Gr 9 MATH: June Exam Medium
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Questions and Answers

Which of the following is a property of natural numbers?

  • When a natural number is subtracted from another natural number, the answer is always a natural number.
  • When you add two or more natural numbers, you get a natural number again. (correct)
  • When a natural number is multiplied by a whole number, the answer is always a fraction.
  • When a natural number is divided by another natural number, the answer is always a natural number.

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

  • -1
  • -0 (correct)
  • 1
  • 0 (correct)

    • Which of the following statements is true about the system of integers?

  • The sum of two integers can never be zero.
  • Each integer has a multiplicative inverse.
  • The system of integers is closed under division.
  • The sum of two integers can be zero. (correct)

    • What is the definition of a rational number?

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

    Which of the following numbers 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 set of real numbers</p> Signup and view all the answers

    Why is 0 included in the system of whole numbers?

    <p>Because we need it to write numbers.</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 difference between the system of whole numbers and the system of integers?

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

    What is the additive inverse of a number?

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

    What is the product of two negative numbers?

    <p>Always positive</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 positive and a negative number?

    <p>Depends on the magnitudes of the numbers involved</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 quotient of a positive number and a negative number?

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

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

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

    What is the purpose of the square root operation?

    <p>To find the positive square root of a number</p> Signup and view all the answers

    What are examples of real-world situations where integers are used?

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

    When adding numbers in columns, which digit do you start with?

    <p>Rightmost digit</p> Signup and view all the answers

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

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

    What is the formula for average speed?

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

    What is the purpose of compensating for errors in calculations?

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

    What is the relationship between the highest common factor and the lowest common multiple of two numbers?

    <p>They can be found using prime factorization</p> Signup and view all the answers

    What is the difference between simple interest and compound interest?

    <p>Simple interest is calculated on the principal amount, while compound interest adds the interest to the principal each year</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 formula for calculating the total HP price?

    <p>Deposit + Total of instalments</p> Signup and view all the answers

    What is the purpose of prime factorization in calculations?

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

    What is the relationship between distance, speed, and time?

    <p>Distance = 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 equivalent of adding a negative number?

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

    What is the order of operations when calculating expressions involving exponents, multiplication, and addition?

    <p>Parentheses, exponents, multiplication and division, addition and subtraction</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

    How do you write a large number in scientific notation?

    <p>By moving the decimal point to the left and the exponent is positive</p> Signup and view all the answers

    What is the purpose of the laws of exponents?

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

    How do you solve exponential equations?

    <p>By rewriting both sides of the equation with the same base, then equating the exponents</p> Signup and view all the answers

    What is the pattern of grey and white squares in the arrangements of blue, yellow, and red tiles?

    <p>The number of grey squares remains constant, while the number of white squares increases</p> Signup and view all the answers

    What is the purpose of investigating and extending patterns?

    <p>To identify the underlying structure of a pattern</p> Signup and view all the answers

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

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

    What is the purpose of identifying constants and variables in a pattern?

    <p>To recognize the relationships between terms</p> Signup and view all the answers

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

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

    What is the term for an expression with one term, such as 3x^2?

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

    What is the purpose of using algebraic expressions?

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

    What is the correct way to write a known number in a product in an algebraic expression?

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

    What is the term for the symbol, often x, 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 different sequences of operations but the same numerical value</p> Signup and view all the answers

    What is the correct way to calculate an expression with brackets?

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

    What is the term for an expression which is a sum of two terms, such as 5x + 4?

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

    What is the term for the number multiplying the variable in an algebraic expression, such as 3 in 3x^2?

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

    What is the purpose of using brackets in algebraic expressions?

    <p>To group numbers and specify the order of operations</p> Signup and view all the answers

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

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

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

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

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

    <p>$4 + 6 - 2$</p> Signup and view all the answers

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

    <p>$4x^2 + 2x - 6$</p> Signup and view all the answers

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

    <p>$5x^2 + 2x + 2$</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 evaluating the expression $x^2 + 2x - 3$ when $x = -1$?

    <p>$-4$</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 simplifying the expression $(2x + 3)(x - 2)$?

    <p>$2x^2 - x - 6$</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 relationship is described when one variable quantity is influenced by another?

    <p>Dependent relationship</p> Signup and view all the answers

    What is a characteristic of a function?

    <p>One output number for each input number</p> Signup and view all the answers

    What type of representation 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 the purpose of a table in function representation?

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

    What is the primary purpose of a graph in function representation?

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

    How can a function described by an expression be represented?

    <p>With a flow diagram, a table, or a graph</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 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 result of multiplying each digit and adding the results in multiplication?

    <p>The product of the numbers being multiplied</p> Signup and view all the answers

    What is the purpose of finding the lowest common multiple (LCM) of two numbers?

    <p>To find the smallest number that is a multiple of each of the two numbers</p> Signup and view all the answers

    What is the formula to calculate the average speed?

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

    What is the purpose of prime factorization in calculations?

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

    What is the relationship between distance, speed, and time?

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

    What is the purpose of calculating the highest common factor (HCF) of two numbers?

    <p>To find the largest number that divides each of the two numbers without leaving a remainder</p> Signup and view all the answers

    What is the difference between simple interest and compound interest?

    <p>Simple interest is calculated on the principal amount, while compound interest is calculated on the principal amount and the interest</p> Signup and view all the answers

    What is the purpose of calculating the ratio of collected apples?

    <p>To compare the collection rates of different people</p> Signup and view all the answers

    What is the purpose of calculating the total HP price?

    <p>To find the deposit plus the total of instalments</p> Signup and view all the answers

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

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

    What is the term for an expression with one term, such as 2x^3?

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

    What is the purpose of using brackets in algebraic expressions?

    <p>To evaluate the expression inside the brackets first</p> Signup and view all the answers

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

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

    What is the correct way to write a known number in a product in an algebraic expression?

    <p>Write the known number first, followed by the variable</p> Signup and view all the answers

    What is the term for an expression which is a sum of two terms, such as 3x + 2?

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

    What is the purpose of equivalent algebraic expressions?

    <p>To evaluate expressions with different sequences of operations</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 term for the number multiplying the variable in an algebraic expression, such as 3 in 3x^2?

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

    What is the purpose of understanding the properties of negative numbers?

    <p>To understand and work with negative numbers effectively in various mathematical contexts</p> Signup and view all the answers

    What is the purpose of identifying constants and variables in a pattern?

    <p>To recognize the relationships between terms</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 correct way to calculate an expression with brackets?

    <p>Evaluate the expression inside the brackets first</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 purpose of using exponents?

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

    What is the rule for calculating expressions involving exponents, multiplication, and addition?

    <p>Follow the order of operations (PEMDAS/BODMAS)</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 writing numbers in 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 purpose of identifying constants and variables in a pattern?

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

    What is the purpose of extending patterns?

    <p>To extend the pattern to a larger number of terms and understand its underlying structure</p> Signup and view all the answers

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

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

    What is the product of a positive and a negative integer?

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

    What is the additive inverse of a number?

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

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

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

    What is the purpose of the distributive property of multiplication over addition?

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

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

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

    What is the relationship between the square of a number and its square root?

    <p>The square of a number is always larger than its square root</p> Signup and view all the answers

    What is the purpose of word problems involving integers?

    <p>To model real-world situations</p> Signup and view all the answers

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

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

    What is the rule for multiplying two negative numbers?

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

    What is the defining characteristic of a function?

    <p>A relationship between two variables where there is only one output number for each input number.</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 another way to represent a function besides a table?

    <p>A flow diagram, a formula, or a graph.</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 an algebraic expression?

    <p>A description of the calculations needed to find the output number that corresponds to a given input number.</p> Signup and view all the answers

    Which of the following is a way to represent a function?

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

    What is the result of applying the rule \frac{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 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 purpose of using the distributive property in algebra?

    <p>To simplify expressions</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 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 purpose of evaluating expressions by substituting specific values for variables?

    <p>To check for equivalence and simplification</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 set of natural numbers smaller than 10?

    <p>A set of numbers between 10 and 50</p> Signup and view all the answers

    What is the purpose of using the distributive property of division?

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

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

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

    What is the purpose of factorizing algebraic expressions?

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

    What is the result of applying the rule '2n + 1' to the input set of even numbers?

    <p>A set of odd numbers</p> Signup and view all the answers

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

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

    Which of the following numbers is not a natural number?

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

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

    <p>The system of integers includes negative 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>The system of real numbers</p> Signup and view all the answers

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

    <p>To write numbers without needing a special symbol for 10, all multiples of 10, and some other numbers</p> Signup and view all the answers

    What is the result of adding 0 to a number?

    <p>The number remains the same</p> Signup and view all the answers

    What is a property of integers?

    <p>The sum of two integers can be zero</p> Signup and view all the answers

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

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

    What is the characteristic of the system of natural numbers under subtraction?

    <p>The answer is not always a natural number.</p> Signup and view all the answers

    What is the characteristic of the system of integers under addition?

    <p>The sum of two integers can be zero.</p> Signup and view all the answers

    What is the definition of a rational number?

    <p>A number that can be expressed as a fraction of two integers.</p> Signup and view all the answers

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

    <p>To make it easier to write numbers.</p> Signup and view all the answers

    What is the characteristic of the system of whole numbers under multiplication?

    <p>The product of two whole numbers is always a whole number.</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 product of a positive and a negative integer?

    <p>Always negative</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 subtracting an additive inverse?

    <p>The original number</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 to its additive inverse?

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

    What is the purpose of the square root operation?

    <p>To find the positive square root of a 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 adding a negative number?

    <p>Subtracting a positive number</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 happens when you subtract a larger number from a smaller number?

    <p>The result is a negative number</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 equivalent of adding a negative number?

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

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

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

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

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

    What is the formula for calculating the average speed?

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

    What is the purpose of the laws of exponents?

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

    What is the purpose of prime factorization in calculations?

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

    How do you solve exponential equations?

    <p>By rewriting both sides with the same base and equating the exponents</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 creating sequences of patterns?

    <p>To identify constants and variables in a pattern.</p> Signup and view all the answers

    What is the relationship between distance, speed, and time?

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

    What is an expression with one term, such as 3x^2?

    <p>Monomial</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 purpose of the highest common factor in calculations?

    <p>To find the greatest common divisor of two numbers</p> Signup and view all the answers

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

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

    What is the difference between simple interest and compound interest?

    <p>Simple interest is calculated on the principal amount, while compound interest is calculated on the principal amount and the interest</p> Signup and view all the answers

    What is the order of operations when calculating expressions involving exponents, multiplication, and addition?

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

    What is the purpose of investigating and extending patterns?

    <p>To identify variables and constants in a pattern</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 term for the symbol, often x, representing the unknown value in an algebraic expression?

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

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

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

    What is the purpose of using brackets in algebraic expressions?

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

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

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

    What is the formula for calculating the lowest common multiple of two numbers?

    <p>Multiply 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 result of performing the calculations within brackets first in an algebraic expression?

    <p>The correct value is obtained</p> Signup and view all the answers

    What is an expression which is a sum of three terms, such as 3x^3 + 2x + 9?

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

    What is the correct way to write a known number in a product in an algebraic expression?

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

    What is the term for the number multiplying the variable in an algebraic expression, such as 3 in 3x^2?

    <p>Coefficient</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 name of 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

    Which of the following is a way to represent a function?

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

    What is the purpose of a flow diagram?

    <p>To describe the calculations needed to determine the output number</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 purpose of a table representation of a function?

    <p>To complete the input numbers and their corresponding function values</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

    How many output numbers can a function have for each input number?

    <p>Exactly one</p> Signup and view all the answers

    What is the correct way to simplify an expression?

    <p>Combine like terms and apply the distributive property only</p> Signup and view all the answers

    What is the result of multiplying (x + 3) by (x + 4)?

    <p>x^2 + 7x + 12</p> Signup and view all the answers

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

    <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 purpose of using the distributive property in algebra?

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

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

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

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

    <p>x^2 + x - 6</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 the result of substituting x = 2 into the expression 2x^2 + 3x - 4?

    <p>8 + 6 - 4</p> Signup and view all the answers

    What is the purpose of using rules and calculations in functions and relationships?

    <p>To determine the output numbers for a given input set</p> Signup and view all the answers

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

    <p>Whole numbers include 0</p> Signup and view all the answers

    Which of the following properties is not true for natural numbers?

    <p>When a natural number is divided by another natural number, the answer is always a natural number</p> Signup and view all the answers

    What type of numbers include 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>π</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

    What is a property of the system of integers?

    <p>The sum of two integers is always an integer</p> Signup and view all the answers

    Why is the system of whole numbers closed under addition and multiplication?

    <p>Because the result of adding or multiplying two whole numbers is always a whole number</p> Signup and view all the answers

    What is the purpose of the system of whole numbers?

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

    What is the purpose of estimating in calculations?

    <p>To simplify calculations and get close to an answer</p> Signup and view all the answers

    What is the result of dividing a number by its highest common factor?

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

    What is the purpose of prime factorization in calculations?

    <p>To express a number as a product of its prime factors</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 formula for calculating the average speed?

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

    What is the difference between simple interest and compound interest?

    <p>Simple interest is calculated on the principal amount, while compound interest is calculated on the principal amount plus interest</p> Signup and view all the answers

    What is equivalent to subtracting a negative number?

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

    What is the correct order of operations when calculating expressions involving exponents, multiplication, and addition?

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

    What is the purpose of the lowest common multiple in calculations?

    <p>To find the common multiples of two or more numbers</p> Signup and view all the answers

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

    <p>The difference between the two numbers</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

    How do you write a large number in scientific notation?

    <p>Move the decimal point to the left, and the exponent is positive</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 relationship between the highest common factor and the lowest common multiple of two numbers?

    <p>The HCF is always less than the LCM</p> Signup and view all the answers

    What is the purpose of the laws of exponents?

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

    What is the purpose of column subtraction?

    <p>To subtract numbers in columns</p> Signup and view all the answers

    How do you solve exponential equations?

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

    What is the pattern of grey and white squares in the arrangements of blue, yellow, and red tiles?

    <p>The number of grey tiles is a constant, and the number of white tiles is a variable</p> Signup and view all the answers

    What is the purpose of investigating and extending patterns?

    <p>To identify constants and variables in a pattern</p> Signup and view all the answers

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

    <p>Depends on the values of the integers</p> Signup and view all the answers

    What is the purpose of using algebraic expressions?

    <p>To represent unknown values and describe relationships</p> Signup and view all the answers

    What is the correct 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 term for an expression with one term, such as 3x^2?

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

    What is the correct way to write a known number in a product in an algebraic expression?

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

    What is the purpose of equivalent algebraic expressions?

    <p>To show different sequences of operations with the same result</p> Signup and view all the answers

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

    <p>Variable</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 term for an expression which is a sum of two terms, such as 5x + 4?

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

    What is the term for the number multiplying the variable in an algebraic expression, such as 3 in 3x^2?

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

    What is the correct way to calculate an expression with brackets?

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

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

    <p>x^2 + (a + b)x + ab</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

    When dividing a polynomial by a monomial, what operation is performed on each term in the polynomial?

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

    What is the purpose of simplifying algebraic expressions?

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

    What is the result of squaring the monomial (2x)?

    <p>4x^2</p> Signup and view all the answers

    What operation is performed first when evaluating an expression without brackets?

    <p>Multiplication and division from left to right.</p> Signup and view all the answers

    What is the convention for writing a known number in a product in an algebraic expression?

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

    What is the purpose of equivalent algebraic expressions?

    <p>To rewrite an expression in a different form.</p> Signup and view all the answers

    When multiplying a polynomial by a monomial, what operation is performed on each term in the polynomial?

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

    What is the formula 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 a common characteristic of a function?

    <p>It can have only one output value for each input value.</p> Signup and view all the answers

    Which of the following is a way to represent a function?

    <p>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 for a given input variable</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 \frac{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 the purpose of a table representation of a function?

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

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

    <p>To provide a visual representation of the relationship</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 additive inverse of a number?

    <p>A number that, when added to the original number, results in zero</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

    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 two negative integers?

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

    What is the purpose of negative numbers?

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

    What is the square root of a number?

    <p>A value that, when multiplied by itself, gives the original number</p> Signup and view all the answers

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

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

    What is the purpose of the square root operation?

    <p>To find the positive square root of a number</p> Signup and view all the answers

    What are some examples of real-world situations where integers are used?

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

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