Gr 9 MATH: June Exam Easy
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Questions and Answers

What is the set of numbers that we use to count called?

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

    • Which operation is not closed under the natural numbers?

  • Subtraction (correct)
  • Addition
  • Multiplication
  • Division (correct)

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

  • To represent negative numbers
  • To count objects
  • To write fractions
  • To write numbers, especially multiples of 10 (correct)

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

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

    What is the set of numbers that includes fractions and negative fractions?

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

    Which of the following is an example of an irrational number?

    <p>√2</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 properties is true for integers?

    <p>The sum of two integers can be zero</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 the product of a positive and a negative number?

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

    What is an algebraic expression indicating in a sequence of operations?

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

    What should be calculated first in an algebraic expression with brackets?

    <p>The expressions in brackets.</p> Signup and view all the answers

    What is the purpose of exponents in mathematics?

    <p>To provide a shorthand method for writing repeated multiplication</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 the correct order of operations when calculating expressions involving exponents?

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

    What is a monomial in algebraic expressions?

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

    What is the meaning of a negative exponent in scientific notation?

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

    What is the purpose of simplifying exponential expressions?

    <p>To make the expression easier to work with</p> Signup and view all the answers

    What is the coefficient in an algebraic expression?

    <p>The number multiplying the variable.</p> Signup and view all the answers

    What is the first step in solving exponential equations?

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

    What is a trinomial in algebraic expressions?

    <p>An expression which is a sum of three terms.</p> Signup and view all the answers

    What is the main focus of geometric patterns?

    <p>Investigating and extending patterns</p> Signup and view all the answers

    What is a variable in algebraic expressions?

    <p>The symbol, often x, representing the unknown value.</p> Signup and view all the answers

    What is a binomial in algebraic expressions?

    <p>An expression which is a sum of two terms.</p> Signup and view all the answers

    What is the purpose of identifying the next number in a pattern?

    <p>To understand the pattern better</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 are equivalent algebraic expressions?

    <p>Expressions with different sequences of operations but the same numerical value.</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 process of dividing a number step-by-step, subtracting multiples of the divisor from the dividend, and continuing the process until the remainder is less than the divisor?

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

    What is the smallest common multiple of two or more numbers called?

    <p>Lowest Common Multiple</p> Signup and view all the answers

    What is the process of expressing a number as a product of its prime factors?

    <p>Prime factorization</p> Signup and view all the answers

    What is the formula to calculate average speed?

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

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

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

    How is simple interest calculated?

    <p>On the principal amount without adding the interest to the principal each year</p> Signup and view all the answers

    What is the formula to calculate distance?

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

    What is the ratio of the numbers of apples collected by different people used to compare?

    <p>Their collection rates</p> Signup and view all the answers

    What is the highest number that divides each of two or more numbers without leaving a remainder called?

    <p>Highest Common Factor</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 to a positive number?

    <p>The result is the same as subtracting the corresponding 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 additive inverse of a number?

    <p>The corresponding negative 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 result of dividing a positive number by a negative number?

    <p>Negative</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 the purpose of negative numbers?

    <p>Both a and b</p> Signup and view all the answers

    What can be modeled using integers and the rules of addition, subtraction, multiplication, and division?

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

    What is the purpose of using brackets in algebraic expressions?

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

    Which of the following is an example of the distributive property?

    <p>2(x + 3) = 2x + 6</p> Signup and view all the answers

    What is the result of multiplying (x + 2) by (x + 3)?

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

    What is the result of dividing (x^2 + 3x - 4) by (x + 1)?

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

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

    <p>2(x^2 + 2x - 3)</p> Signup and view all the answers

    What is the square of the binomial (x + 3)?

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

    What is the result of substituting x = 2 into the expression 2x^2 + 3x - 4?

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

    What is the rule for calculating the output numbers when the input is multiplied by 5 and the result is subtracted from 50?

    <p>50 - 5x</p> Signup and view all the answers

    What is the output number when the input is 4 and the rule is 2n + 1?

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

    Which of the following is an equivalent form of the expression 2x^2 + 3x - 4?

    <p>2(x^2 + 2x - 3)</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 type of numbers does the rule $\frac{x}{10} + 10$ result in when applied 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 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 is the purpose of a flow diagram?

    <p>To illustrate the calculations needed to determine the output number for a given input variable</p> Signup and view all the answers

    What is a characteristic of a function?

    <p>There is only one output number for each input number</p> Signup and view all the answers

    How can a function be represented?

    <p>Using a flow diagram, a table, or a graph</p> Signup and view all the answers

    What is the purpose of a table representation of a function?

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

    What is the main difference between the natural numbers and the whole numbers?

    <p>The natural numbers do not include 0, while the whole numbers do.</p> Signup and view all the answers

    What is a common property shared by the natural numbers and whole numbers?

    <p>They are both closed under addition and multiplication.</p> Signup and view all the answers

    What is the system of integers extended to include?

    <p>Negative 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 an example of an irrational number?

    <p>√2</p> Signup and view all the answers

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

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

    What is a property of the system of natural numbers?

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

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

    <p>To be used as an identity element for addition.</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 process of dividing a number step-by-step, subtracting multiples of the divisor from the dividend, and continuing the process until the remainder is less than the divisor?

    <p>Long Division</p> Signup and view all the answers

    What is the smallest common multiple of two or more numbers called?

    <p>Lowest Common Multiple</p> Signup and view all the answers

    What is the process of expressing a number as a product of its prime factors?

    <p>Prime Factorization</p> Signup and view all the answers

    What is the formula to calculate average speed?

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

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

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

    How is simple interest calculated?

    <p>On the principal amount without adding the interest to the principal each year.</p> Signup and view all the answers

    What is the ratio of the numbers of apples collected by different people used to compare?

    <p>Collection rates</p> Signup and view all the answers

    What is the highest number that divides each of two or more numbers without leaving a remainder called?

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

    What is the formula to calculate distance?

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

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

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

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

    <p>Division, Multiplication, Addition, Subtraction</p> Signup and view all the answers

    What describes the calculations needed to find the output number that corresponds to a given input number?

    <p>Algebraic Expression</p> Signup and view all the answers

    What can be used to visually represent the relationship between two variables?

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

    What is the purpose of the distributive property?

    <p>To expand the product of two binomials</p> Signup and view all the answers

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

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

    What shows the calculations performed to produce the output numbers and indicates which output numbers correspond to which input numbers?

    <p>Flow Diagram</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 can be completed to show the input numbers and their corresponding function values?

    <p>Table</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 result of dividing the polynomial $x^2 + 3x - 4$ by the monomial $x - 1$?

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

    What is the purpose of factorising algebraic expressions?

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

    What is one way to determine which number is linked to a specific value of the other variable?

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

    What is an algebraic expression used to describe?

    <p>A relationship between two variables</p> Signup and view all the answers

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

    <p>3</p> Signup and view all the answers

    What is the distributive property of division?

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

    What is the purpose of brackets in algebraic expressions?

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

    What is the result of evaluating the expression $(5x)^2$?

    <p>25x^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 equivalent of subtracting a negative number?

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

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

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

    What is the purpose of exponents in mathematics?

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

    What is the order of operations when calculating expressions involving exponents?

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

    What is the meaning of a negative exponent in scientific notation?

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

    What is the purpose of simplifying exponential expressions?

    <p>To rewrite the expression in a more concise form</p> Signup and view all the answers

    What is the first step in solving exponential equations?

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

    What is the main focus of geometric patterns?

    <p>Investigating and extending patterns</p> Signup and view all the answers

    What is an algebraic expression indicating?

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

    What is the purpose of identifying the next number in a pattern?

    <p>To predict the number of black tiles in future arrangements</p> Signup and view all the answers

    What operation should be performed first in an algebraic expression with brackets?

    <p>Calculations within the brackets</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 in algebraic expressions?

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

    What is the coefficient in an algebraic expression?

    <p>The number multiplying the variable</p> Signup and view all the answers

    What is a trinomial in algebraic expressions?

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

    What is the purpose of simplifying algebraic expressions?

    <p>To make the expression easier to understand</p> Signup and view all the answers

    What is a variable in algebraic expressions?

    <p>The symbol representing the unknown value</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 are equivalent algebraic expressions?

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

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

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

    What is the additive inverse of a number?

    <p>A number that has the same magnitude but opposite sign</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 product of two negative numbers?

    <p>A positive 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 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 result of dividing a positive number by a negative number?

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

    What is the square root of a number?

    <p>A number that is squared to give the original number</p> Signup and view all the answers

    What can be modeled using integers and the rules of addition, subtraction, multiplication, and division?

    <p>Temperature changes, depths below sea level, and financial transactions</p> Signup and view all the answers

    What is the purpose of forming a sequence with dots?

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

    What is done first in an expression with brackets?

    <p>Calculations within the brackets</p> Signup and view all the answers

    What is a term with a single variable and coefficient?

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

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

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

    What is the purpose of identifying patterns in algebraic expressions?

    <p>To compare sequences and identify relationships</p> Signup and view all the answers

    What is the term for the numerical coefficient in a monomial?

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

    What is the purpose of writing algebraic expressions?

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

    What is an expression with three terms?

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

    What is the convention for writing algebraic expressions?

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

    What is the order of operations when calculating expressions without brackets?

    <p>Multiplication and division first, followed by addition and subtraction</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 process of expressing a number as a product of its prime factors?

    <p>Prime factorization</p> Signup and view all the answers

    What is the formula to calculate average speed?

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

    What is the highest number that divides each of two or more numbers without leaving a remainder called?

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

    What is the process of dividing a number step-by-step, subtracting multiples of the divisor from the dividend, and continuing the process until the remainder is less than the divisor?

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

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

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

    What is the purpose of using prime factorization?

    <p>To find the LCM and HCF of two numbers</p> Signup and view all the answers

    What is the formula to calculate distance?

    <p>Average speed × Time</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 ratio of the numbers of apples collected by different people used to compare?

    <p>Their rates of collection</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

    How is simple interest calculated?

    <p>On the principal amount without adding the interest to the principal each year</p> Signup and view all the answers

    What is the purpose of combining like terms when simplifying an algebraic expression?

    <p>To make the expression easier to evaluate</p> Signup and view all the answers

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

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

    What is the purpose of exponents in mathematics?

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

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

    <p>A polynomial with each term multiplied by the monomial</p> Signup and view all the answers

    What is the correct order of operations when calculating expressions involving exponents?

    <p>Parentheses, Exponents, Multiplication and Division, Addition and Subtraction</p> Signup and view all the answers

    What is the distributive property of division?

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

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

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

    What is the meaning of a negative exponent in scientific notation?

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

    What is the purpose of substituting specific values for variables in an algebraic expression?

    <p>To evaluate the expression for a given input</p> Signup and view all the answers

    What is the purpose of simplifying exponential expressions?

    <p>To use the laws of exponents to simplify expressions</p> Signup and view all the answers

    What is the main focus of geometric patterns?

    <p>Investigating and extending patterns</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 a given input?

    <p>The output depends on the input value</p> Signup and view all the answers

    What is a common property of natural numbers and whole numbers?

    <p>They are closed under addition and multiplication</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 purpose of identifying the next number in a pattern?

    <p>To predict the next number in the pattern</p> Signup and view all the answers

    What is an equivalent algebraic expression?

    <p>An expression with different sequence of operations but same result</p> Signup and view all the answers

    What is the main difference between natural numbers and whole numbers?

    <p>Natural numbers do not include 0, while whole numbers do</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 a characteristic of integers?

    <p>They can be zero or have an additive inverse</p> Signup and view all the answers

    What is the purpose of factoring algebraic expressions?

    <p>To simplify the expression</p> Signup and view all the answers

    What is a characteristic of rational numbers?

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

    What is the result of squaring a binomial (a - b)?

    <p>a^2 - 2ab + b^2</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 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 a property of the system of natural numbers?

    <p>It is closed under addition and multiplication</p> Signup and view all the answers

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

    <p>To write numbers and provide a place value</p> Signup and view all the answers

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

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

    How can a function be represented?

    <p>Using a flow diagram, a table, and a graph</p> Signup and view all the answers

    What does a flow diagram show?

    <p>The calculations performed to produce the output numbers and the corresponding input numbers</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 that corresponds to a given input number</p> Signup and view all the answers

    If one variable quantity is influenced by another, what is the result?

    <p>A relationship between the two variables</p> Signup and view all the answers

    What is a table used for in function representation?

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

    What is the purpose of a graph in function representation?

    <p>To visually represent the function</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

    When adding a positive and a negative number, what determines the result?

    <p>The magnitude of the numbers involved</p> Signup and view all the answers

    What is the effect of subtracting a negative number?

    <p>It is the same as adding a positive 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 product of two negative numbers?

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

    What does the distributive property of multiplication over addition state?

    <p>a(b + c) = ab + ac</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 square root of a number?

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

    What are negative numbers used for?

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

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

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

    What can be modeled using integers and the rules of addition, subtraction, multiplication, and division?

    <p>Real-world situations</p> Signup and view all the answers

    What is true about the system of natural numbers?

    <p>It is closed under addition and multiplication</p> Signup and view all the answers

    What is the main difference between the system of whole numbers and the system of natural numbers?

    <p>The system of whole numbers includes 0</p> Signup and view all the answers

    What is true about the sum of two integers?

    <p>It can be zero</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 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 a property of the system of integers?

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

    What is the purpose of the system of integers?

    <p>To include negative numbers</p> Signup and view all the answers

    What is true about the system of whole numbers and the system of integers?

    <p>The system of whole numbers is a subset of the system of integers</p> Signup and view all the answers

    What is the result of adding a positive number 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 from a positive number?

    <p>Increases the result</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 additive inverse of a number?

    <p>A number that adds up to 0</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 result of dividing a positive number by a negative number?

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

    What is the square root of a number?

    <p>The positive number that when multiplied by itself gives the original 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 can be modeled using integers and the rules of addition, subtraction, multiplication, and division?

    <p>Real-world situations</p> Signup and view all the answers

    What is the purpose of estimating in calculations?

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

    What is the process of dividing a number step-by-step, subtracting multiples of the divisor from the dividend, and continuing the process until the remainder is less than the divisor?

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

    What is the smallest common multiple of two or more numbers called?

    <p>Lowest Common Multiple</p> Signup and view all the answers

    What is the process of expressing a number as a product of its prime factors?

    <p>Prime factorization</p> Signup and view all the answers

    What is the formula to calculate average speed?

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

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

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

    How is simple interest calculated?

    <p>On the principal amount without adding the interest to the principal each year</p> Signup and view all the answers

    What is the ratio of the numbers of apples collected by different people used to compare?

    <p>Their collection rates</p> Signup and view all the answers

    What is the highest number that divides each of two or more numbers without leaving a remainder called?

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

    What is the formula to calculate distance?

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

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

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

    What is the equivalent of subtracting a negative number in integer operations?

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

    What is the result of the product of a positive and a negative number in integer operations?

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

    What is the purpose of exponents in mathematics?

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

    What is the correct order of operations when calculating expressions involving exponents?

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

    What does a negative exponent represent in scientific notation?

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

    What is the purpose of simplifying exponential expressions?

    <p>To make the expressions easier to understand and solve</p> Signup and view all the answers

    What is the main focus of geometric patterns?

    <p>Investigating and extending geometric patterns</p> Signup and view all the answers

    What is the purpose of identifying the next number in a pattern?

    <p>To predict the next arrangement</p> Signup and view all the answers

    What is the benefit of using scientific notation to express very large or very small numbers?

    <p>It provides a simple and concise way to express very large or very small numbers</p> Signup and view all the answers

    What is the purpose of identifying variables in algebraic expressions?

    <p>To represent the unknown value</p> Signup and view all the answers

    What is the rule for performing calculations in an algebraic expression with brackets?

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

    What is a trinomial in algebraic expressions?

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

    What is the purpose of equivalent algebraic expressions?

    <p>To represent the same numerical value</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 the result of performing multiplication and division in an algebraic expression without brackets?

    <p>Perform multiplication and division first</p> Signup and view all the answers

    What is the purpose of monomials, binomials, and trinomials in algebraic expressions?

    <p>To classify algebraic expressions based on the number of terms</p> Signup and view all the answers

    What is the role of the coefficient in an algebraic expression?

    <p>To multiply the variable term</p> Signup and view all the answers

    What is the purpose of algebraic expressions?

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

    What is the rule for performing calculations in an algebraic expression without brackets?

    <p>Perform multiplication and division first</p> Signup and view all the answers

    What happens when the rule ( x - 1000 ) is applied to natural numbers smaller than 1000?

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

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

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

    How can a function be represented?

    <p>By a table, flow diagram, formula, or graph.</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 can be used to complete a table to show the input numbers and their corresponding function values?

    <p>A formula or a flow diagram.</p> Signup and view all the answers

    What is the purpose of a graph?

    <p>To provide a visual representation of the relationship.</p> Signup and view all the answers

    How many ways can a function be represented?

    <p>Four ways.</p> Signup and view all the answers

    What is the rule ( rac{x}{10} + 10 ) applied to?

    <p>Natural numbers smaller than 10.</p> Signup and view all the answers

    What is the purpose of combining like terms when simplifying an expression?

    <p>To reduce the number of terms in the expression</p> Signup and view all the answers

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

    <p>A polynomial with the same degree</p> Signup and view all the answers

    How do you evaluate the expression $(a + b)^2$?

    <p>By expanding the product using the distributive property</p> Signup and view all the answers

    What is the purpose of substituting specific values for variables in an algebraic expression?

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

    What is the rule for 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 distributive property of multiplication over addition?

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

    What is the purpose of applying the distributive property in algebraic expressions?

    <p>To expand the product of binomials</p> Signup and view all the answers

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

    <p>A polynomial with the same degree</p> Signup and view all the answers

    What is the purpose of using brackets in algebraic expressions?

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

    What is the result of applying the rule of multiplication to a binomial?

    <p>A polynomial with the same degree</p> Signup and view all the answers

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