EQAO Grade 9 Mathematics Past Paper 2023 PDF

Resource: Released Questions Grade 9 Assessment of Mathematics November 2023 Mathematics In This Resource:...

Resource: Released Questions Grade 9 Assessment of Mathematics November 2023 Mathematics In This Resource: Details of the Assessment Results Reported Definitions of the Categories of Knowledge and Skills Impact of Answer Options Suggested Uses for This Resource Questions Details of the Questions This resource is provided to support educators with the EQAO Grade 9 Assessment of Mathematics. Each question on the assessment is mapped to a category of knowledge and skills and an overall and a specific expectation in The Ontario Curriculum, Grade 9: Mathematics (2021). This resource includes the definitions of the categories of knowledge and skills as well as examples of adapted assessment questions. Detailed information about each question, including the overall expectation and category of knowledge and skills to which the question is mapped, and the correct answer, are provided. For more information about the assessment design, refer to the Framework at www.eqao.com. DETAILS OF THE ASSESSMENT The EQAO Grade 9 Assessment of Mathematics During each stage of the assessment, students complete is an online assessment completed by students at questions mapped to each category of knowledge and the end of the Grade 9 mathematics course. The skills assessed. The category assigned to each question assessment uses a multi-stage computer adaptive assumes that students have been taught the knowledge testing model that adapts to the individual student’s and skills outlined in the Grade 9 mathematics curriculum, performance as the student progresses through the as the EQAO assessment is completed near the end of stages of the assessment (e.g., based on a student’s the Grade 9 mathematics course. performance in Stage 1, the student will be routed to Regardless of how students are routed as they progress a set of questions that is overall easier or more difficult through the stages of the assessment, students in Stage 2). Though students are routed to different complete the same number of questions from each of question sets, outcomes are put on the same scale, the various strands assessed, as the assessment follows and overall levels of achievement are comparable. a blueprint. The blueprint, which can be found in the The EQAO Grade 9 Assessment of Mathematics Framework, defines how many questions a student will assesses the knowledge and skills that are defined complete from each strand. This makes the assessment in the expectations found in The Ontario Curriculum, comparable from year to year. (For more information, see Grade 9: Mathematics (2021). The questions assess www.eqao.com.) students’ knowledge and skills in the strands: Number RESULTS REPORTED Algebra The EQAO Grade 9 Assessment of Mathematics is a Data standards-referenced large-scale assessment based on Geometry and Measurement the expectations and standards (levels of achievement) Financial Literacy for student proficiency in The Ontario Curriculum. EQAO reports an overall level of achievement in mathematics Although the assessment does not measure the content for each student. EQAO does not provide scores by in the Mathematical Thinking and Making Connections strand or by category of knowledge and skills at the strand, students will be required to apply mathematical student level, as each student does not complete processes while completing the assessment. The enough questions mapped to each strand or skill to assessment does not measure the content in the Social- report on each accurately. However, through the EQAO Emotional Learning (SEL) Skills in Mathematics strand. secure reporting tool, the agency provides reports by Each question on the assessment is mapped to an strand and skill at the school, board and provincial levels overall and a specific curriculum expectation. Each for schools and boards to use for improvement planning. question is also mapped to one of these categories of knowledge and skills: Knowledge and Understanding (KU) Application (AP) Thinking (TH) Questions in the mathematics assessment do not assess the Communication category of knowledge and skills. EQAO Resource: Released Questions, November 2023 2 DEFINITIONS OF THE CATEGORIES OF KNOWLEDGE AND SKILLS EQAO has adapted the definitions of the three categories below from the achievement chart for mathematics found in the Ontario mathematics curriculum. This section outlines the definitions EQAO uses to determine the category for each question on the assessment. An example is provided for each category. Knowledge and Understanding A question is mapped to Knowledge and Understanding Example if in order to answer the question students must This table of values shows information about the demonstrate only linear relationship between the cost of an activity and the number of people participating. subject-specific content (knowledge) and/or comprehension of its meaning and significance Number of Cost of (understanding). people activity ($) 0 50 These questions assess basic knowledge and/or understanding of concepts. 1 70 2 90 Which statement about this table of values is true? A The initial cost is $50. B The initial cost is $70. C The cost per person is $50. D The cost per person is $70. Correct answer: A To answer this question, students need to select the correct statement. They can identify the initial cost directly from the table of values and do not need to select a tool to determine the answer. EQAO Resource: Released Questions, November 2023 3 Application A question is mapped to Application if in order to answer Example the question students must either This table of values shows information about the linear relationship between the cost of an activity select the appropriate tool or and the number of people participating. get the necessary information and “fit” it to the problem. Number of Cost of people activity ($) The category that a question is mapped to may change 0 50 from Knowledge and Understanding to Application if a context is added or if a tool required to answer the 10 250 question is not provided. 20 450 What is the cost per person for this activity? A $20 B $50 C $200 D $250 Correct answer: A Students must select the tool they will use as they need to determine the rate of change. This could be done through a variety of strategies using the information in the table of values. EQAO Resource: Released Questions, November 2023 4 Thinking A question is mapped to Thinking if in order to answer Example the question students must either This table of values shows information about the linear relationship between the cost of an activity select and sequence a variety of tools or and the number of people participating. demonstrate a critical thinking process (e.g., reasoning). Number of Cost of people activity ($) Students may need to make a plan to answer these 10 250 questions. 20 450 40 850 If the total cost for the activity is $750, how many people participate? A 25 people B 30 people C 35 people D 37 people Correct answer: C Students need to make a plan to answer this question. They may first determine the rate of change and the initial value using the information in the table of values and then use those two values to determine the answer. There are multiple ways to solve this question. EQAO Resource: Released Questions, November 2023 5 IMPACT OF ANSWER OPTIONS When two questions are similar in content, the answer options can affect the category of knowledge and skills to which the question is mapped. Consider these two versions. Version 1 Version 2 This cube and pyramid have the same height This cube and pyramid have the same height and base area. and base area. Complete the following statement. The volume of the pyramid is 12 cm3. The volume of the cube is _________ [the same as, What is the volume of the cube? two times larger than, three times larger than, three times smaller than] the volume of the pyramid. A 4 cm3 B 6 cm3 Correct answer: three times larger than C 24 cm3 This question is mapped to the Knowledge and D 36 cm3 Understanding category. In the curriculum students learn about the relationships between the volume of Correct answer: D prisms and pyramids with the same height and base area. Students state the relationship between the In the curriculum students learn about the relationships volume of these two objects. between the volume of prisms and pyramids with the same height and base area. Students must use the relationship between the volume of these two objects to determine the volume of the cube given the volume of the pyramid. Therefore, this question is mapped to Application, as the tool is not given. EQAO Resource: Released Questions, November 2023 6  SUGGESTED USES FOR THIS RESOURCE Here is a suggested list of how the example questions can be used in the classroom: Use questions without including the answer options. Students can answer the question and then discuss the steps required and other possible answers, including those arrived at through common errors or misconceptions. Discuss whether there are multiple methods that can be used to answer the question. Students can then compare their answer to the given options. Use technology in the classroom to have students record answers instantly, which will allow for discussion of correct answers and the common errors or misconceptions associated with the incorrect options. The discussion can lead to a deeper understanding of concepts and assist students in correcting their own misconceptions. Use questions as part of a pre- and post-assessment on a topic to show students their improved understanding within a unit. Use questions when spiralling as a method to revisit topics. Encourage students to use manipulatives, and model how to use them effectively. For example, graphing applications can be used with questions mapped to expectations in the Algebra strand as well as those mapped to other strands, such as Data, or Geometry and Measurement. EQAO Resource: Released Questions, November 2023 7 QUESTIONS These questions were adapted from the EQAO Grade 9 Assessment of Mathematics for use in the classroom. This section provides the overall expectation and the category of knowledge and skills for each question. B. NUMBER B1. Development of Numbers and Number Sets demonstrate an understanding of the development and use of numbers, and make connections between sets of numbers 1 How many real numbers are between 0 and 10? 3 Set C and Set D are given. KU TH Set C = {3, 6, 9, 12,...} A an infinite number Set D is the set of integers that are multiples of 5. B 9 Select the statement that correctly describes the numbers that are common to both Set C 10 and Set D. C D 100 The common numbers are always A divisible by 9. The common numbers are always B multiples of 15. 2 Which statement about rational numbers The common numbers are always AP is correct? C odd numbers. There are no common numbers A A rational number is always positive. D between Set C and Set D. A rational number can be written B as a fraction. The square root of any number is C a rational number. A rational number in its decimal form D is a non-ending, non-repeating decimal. EQAO Resource: Released Questions, November 2023 8 B2. Powers represent numbers in various ways, evaluate powers, and simplify expressions by using the relationships between powers and their exponents 4 Which value is equivalent to 3.5 × 105? 6 Select the expression that has the value KU TH that is the least. A 350 B 35 000 A ( ) 1 (43)2 4 44 C 350 000 B ( ) 1 43 2 44 2 D 3 500 000 C ( ) 1 (43)2 2 44 5 AP An equation is shown. (x6y3)(x y8) D ( ) 1 43 4 44 2 x3y4 = x12y Select the values that make this equation true: = _______ [6, 7, 9] and  = _______ [6, 7, 9]. EQAO Resource: Released Questions, November 2023 9 B3. Number Sense and Operations apply an understanding of rational numbers, ratios, rates, percentages, and proportions, in various mathematical contexts, and to solve problems 5 7 Which rational number is equivalent to – ? 9 There are 42 students: 6 KU TH 6 of the students are members of a school 7 club; – 10 1 A 4 of the students who are members of a 12 school club are members of the school environmental club. –5 How many of these students are members B – 6 of a school club but are not members of the school environmental club? 10 C 12 A 18 students B 24 students 5 D 6 C 27 students D 36 students 8 The temperature is measured five times. AP The first temperature measured is 7 °C. The temperature goes down by 13 °C, up by 4 °C, down by 9 °C, and then up by 1°C. What is the final temperature measured? A –20 °C B –10 °C C 10 °C D 17 °C EQAO Resource: Released Questions, November 2023 10 C. ALGEBRA C1. Algebraic Expressions and Equations demonstrate an understanding of the development and use of algebraic concepts and of their connection to numbers, using various tools and representations 10 What is a simplified form of this expression? 12 There are a total of 90 red and yellow tiles. KU TH –3x(4x2 – 5) There are 5 times as many red tiles as yellow tiles. –12x2 – 15x How many red tiles are there? A B –12x3 – 5 A 15 tiles C –12x2 + 15 B 18 tiles D –12x3 + 15x C 72 tiles D 75 tiles 11 For each expression, select the appropriate AP choice. Equivalent to Equivalent to 4n – 2 4n – 8 (3n – 4) + (n + 2) 4(n – 2) (5n + 6) – (n + 8) EQAO Resource: Released Questions, November 2023 11 C2. Coding apply coding skills to represent mathematical concepts and relationships dynamically, and to solve problems, in algebra and across the other strands 13 When creating pseudocode, Suchen uses this KU expression. distance > (8 * minutes + 15) What is distance an example of in this pseudocode? A a variable B an equation C a constant D an inequality 14 This pseudocode is used to determine the value AP of a variable in an equation. variableB = 0 variableC = 0 output "Enter the value of variable B." store input as variableB output "Enter the value of variable C." store input as variableC variableA = ((5 * variableC) – variableB)/4 output "The value of variable A is ", variableA, "." What is the value of variableA if the program is run and 2 is entered for variableB and 6 is entered for variableC? A 1 B 2.25 C 7 D 7.5 EQAO Resource: Released Questions, November 2023 12 C2. Coding (continued) 15 Pseudocode is written to determine if a given point TH is above the liney = –4x + 12. Select the correct parts of the code to complete A initialValue this pseudocode. rateOfChange = –4 B rateOfChange initialValue = 12 output "Enter the x-coordinate of the point." C yInput store user input as xInput output "Enter the y-coordinate of the point." D yInput = yValue store user input as yInput yValue = ________ * xInput + ________ if __________ E yInput < yValue output "The point is above the line." else F yInput > yValue output "The point is not above the line." EQAO Resource: Released Questions, November 2023 13 C3. Application of Relations represent and compare linear and non-linear relations that model real-life situations, and use these representations to make predictions 16 The equation H = 5 + 1.5t represents the 17 This graph shows the relationship between KU relationship between the height of a plant, AP the total mass of a basket, in grams, and the H, in centimetres, and time, t, in days. amount of time spent picking berries, in minutes, for two baskets. Which statement is true? Total Mass of Basket vs. Amount of Time Spent Picking Berries A The initial height of the plant is 1.5 cm. M Basket 1 800 Total mass of basket (g) B The initial height of the plant is 5 cm. 700 600 Basket 2 The height of the plant increases 5 cm 500 C each day. 400 300 The height of the plant increases 6.5 cm 200 D each day. 100 t 0 10 20 30 40 50 60 70 80 Amount of time spent picking berries (min) Which statement is true about the graph? The initial mass of Basket 1 is 200 g A more than the initial mass of Basket 2. At 30 minutes, the total mass of B Basket 1 and that of Basket 2 are the same. The total mass of Basket 1 will always C be greater than the total mass of Basket 2. At 30 minutes, the difference between D the total mass of Basket 1 and that of Basket 2 is 200 g. EQAO Resource: Released Questions, November 2023 14 C3. Application of Relations (continued) 18 Information about two linear relationships is shown on TH these graphs. Graph A Graph B y y 100 100 80 80 60 60 40 40 20 20 x x 0 2 4 6 8 0 2 4 6 8 Select the options that correctly complete these statements. The rate of change of Graph A is ______________ [greater than, less than, the same as] the rate of change of Graph B. The initial value for Graph A is ______________ [greater than, less than, the same as] the initial value for Graph B. At x = 10, Graph A has a y-value that is ______________ [greater than, less than, the same as] the y-value in Graph B. EQAO Resource: Released Questions, November 2023 15 C4. Characteristics of Relations demonstrate an understanding of the characteristics of various representations of linear and non-linear relations, using tools, including coding when appropriate 19 This table of values shows the relationship 20 Which inequality corresponds to this graph? KU between the total rental cost of a bicycle, C, AP in dollars, and time, t, in hours. y Total rental 4 Time, t cost, C (h) 3 ($) 2 0 30.00 1 1 37.50 x –4 –3 –2 –1 0 2 45.00 1 2 3 4 3 52.50 –1 –2 Which equation represents this relationship? –3 –4 A C = 30t B C = 30t + 7.5 2x – y ≤ – 2 A C C = 7.5t 2x + y ≤ – 2 B D C = 7.5t + 30 x – 2y ≤ – 2 C D x + 2y ≤ – 2 EQAO Resource: Released Questions, November 2023 16 C4. Characteristics of Relations (continued) 21 Information about three different linear relations is given. TH Relation 1 Relation 2 Relation 3 y y= 3x+6 x y 5 3 30 5 6 25 9 20 12 15 x 15 10 –5 0 5 –5 Which statement about the relations is true? Relation 1 and Relation 3 have the same slope, while Relation 2 A and Relation 3 have different y-intercepts. Relation 1 and Relation 2 have the same y-intercept, while B Relation 1 and Relation 3 have different slopes. Relation 2 and Relation 3 have the same slope, while Relation 1 C and Relation 2 have different slopes. Relation 1 and Relation 2 have the same y-intercept, while D Relation 1 and Relation 3 have the same y-intercept. EQAO Resource: Released Questions, November 2023 17 D. DATA D1. Collection, Representation, and Analysis of Data describe the collection and use of data, and represent and analyse data involving one and two variables 22 A correlation coefficient, r, represents the 24 A bag contains 5 tomatoes that each have KU strength of a linear relationship between two TH a different mass. The mean and median variables. masses of the tomatoes are determined. Which option represents the strongest negative The tomato with the smallest mass is replaced linear correlation? with a tomato that has a larger mass than the other tomatoes. How will the new mean and new median A r = –0.95 masses of the 5 tomatoes be different after the tomato is replaced? B r = 1.0 The new mean mass and the new C r = –0.05 A median mass are both greater. D r=0 The new mean mass and the new B median mass are both less. The new mean mass is greater, and C the new median mass is less. 23 This box plot represents the score out of 90 AP received by students on a driver’s education The new mean mass is less, and D exam. the new median mass is greater. 62 66 70 74 78 82 86 90 Driver’s education exam score (out of 90) 75% of students pass the exam. What is the minimum score needed to pass the exam? A 62 B 72 C 80 D 84 EQAO Resource: Released Questions, November 2023 18 D2. Mathematical Modelling apply the process of mathematical modelling, using data and mathematical concepts from other strands, to represent, analyse, make predictions, and provide insight into real-life situations 25 Select the option that does not require the use 26 This scatter plot represents the relationship KU of mathematical modelling. AP between the number of drinks sold, N, in a store and the outdoor temperature, T, in degrees Celsius, at lunchtime. A analyzing real-life situations N 160 B representing real-life situations 140 120 100 predicting the outcome of real-life C 80 situations 60 40 D giving solutions to real-life situations 20 0 T –16 –8 8 16 24 32 Select the TWO statements about this scatter plot that are true. A The data point (–16, 140) is an outlier. The number of drinks sold does not B depend on the outdoor temperature at lunchtime. There is a positive correlation between C the outdoor temperature at lunchtime and the number of drinks sold. There is a negative correlation between D the outdoor temperature at lunchtime and the number of drinks sold. EQAO Resource: Released Questions, November 2023 19 D2. Mathematical Modelling (continued) 27 The results of a survey of 80 students are shown. TH Students who like Students who do not like broccoli broccoli Students who like 42 18 carrots Students who do not like carrots ? 9 Which statement is correct based on the data? A 60% of students like carrots. B Most students who like carrots don’t like broccoli. C 14% of students like broccoli but do not like carrots. D More students like broccoli than like carrots. EQAO Resource: Released Questions, November 2023 20 E. GEOMETRY AND MEASUREMENT E1. Geometric and Measurement Relationships demonstrate an understanding of the development and use of geometric and measurement relationships, and apply these relationships to solve problems, including problems involving real-life situations 28 A frame is in the shape of a rectangle. 29 What are the values of x, y and z? KU AP A second rectangular frame has triple the length and one third of the width of the first frame. x Complete this statement. The area of the second frame is _____________ the area of the first frame. O 44° A the same as z y B half the size of C three times the size of A x = 44°, y = 44°, z = 44° D six times the size of B x = 44°, y = 92°, z = 44° C x = 68°, y = 68°, z = 68° D x = 44°, y = 68°, z = 68° EQAO Resource: Released Questions, November 2023 21 E1. Geometric and Measurement Relationships (continued) 30 The dimensions of a silo are given. TH 12 m Total height 20 m 8m Hint: Use the side-length relationship for right triangles, a2 + b2 = c2. Which value is closest to the total height of the silo? A 24 m B 29 m C 32 m D 34 m EQAO Resource: Released Questions, November 2023 22 F. FINANCIAL LITERACY F1. Financial Decisions demonstrate the knowledge and skills needed to make informed financial decisions 31 A person creates a monthly budget and 32 This graph represents the relationship between KU determines the monthly income will be $2800. AP the value of a refrigerator, in dollars, and the number of years since its purchase. The person’s expenses are shown in this table. Value of Refrigerator vs. Years Monthly Expenses Cost V 1000 Rent $1500 Value of refrigerator ($) Utililties $350 750 Food $400 Other $345 500 Select the TWO statements that are true about 250 the person’s budget. The budget needs to be modified, t 0 5 10 15 20 A because the monthly expenses are more than the monthly income. Years Complete this statement. The budget does not need to be B modified, because the monthly expenses After approximately 10 years, the value of the are less than the monthly income. refrigerator will have ___________ [appreciated, depreciated] by ______ [25%, 40%, 50%, 75%] of its initial purchase value. If the rent goes up by $205, the monthly C expenses will be the same amount as the monthly income. If the utilities go down by $205, the D monthly expenses will be the same amount as the monthly income. EQAO Resource: Released Questions, November 2023 23 F1. Financial Decisions (continued) 33 A person gets a loan to make a $3000 TH purchase. Which borrowing situation will allow this person to pay the loan off in the least amount of time at 0% interest? making a $300 down payment and A monthly payments of $75 making a $600 down payment and B monthly payments of $50 making a $300 down payment and C biweekly payments of $50 making a $600 down payment and D biweekly payments of $30 EQAO Resource: Released Questions, November 2023 24 DETAILS OF THE QUESTIONS question overall cognitive key legend number expectation skill 1 B1 KU A Cognitive Skill 2 B1 AP B KU—Knowledge and Understanding 3 B1 TH B AP—Application 4 B2 KU C TH—Thinking 5 B2 AP * 6 B2 TH D 7 B3 KU A 8 B3 AP B * See next page for solutions to questions 5, 11, 15, 18, 32. 9 B3 TH C 10 C1 KU D 11 C1 AP * 12 C1 TH D 13 C2 KU A 14 C2 AP C 15 C2 TH * 16 C3 KU B 17 C3 AP B 18 C3 TH * 19 C4 KU D 20 C4 AP C 21 C4 TH A 22 D1 KU A 23 D1 AP B 24 D1 TH A 25 D2 KU D 26 D2 AP A, C 27 D2 TH C 28 E1 KU A 29 E1 AP C 30 E1 TH B 31 F1 KU B, C 32 F1 AP * 33 F1 TH C EQAO Resource: Released Questions, November 2023 25 * Solutions for questions 5 An equation is shown. AP (x6y3)(x y8) xy 3 4 = x12y Select the values that make this equation true: 9 = _______ 7 [6, 7, 9] and  = _______ [6, 7, 9]. 11 For each expression, select the appropriate AP choice. Equivalent to Equivalent to 4n – 2 4n – 8 (3n – 4) + (n + 2)  4(n – 2)  (5n + 6) – (n + 8)  15 Pseudocode is written to determine if a given point TH is above the line y = –4x + 12. Select the correct parts of the code to complete A initialValue this pseudocode. rateOfChange = –4 B rateOfChange initialValue = 12 output "Enter the x-coordinate of the point." C yInput store user input as xInput output "Enter the y-coordinate of the point." D yInput = yValue store user input as yInput B yValue = ________ A * xInput + ________ F if __________ E yInput < yValue output "The point is above the line." else F yInput > yValue output "The point is not above the line." EQAO Resource: Released Questions, November 2023 26 * Solutions for questions (continued) 18 Information about two linear relationships is shown on TH these graphs. Graph A Graph B y y 100 100 80 80 60 60 40 40 20 20 x x 0 2 4 6 8 0 2 4 6 8 Select the options that correctly complete these statements. less than The rate of change of Graph A is ______________ [greater than, less than, the same as] the rate of change of Graph B. greater than [greater than, The initial value for Graph A is ______________ less than, the same as] the initial value for Graph B. At x = 10, Graph A has a y-value that is ______________ less than [greater than, less than, the same as] the y-value in Graph B. EQAO Resource: Released Questions, November 2023 27 * Solutions for questions (continued) 32 This graph represents the relationship between AP the value of a refrigerator, in dollars, and the number of years since its purchase. Value of Refrigerator vs. Years V 1000 Value of refrigerator ($) 750 500 250 t 0 5 10 15 20 Years Complete this statement. After approximately 10 years, the value of the depreciated [appreciated, refrigerator will have ___________ 75% [25%, 40%, 50%, 75%] depreciated] by ______ of its initial purchase value. EQAO Resource: Released Questions, November 2023 28 Education Quality and Accountability Office Information Centre: 1-888-327-7377 (Ontario) or 416-916-0708 (outside Ontario) | e-mail | eqao.com November 2023