Gr 9 MATH: June Exam Mix
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Questions and Answers

What are the numbers used to count called?

  • Natural Numbers (correct)
  • Real Numbers
  • Whole Numbers
  • Rational Numbers

    • What is the result of adding two or more natural numbers?

  • Always a rational number
  • Always a natural number (correct)
  • Always an irrational number
  • Always an integer

    • What is the result of subtracting a natural number from another natural number?

  • Always a natural number
  • Not always a natural number (correct)
  • Always an irrational number
  • Always an integer

    • What is the result of dividing a natural number by another natural number?

    <p>Not always a natural number</p> Signup and view all the answers

    What is the purpose of 0 in the system of whole numbers?

    <p>To represent the absence of quantity</p> Signup and view all the answers

    What is an additive inverse of an integer?

    <p>A number that when added gives 0</p> Signup and view all the answers

    What are numbers that can be expressed as the quotient of two integers?

    <p>Rational numbers</p> Signup and view all the answers

    What is an example of an irrational number?

    <p>(\sqrt{2})</p> Signup and view all the answers

    What is the result of subtracting a larger number from a smaller number?

    <p>A negative number</p> Signup and view all the answers

    What is the effect of adding a negative number?

    <p>It decreases the value</p> Signup and view all the answers

    What is the product of two negative numbers?

    <p>A positive number</p> Signup and view all the answers

    What is the quotient of a positive number and a negative number?

    <p>A negative number</p> Signup and view all the answers

    What is the additive inverse of a number?

    <p>The negative of the number</p> Signup and view all the answers

    What is the result of adding a number and its additive inverse?

    <p>Zero</p> Signup and view all the answers

    What is the distributive property of multiplication over addition?

    <p>a(b + c) = ab + ac</p> Signup and view all the answers

    What is the square root of a number?

    <p>The positive square root</p> Signup and view all the answers

    What is an example of a real-world situation where integers are used?

    <p>All of the above</p> Signup and view all the answers

    What type of numbers are -7 and -500?

    <p>Integers</p> Signup and view all the answers

    What is the result of subtracting a larger number from a smaller number?

    <p>A negative number</p> Signup and view all the answers

    What is the equivalent of subtracting a negative number?

    <p>Adding a positive number</p> Signup and view all the answers

    What is the rule for multiplying a positive and a negative number?

    <p>The result is always negative</p> Signup and view all the answers

    What is the purpose of exponents in mathematical notation?

    <p>To provide a shorthand method for writing repeated multiplication</p> Signup and view all the answers

    What is the rule for calculating powers in mixed operations?

    <p>Powers should be calculated before performing multiplication and division</p> Signup and view all the answers

    What does a negative exponent represent?

    <p>The reciprocal of the base raised to the positive exponent</p> Signup and view all the answers

    What is the purpose of scientific notation?

    <p>To express very large or very small numbers</p> Signup and view all the answers

    What is the next step in solving an exponential equation?

    <p>Rewrite both sides of the equation with the same base</p> Signup and view all the answers

    What is the purpose of investigating and extending geometric patterns?

    <p>To analyze and describe patterns</p> Signup and view all the answers

    What is the purpose of estimating in calculations?

    <p>To get close to an answer without performing precise calculations</p> Signup and view all the answers

    What is the next step in identifying a pattern in a geometric arrangement?

    <p>Analyze the arrangement and identify the pattern</p> Signup and view all the answers

    How is long division performed?

    <p>By dividing the number step-by-step, subtracting multiples of the divisor from the dividend</p> Signup and view all the answers

    What is the lowest common multiple of two or more numbers?

    <p>The smallest number that is a multiple of each of them</p> Signup and view all the answers

    How is the highest common factor of two numbers found?

    <p>By identifying the common prime factors of the numbers and multiplying them</p> Signup and view all the answers

    What is the formula for calculating average speed?

    <p>Average speed = Distance / Time</p> Signup and view all the answers

    What is the difference between the HP price and the cash price?

    <p>The interest</p> Signup and view all the answers

    What is the formula for calculating the distance?

    <p>Distance = Average speed × Time</p> Signup and view all the answers

    What is the term for the largest number that divides each of two or more numbers without leaving a remainder?

    <p>Highest Common Factor</p> Signup and view all the answers

    What is the purpose of compensating for errors in calculations?

    <p>To correct errors introduced by rounding</p> Signup and view all the answers

    What is the formula for calculating time?

    <p>Time = Distance / Average speed</p> Signup and view all the answers

    What is an algebraic expression?

    <p>A sequence of operations that can be described in words and diagrams</p> Signup and view all the answers

    What is the order of operations in an algebraic expression without brackets?

    <p>Multiplication and division first, then addition and subtraction</p> Signup and view all the answers

    What is a monomial?

    <p>An expression with one term</p> Signup and view all the answers

    What is the purpose of brackets in an algebraic expression?

    <p>To indicate the order of operations</p> Signup and view all the answers

    What is the term for the symbol representing the unknown value?

    <p>Variable</p> Signup and view all the answers

    What is the correct order of operations with brackets?

    <p>Perform calculations within brackets first</p> Signup and view all the answers

    What is a binomial?

    <p>An expression with two terms</p> Signup and view all the answers

    What is the convention for writing algebraic expressions?

    <p>Write the known number first in a product</p> Signup and view all the answers

    What is equivalent to an algebraic expression?

    <p>A sequence of operations with the same result</p> Signup and view all the answers

    What do you call the number multiplying the variable in an algebraic expression?

    <p>Coefficient</p> Signup and view all the answers

    What is the result of applying the rule $x - 1000$ to natural numbers smaller than 1000?

    <p>Negative numbers</p> Signup and view all the answers

    What is the result of applying the rule $rac{x}{10} + 10$ to natural numbers smaller than 10?

    <p>Positive numbers between 10 and 11</p> Signup and view all the answers

    What is the result of applying the rule $30x + 2$ to positive fractions with denominators 2, 3, and 5?

    <p>Positive numbers greater than 2</p> Signup and view all the answers

    What is a relationship between two variables where one variable quantity is influenced by another?

    <p>Function</p> Signup and view all the answers

    What is a diagram that illustrates the calculations needed to determine the output number for a given input variable?

    <p>Flow Diagram</p> Signup and view all the answers

    What is a representation of a function that provides a visual picture of the relationship?

    <p>Graph</p> Signup and view all the answers

    How many ways can a function be represented?

    <p>4</p> Signup and view all the answers

    What is the characteristic of a function that ensures each input number corresponds to only one output number?

    <p>One input, one output</p> Signup and view all the answers

    What is the purpose of brackets in algebraic expressions?

    <p>To specify the order of operations when necessary</p> Signup and view all the answers

    What is the result of multiplying a polynomial by a monomial?

    <p>Each term in the polynomial is multiplied by the monomial</p> Signup and view all the answers

    What is the formula for the square of a binomial (a + b)?

    <p>a^2 + 2ab + b^2</p> Signup and view all the answers

    What is the distributive property of division?

    <p>Both (x + y)/z = x/z + y/z and (x - y)/z = x/z - y/z</p> Signup and view all the answers

    What is the purpose of simplifying algebraic expressions?

    <p>To combine like terms and eliminate any parentheses</p> Signup and view all the answers

    What is the result of evaluating the expression (x + 3)(x + 2)?

    <p>x^2 + 5x + 6</p> Signup and view all the answers

    What is the formula for the cube of a monomial (2x)?

    <p>8x^3</p> Signup and view all the answers

    What is the purpose of the distributive property in algebra?

    <p>To simplify expressions and expand products</p> Signup and view all the answers

    What is the result of substituting a value into an algebraic expression?

    <p>A numerical value</p> Signup and view all the answers

    What is the formula for the square root of a monomial (16x^2)?

    <p>4x</p> Signup and view all the answers

    Which of the following is a property of the system of whole numbers?

    <p>The system is closed under addition and multiplication.</p> Signup and view all the answers

    What is the identity element for addition in the system of whole numbers?

    <p>0</p> Signup and view all the answers

    Which of the following is a characteristic of rational numbers?

    <p>They can be expressed as the quotient of two integers.</p> Signup and view all the answers

    What is the set of numbers that includes both rational and irrational numbers?

    <p>The set of real numbers.</p> Signup and view all the answers

    What is the characteristic of the system of integers that is not found in the system of whole numbers?

    <p>The system includes negative numbers.</p> Signup and view all the answers

    What is a characteristic of irrational numbers?

    <p>They cannot be expressed as a fraction.</p> Signup and view all the answers

    What is the result of adding a negative number to a positive number?

    <p>Depends on the magnitudes of the numbers</p> Signup and view all the answers

    What is the purpose of the number 0 in the system of whole numbers?

    <p>To represent the absence of quantity.</p> Signup and view all the answers

    What is the additive inverse of a number?

    <p>The number multiplied by -1</p> Signup and view all the answers

    What is the sum of two integers that can be?

    <p>Zero or non-zero.</p> Signup and view all the answers

    What is the rule for multiplying a positive and a negative number?

    <p>The product is always negative</p> Signup and view all the answers

    What is the equivalent of subtracting a negative number?

    <p>Adding the corresponding positive number</p> Signup and view all the answers

    What is the result of subtracting a larger number from a smaller number?

    <p>A negative number</p> Signup and view all the answers

    What is the purpose of negative numbers?

    <p>To extend the number system for practical purposes</p> Signup and view all the answers

    What is the distributive property of multiplication over addition?

    <p>a(b + c) = ab + bc</p> Signup and view all the answers

    What is the result of adding a number and its additive inverse?

    <p>Zero</p> Signup and view all the answers

    What is the rule for dividing a positive number by a negative number?

    <p>The quotient is always negative</p> Signup and view all the answers

    What is the result of subtracting an additive inverse?

    <p>Adding the corresponding positive number</p> Signup and view all the answers

    What is the result of subtracting a larger number from a smaller number?

    <p>A negative number</p> Signup and view all the answers

    What is the equivalent of subtracting a negative number?

    <p>Adding a positive number</p> Signup and view all the answers

    What is the rule for multiplying a positive and a negative number?

    <p>The result is always negative</p> Signup and view all the answers

    What does a negative exponent represent?

    <p>A reciprocal of the base raised to the positive exponent</p> Signup and view all the answers

    What is the purpose of scientific notation?

    <p>To express very large numbers in a simpler form</p> Signup and view all the answers

    What is the next step in solving an exponential equation?

    <p>Rewrite both sides of the equation with the same base</p> Signup and view all the answers

    What is the purpose of investigating and extending geometric patterns?

    <p>To identify the pattern and make predictions</p> Signup and view all the answers

    What is the purpose of estimating in calculations?

    <p>To get a close approximation of the answer</p> Signup and view all the answers

    What is the law of exponents that states $a^m imes a^n = a^{m+n}$?

    <p>The product of powers</p> Signup and view all the answers

    How do you find the LCM of two numbers?

    <p>By multiplying all the prime factors of both numbers, without repeating any factors</p> Signup and view all the answers

    What is the formula for calculating average speed?

    <p>Average speed = Distance / Time</p> Signup and view all the answers

    What is the order of operations in an expression involving exponents, multiplication, and addition?

    <p>Parentheses, exponents, multiplication, addition</p> Signup and view all the answers

    What is the purpose of compensating for errors in calculations?

    <p>To correct errors introduced by rounding</p> Signup and view all the answers

    What is the result of applying the law of exponents $a^m \div a^n = a^{m-n}$?

    <p>The difference of the exponents</p> Signup and view all the answers

    What is the term for the largest number that divides each of two or more numbers without leaving a remainder?

    <p>Highest Common Factor (HCF)</p> Signup and view all the answers

    How do you find the HCF of two numbers?

    <p>By multiplying the common prime factors of the numbers</p> Signup and view all the answers

    What is the difference between the HP price and the cash price?

    <p>The interest paid</p> Signup and view all the answers

    How do you calculate the distance?

    <p>Distance = Average speed × Time</p> Signup and view all the answers

    What is the formula for calculating time?

    <p>Time = Distance / Average speed</p> Signup and view all the answers

    What is the purpose of prime factorization?

    <p>To express a number as a product of its prime factors</p> Signup and view all the answers

    What is the purpose of an algebraic expression?

    <p>To indicate a sequence of operations</p> Signup and view all the answers

    What is the term for the number that multiplies the variable in an algebraic expression?

    <p>Coefficient</p> Signup and view all the answers

    What is the rule for evaluating algebraic expressions without brackets?

    <p>Perform multiplication and division before addition and subtraction</p> Signup and view all the answers

    What is the term for an expression with three terms?

    <p>Trinomial</p> Signup and view all the answers

    What is the purpose of brackets in an algebraic expression?

    <p>To perform calculations first</p> Signup and view all the answers

    What is the convention for writing algebraic expressions?

    <p>Write a known number first in a product</p> Signup and view all the answers

    What is an equivalent algebraic expression?

    <p>An expression with different sequences of operations but the same numerical value</p> Signup and view all the answers

    What is the term for the symbol representing the unknown value?

    <p>Variable</p> Signup and view all the answers

    What is the correct order of operations when brackets are present in an algebraic expression?

    <p>Perform calculations within brackets first, then multiplication and division, then addition and subtraction</p> Signup and view all the answers

    What is the purpose of a flow diagram in algebraic expressions?

    <p>To represent a sequence of operations</p> Signup and view all the answers

    What is the result of applying the rule 30x + 2 to positive fractions with denominators 2, 3, and 5?

    <p>Positive numbers greater than 2</p> Signup and view all the answers

    What represents the relationship between two variables where there is only one output number for each input number?

    <p>A function</p> Signup and view all the answers

    What is used to visually represent the relationship between two variables?

    <p>A graph</p> Signup and view all the answers

    What is used to describe the calculations needed to find the output number that corresponds to a given input number?

    <p>A formula</p> Signup and view all the answers

    What is the purpose of a flow diagram?

    <p>To illustrate the calculations needed to determine the output number</p> Signup and view all the answers

    What is the purpose of a table representation?

    <p>To show the input numbers and their corresponding function values</p> Signup and view all the answers

    How many different ways can a function be represented?

    <p>Multiple ways</p> Signup and view all the answers

    What is true about the application of a rule to a given input number?

    <p>It produces only one output number</p> Signup and view all the answers

    What is the purpose of using brackets in algebraic expressions?

    <p>To specify the order of operations when necessary</p> Signup and view all the answers

    What is the distributive property of multiplication over addition?

    <p>a(b + c) = ab + ac</p> Signup and view all the answers

    What is the result of evaluating the expression $(2x + 3)(x - 2)$?

    <p>$2x^2 + x - 12$</p> Signup and view all the answers

    What is the result of dividing a polynomial by a monomial?

    <p>Each term in the polynomial is divided by the monomial</p> Signup and view all the answers

    What is the result of evaluating the expression $(3x)^2$?

    <p>$9x^2$</p> Signup and view all the answers

    What is the equivalent of the expression $(x + 2)(x + 3)$?

    <p>$x^2 + 5x + 6$</p> Signup and view all the answers

    What is the convention for writing algebraic expressions?

    <p>Write the coefficient first, then the variable</p> Signup and view all the answers

    What is the result of applying the rule $2x + 1$ to the input $x = 3$?

    <p>7</p> Signup and view all the answers

    What is the result of evaluating the expression $(x - 2)(x + 3)$?

    <p>$x^2 - x + 6$</p> Signup and view all the answers

    What is the equivalent of the expression $(a + b)^2$?

    <p>$a^2 + 2ab + b^2$</p> Signup and view all the answers

    What is the result of adding a positive and a negative number?

    <p>Depends on the magnitudes of the numbers involved</p> Signup and view all the answers

    What is the effect of subtracting a negative number?

    <p>It has the same effect as adding a positive number</p> Signup and view all the answers

    What is the product of two negative numbers?

    <p>Positive</p> Signup and view all the answers

    What is the rule for multiplying a positive and a negative number?

    <p>The product is always negative</p> Signup and view all the answers

    What is the purpose of integers in real-world applications?

    <p>To model temperature changes and financial transactions</p> Signup and view all the answers

    Which of the following numbers is a natural number?

    <p>1</p> Signup and view all the answers

    What is the result of subtracting an additive inverse from a number?

    <p>The result is always zero</p> Signup and view all the answers

    What is the distributive property of multiplication over addition?

    <p>$a(b + c) = ab + bc$</p> Signup and view all the answers

    What is the purpose of 0 in the system of whole numbers?

    <p>To represent the absence of quantity</p> Signup and view all the answers

    What is the equivalent of adding a negative number?

    <p>Subtracting a positive number</p> Signup and view all the answers

    Which of the following properties is true for the system of whole numbers?

    <p>Closed under addition and multiplication</p> Signup and view all the answers

    What is an integer that is not a natural number?

    <p>-1</p> Signup and view all the answers

    What is the result of adding an integer and its additive inverse?

    <p>The result is always zero</p> Signup and view all the answers

    Which of the following is a characteristic of irrational numbers?

    <p>Cannot be expressed as a fraction of two integers</p> Signup and view all the answers

    What is the purpose of negative numbers in the number system?

    <p>To extend the number system for practical purposes</p> Signup and view all the answers

    What is the set of numbers that includes both rational and irrational numbers?

    <p>Real numbers</p> Signup and view all the answers

    Which of the following is a property of integers?

    <p>Each integer has an additive inverse</p> Signup and view all the answers

    What is the result of adding 0 to a number?

    <p>The result is always the number you start with</p> Signup and view all the answers

    What is the result of subtracting a larger number from a smaller number?

    <p>A negative number</p> Signup and view all the answers

    What is the equivalent of adding a negative number?

    <p>Subtracting the corresponding positive number</p> Signup and view all the answers

    What is the result of multiplying a positive number and a negative number?

    <p>A negative number</p> Signup and view all the answers

    What is the rule for calculating powers in mixed operations?

    <p>Calculate powers before performing multiplication and division</p> Signup and view all the answers

    What does a negative exponent represent?

    <p>The reciprocal of the base raised to the positive exponent</p> Signup and view all the answers

    What is the purpose of scientific notation?

    <p>To express very large or very small numbers in a compact form</p> Signup and view all the answers

    What is the next step in solving an exponential equation?

    <p>Rewrite both sides of the equation with the same base</p> Signup and view all the answers

    What is the purpose of investigating and extending geometric patterns?

    <p>To identify and extend patterns in arrangements</p> Signup and view all the answers

    What is the result of adding a number and its additive inverse?

    <p>Zero</p> Signup and view all the answers

    What is the effect of adding an integer to its additive inverse?

    <p>It results in zero</p> Signup and view all the answers

    What is the main purpose of estimating in calculations?

    <p>To get close to an answer without performing precise calculations</p> Signup and view all the answers

    How do you find the lowest common multiple of two numbers?

    <p>By multiplying all the prime factors of both numbers, without repeating any factors unless they appear more than once in one of the numbers</p> Signup and view all the answers

    What is the formula for calculating average speed?

    <p>Distance / Time</p> Signup and view all the answers

    What is the term for the largest number that divides each of two or more numbers without leaving a remainder?

    <p>Highest Common Factor</p> Signup and view all the answers

    How do you find the highest common factor of two numbers?

    <p>By multiplying the common prime factors of the numbers</p> Signup and view all the answers

    What is the purpose of compensating for errors in calculations?

    <p>To correct errors introduced by rounding</p> Signup and view all the answers

    What is the formula for calculating distance?

    <p>Average speed × Time</p> Signup and view all the answers

    How do you calculate the simple interest on a principal amount?

    <p>By calculating the interest on the principal amount without adding it to the principal each year</p> Signup and view all the answers

    What is the difference between the HP price and the cash price?

    <p>The interest amount</p> Signup and view all the answers

    What is the purpose of prime factorization?

    <p>To express a number as a product of its prime factors</p> Signup and view all the answers

    What is the purpose of algebraic language?

    <p>To describe a sequence of operations</p> Signup and view all the answers

    What is the correct order of operations when brackets are present in an algebraic expression?

    <p>Perform the calculations within the brackets first, then multiplication and division</p> Signup and view all the answers

    What is the term for an expression with one term?

    <p>Monomial</p> Signup and view all the answers

    What is the purpose of convention in writing algebraic expressions?

    <p>To avoid ambiguity</p> Signup and view all the answers

    What is the result of applying the order of operations in the expression $12 + 3x$ when $x = 5$?

    <p>Multiply 5 by 3, then add 12</p> Signup and view all the answers

    What is the term for the symbol representing the unknown value in an algebraic expression?

    <p>Variable</p> Signup and view all the answers

    What is the purpose of equivalent algebraic expressions?

    <p>To have the same numerical value for any given value of the variable</p> Signup and view all the answers

    What is the convention for writing algebraic expressions when there are no brackets?

    <p>Perform multiplication and division before addition and subtraction</p> Signup and view all the answers

    What is the term for an expression which is a sum of two terms?

    <p>Binomial</p> Signup and view all the answers

    What is the term for the number multiplying the variable in an algebraic expression?

    <p>Coefficient</p> Signup and view all the answers

    What is the term for a relationship between two variables in which there is only one output number for each input number?

    <p>Function</p> Signup and view all the answers

    What does a flow diagram illustrate in a function?

    <p>The calculations needed to determine the output number</p> Signup and view all the answers

    What is the purpose of a table in representing a function?

    <p>To complete the input numbers and their corresponding function values</p> Signup and view all the answers

    What is the benefit of representing a function using a graph?

    <p>It provides a visual representation of the relationship</p> Signup and view all the answers

    How many different ways can a function be represented?

    <p>4</p> Signup and view all the answers

    What is the result of applying the rule 30x + 2 to positive fractions with denominators 2, 3, and 5?

    <p>Positive numbers greater than 2</p> Signup and view all the answers

    What is the relationship between variables if one variable quantity is influenced by another?

    <p>There is an influence</p> Signup and view all the answers

    What is the purpose of an algebraic expression?

    <p>To describe the calculations needed to find the output number</p> Signup and view all the answers

    What is the result of applying the distributive property to the expression (a + b)(a - b)?

    <p>a^2 - b^2</p> Signup and view all the answers

    Which of the following is a correct simplification of the expression 2x + 5x?

    <p>7x</p> Signup and view all the answers

    What is the result of dividing the polynomial 6x^2 + 12x by the monomial 2x?

    <p>3x + 6</p> Signup and view all the answers

    What is the simplified form of the expression (x + 3)^2?

    <p>x^2 + 6x + 9</p> Signup and view all the answers

    What is the result of evaluating the expression 2x^2 + 3x - 1 when x = 4?

    <p>45</p> Signup and view all the answers

    What is the result of applying the rule 'multiply a number by 5 and subtract the result from 50' to the input 6?

    <p>20</p> Signup and view all the answers

    What is the equivalent expression for the given rule '2n + 1' when applied to even numbers?

    <p>n + 1</p> Signup and view all the answers

    What is the result of evaluating the expression (x - 2)(x + 3) when x = 5?

    <p>27</p> Signup and view all the answers

    What is the convention for writing algebraic expressions involving the product of a number and a variable?

    <p>Write the number first, then the variable</p> Signup and view all the answers

    What is the result of simplifying the expression 3x^2 + 6x + 2x^2 + 4x?

    <p>5x^2 + 10x</p> Signup and view all the answers

    Which set of numbers is not closed under division?

    <p>Natural numbers</p> Signup and view all the answers

    What is the term for the set of numbers that includes both rational and irrational numbers?

    <p>Real numbers</p> Signup and view all the answers

    What is the additive inverse of an integer?

    <p>An integer of the same absolute value but opposite sign</p> Signup and view all the answers

    What is a characteristic of irrational numbers?

    <p>They cannot be expressed as a fraction of two integers</p> Signup and view all the answers

    What is the purpose of 0 in the system of whole numbers?

    <p>To write numbers without a special symbol for 10</p> Signup and view all the answers

    What is a characteristic of natural numbers?

    <p>They can be used to count</p> Signup and view all the answers

    What is the system of integers extended from?

    <p>Natural numbers</p> Signup and view all the answers

    What is a characteristic of rational numbers?

    <p>They can be expressed as the quotient of two integers</p> Signup and view all the answers

    What is the purpose of compensating for errors in calculations?

    <p>To correct the rounding errors introduced in estimation</p> Signup and view all the answers

    What is the formula for calculating average speed?

    <p>Distance ÷ Time</p> Signup and view all the answers

    What is the term for the largest number that divides each of two or more numbers without leaving a remainder?

    <p>Highest Common Factor (HCF)</p> Signup and view all the answers

    What is the difference between the HP price and the cash price?

    <p>The interest amount</p> Signup and view all the answers

    What is the result of subtracting a negative number from a positive number?

    <p>Depends on the magnitudes of the numbers</p> Signup and view all the answers

    How is the Lowest Common Multiple (LCM) of two numbers found?

    <p>By multiplying all the prime factors of both numbers</p> Signup and view all the answers

    Which of the following is a property of adding integers?

    <p>Commutative property</p> Signup and view all the answers

    What is the purpose of estimating in calculations?

    <p>To get a close approximation of the answer</p> Signup and view all the answers

    What is the formula for calculating distance?

    <p>Average speed × Time</p> Signup and view all the answers

    What is the result of adding a number and its additive inverse?

    <p>Always 0</p> Signup and view all the answers

    What is the product of two negative integers?

    <p>Always positive</p> Signup and view all the answers

    What is the term for the symbol representing the unknown value in an algebraic expression?

    <p>Variable</p> Signup and view all the answers

    What is the result of subtracting an additive inverse from a number?

    <p>Always the original number</p> Signup and view all the answers

    What is the purpose of prime factorization?

    <p>To express a number as a product of its prime factors</p> Signup and view all the answers

    What is the purpose of negative numbers in the number system?

    <p>Both A and B</p> Signup and view all the answers

    What is the formula for calculating time?

    <p>Distance ÷ Average speed</p> Signup and view all the answers

    What is the result of adding a positive and a negative number?

    <p>Depends on the magnitudes of the numbers</p> Signup and view all the answers

    What is the distributive property of multiplication over addition?

    <p>a(b + c) = ab + ac</p> Signup and view all the answers

    What is the result of multiplying a positive and a negative integer?

    <p>Always negative</p> Signup and view all the answers

    What is the purpose of exponents in mathematical notation?

    <p>To indicate repeated multiplication</p> Signup and view all the answers

    When solving an equation involving subtracting a larger number from a smaller one, what type of number is the result?

    <p>Negative</p> Signup and view all the answers

    What is the result of adding the additive inverse of an integer to the integer itself?

    <p>Zero</p> Signup and view all the answers

    What is the purpose of exponents in mathematical notation?

    <p>To represent repeated multiplication</p> Signup and view all the answers

    What is the rule for calculating powers in mixed operations?

    <p>Calculate exponents and then multiplication and division</p> Signup and view all the answers

    What does a negative exponent represent?

    <p>The reciprocal of the base raised to the positive exponent</p> Signup and view all the answers

    What is the purpose of scientific notation?

    <p>To express very large or very small numbers in a more readable form</p> Signup and view all the answers

    When converting a number from scientific notation to decimal form, what do you do?

    <p>Move the decimal point to the left according to the exponent</p> Signup and view all the answers

    What is the first step in solving an exponential equation?

    <p>Rewrite both sides of the equation with the same base</p> Signup and view all the answers

    What is the purpose of investigating and extending geometric patterns?

    <p>To describe the patterns of different shapes and colors</p> Signup and view all the answers

    When analyzing geometric arrangements, what do you identify?

    <p>The pattern of different shapes and colors</p> Signup and view all the answers

    What is the purpose of an algebraic expression?

    <p>To represent a sequence of calculations</p> Signup and view all the answers

    What is the term for an expression with one term?

    <p>Monomial</p> Signup and view all the answers

    What operation should be performed first in an algebraic expression without brackets?

    <p>Multiplication and division</p> Signup and view all the answers

    What is the term for the number multiplying the variable in an algebraic expression?

    <p>Coefficient</p> Signup and view all the answers

    What is the purpose of brackets in an algebraic expression?

    <p>To indicate the order of operations</p> Signup and view all the answers

    What is the term for an expression which is a sum of two terms?

    <p>Binomial</p> Signup and view all the answers

    What is the convention for writing algebraic expressions?

    <p>Omit the multiplication sign</p> Signup and view all the answers

    What is the relationship between equivalent algebraic expressions?

    <p>They have different sequences of operations but the same numerical value</p> Signup and view all the answers

    What is the term for the symbol representing the unknown value in an algebraic expression?

    <p>Variable</p> Signup and view all the answers

    What operation should be performed next in an expression without brackets, after multiplication and division?

    <p>Addition and subtraction</p> Signup and view all the answers

    What is the result of expanding the product of two binomials (a + b)(a - b)?

    <p>a^2 - 2ab + b^2</p> Signup and view all the answers

    What is the result of dividing a polynomial by a monomial?

    <p>Each term in the polynomial is divided by the monomial</p> Signup and view all the answers

    What is the equivalent of the algebraic expression (a + b)^2?

    <p>a^2 + 2ab + b^2</p> Signup and view all the answers

    What is the result of evaluating the expression (x + 2)(x + 3) when x = 1?

    <p>10</p> Signup and view all the answers

    What is the result of simplifying the expression 2x + 3x + 5x?

    <p>8x + 5</p> Signup and view all the answers

    What is the result of finding the square root of 16x^2?

    <p>4x</p> Signup and view all the answers

    What is the result of applying the rule x^2 + 5x - 2 to the input x = 2?

    <p>14</p> Signup and view all the answers

    What is the equivalent of the algebraic expression (a - b)^2?

    <p>a^2 - 2ab + b^2</p> Signup and view all the answers

    What is the result of multiplying a polynomial by a monomial?

    <p>Each term in the polynomial is multiplied by the monomial</p> Signup and view all the answers

    What is the result of evaluating the expression 2x^2 + 3x - 5 when x = -1?

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

    What is the primary characteristic of a function?

    <p>It is a relationship between two variables with only one output number for each input number</p> Signup and view all the answers

    What is the purpose of a flow diagram in representing a function?

    <p>To illustrate the calculations needed to determine the output number</p> Signup and view all the answers

    What is the benefit of using a graph to represent a function?

    <p>It provides a visual representation of the relationship between the variables</p> Signup and view all the answers

    What is the result of applying the rule $30x + 2$ to positive fractions with denominators 2, 3, and 5?

    <p>Positive numbers greater than 2</p> Signup and view all the answers

    What can be used to determine which output number corresponds to a specific input number?

    <p>All of the above</p> Signup and view all the answers

    What is a common way to represent a function?

    <p>In multiple ways, including a formula, table, graph, and flow diagram</p> Signup and view all the answers

    What is the term for a relationship between two variables where each input number corresponds to only one output number?

    <p>Function</p> Signup and view all the answers

    What is the benefit of using a table to represent a function?

    <p>It clearly indicates which output value corresponds to each input value</p> Signup and view all the answers

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