Gr 9 MATH: Term Test 1
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Questions and Answers

What is the purpose of estimating in calculations?

  • To get an exact answer
  • To get close to an answer without performing precise calculations (correct)
  • To round off numbers to more than 2 decimal places
  • To simplify calculations by adding extra digits

    • What is the result of multiplying each digit and adding the results in multiplication?

  • An expanded notation (correct)
  • The estimated answer
  • The correct answer
  • The product of the numbers

    • What is the term for the smallest common multiple of two or more numbers?

  • Lowest Common Multiple (correct)
  • Greatest Common Multiple
  • Smallest Common Factor
  • Highest Common Factor

    • What is the purpose of prime factorization?

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

    What is the formula to calculate the 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 in hire purchase?

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

    What is the primary focus of creating patterns with black and grey squares?

    <p>Identifying constants and variables</p> Signup and view all the answers

    What is the type of interest that is calculated on the principal amount without adding the interest to the principal each year?

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

    What is the goal of extending sequences and describing how they are formed?

    <p>To understand how sequences are formed</p> Signup and view all the answers

    What is the purpose of writing the next terms in given sequences?

    <p>To identify patterns in sequences</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 is the ratio between the numbers of apples collected by different people used?

    <p>To compare their collection rates</p> Signup and view all the answers

    What is an essential step in creating a sequence by repeatedly adding a specific number?

    <p>Determining the starting point of the sequence</p> Signup and view all the answers

    What is the result of subtracting multiples of the divisor from the dividend in long division?

    <p>A quotient and a remainder</p> Signup and view all the answers

    What is the main objective of using instructions to form sequences?

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

    What is the primary focus of formulating relationships between terms in sequences?

    <p>Checking the results of formulated sequences</p> Signup and view all the answers

    Which of the following operations is the system of natural numbers not closed under?

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

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

    <p>To enable the writing of numbers</p> Signup and view all the answers

    Which property is unique to the system of integers?

    <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

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

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

    What is the relationship between the system of whole numbers and the system of natural numbers?

    <p>The system of natural numbers is a subset of the system of whole numbers</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 set of numbers includes both rational and irrational numbers?

    <p>Real 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 equivalent of adding a negative number?

    <p>Subtracting 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, multiplication, and addition?

    <p>Parentheses, Exponents, Multiplication, Addition, 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

    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

    How do you write numbers 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 the laws of exponents?

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

    What is the purpose of investigating and extending geometric patterns?

    <p>To predict the number of black tiles in future arrangements</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 additive inverse of 5?

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

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

    <p>It depends on the magnitudes of the numbers involved.</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 purpose of negative numbers?

    <p>To provide solutions for equations and to extend the number system.</p> Signup and view all the answers

    What is the square root of a number x?

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

    What is the result of subtracting a negative number?

    <p>It is equivalent to adding the corresponding positive number.</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 adding an additive inverse?

    <p>The result is 0.</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 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 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 simplify multiplication</p> Signup and view all the answers

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

    <p>Exponents, multiplication, addition</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 compact form</p> Signup and view all the answers

    How do you write numbers in scientific notation?

    <p>Move the decimal point to the left, and the exponent n is positive</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 investigating and extending geometric patterns?

    <p>To identify relationships between terms in a sequence</p> Signup and view all the answers

    Which of the following properties of natural numbers states that when a natural number is subtracted from another natural number, the answer is not always a natural number?

    <p>Not closure under subtraction</p> Signup and view all the answers

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

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

    Which set of numbers includes both rational and irrational numbers?

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

    What is the additive inverse of a number in the system of integers?

    <p>A number that when added to the original number gives 0</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 relationship between the system of whole numbers and the system of natural numbers?

    <p>The system of natural numbers is a subset of the system of whole 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

    Which property is unique to the system of integers?

    <p>Existence of additive inverses</p> Signup and view all the answers

    When subtracting a larger number from a smaller number, what is the result?

    <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 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 negative numbers?

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

    What is the square root of a number x?

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

    What is the result of subtracting a negative number?

    <p>Adding the corresponding positive number</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 adding an additive inverse?

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

    What is the rule for multiplying two negative numbers?

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

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

    <p>For modeling real-world situations such as temperature changes, depths below sea level, and financial transactions</p> Signup and view all the answers

    What is the primary purpose of creating patterns with black and grey squares?

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

    What is the benefit of extending sequences and describing how they are formed?

    <p>To identify relationships between terms and their positions</p> Signup and view all the answers

    What is the primary focus of writing the next terms in given sequences?

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

    What is the purpose of using instructions to form sequences?

    <p>To create sequences with different operations</p> Signup and view all the answers

    What is the primary focus of formulating relationships between terms in sequences?

    <p>To identify relationships between terms and their positions</p> Signup and view all the answers

    What is the benefit of creating sequences with different operations?

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

    What is the purpose of rounding off numbers in calculations?

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

    What is the method 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 term for the product of prime factors of a number?

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

    What is the formula to calculate the selling price of an item after a discount?

    <p>Selling price = Marked price - Discount</p> Signup and view all the answers

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

    <p>Ratio and rate</p> Signup and view all the answers

    What is the term for the amount of money paid as interest in a hire purchase?

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

    What is the method of calculating the average speed for different sections of a journey?

    <p>By dividing the total distance by the total time</p> Signup and view all the answers

    What is the purpose of prime factorization in calculating the HCF and LCM of two numbers?

    <p>To find the prime factors of the two numbers</p> Signup and view all the answers

    What is the term for the rate at which someone collects apples?

    <p>Apples per minute</p> Signup and view all the answers

    What is the purpose of calculating the HCF and LCM of two numbers?

    <p>To find the common multiples and factors of the two numbers</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

    Which of the following is an example of exponential notation?

    <p>5^2</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

    What is the result of the product of two negative numbers?

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

    How do you write a large number in scientific notation?

    <p>Move the decimal point to the right and the exponent is positive</p> Signup and view all the answers

    What is the purpose of geometric patterns?

    <p>To investigate and extend sequences</p> Signup and view all the answers

    What is the result of adding a positive and a negative number with the same absolute value?

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

    What is the purpose of integer exponents?

    <p>To represent the reciprocal of a 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, Division, Addition, Subtraction</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 property that makes the system of whole numbers closed under addition?

    <p>Identity element for addition</p> Signup and view all the answers

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

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

    Which of the following numbers is NOT a rational number?

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

    What is the property that makes the system of integers different from the system of whole numbers?

    <p>Closure under subtraction</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>The set of real numbers</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 property that is unique to the system of natural numbers?

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

    When subtracting a larger number from a smaller number, what is the result?

    <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 product of two negative numbers?

    <p>A positive number</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 purpose of currency exchange?

    <p>To convert one currency to another</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 subtracting a negative number?

    <p>Adding the corresponding positive number</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 purpose of negative numbers?

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

    What is the result of adding an additive inverse?

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

    What is the primary technique used to identify patterns in sequences?

    <p>Analyzing the relationship between terms and their positions</p> Signup and view all the answers

    What is the main goal of formulating relationships between terms in sequences?

    <p>To check the results of the formulated relationships</p> Signup and view all the answers

    What is the key difference between creating sequences with different operations and creating sequences with different starting points?

    <p>The type of operation used to form the sequence</p> Signup and view all the answers

    What is the purpose of using instructions to form sequences?

    <p>To create a sequence with a specific pattern</p> Signup and view all the answers

    What is the primary focus of creating patterns with black and grey squares?

    <p>Identifying constants and variables in the pattern</p> Signup and view all the answers

    What is the main objective of developing your own pattern and describing the variables?

    <p>To identify the relationship between the variables and the pattern</p> Signup and view all the answers

    When performing long division, what is the purpose of subtracting multiples of the divisor from the dividend?

    <p>To find the remainder of the division</p> Signup and view all the answers

    What is the relationship between the average speed, distance, and time in a journey?

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

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

    <p>To determine the common multiples of the numbers</p> Signup and view all the answers

    What is the result of using the formula Distance = Average speed × Time to find the distance traveled?

    <p>The result is the distance traveled</p> Signup and view all the answers

    What is the purpose of compensating for errors in estimating calculations?

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

    What is the result of using the formula Time = Distance / Average speed to find the time taken?

    <p>The result is the time taken to travel the distance</p> Signup and view all the answers

    What is the purpose of finding the highest common factor (HCF) of two or more numbers?

    <p>To determine the common factors of the numbers</p> Signup and view all the answers

    What is the result of using the formula Average speed = Distance / Time to find the average speed?

    <p>The result is the average speed of the journey</p> Signup and view all the answers

    What is the purpose of using prime factorization in calculations?

    <p>To determine the highest common factor and lowest common multiple of two numbers</p> Signup and view all the answers

    What is the relationship between the cost price, marked price, and selling price in percentage calculations?

    <p>The selling price is the marked price minus the discount</p> Signup and view all the answers

    What is the primary goal of identifying constants and variables in patterns with black and grey squares?

    <p>To understand the relationships between terms and their positions</p> Signup and view all the answers

    What is the main purpose of creating sequences with different operations?

    <p>To create sequences with different starting points and operations</p> Signup and view all the answers

    What is the primary focus of formulating relationships between terms in sequences?

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

    What is the primary goal of developing your own pattern?

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

    What is the main purpose of using instructions to form sequences?

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

    What is the primary goal of comparing sequences by identifying relationships?

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

    What is the primary characteristic of natural numbers that makes them closed under addition?

    <p>The result of adding two or more natural numbers is always a natural number.</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>Whole numbers include 0, but natural numbers do not.</p> Signup and view all the answers

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

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

    What is the definition of rational numbers?

    <p>Numbers that can be expressed as the quotient 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 relationship between the system of real numbers and the system of rational numbers?

    <p>The system of real numbers is a superset of the system of rational numbers.</p> Signup and view all the answers

    What is the property of the system of natural numbers that is not true for the system of whole numbers?

    <p>The system of natural numbers is closed under subtraction.</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 result of subtracting a larger number from a smaller number in the context of integers?

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

    What is the equivalent of adding a negative number in the context of integers?

    <p>Subtracting the corresponding positive 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 equivalent of adding a negative number?

    <p>Subtracting 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 the context of integers?

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

    What is the purpose of exponents in the context of exponential notation?

    <p>To represent multiplication of a number by itself</p> Signup and view all the answers

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

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

    What is the purpose of negative numbers?

    <p>To provide solutions for equations</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 in the context of exponential notation?

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

    What is the square root of a number x?

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

    What is the purpose of scientific notation in the context of very large or very small numbers?

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

    What is the result of subtracting a negative number?

    <p>Equivalent to adding a positive number</p> Signup and view all the answers

    How do you write numbers 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 distributive property of multiplication over addition?

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

    What is the result of adding an additive inverse?

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

    What is the purpose of the laws of exponents in the context of exponential notation?

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

    What is the primary focus of investigating and extending geometric patterns in the context of numeric and geometric patterns?

    <p>To analyze the patterns of grey and white squares in the arrangement</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 result of the product of two negative numbers?

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

    What is the main difference between the LCM and HCF of two numbers?

    <p>LCM is the largest number that divides each of them, while HCF is the smallest number that divides each of them</p> Signup and view all the answers

    How can you calculate the average speed for a journey with multiple sections?

    <p>By calculating the total distance traveled and dividing it by the total time taken</p> Signup and view all the answers

    What is the formula to calculate the interest in a simple interest calculation?

    <p>Interest = Principal × Rate × Time</p> Signup and view all the answers

    What is the purpose of long division in whole number calculations?

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

    What is the result of compensating for errors introduced by rounding in calculations?

    <p>A more accurate answer</p> Signup and view all the answers

    What is the purpose of adding in columns in whole number calculations?

    <p>To perform addition by writing numbers in columns and adding each digit starting from the rightmost digit</p> Signup and view all the answers

    What is the formula to calculate the time in a distance, speed, and time calculation?

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

    What is the purpose of prime factorization in whole number 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 multiplying a positive number by a negative number?

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

    What is the purpose of estimating in whole number calculations?

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

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