264 Questions
What is the set of numbers that we use to count called?
Natural Numbers
Which operation is not closed under the natural numbers?
Subtraction
What is the purpose of 0 in the system of whole numbers?
To write numbers, especially multiples of 10
What is the identity element for addition in the system of whole numbers?
0
What is the set of numbers that includes fractions and negative fractions?
Rational Numbers
Which of the following is an example of an irrational number?
√2
What is the set of numbers that includes both rational and irrational numbers?
Real Numbers
Which of the following properties is true for integers?
The sum of two integers can be zero
What is the result of subtracting a larger number from a smaller number?
A negative number
What is the equivalent of adding a negative number?
Subtracting the corresponding positive number
What is the result of the product of a positive and a negative number?
A negative number
What is an algebraic expression indicating in a sequence of operations?
A sequence of operations that can also be described in words or flow diagrams.
What should be calculated first in an algebraic expression with brackets?
The expressions in brackets.
What is the purpose of exponents in mathematics?
To provide a shorthand method for writing repeated multiplication
What is the order of operations in an algebraic expression without brackets?
Multiplication and division first, then addition and subtraction.
What is the correct order of operations when calculating expressions involving exponents?
Parentheses, exponents, multiplication, division, addition, subtraction
What is a monomial in algebraic expressions?
An expression with one term.
What is the meaning of a negative exponent in scientific notation?
The reciprocal of the base raised to the positive exponent
What is the purpose of simplifying exponential expressions?
To make the expression easier to work with
What is the coefficient in an algebraic expression?
The number multiplying the variable.
What is the first step in solving exponential equations?
Rewrite both sides of the equation with the same base
What is a trinomial in algebraic expressions?
An expression which is a sum of three terms.
What is the main focus of geometric patterns?
Investigating and extending patterns
What is a variable in algebraic expressions?
The symbol, often x, representing the unknown value.
What is a binomial in algebraic expressions?
An expression which is a sum of two terms.
What is the purpose of identifying the next number in a pattern?
To understand the pattern better
What is the convention for writing algebraic expressions?
Write a known number first in a product.
What are equivalent algebraic expressions?
Expressions with different sequences of operations but the same numerical value.
What is the purpose of estimating in calculations?
To get close to an answer without performing precise calculations
What is the process of dividing a number step-by-step, subtracting multiples of the divisor from the dividend, and continuing the process until the remainder is less than the divisor?
Long division
What is the smallest common multiple of two or more numbers called?
Lowest Common Multiple
What is the process of expressing a number as a product of its prime factors?
Prime factorization
What is the formula to calculate average speed?
Distance / Time
What is the difference between the HP price and the cash price called?
Interest
How is simple interest calculated?
On the principal amount without adding the interest to the principal each year
What is the formula to calculate distance?
Average speed × Time
What is the ratio of the numbers of apples collected by different people used to compare?
Their collection rates
What is the highest number that divides each of two or more numbers without leaving a remainder called?
Highest Common Factor
What is the result of subtracting a larger number from a smaller number?
A negative number
What is the effect of adding a negative number to a positive number?
The result is the same as subtracting the corresponding positive number
What is the product of two negative numbers?
Positive
What is the additive inverse of a number?
The corresponding negative number
What is the result of adding a number and its additive inverse?
Zero
What is the distributive property of multiplication over addition?
a(b + c) = ab + ac
What is the result of dividing a positive number by a negative number?
Negative
What is the square root of a number?
The positive square root
What is the purpose of negative numbers?
Both a and b
What can be modeled using integers and the rules of addition, subtraction, multiplication, and division?
All of the above
What is the purpose of using brackets in algebraic expressions?
To indicate the order of operations
Which of the following is an example of the distributive property?
2(x + 3) = 2x + 6
What is the result of multiplying (x + 2) by (x + 3)?
x^2 + 5x + 6
What is the result of dividing (x^2 + 3x - 4) by (x + 1)?
x + 2
What is the result of simplifying the expression 2x^2 + 4x - 3?
2(x^2 + 2x - 3)
What is the square of the binomial (x + 3)?
x^2 + 6x + 9
What is the result of substituting x = 2 into the expression 2x^2 + 3x - 4?
10
What is the rule for calculating the output numbers when the input is multiplied by 5 and the result is subtracted from 50?
50 - 5x
What is the output number when the input is 4 and the rule is 2n + 1?
7
Which of the following is an equivalent form of the expression 2x^2 + 3x - 4?
2(x^2 + 2x - 3)
What is the result of applying the rule $x - 1000$ to natural numbers smaller than 1000?
Negative numbers
What type of numbers does the rule $\frac{x}{10} + 10$ result in when applied to natural numbers smaller than 10?
Positive numbers between 10 and 11
What is the result of applying the rule $30x + 2$ to positive fractions with denominators 2, 3, and 5?
Positive numbers greater than 2
What is the term for a relationship between two variables in which there is only one output number for each input number?
Function
What is the purpose of a flow diagram?
To illustrate the calculations needed to determine the output number for a given input variable
What is a characteristic of a function?
There is only one output number for each input number
How can a function be represented?
Using a flow diagram, a table, or a graph
What is the purpose of a table representation of a function?
To show the input numbers and their corresponding function values
What is the main difference between the natural numbers and the whole numbers?
The natural numbers do not include 0, while the whole numbers do.
What is a common property shared by the natural numbers and whole numbers?
They are both closed under addition and multiplication.
What is the system of integers extended to include?
Negative numbers.
What is a characteristic of rational numbers?
They can be expressed as the quotient of two integers.
What is an example of an irrational number?
√2
What is the set of numbers that includes both rational and irrational numbers?
The real numbers.
What is a property of the system of natural numbers?
It is closed under addition and multiplication.
What is the purpose of the number 0 in the system of whole numbers?
To be used as an identity element for addition.
What is the purpose of estimating in calculations?
To get close to an answer without performing precise calculations
What is the process of dividing a number step-by-step, subtracting multiples of the divisor from the dividend, and continuing the process until the remainder is less than the divisor?
Long Division
What is the smallest common multiple of two or more numbers called?
Lowest Common Multiple
What is the process of expressing a number as a product of its prime factors?
Prime Factorization
What is the formula to calculate average speed?
Distance / Time
What is the difference between the HP price and the cash price called?
Interest
How is simple interest calculated?
On the principal amount without adding the interest to the principal each year.
What is the ratio of the numbers of apples collected by different people used to compare?
Collection rates
What is the highest number that divides each of two or more numbers without leaving a remainder called?
Highest Common Factor
What is the formula to calculate distance?
Distance = Average speed × Time
What is a relationship between two variables in which there is only one output number for each input number called?
Function
What is the correct order of operations in an algebraic expression without brackets?
Division, Multiplication, Addition, Subtraction
What describes the calculations needed to find the output number that corresponds to a given input number?
Algebraic Expression
What can be used to visually represent the relationship between two variables?
Graph
What is the purpose of the distributive property?
To expand the product of two binomials
What is the result of evaluating the expression $(2x)^3$?
8x^3
What shows the calculations performed to produce the output numbers and indicates which output numbers correspond to which input numbers?
Flow Diagram
What is the convention for writing algebraic expressions?
Write a known number first in a product
What can be completed to show the input numbers and their corresponding function values?
Table
How many ways can a function be represented?
4
What is the result of dividing the polynomial $x^2 + 3x - 4$ by the monomial $x - 1$?
$x + 4$
What is the purpose of factorising algebraic expressions?
To simplify expressions
What is one way to determine which number is linked to a specific value of the other variable?
Table
What is an algebraic expression used to describe?
A relationship between two variables
What is the result of evaluating the expression $x^2 + 2x - 3$ when $x = 2$?
3
What is the distributive property of division?
$(x + y)/z = x/z + y/z$
What is the purpose of brackets in algebraic expressions?
To indicate the order of operations
What is the result of evaluating the expression $(5x)^2$?
25x^2
What is the result of subtracting a larger number from a smaller number?
A negative number
What is the equivalent of subtracting a negative number?
Adding a positive number
What is the result of the product of a positive and a negative number?
A negative number
What is the purpose of exponents in mathematics?
To provide a shorthand method for writing repeated multiplication
What is the order of operations when calculating expressions involving exponents?
Parentheses, exponents, multiplication, division, addition, subtraction
What is the meaning of a negative exponent in scientific notation?
The reciprocal of the base raised to the positive exponent
What is the purpose of simplifying exponential expressions?
To rewrite the expression in a more concise form
What is the first step in solving exponential equations?
Rewrite both sides of the equation with the same base
What is the main focus of geometric patterns?
Investigating and extending patterns
What is an algebraic expression indicating?
a sequence of operations
What is the purpose of identifying the next number in a pattern?
To predict the number of black tiles in future arrangements
What operation should be performed first in an algebraic expression with brackets?
Calculations within the brackets
What is the order of operations in an algebraic expression without brackets?
Multiplication and division first, then addition and subtraction
What is a monomial in algebraic expressions?
An expression with one term
What is the coefficient in an algebraic expression?
The number multiplying the variable
What is a trinomial in algebraic expressions?
An expression with three terms
What is the purpose of simplifying algebraic expressions?
To make the expression easier to understand
What is a variable in algebraic expressions?
The symbol representing the unknown value
What is the convention for writing algebraic expressions?
Write the coefficient first, then the variable
What are equivalent algebraic expressions?
Expressions with the same numerical value for any given value of the variable
What is the result of subtracting a negative number from a positive number?
A positive number
What is the additive inverse of a number?
A number that has the same magnitude but opposite sign
What is the result of adding a positive and a negative number?
Depends on the magnitudes of the numbers
What is the product of two negative numbers?
A positive number
What is the purpose of negative numbers?
To extend the number system for practical purposes
What is the result of adding a number and its additive inverse?
Zero
What is the distributive property of multiplication over addition?
a(b + c) = ab + ac
What is the result of dividing a positive number by a negative number?
A negative number
What is the square root of a number?
A number that is squared to give the original number
What can be modeled using integers and the rules of addition, subtraction, multiplication, and division?
Temperature changes, depths below sea level, and financial transactions
What is the purpose of forming a sequence with dots?
To analyze the pattern
What is done first in an expression with brackets?
Calculations within the brackets
What is a term with a single variable and coefficient?
Monomial
What is the result of multiplying a positive number by a negative number?
A negative number
What is the purpose of identifying patterns in algebraic expressions?
To compare sequences and identify relationships
What is the term for the numerical coefficient in a monomial?
Coefficient
What is the purpose of writing algebraic expressions?
To describe sequences of operations
What is an expression with three terms?
Trinomial
What is the convention for writing algebraic expressions?
Write the known number first
What is the order of operations when calculating expressions without brackets?
Multiplication and division first, followed by addition and subtraction
What is the purpose of estimating in calculations?
To get close to an answer without performing precise calculations
What is the process of expressing a number as a product of its prime factors?
Prime factorization
What is the formula to calculate average speed?
Distance / Time
What is the highest number that divides each of two or more numbers without leaving a remainder called?
Highest Common Factor (HCF)
What is the process of dividing a number step-by-step, subtracting multiples of the divisor from the dividend, and continuing the process until the remainder is less than the divisor?
Long division
What is the difference between the HP price and the cash price called?
Interest
What is the purpose of using prime factorization?
To find the LCM and HCF of two numbers
What is the formula to calculate distance?
Average speed × Time
What is the result of subtracting a larger number from a smaller number?
A negative number
What is the ratio of the numbers of apples collected by different people used to compare?
Their rates of collection
What is the equivalent of adding a negative number?
Subtracting a positive number
How is simple interest calculated?
On the principal amount without adding the interest to the principal each year
What is the purpose of combining like terms when simplifying an algebraic expression?
To make the expression easier to evaluate
What is the result of the product of a positive and a negative number?
A negative number
What is the purpose of exponents in mathematics?
To indicate repeated multiplication
What is the result of multiplying a polynomial by a monomial?
A polynomial with each term multiplied by the monomial
What is the correct order of operations when calculating expressions involving exponents?
Parentheses, Exponents, Multiplication and Division, Addition and Subtraction
What is the distributive property of division?
Both of the above
What is the formula for expanding the square of a binomial (a + b)?
a^2 + 2ab + b^2
What is the meaning of a negative exponent in scientific notation?
The reciprocal of the base raised to the positive exponent
What is the purpose of substituting specific values for variables in an algebraic expression?
To evaluate the expression for a given input
What is the purpose of simplifying exponential expressions?
To use the laws of exponents to simplify expressions
What is the main focus of geometric patterns?
Investigating and extending patterns
What is the result of applying the rule 'multiply a number by 5 and subtract the result from 50' to a given input?
The output depends on the input value
What is a common property of natural numbers and whole numbers?
They are closed under addition and multiplication
What is the convention for writing algebraic expressions?
Write the coefficient first, then the variable
What is the purpose of identifying the next number in a pattern?
To predict the next number in the pattern
What is an equivalent algebraic expression?
An expression with different sequence of operations but same result
What is the main difference between natural numbers and whole numbers?
Natural numbers do not include 0, while whole numbers do
What is the result of adding a number and its additive inverse?
Zero
What is a characteristic of integers?
They can be zero or have an additive inverse
What is the purpose of factoring algebraic expressions?
To simplify the expression
What is a characteristic of rational numbers?
They can be expressed as a quotient of two integers
What is the result of squaring a binomial (a - b)?
a^2 - 2ab + b^2
What is an example of an irrational number?
\sqrt{2}
What is the set of numbers that includes both rational and irrational numbers?
The set of real numbers
What is a property of the system of natural numbers?
It is closed under addition and multiplication
What is the purpose of the number 0 in the system of whole numbers?
To write numbers and provide a place value
What is a relationship between two variables where there is only one output number for each input number?
Function
How can a function be represented?
Using a flow diagram, a table, and a graph
What does a flow diagram show?
The calculations performed to produce the output numbers and the corresponding input numbers
What is the purpose of an algebraic expression?
To describe the calculations needed to find the output number that corresponds to a given input number
If one variable quantity is influenced by another, what is the result?
A relationship between the two variables
What is a table used for in function representation?
To complete the input numbers and their corresponding function values
What is the purpose of a graph in function representation?
To visually represent the function
What is the result of applying the rule $x - 1000$ to natural numbers smaller than 1000?
Negative numbers
When adding a positive and a negative number, what determines the result?
The magnitude of the numbers involved
What is the effect of subtracting a negative number?
It is the same as adding a positive number
What is the result of adding a number and its additive inverse?
Zero
What is the product of two negative numbers?
A positive number
What does the distributive property of multiplication over addition state?
a(b + c) = ab + ac
What is the result of subtracting a larger number from a smaller number?
A negative number
What is the square root of a number?
The positive square root
What are negative numbers used for?
To extend the number system for practical purposes
What is the result of adding a negative number to a positive number?
It depends on the magnitudes of the numbers
What can be modeled using integers and the rules of addition, subtraction, multiplication, and division?
Real-world situations
What is true about the system of natural numbers?
It is closed under addition and multiplication
What is the main difference between the system of whole numbers and the system of natural numbers?
The system of whole numbers includes 0
What is true about the sum of two integers?
It can be zero
What is a characteristic of irrational numbers?
They cannot be expressed as a fraction of two integers
What is the set of numbers that includes both rational and irrational numbers?
The set of real numbers
What is a property of the system of integers?
Each integer has an additive inverse
What is the purpose of the system of integers?
To include negative numbers
What is true about the system of whole numbers and the system of integers?
The system of whole numbers is a subset of the system of integers
What is the result of adding a positive number and a negative number?
Depends on the magnitudes of the numbers involved
What is the effect of subtracting a negative number from a positive number?
Increases the result
What is the product of two negative numbers?
Positive
What is the additive inverse of a number?
A number that adds up to 0
What is the result of adding a number and its additive inverse?
Zero
What is the distributive property of multiplication over addition?
a(b + c) = ab + ac
What is the result of dividing a positive number by a negative number?
Negative
What is the square root of a number?
The positive number that when multiplied by itself gives the original number
What is the purpose of negative numbers?
To extend the number system for practical purposes
What can be modeled using integers and the rules of addition, subtraction, multiplication, and division?
Real-world situations
What is the purpose of estimating in calculations?
To get a close answer without performing precise calculations
What is the process of dividing a number step-by-step, subtracting multiples of the divisor from the dividend, and continuing the process until the remainder is less than the divisor?
Long division
What is the smallest common multiple of two or more numbers called?
Lowest Common Multiple
What is the process of expressing a number as a product of its prime factors?
Prime factorization
What is the formula to calculate average speed?
Distance / Time
What is the difference between the HP price and the cash price called?
Interest
How is simple interest calculated?
On the principal amount without adding the interest to the principal each year
What is the ratio of the numbers of apples collected by different people used to compare?
Their collection rates
What is the highest number that divides each of two or more numbers without leaving a remainder called?
Highest Common Factor
What is the formula to calculate distance?
Average speed × Time
What is the result of subtracting a larger number from a smaller number in integer operations?
A negative number
What is the equivalent of subtracting a negative number in integer operations?
Adding a positive number
What is the result of the product of a positive and a negative number in integer operations?
A negative number
What is the purpose of exponents in mathematics?
To represent repeated multiplication
What is the correct order of operations when calculating expressions involving exponents?
Parentheses, exponents, multiplication, division, addition, subtraction
What does a negative exponent represent in scientific notation?
The reciprocal of the base raised to the positive exponent
What is the purpose of simplifying exponential expressions?
To make the expressions easier to understand and solve
What is the main focus of geometric patterns?
Investigating and extending geometric patterns
What is the purpose of identifying the next number in a pattern?
To predict the next arrangement
What is the benefit of using scientific notation to express very large or very small numbers?
It provides a simple and concise way to express very large or very small numbers
What is the purpose of identifying variables in algebraic expressions?
To represent the unknown value
What is the rule for performing calculations in an algebraic expression with brackets?
Perform the calculations inside the brackets first
What is a trinomial in algebraic expressions?
An expression with three terms
What is the purpose of equivalent algebraic expressions?
To represent the same numerical value
What is the convention for writing algebraic expressions?
Write the known number first in a product
What is the result of performing multiplication and division in an algebraic expression without brackets?
Perform multiplication and division first
What is the purpose of monomials, binomials, and trinomials in algebraic expressions?
To classify algebraic expressions based on the number of terms
What is the role of the coefficient in an algebraic expression?
To multiply the variable term
What is the purpose of algebraic expressions?
To indicate a sequence of operations
What is the rule for performing calculations in an algebraic expression without brackets?
Perform multiplication and division first
What happens when the rule ( x - 1000 ) is applied to natural numbers smaller than 1000?
The result is always negative.
What is the relationship between variables in which one variable quantity is influenced by another?
A function.
How can a function be represented?
By a table, flow diagram, formula, or graph.
What is the purpose of a flow diagram?
To illustrate the calculations needed to determine the output number.
What can be used to complete a table to show the input numbers and their corresponding function values?
A formula or a flow diagram.
What is the purpose of a graph?
To provide a visual representation of the relationship.
How many ways can a function be represented?
Four ways.
What is the rule ( rac{x}{10} + 10 ) applied to?
Natural numbers smaller than 10.
What is the purpose of combining like terms when simplifying an expression?
To reduce the number of terms in the expression
What is the result of multiplying a polynomial by a monomial?
A polynomial with the same degree
How do you evaluate the expression $(a + b)^2$?
By expanding the product using the distributive property
What is the purpose of substituting specific values for variables in an algebraic expression?
All of the above
What is the rule for dividing a polynomial by a monomial?
Each term in the polynomial is divided by the monomial
What is the distributive property of multiplication over addition?
a(b + c) = ab + ac
What is the purpose of applying the distributive property in algebraic expressions?
To expand the product of binomials
What is the result of multiplying a polynomial by a monomial?
A polynomial with the same degree
What is the purpose of using brackets in algebraic expressions?
To indicate the order of operations
What is the result of applying the rule of multiplication to a binomial?
A polynomial with the same degree
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