume of a sphere can be calculated

using the formula: � � � !" .


33. Given that both the equilateral triangle and the square shown below have a perimeter of 12 cm, which one contains the greater area? Explain your reasoning. (3 points)

mathematics 10 examination january 2013jameswisemanwestkings.weebly.com/uploads/3/2/0/1/... ·...

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