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

What is the formula to calculate the average speed?

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

What is the difference between the HP price and the cash price in hire purchase?

<p>Interest (A)</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 (B)</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 (B)</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 (D)</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 (A)</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 (C)</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 (A)</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 (B)</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 (A)</p> Signup and view all the answers

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

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

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

<p>Subtraction (B), Division (C)</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 (A)</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 (B)</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 (B)</p> Signup and view all the answers

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

<p>√2 (D)</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 (B)</p> Signup and view all the answers

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

<p>-0 (A), 0 (B)</p> Signup and view all the answers

Which set of numbers includes both rational and irrational numbers?

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

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

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

What is the equivalent of adding a negative number?

<p>Subtracting a positive number (D)</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 (C)</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 (D)</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 (A)</p> Signup and view all the answers

What does a negative exponent represent?

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

What is the purpose of the laws of exponents?

<p>To simplify expressions involving exponents (C)</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 (C)</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. (B)</p> Signup and view all the answers

What is the additive inverse of 5?

<p>-5 (B)</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. (C)</p> Signup and view all the answers

What is the product of two negative numbers?

<p>Positive. (B)</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. (A)</p> Signup and view all the answers

What is the square root of a number x?

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

What is the distributive property of multiplication over addition?

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

What is the result of adding an additive inverse?

<p>The result is 0. (B)</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. (D)</p> Signup and view all the answers

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

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

What is the equivalent of adding a negative number?

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

What is the purpose of exponents in mathematics?

<p>To simplify multiplication (A)</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 (A)</p> Signup and view all the answers

What does a negative exponent represent?

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

What is the purpose of the laws of exponents?

<p>To simplify expressions involving exponents (A)</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 (A)</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 (D)</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 (B)</p> Signup and view all the answers

Which set of numbers includes both rational and irrational numbers?

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

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

<p>√2 (C)</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 (D)</p> Signup and view all the answers

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

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

Which property is unique to the system of integers?

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

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

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

What is the equivalent of adding a negative number?

<p>Subtracting a positive number (D)</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 (B)</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 (D)</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 (C)</p> Signup and view all the answers

What is the result of subtracting a negative number?

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

What is the distributive property of multiplication over addition?

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

What is the result of adding an additive inverse?

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

What is the rule for multiplying two negative numbers?

<p>The result is always positive (D)</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 (C)</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 (A)</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 (C)</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 (C)</p> Signup and view all the answers

What is the purpose of using instructions to form sequences?

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

What is the benefit of creating sequences with different operations?

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

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

<p>Prime factorization (C)</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 (D)</p> Signup and view all the answers

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

<p>Ratio and rate (B)</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 (B)</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 (B)</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 (C)</p> Signup and view all the answers

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

<p>Apples per minute (D)</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 (B)</p> Signup and view all the answers

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

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

Which of the following is an example of exponential notation?

<p>5^2 (C)</p> Signup and view all the answers

What is the purpose of the laws of exponents?

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

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

<p>A positive number (D)</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 (B)</p> Signup and view all the answers

What is the purpose of geometric patterns?

<p>To investigate and extend sequences (A)</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 (D)</p> Signup and view all the answers

What is the purpose of integer exponents?

<p>To represent the reciprocal of a number (A)</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 (C)</p> Signup and view all the answers

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

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

Which of the following numbers is NOT a rational number?

<p>√2 (B)</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 (A)</p> Signup and view all the answers

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

<p>Ï€ (A)</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 (D)</p> Signup and view all the answers

What is the additive inverse of a number?

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

What is the property that is unique to the system of natural numbers?

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

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

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

What is the equivalent of adding a negative number?

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

What is the product of two negative numbers?

<p>A positive number (D)</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 (B)</p> Signup and view all the answers

What is the purpose of currency exchange?

<p>To convert one currency to another (C)</p> Signup and view all the answers

What is the distributive property of multiplication over addition?

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

What is the result of subtracting a negative number?

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

What is the additive inverse of a number?

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

What is the purpose of negative numbers?

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

What is the result of adding an additive inverse?

<p>Zero (D)</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 (B)</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 (A)</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 (B)</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 (C)</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 (B)</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 (B)</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 (C)</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 (C)</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 (D)</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 (C)</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 (C)</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 (C)</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 (D)</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 (C)</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 (C)</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 (C)</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 (B)</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 (C)</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 (A)</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 (D)</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 (D)</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 (C)</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. (D)</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. (D)</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. (A)</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. (A)</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. (B)</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. (B)</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. (D)</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. (B)</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 (A)</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 (C)</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 (C)</p> Signup and view all the answers

What is the equivalent of adding a negative number?

<p>Subtracting a positive number (A)</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 (C)</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 (D)</p> Signup and view all the answers

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

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

What is the purpose of negative numbers?

<p>To provide solutions for equations (C), To extend the number system for practical purposes (D)</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 (B)</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 (B)</p> Signup and view all the answers

What is the square root of a number x?

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

What is the result of subtracting a negative number?

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

What is the distributive property of multiplication over addition?

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

What is the result of adding an additive inverse?

<p>The result is always zero (A)</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 (D)</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 (A)</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 (B)</p> Signup and view all the answers

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

<p>Always positive (C)</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 (B)</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 (B)</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 (D)</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 (D)</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 (D)</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 (C)</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 (B)</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 (D)</p> Signup and view all the answers

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

<p>A negative number (C)</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 (D)</p> Signup and view all the answers

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