Math Concepts and Rational Numbers Quiz

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Questions and Answers

How many real numbers exist between 0 and 10?

  • 9
  • 100
  • An infinite number (correct)
  • 10

Which statement about rational numbers is accurate?

  • A rational number in its decimal form is a non-ending, non-repeating decimal.
  • The square root of any number is a rational number.
  • A rational number is always positive.
  • A rational number can be written as a fraction. (correct)

Set C is defined as {3, 6, 9, 12,...}, and Set D is the set of integers that are multiples of 5. What characterizes the numbers common to both sets?

  • The common numbers are always multiples of 15. (correct)
  • The common numbers are always divisible by 9.
  • The common numbers are always odd numbers.
  • There are no common numbers between Set C and Set D.

Which value is equivalent to $3.5 \times 10^5$?

<p>350000 (B)</p> Signup and view all the answers

Which of the following properties is NOT necessarily true for rational numbers?

<p>They can be expressed as a terminating decimal. (D)</p> Signup and view all the answers

Considering Set A, which includes all integers divisible by 3, and Set B, which includes all odd numbers, which is true?

<p>Some elements in Set A are also in Set B. (A)</p> Signup and view all the answers

How can the number 0.000078 be represented using powers of ten?

<p>$7.8 \times 10^{-5}$ (B)</p> Signup and view all the answers

Which of the following statements correctly explains the difference between integers and real numbers?

<p>All integers are real numbers, but not all real numbers are integers. (B)</p> Signup and view all the answers

What does the y-axis on the graph represent?

<p>The mass of the berries in grams (C)</p> Signup and view all the answers

What is the initial mass of berries in Basket 1?

<p>200 grams (D)</p> Signup and view all the answers

At what time do both baskets have the same mass?

<p>Approximately 20 minutes (A)</p> Signup and view all the answers

Which basket is filling up faster?

<p>Basket 1 (C)</p> Signup and view all the answers

After 40 minutes, what is the approximate mass of berries in Basket 2?

<p>200 grams (D)</p> Signup and view all the answers

What is the approximate difference in berry mass between the two baskets at 10 minutes?

<p>150 grams (C)</p> Signup and view all the answers

If the trend continues, what will happen to the difference in mass between Basket 1 and Basket 2?

<p>The difference will keep increasing (C)</p> Signup and view all the answers

If $6/7$ of 42 students are in a club, and $1/4$ of those club members are in the environmental club, how many are in a club but not the environmental club?

<p>18 students (A)</p> Signup and view all the answers

A temperature starts at $7$ C and then changes by $-13$ C, $+4$ C, $-9$ C, and $+1$ C. What is the final temperature?

<p>-10 C (D)</p> Signup and view all the answers

Simplify the expression: $-3x(4x^2 - 5)$

<p>$-12x^3 + 15x$ (B)</p> Signup and view all the answers

If there are 90 red and yellow tiles, and there are 5 times as many red tiles as yellow tiles, which equation represents how to find Y (the amount of yellow tiles?)

<p>$Y + 5Y = 90$ (D)</p> Signup and view all the answers

If $6/7$ of 42 students are in a club, how many students are not in a club?

<p>6 students (D)</p> Signup and view all the answers

If a temperature goes up by $a$ degrees, then goes down by $b$ degrees, which algebraic expression represents the change in temperature?

<p>$a-b$ (A)</p> Signup and view all the answers

What is the coefficient of the $x^3$ term in the simplified expression of $-3x (4x^2 - 5)$

<p>-12 (A)</p> Signup and view all the answers

If the total number of tiles is 90, and there are 5 times as many red tiles as yellow tiles, how many red tiles are there?

<p>75 (C)</p> Signup and view all the answers

What can be said about the rate of change of Graph A compared to Graph B?

<p>Graph A has a greater rate of change than Graph B. (C)</p> Signup and view all the answers

How do the initial values of Graph A and Graph B compare?

<p>The initial value for Graph A is the same as that for Graph B. (B)</p> Signup and view all the answers

At x = 10, the y-value of Graph A is compared to Graph B. What is the relationship?

<p>The y-value of Graph A is greater than that of Graph B. (C)</p> Signup and view all the answers

Which statement is true regarding the slopes of the two graphs?

<p>Graph A has a slope that is steeper than Graph B. (A)</p> Signup and view all the answers

If the equations of Graph A and Graph B are linear, which of the following could represent their equations?

<p>Graph A: y = 10x, Graph B: y = 5x (A)</p> Signup and view all the answers

Which statement about the data point (–16, 140) is true?

<p>It is an outlier. (D)</p> Signup and view all the answers

What does the scatter plot primarily illustrate?

<p>The relationship between drinks sold and temperature. (C)</p> Signup and view all the answers

Which correlation exists between the outdoor temperature at lunchtime and the number of drinks sold?

<p>There is a positive correlation. (B)</p> Signup and view all the answers

In the context of the scatter plot, how does temperature affect drink sales?

<p>Higher temperatures lead to more drinks sold. (A)</p> Signup and view all the answers

What can be inferred about the data represented in the scatter plot?

<p>The plot indicates a linear relationship. (C)</p> Signup and view all the answers

Which of the following statements is NOT true based on the scatter plot?

<p>The outdoor temperature has an inverse effect. (C)</p> Signup and view all the answers

How many total data points are suggested in the scatter plot?

<p>80 (D)</p> Signup and view all the answers

If the temperature is set at 0 degrees, what can be predicted about drink sales?

<p>Sales will likely be low. (D)</p> Signup and view all the answers

According to the provided definitions, what is the primary distinction between a 'knowledge and understanding' question and an 'application' question?

<p>Knowledge questions test basic recall, while application questions require tool selection or information fitting. (D)</p> Signup and view all the answers

If a table of values presents a linear relationship, and a student needs to calculate the cost per person, which type of cognitive domain would this question fall into?

<p>Application (A)</p> Signup and view all the answers

In the context of a linear relationship shown in a table, if the 'cost of activity' is $60 when the 'number of people' is zero, what does this value specifically represent?

<p>The initial or fixed cost of the activity. (D)</p> Signup and view all the answers

A table shows a 'Cost of activity' of $120 for zero people and $200 for 4 people. What is the additional cost for each person?

<p>$20 (C)</p> Signup and view all the answers

Which of the following scenarios best represents a question that requires 'application' rather than just 'knowledge and understanding'?

<p>Calculating the total cost after calculating the cost per person from a table. (D)</p> Signup and view all the answers

In a table showing a linear relationship between the number of people and the cost, what would indicate a higher 'cost per person'?

<p>A larger difference in cost for a larger difference in the number of people. (C)</p> Signup and view all the answers

Given a table, if the cost of an activity is $50 for 0 people, and $150 for 5 people, what is the cost of an activity for 10 people?

<p>$250 (C)</p> Signup and view all the answers

If a question requires selecting a specific formula from multiple choices when given a word problem that displays a linear relationship, is it more likely to be categorized as 'knowledge and understanding' or 'application'?

<p>Application (C)</p> Signup and view all the answers

Flashcards

Initial Cost

The initial cost of an activity, before any people participate.

Cost Per Person

The cost of an activity for each additional person.

Table of Values

A table showing how the cost of an activity changes as the number of participants grows.

Linear Relationship

The relationship between cost and the number of people involved in an activity.

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Application Question

A question where you need to apply a specific strategy or tool to find the answer.

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Selecting the Appropriate Tool

The process of choosing the right tool or method to solve a problem.

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Fitting Information

A technique that uses values from a table to determine patterns or rules.

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Knowledge and Understanding Questions

Questions that test basic knowledge or understanding of concepts.

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Rational Numbers

A set of numbers that can be written as a fraction, where the numerator and denominator are integers and the denominator is not zero.

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Rational Number (Decimal Form)

A number that can be written as a decimal that either terminates or repeats.

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Irrational Number

A number that cannot be written as a fraction, its decimal representation continues without repeating.

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Real Number

Any number that can be plotted on a number line.

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Power

A number raised to a power, indicating repeated multiplication.

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Exponent

The number of times a base is multiplied by itself in a power.

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Arithmetic Sequence

A set of numbers that follow a pattern of adding a constant value to each consecutive term.

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Geometric Sequence

A set of numbers that follow a pattern of multiplying each consecutive term by a constant value.

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Simplified form of an expression

A simplified form of an expression is an equivalent expression with no parentheses and like terms combined.

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Variable

A variable that represents the unknown in a mathematical equation or expression.

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Substitution

The process of replacing a variable in an expression with its numerical value.

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Expression

A mathematical expression that includes variables, numbers, and operations.

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Equation

A mathematical equation that involves variables, numbers, and operations, and sets two expressions equal to each other.

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Algebraic expression

A mathematical expression that includes variables, exponents, numbers, and operations.

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Rate of change

The rate of change is a measure of how much the output (y-value) changes for every unit change in the input (x-value). It tells us how steep the line is on a graph.

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Initial Value

The initial value is the y-value when x is 0, representing the starting point of a relationship.

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Comparing Rate of Change

Graph A rises more quickly than Graph B, signifying a faster rate of change.

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Comparing Initial Value

Graph A starts at a lower y-value than Graph B, indicating a smaller initial value.

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Y-intercept

The point on the y-axis where the line intersects.

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Initial Mass

The amount of something at the beginning, before any changes occur.

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Outlier

A data point that is significantly different from the other data points in a set.

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Positive Correlation

When two variables increase or decrease together. The points on a scatter plot generally move upwards from left to right.

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Negative Correlation

When one variable increases as the other decreases. The points on a scatter plot generally move downwards from left to right.

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No correlation

When two variables have no clear relationship. The points on a scatter plot are scattered randomly.

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Scatter Plot

A visual representation that shows the relationship between two variables. Each point represents a pair of values.

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Mode

The value that occurs most frequently in a set of data.

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Median

The middle value in a set of data that is ordered from least to greatest.

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Mean

The average of all values in a set of data.

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Study Notes

Released Grade 9 Mathematics Assessment Questions

  • This resource supports educators using the EQAO Grade 9 Assessment of Mathematics (2021).
  • Each question maps to a knowledge category and an overall and specific expectation in The Ontario Curriculum.
  • Definitions of knowledge and skills categories are included, along with adapted assessment questions.
  • Detailed information about each question, including its overall expectation, knowledge category, and correct answer, is provided.
  • The assessment is online, computer adaptive and completed at the end of the Grade 9 course.
  • It assesses knowledge and skills in number, algebra, data, geometry and measurement, and financial literacy.
  • Mathematical thinking and making connections, and social emotional learning are not assessed.
  • Students complete questions related to the categories of knowledge and skills throughout the assessment.
  • The assessment questions follow a blueprint, and each student completes a comparable number of questions from each strand, enabling year-to-year comparison.
  • The EQAO Grade 9 Assessment reports overall achievement levels, not scores per strand or knowledge category for individual students.
  • Detailed reports on a strand/skill basis are available at the school, board, and provincial levels.

Definitions of Knowledge and Skills Categories

  • Knowledge and Understanding: Questions in this category require students to demonstrate knowledge of subject-specific content and understanding of its meaning and significance.
  • Example: A question about the linear relationship between the cost of an activity and the number of people participating.
  • Application: Questions in this category require students either to select the appropriate tool or gather and apply necessary information to solve a problem.
    • Example: A question about calculating the cost per person for an activity given a table of values.
  • Thinking: Questions in this category require students to select and sequence tools or demonstrate a critical thinking process (e.g., reasoning). Students must make a plan to answer the question.
  • Example: A question using a table of values to determine the number of people participating in an activity given a specific total cost.

Suggested Uses in Class

  • Questions can be used without answer options to encourage student discussion about methods and common errors.
  • Technology can be used to record instant student responses for discussions about correct answers and errors.
  • Questions can be used as pre- and post-assessments, or as revision tools.
  • Manipulatives and examples are recommended for students to use with questions.

Data Analysis, Collection, and Representation

  • A correlation coefficient (r) represents the strength of a linear relationship between two variables.
  • A strong negative correlation (correlation coefficient closest to -1) indicates a strong inverse relationship.
  • A correlation coefficient of 0 indicates no linear correlation.
  • Box plots visually represent data distribution.

Geometric and Measurement Relationships

  • Geometric problems often involve relationships, like between a rectangular frame and a second frame with altered dimensions.
  • Area calculations and characteristics of 2D and 3D shapes are necessary.

Financial Literacy

  • Students can create monthly budgets.
  • Monthly expenses are compared to the monthly income to modify the budget or check for its adequacy.

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