Name: Teacher: School: Contents:

Name: Teacher: School: Contents: Key Words... 1 Tools and Strategies... 2 Open Response Rubric... 3 EQAO Formula Sheet... 5 Sample Questions from the 2014 Assessment... 7 Sample Questions from the 2013 Assessment... 29 Sample Questions from the 2012 Assessment... 49 2014-2015

Key Words Throughout the assessment, key words are used to identify the type of response required from you. The Key words are explained below. Refer to this sheet to make sure you are responding fully to each question. Compare: Tell what is the same and what is different. Describe: Use words to create a mental picture for the reader. Determine: Use mathematics to find a solution to the problem. List: Use point form. Explain: Use words and symbols to make your solution clear. Justify: Give reasons and evidence to show your answer is correct. Show your work: Record all calculations and all the steps you went through to get your answer. You may use words, numbers, graphs, diagrams, symbols and/or charts. DPCDSB 1

Tools you should have access to: Pencil, ruler and eraser Scientific or Graphing calculator (You may not share with another student ) Manipulatives ( examples: fraction pieces, algebra tiles, linking cubes, integer counters, 3D solids, 2D shapes ) Strategies for Multiple Choice Questions: 1. Cover the question choices and read the question stem carefully and highlight key words with a highlighter, especially the key words on the previous page. 2. Look at the choices and eliminate any of the responses that are not possible. 3. There is only one answer per question. Choose the best possible answer and shade your choice on the answer sheet. 4. Answer every question; there are no penalties for guessing. 5. Questions that have a graph are drawn to scale. Questions that have a diagram are usually not drawn to scale. Strategies for Open Response Questions: 1. These questions are asking you to show what you know and what you can do. Complete solutions including any rough work are expected for these quest ions. Give as much information as you can. 2. Read the quest ion carefully and highlight any key words or information with a highlighter. 3. Write your solution in the space provided. Try to give a clear well organized solution to illustrate your complete understanding and ability to communicate. Write your solutions so they can be understood by someone who does not know your work. 4. Don t erase any of your calculations, drawing or reasoning. Scorers want to see all your work. 5. Use the list of key words on the previous page to help you decide what is expected in your answer. For example, show your work means, record all calculations and all the steps you went through to get your answer. You may use words, numbers, graphs, diagrams, symbols and/or charts. 6. The problems in these questions often have more than one way of being solved. Be sure to clearly explain your solution using graphs, tables, pictures numbers or words. 7. When using a calculator, write down all the numbers you use and the operations you carry out. For example to find the area of a circle with diameter 7cm you need to write 3.5 38.485. DPCDSB 2

Open Response Rubric Code B I 10 20 30 40 Descriptor blank: nothing written or drawn in response to the question illegible: cannot be read; completely crossed out/erased; not written in English irrelevant content: does not attempt assigned question (e.g., comment on the task, drawings,?,!, I don t know ) off topic: no relationship of written work to the question demonstration of limited understanding of concepts and/or procedures application of knowledge and skills shows limited effectiveness due to o misunderstanding of concepts o incorrect selection or misuse of procedures problem solving process shows limited effectiveness due to o minimal evidence of a solution process o limited identification of important elements of the problem o too much emphasis on unimportant elements of the problem o no conclusions presented o conclusion presented without supporting evidence demonstration of some understanding of concepts and/or procedures application of knowledge and skills shows some effectiveness due to o partial understanding of the concepts o errors and/or omissions in the application of the procedures problem solving process shows some effectiveness due to o an incomplete solution process o identification of some of the important elements of the problem o some understanding of the relationships between important elements of the problem o simple conclusions with little supporting evidence demonstration of considerable understanding of concepts and/or procedures application of knowledge and skills shows considerable effectiveness due to o an understanding of most of the concepts o minor errors and/or omissions in the application of the procedures problem solving process shows considerable effectiveness due to o a solution process that is nearly complete o identification of most of the important elements of the problem o a considerable understanding of the relationships between important elements of the problem o appropriate conclusions with supporting evidence demonstration of thorough understanding of concepts and/or procedures application of knowledge and skills shows a high degree of effectiveness due to o a thorough understanding of the concepts o an accurate application of the procedures (any minor errors and/or omissions do not detract from the demonstration of a thorough understanding) problem solving process shows a high degree of effectiveness due to o a complete solution process o identification of all important elements of the problem o a thorough understanding of the relationships between all of the important elements of the problem o appropriate conclusions with thorough and insightful supporting evidence DPCDSB 3

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Formula Sheet Grade 9 Academic Geometric Figure Perimeter Area Rectangle l w P = l + l + w + w or P = 2(l + w) A = lw Parallelogram P = b + b + c + c A = bh h b c or P = 2(b + c) Triangle a h c P = a + b + c bh A = 2 or b A = 1 2 bh Trapezoid c a h b d P = a + b + c + d (a + b)h A = 2 or A = 1 2 (a + b)h Circle r C = πd or A = πr 2 d C = 2πr Ffla2_9e_0113 DPCDSB 5

Geometric Figure Surface Area Volume Cylinder r h A base = πr 2 A lateral surface = 2πrh A total = 2A base + A lateral surface = 2πr 2 + 2πrh V = (A base )(height) V = πr 2 h Sphere r A = 4πr 2 4 V = 3 πr 3 or V = 4πr 3 3 Cone h r s A lateral surface = πrs A base = πr 2 A total = A lateral surface + A base A total = πrs + πr 2 V = (A base)(height) 3 V = 1 3 πr 2 h or V = πr 2 h 3 Squarebased pyramid b h s b A triangle = A base = b 2 1 2 bs A total = 4A triangle + A base A total = 2bs + b 2 V = (A base)(height) 3 V = 1 3 b 2 h or V = b 2 h 3 Rectangular prism A = 2(wh + lw + lh) V = (A base )(height) h l w V = lwh Triangular prism c a h l b A base = 1 2 bl A rectangles = ah + bh + ch A total = A rectangles + 2A base A total = ah + bh + ch + bl V = (A base )(height) V = 1 2 blh or V = blh 2 DPCDSB 6 Ffla2_9e_0113

Grade 9 Assessment of Mathematics 2014 Released Assessment Questions: Academic Student Answer Sheet Your multiple-choice answers must be entered on this sheet. To indicate your answer, use a pencil to fill in the circle completely. Like this: Not like this: Do not fill in more than one answer to a question. Do not leave a question blank. Cleanly erase any answer you wish to change and fill in the circle for your new answer. 1. a b c d 9. a b c d 17. a b c d 25. a b c d 2. a b c d 10. a b c d 18. a b c d 26. a b c d 3. a b c d 11. a b c d 19. a b c d 27. a b c d 4. a b c d 12. a b c d 20. a b c d 28. a b c d 5. a b c d 13. Respond in booklet. 21. a b c d 29. a b c d 6. Respond in booklet. 14. Respond in booklet. 22. Respond in booklet. 30. Respond in booklet. 7. a b c d 15. a b c d 23. Respond in booklet. 31. Respond in booklet. 8. a b c d 16. a b c d 24. a b c d End of Assessment Print Student Name: Student Signature: Student Answer Sheet Released Assessment Questions DPCDSB 7

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Academic Grade 9 Assessment of Mathematics 2014 RELEASED ASSESSMENT QUESTIONS Record your answers to the multiple-choice questions on the Student Answer Sheet (2014, Academic). Please note: The format of this booklet is different from that used for the assessment. The questions themselves remain the same. DPCDSB 9

Multiple-Choice Grade 9 Assessment of Mathematics, 2014 The following is the formula for the area of a circle: A = πr 2 If the radius of a circle is 1.25 cm, which of the following is closest to its area? a 15.4 cm 2 b 7.9 cm 2 c 4.9 cm 2 d 3.9 cm 2 Marc has a garden that is made up of three square sections. He builds a fence on one side of the garden as shown below. M A T R I X l Area = 11.56 m 2 Area = 6.76 m 2 What goes in the to complete the equation below? a 3x 9 b 3x 4 c 16x 9 d 16x 4 (8x 3 )( ) 24x 12 A cellphone company offers four choices for purchasing talk time. Which of the following has the lowest cost per minute? a 200 minutes for $24.50 b 550 minutes for $68.00 c 700 minutes for $80.25 d 850 minutes for $99.50 Area = 21.16 m 2 Which of the following is closest to the length of the fence, l? a b c d 19.7 m 10.6 m 9.9 m 6.3 m What is the value of x in the equation a 4 b 35 8 4(2x 1) = 36? c 37 8 d 5 DPCDSB 10 2 Academic

Grade 9 Assessment of Mathematics, 2014 Open-Response Share the Profits Three partners, Luc, Deborah and Melanie, share the profits of a business in the ratio 2:3:7 respectively. The profit for this year is $176 496. Determine the share of the profit for each partner. Show your work. Academic 3 DPCDSB 11

Multiple-Choice Grade 9 Assessment of Mathematics, 2014 Four stores hire people to deliver flyers. Each pays a different amount per flyer delivered. The points on the graph below show the total pay for a certain number of flyers delivered for each of the stores. P Total Pay vs. Number of Flyers 70 60 Store Z Total pay ($) 50 40 30 Store X Store Y 20 Store W 10 0 100 200 300 400 500 600 n Number of flyers Which store will pay $45 for 450 flyers delivered? a b c d Store W Store X Store Y Store Z DPCDSB 12 4 Academic

Grade 9 Assessment of Mathematics, 2014 Multiple-Choice The total yearly cost of a museum membership is made up of a fee of $25, plus $5 per visit. c C Which graph best represents the relationship between total yearly cost, C, and number of visits, n? a C 0 n d C 0 n b C 0 n 0 n Gertrude sells shoes. Her total pay each week is made up of a base salary and a commission of 15% of her sales that week. One week, her total pay is $167.50 and she has $850 in sales. Which equation below represents the relationship between her total pay, P, each week and sales, s? a P = 15s b P = 40 0.15s c P = 850 0.15s d P = 167.50 0.15s Academic 5 DPCDSB 13

Multiple-Choice Grade 9 Assessment of Mathematics, 2014 Which of the following shows data from a non-linear relation? a n 1 2 3 4 P 8 5 2 1 What is the value of P in the equation below when r = 7? a b 14 10 c 14 d 18 P = 4 2r b n 5 10 15 20 P 3.25 4.00 4.75 5.50 c n 2 4 6 8 P 8 8 1 3 2 8 3 9 d n 3 6 9 P 25 16 9 12 4 DPCDSB 14 6 Academic

Grade 9 Assessment of Mathematics, 2014 Multiple-Choice The table below shows information about the linear relationship between Ben s total savings and the number of months he saves money. Number of months, n 3 6 9 12 Total savings, S ($) 345 540 735 930 Which of the following represents this relationship? a S = 65n 345 b S = 195n 150 c d Total savings ($) Total savings ($) S 500 400 300 200 100 0 S 500 400 300 200 100 0 Total Savings vs. Number of Months 1 2 3 4 5 Number of months Total Savings vs. Number of Months 1 2 3 4 5 Number of months n n Academic 7 DPCDSB 15

Open-Response Grade 9 Assessment of Mathematics, 2014 More Money, Please! The graph below shows information about the amount of money, A, in Shreya s bank account and the number of months, n, she has had the account. A Amount of Money in Account vs. Number of Months 120 110 100 Amount of money in account ($) 90 80 70 60 50 40 30 20 10 0 1 2 3 4 5 Number of months 6 7 8 n Draw the line of best fit for the data. Determine the equation of your line of best fit. Show your work. DPCDSB 16 8 Academic

Grade 9 Assessment of Mathematics, 2014 Open-Response Roll with It! The total cost at an amusement park is made up of an admission fee and a cost per ride. Information about the total cost for n rides last year is shown below. 50 45 C Total Cost vs. Number of Rides Last year 40 35 Total cost ($) 30 25 20 15 10 5 0 2 4 6 8 10 12 14 Number of rides n This year, the cost per ride is reduced from last year, but the total cost for 10 rides is the same. Determine a possible equation for the total cost, C, for this year. Include an admission fee and a cost per ride. Justify your answer. Academic 9 DPCDSB 17

Multiple-Choice Grade 9 Assessment of Mathematics, 2014 The equation of a line is 5x 2y 10 = 0. Which of the following expresses this equation in the form y = mx + b? a y = 5 2 x 5 b y = 5 2 x 10 c y = 5 2 x 5 d y = 5 2 x 10 A formula for determining the slope of a line M is given below. A m y 2 T y 1 R x 2 x 1 I X What is the slope of the line that passes through the points (2, 3) and (5, 6)? a 11 b 3 c 1 3 d 1 11 DPCDSB 18 10 Academic

Grade 9 Assessment of Mathematics, 2014 Multiple-Choice Consider the line represented by the equation y = 3x 2. A new line is formed by decreasing the slope and increasing the y-intercept. c y 6 4 Which of the following could be the graph of the new line? 2 6 4 2 0 2 4 6 x a y 2 6 4 4 6 2 6 4 2 0 2 4 6 x d y 6 2 4 4 2 6 6 4 2 0 2 4 6 x b y 2 6 4 4 6 2 6 4 2 0 2 4 6 x 2 4 6 Academic 11 DPCDSB 19

Multiple-Choice Grade 9 Assessment of Mathematics, 2014 Lee thinks of a line represented by the equation y = 4x + 6. Which line on the graph below is steeper than Lee s line and has a y-intercept that has half the value of Lee s line? 3 a b c d p q r u q 2 p 6 4 2 y 1 0 1 2 3 2 4 6 A line has a y-intercept of 4 and a slope of 3. Which equation represents this line? a y = 4x 3 b y = 4x 3 c d y = 4 3x y = 4 3x u r x The table below shows information about the total cost to rent a car and the distance driven. Distance driven, d (km) 100 200 300 400 Total cost, C ($) 65 80 95 110 What information would the C-intercept and slope of the graph of this linear relationship give? a b c d There is no fixed fee, and the cost per kilometre is $0.15. There is no fixed fee, and the cost per kilometre is $0.65. There is a $50 fixed fee, and the cost per kilometre is $0.15. There is a $50 fixed fee, and the cost per kilometre is $0.65. Jared uses the equation C = 30n to determine the cost, C, in dollars, for renting a car for n days, where n is a whole number. If Jared can spend a maximum of $200 on the rental, which of the following describes the possible values of n? a 7, 8, 9,... b 6, 7, 8, 9,... c 0, 1, 2, 3, 4, 5, 6 d 0, 1, 2, 3, 4, 5, 6, 7 DPCDSB 20 12 Academic

Grade 9 Assessment of Mathematics, 2014 Open-Response Is It a Line? Determine whether each of the relations in the chart below is linear or non-linear. Justify your answers. You may use the grid if you wish. 2x + 6y = 18 y = 4x 2 + 3 Circle one: Linear Non-linear Circle one: Linear Non-linear Justification Justification y x Academic 13 DPCDSB 21

Open-Response Grade 9 Assessment of Mathematics, 2014 Movie Night There are two payment options for downloading movies from a Web site. Option A: Pay $30 for a membership and $2 per movie downloaded. Option B: Shown on the grid below. 64 C Total Cost vs. Number of Movies 60 56 Option B 52 48 44 Total cost ($) 40 36 32 28 24 20 16 12 8 4 0 1 2 3 4 5 6 7 8 9 10 11 Number of movies n Determine under which conditions a person should select Option A and under which conditions a person should select Option B. Justify your answer. DPCDSB 22 14 Academic

Grade 9 Assessment of Mathematics, 2014 The diagram below is made of a right triangle and three squares. Multiple-Choice The 5 km of highway between City X and City Y is closed. There are two possible detour routes: one through Town A and one through Town B, as shown in the diagram below. Town A m r p 12 km Which of the following is represented by this diagram? a p 2 = r 2 m 2 b p 2 = m 2 r 2 c r 2 = p 2 m 2 d r 2 = m 2 p 2 City X 5 km Town B 3 km City Y How much shorter is the detour through Town B than the detour through Town A? a b c d 7 km 9 km 16 km 18 km Academic 15 DPCDSB 23

Multiple-Choice Grade 9 Assessment of Mathematics, 2014 The sign below is made up of a rectangle and a semicircle. The container pictured below is made up of a cone and a cylinder. The cone and the cylinder have the same height. 15 cm 10 cm 40 cm 30 cm Which of the following is closest to the area of the sign? a 347 cm 2 b 653 cm 2 c 1007 cm 2 d 1410 cm 2 12 cm Which of the following is closest to the volume of the container? a 2261 cm 3 b 3016 cm 3 c 3393 cm 3 d 4524 cm 3 What is the value of x in the diagram below? 38 x a b c d 38 71 104 161 DPCDSB 24 16 Academic

Grade 9 Assessment of Mathematics, 2014 Multiple-Choice The sum of the interior angles of a polygon is 2700. How many sides does the polygon have? a 19 b 17 c 15 d 13 Academic 17 DPCDSB 25

Open-Response Grade 9 Assessment of Mathematics, 2014 Coated Cones An ice cream store offers chocolate-coated cones as shown in the diagram below. 6 cm 10 cm The cone is open topped, and the entire outside is coated in chocolate. Determine the area of the surface that is coated in chocolate. Show your work. DPCDSB 26 18 Academic

Grade 9 Assessment of Mathematics, 2014 Open-Response Daring Diagram A diagram is shown below. x x x 100 y 100 85 70 Complete the table below with the values of x and y. Justify your answers using geometric properties. Value Justification using geometric properties x y Academic 19 DPCDSB 27

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