Gr 9 MATH: June Exam Medium
264 Questions
0 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to Lesson

Podcast

Play an AI-generated podcast conversation about this lesson

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

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

<p>√2 (C)</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 (A)</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. (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 difference between the system of whole numbers and the system of integers?

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

What is the additive inverse of a number?

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

What is the product of two negative numbers?

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

What is the purpose of negative numbers?

<p>To extend the number system for practical purposes (B)</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 (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 quotient of a positive number and a negative number?

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

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

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

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

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

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

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

What is the formula for average speed?

<p>Distance / Time (C)</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 (D)</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 (D)</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 (C)</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 (A)</p> Signup and view all the answers

What is the formula for calculating the total HP price?

<p>Deposit + Total of instalments (D)</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 (C)</p> Signup and view all the answers

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

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

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

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

What does a negative exponent represent?

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

What is the purpose of the laws of exponents?

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

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

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

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

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

What is the purpose of using algebraic expressions?

<p>To describe a sequence of operations (D)</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 (C)</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 (B)</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 (D)</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 (A)</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 (D)</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 (C)</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 (D)</p> Signup and view all the answers

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

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

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

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

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

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

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

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

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

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

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

<p>$4x$ (D)</p> Signup and view all the answers

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

<p>$-4$ (B)</p> Signup and view all the answers

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

<p>$7$ (B)</p> Signup and view all the answers

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

<p>$2x^2 - x - 6$ (A)</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 (C)</p> Signup and view all the answers

What type of relationship is described when one variable quantity is influenced by another?

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

What is a characteristic of a function?

<p>One output number for each input number (B)</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 (B)</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 (B)</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 (A)</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 (A)</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 (D)</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 (B)</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 (A)</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 (A)</p> Signup and view all the answers

What is the formula to calculate the average speed?

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

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

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

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

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

What is the purpose of equivalent algebraic expressions?

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

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

What is the equivalent of subtracting a negative number?

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

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

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

What does a negative exponent represent?

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

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

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

What is the additive inverse of a number?

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

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

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

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

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

What is the purpose of word problems involving integers?

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

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

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

What is the rule for multiplying two negative numbers?

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

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

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

What is the purpose of using the distributive property in algebra?

<p>To simplify expressions (C)</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 (D)</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 (C)</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 (D)</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 (C)</p> Signup and view all the answers

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

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

What is the purpose of factorizing algebraic expressions?

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

Which of the following numbers is not a natural number?

<p>0 (A)</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. (D)</p> Signup and view all the answers

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

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

What is the result of adding 0 to a number?

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

What is a property of integers?

<p>The sum of two integers can be zero (B)</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. (B)</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. (B)</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. (A)</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. (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. (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. (B)</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. (D)</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. (D)</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 (C)</p> Signup and view all the answers

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

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

What is the purpose of negative numbers?

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

What is the result of subtracting an additive inverse?

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

What is the distributive property of multiplication over addition?

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

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

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

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

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

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

<p>A negative number (D)</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 (A)</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 (A)</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 multiplying a positive and a negative number?

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

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

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

What is the formula for calculating the average speed?

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

What is the purpose of the laws of exponents?

<p>To simplify expressions involving exponents (B)</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 (C)</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 (C)</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 creating sequences of patterns?

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

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

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

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

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

What is the purpose of compensating for errors in calculations?

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

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

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

What is the purpose of using brackets in algebraic expressions?

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

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

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

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

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

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

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

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

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

What is the purpose of using the distributive property in algebra?

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

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

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

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

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

What is the purpose of factorising algebraic expressions?

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

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

<p>Whole numbers include 0 (A)</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 (B), When a natural number is subtracted from another natural number, the answer is always a natural number (C)</p> Signup and view all the answers

What type of numbers include fractions and negative fractions?

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

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

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

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

<p>Real numbers (C)</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 (A), The sum of two integers can be zero (D)</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 (D)</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 (A)</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 (D)</p> Signup and view all the answers

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

<p>1 (C)</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 (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 (B)</p> Signup and view all the answers

What is the formula for calculating the average speed?

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

What is equivalent to subtracting a negative number?

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

What does a negative exponent represent?

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

What is the purpose of compensating for errors in calculations?

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

What is the purpose of the laws of exponents?

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

What is the purpose of column subtraction?

<p>To subtract numbers in columns (A)</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 (A)</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 (C)</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 (B)</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 (C)</p> Signup and view all the answers

What is the purpose of using algebraic expressions?

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

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

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

What is the purpose of using brackets in algebraic expressions?

<p>To indicate the order of operations (C)</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 (A)</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 (B)</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 (D)</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 (D)</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 (B)</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. (C)</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. (D)</p> Signup and view all the answers

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

<p>4x^2 (D)</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. (B)</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. (B)</p> Signup and view all the answers

What is the purpose of equivalent algebraic expressions?

<p>To rewrite an expression in a different form. (B)</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. (B)</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. (A)</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. (C)</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 (A)</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 (A)</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 (A)</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 (B)</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 (B)</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 (D)</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 (B)</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 (A)</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 (C)</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 (B)</p> Signup and view all the answers

What is the distributive property of multiplication over addition?

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

What is the result of multiplying two negative integers?

<p>Always positive (C)</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 square root of a number?

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

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

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

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

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

Flashcards are hidden until you start studying

Use Quizgecko on...
Browser
Browser