941 Questions
What is the result of applying the commutative property of addition?
a + b = b + a
Which property states that when adding or multiplying three or more numbers, the way in which the numbers are grouped does not affect the result?
Associative Property
What is the distributive property of multiplication over subtraction?
a × (b - c) = a × b - a × c
What is the result of applying the additive property of 0?
a + 0 = a
What is the purpose of a summary table for multiplication?
To practice and reinforce the multiplication of various numbers
What is estimating in the context of whole numbers?
Trying to get close to an answer without actual calculations
What is the result of applying the multiplicative property of 1?
a × 1 = a
Which property does not apply to subtraction and division?
Commutative Property
What is the main advantage of rounding off numbers?
To make quick decisions and check the reasonableness of results
What is the purpose of compensating in rounding off?
To adjust for errors introduced by rounding
Which method of addition involves breaking down numbers into parts?
Expanded Notation
What is the borrowing technique used for in subtraction?
To borrow from the next left column
Which method of multiplication involves breaking down the multiplication into smaller parts?
Multiplication in Parts
What is the purpose of carrying over in multiplication?
To write down the last digit of the product
What is the main advantage of using multiples of a thousand for estimation?
To make quick decisions and check the reasonableness of results
What is the purpose of step-by-step division?
To divide the number step-by-step
Why is it important to align numbers by their place values in column addition and subtraction?
To ensure accurate addition and subtraction
What is the result of long division when you can't go any further?
The remainder
What is the definition of a multiple of a number?
A multiple of a number is the product of that number and an integer.
What is the definition of a factor of a number?
A factor is a number that divides exactly into another number.
What is the definition of a prime number?
A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.
What is the purpose of finding the Least Common Multiple (LCM)?
To find the smallest multiple that two or more numbers have in common.
What is the purpose of finding the Highest Common Factor (HCF)?
To find the largest number that divides two or more numbers without leaving a remainder.
What is the definition of a rate?
A rate describes how one quantity changes in relation to another.
What is the formula for Distance and Time Calculations?
Distance = Speed × Time
What is the purpose of finding the ratio of two or more quantities?
To compare the quantities.
How do you determine if a number is prime?
By checking if it can be divided evenly by any prime numbers smaller than its square root.
What is the purpose of prime factorization?
To express a number as the product of its prime factors.
What is the purpose of scaling quantities in recipes?
To use the ratio of ingredients to the number of servings
What is the formula for calculating simple interest?
Interest = Principal × Rate × Time
What is the result of adding a positive integer to its additive inverse?
Zero
What is the result of subtracting a positive integer from another positive integer?
The result can be either positive or negative
What is the product of two negative integers?
A positive integer
What is the result of subtracting a positive integer from its additive inverse?
A negative integer
What is the purpose of comparing ratios?
To determine which shapes are more similar
Which property states that the order of multiplication does not change the product?
Commutative Property
What is the result of multiplying two negative integers?
The result is always positive
What is the result of adding a negative integer to its additive inverse?
Zero
What is the purpose of calculating the absolute value of an integer?
To find the distance between the number and zero on the number line
What is the result of adding a negative integer to a positive integer?
The result can be either positive or negative
What is the product of a positive integer and a negative integer?
A negative integer
What is the formula for calculating the selling price?
Selling Price = Marked Price - Discount
Which property states that the order of addition does not change the sum?
Commutative Property
What is the result of subtracting a negative integer from its additive inverse?
A positive integer
What is the result of dividing a positive integer by a negative integer?
The result is always negative
What is the result of multiplying a positive integer by its additive inverse?
Zero
What is the purpose of calculating the cube of an integer?
To find the result of raising an integer to the power of three
What is the result of multiplying a negative integer by its additive inverse?
Zero
What is the property that states that changing the order of numbers does not change the sum in addition?
Commutative Property
What is the result of adding a number to its additive inverse?
0
What is the property that states that changing the grouping of numbers does not change the sum in addition?
Associative Property
What is the purpose of the additive inverse in integer operations?
To find the opposite of a number
What is the result of multiplying an integer by 1?
The original number
What is the property that states that multiplication distributes over addition?
Distributive Property
What is the absolute value of an integer?
The distance between the number and 0 on the number line
What is the result of subtracting an integer from itself?
0
What is the property that states that the order of numbers does not change the product in multiplication?
Commutative Property
What is the formula for equivalent fractions?
(a × k) / (b × k) = a / b
What is the first step in adding or subtracting decimal fractions?
Align the decimal points
How do you convert a decimal fraction to a whole number for multiplication?
Multiply by a power of 10
What is the purpose of multiplying both the dividend and the divisor by a power of 10 in dividing decimal fractions?
To convert the divisor to a whole number
What is the result of adding an integer and its additive inverse?
Zero
What is the symbol used to indicate that one integer is greater than another?
What is the property of multiplication that states that the order of multiplication does not change the product?
Commutative Property
What is the purpose of dividing the total amount by a certain number of people to divide amounts equally?
To find the amount each person gets
What is the technique used to multiply decimal fractions?
Convert to whole numbers, multiply, and adjust the decimal place
What is the purpose of converting the divisor to a whole number in dividing decimal fractions?
To make the divisor a whole number
What is the result of multiplying an integer by its additive inverse?
Zero
What is the first step in adding or subtracting fractions?
Find the least common multiple of the denominators
What is the result of multiplying two fractions together?
A fraction with a numerator equal to the product of the numerators and a denominator equal to the product of the denominators
What is the reciprocal of a fraction?
A fraction with the numerator and denominator swapped
What is the purpose of finding the greatest common divisor when simplifying a fraction?
To divide both the numerator and denominator by the GCD
How do you convert a fraction to a decimal?
By dividing the numerator by the denominator
What is the purpose of converting a fraction to a percentage?
To compare the fraction to a whole
What is a mixed number?
A combination of a whole number and a fraction
What is the purpose of equivalent fractions?
To represent the same value
What is the result of dividing a fraction by a whole number?
A fraction with a numerator equal to the quotient of the numerator and the whole number
What is the purpose of finding a fraction of a fraction?
To multiply the fractions together
What is the formula for the nth triangular number?
T_n = n(n+1)/2
What is the type of progression that follows the formula T_n = T_1 + (n-1) * d?
Arithmetic progression
What is the relationship between the number of learners at a school and the number of classrooms needed?
Variable relationship
What is the purpose of a flow diagram?
All of the above
What is the term for different expressions that represent the same value or relationship?
Equivalent forms
What is the commutative property of multiplication?
a × b = b × a
What is the additive inverse of an integer?
A number that is added to the integer to get zero
What is the formula for the nth square number?
T_n = n^2
What is the term for a variable quantity that is influenced by another variable quantity?
Dependent quantity
What is the purpose of an open number sentence?
To find the value of a missing number
What is the result of subtracting a negative integer from another integer?
It increases the value
What is the relationship between the number of identical houses to be built and the number of bricks required?
Variable relationship
What is the purpose of finding the relationship between variables?
To understand the connections between quantities
What is the purpose of using the distributive property of multiplication?
To expand a product of two or more numbers
What is the term for a diagram that shows the calculations needed to produce output numbers from input numbers?
Flow diagram
What is the result of adding a positive integer to its additive inverse?
It results in zero
What is the formula for the nth term of a sequence with a constant difference?
Tn = T1 + (n - 1) × d
What is the result of multiplying a positive integer by a negative integer?
It results in a negative integer
What is the purpose of using the associative property of addition?
To reorder the numbers in a sum without changing the result
What is the formula for the nth term of a linear sequence?
Tn = an + b
What is the process of finding an equivalent fraction in its simplest form?
Simplifying fractions
What is the method used to convert a decimal to a fraction?
Write the decimal as a fraction with a denominator of a power of 10 and then simplify
What is the property that allows us to multiply a single term by each term within a parenthesis?
Distributive property
What is the result of combining like terms in an algebraic expression?
Simplifying the expression
What is the purpose of using common denominators when adding or subtracting fractions?
To enable the addition or subtraction of fractions
What is the term for expressions that yield the same value for all values of the variables?
Equivalent algebraic expressions
What is the process of dividing each term in the numerator by the denominator in an algebraic fraction?
Simplifying the quotient expression
What is the purpose of using the distributive property when expanding algebraic expressions?
To multiply a single term by each term within a parenthesis
What are the terms that have the same variable(s) raised to the same power?
Like terms
What is the result of multiplying both the numerator and the denominator of a fraction by the same number?
An equivalent fraction
What is the result of multiplying a positive integer and a negative integer?
Always negative
What is the purpose of expressing large numbers in scientific notation?
To make numbers easier to read and write
What is the result of adding a positive integer and its additive inverse?
Zero
What is the rule for multiplying powers with the same base?
Add the exponents
What is the purpose of the distributive property of multiplication?
To expand a product of a single number and a sum of two numbers
What is the result of dividing a negative integer by a positive integer?
Always negative
What is the rule for raising a power to another power?
Multiply the exponents
What is the purpose of finding the cube of an integer?
To raise a number to a power of three
What is the result of subtracting a negative integer from a positive integer?
Always positive
What is the purpose of squaring a fraction?
To raise the fraction to a power of two
What is the formula for dividing a fraction by another fraction?
$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$
What is the formula for calculating a fraction of a fraction?
$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$
How is a fraction simplified?
By dividing both the numerator and denominator by their greatest common divisor
What is the formula for converting a fraction to a percentage?
Percentage = $\frac{a}{b} \times 100$
What is the formula for converting a percentage to a fraction?
Fraction = $\frac{\text{Percentage}}{100}$
What is the method to find a percentage of a given number?
Convert the percentage to a decimal and multiply by the number
What is the formula for increasing a number by a percentage?
Increased Value = Original Number + ($\frac{\text{Percentage}}{100} \times \text{Original Number}$)
What is the formula for decreasing a number by a percentage?
Decreased Value = Original Number - ($\frac{\text{Percentage}}{100} \times \text{Original Number}$)
What is the formula for calculating the percentage change?
Percentage Change = ($\frac{\text{New Value} - \text{Original Value}}{\text{Original Value}}$) \times 100
How are decimal fractions added and subtracted?
By aligning the decimal points
When adding or multiplying three or more numbers, which property ensures that the result does not change when the numbers are regrouped?
Associative Property
What is the purpose of using the distributive property in multiplication?
To simplify complex calculations
What is the result of multiplying a number by 1?
The number remains the same
Which property states that the order of numbers does not change the result in addition?
Commutative Property
What is the purpose of estimating in whole number calculations?
To get close to an exact answer without precise calculations
Which property helps to simplify calculations by allowing us to change the order of numbers in addition and multiplication?
Commutative Property
What is the purpose of using a summary table for multiplication?
To practice and reinforce multiplication of various numbers
What is the result of adding a number to 0?
The number remains the same
What is the purpose of estimating products in mathematics?
To make quick decisions and check the reasonableness of results
When simplifying calculations, what can you round numbers to?
The nearest ten, hundred, or thousand
What is the main idea behind column addition?
Adding numbers vertically by their place values
What is the purpose of compensating in rounding off?
To adjust for errors introduced by rounding
What is the main idea behind multiplication in parts?
Breaking down the multiplication into smaller parts and summing the partial products
What is the purpose of carrying over in multiplication?
To write down the partial product and carry over extra values
What is the main idea behind long division?
Breaking down the division into smaller, manageable steps
What is the purpose of step-by-step division?
To divide the dividend by the divisor step-by-step
What is the purpose of remainder handling in long division?
To continue dividing until you can't go any further
Why is it important to align numbers by their place values in column addition and subtraction?
To ensure accurate calculations
What is the result of subtracting a positive integer from itself?
Zero
What is the product of two positive integers?
Always positive
What is the result of adding a positive integer to its multiplicative inverse?
One
What is the result of subtracting a negative integer from a positive integer?
A larger positive integer
What is the cube root of a negative integer?
A negative integer
What is the result of adding a positive integer to its additive inverse?
Zero
What is the result of multiplying a positive integer by its multiplicative inverse?
One
What is the result of subtracting a positive integer from its additive inverse?
A negative integer
What is the result of adding a negative integer to its additive inverse?
Zero
What is the result of multiplying two negative integers?
A positive integer
What is the purpose of comparing ratios?
To determine which shapes or objects are more similar
How do you calculate the selling price when a discount is applied?
Subtract the discount from the marked price
What is the result of multiplying two negative integers?
A positive integer
What is the purpose of scaling quantities in recipes?
To use the ratio of ingredients to the number of servings
What is the process of expressing a number as the product of its prime factors?
Prime factorization
What is the formula for calculating simple interest?
Interest = Principal × Rate × Time
What is a prime number?
A natural number greater than 1 with only two distinct positive divisors: 1 and itself
What is the Highest Common Factor (HCF)?
The largest number that divides two or more numbers without leaving a remainder
What is the result of adding a positive integer to its additive inverse?
Zero
What is the purpose of calculating the absolute value of an integer?
To determine the distance between the number and zero on the number line
How do you determine if a number is prime?
By checking if it can be divided evenly by any prime numbers smaller than its square root
What is the purpose of finding the Least Common Multiple (LCM)?
To find a common denominator for adding fractions
What is the result of subtracting a positive integer from its additive inverse?
A negative integer
What is the result of multiplying a positive integer by a negative integer?
A negative integer
What is a multiple of a number?
The product of a number and an integer
What is the purpose of calculating the cube of an integer?
To calculate the cube of an integer
What is a factor of a number?
A number that divides another number exactly
What is the formula for Distance and Time Calculations?
Distance = Speed × Time
What is the purpose of calculating rates?
To find the time required to complete a task
What is the purpose of describing patterns?
To identify the relationship between quantities
Which property of integers states that changing the order of numbers does not change the sum?
Commutative Property
What is the result of adding a positive integer to its additive inverse?
Zero
What is the purpose of finding the additive inverse of an integer?
To find the value that when added to the number, results in zero
Which property of integers states that changing the grouping of numbers does not change the sum?
Associative Property
What is the result of multiplying a positive integer by a negative integer?
A negative integer
What is the formula for finding an equivalent fraction?
(a × k) / (b × k)
What is the purpose of the distributive property of multiplication?
To multiply a number by a sum of numbers
What is the result of adding a negative integer to a positive integer?
Depends on the absolute values of the integers
Which property of integers states that multiplying a number by one does not change the number?
Identity Property
What is the result of subtracting a positive integer from its additive inverse?
Twice the positive integer
What is the formula for finding the number of elements in the nth position of a square number pattern?
$n^2$
What is the formula for finding the number of elements in the nth position of a triangular number pattern?
$n(n + 1)$
What is the relationship between the number of learners at a school and the number of classrooms needed?
More learners require more classrooms
What is the relationship between the number of calls you make and the airtime left on your cell phone?
The more calls you make, the less airtime you have left
What is the relationship between the length of your arm and your ability to finish Mathematics tests quickly?
No direct influence
What is the purpose of a flow diagram?
To show the calculations needed to produce output numbers
What is the relationship between the number of identical houses to be built and the number of bricks required?
More houses require more bricks
What is an equivalent form in mathematics?
A different expression that represents the same value or relationship
What is the purpose of finding the relationship between variables?
To find a specific value of one quantity linked to a value of the other quantity
What is the formula for calculating the number of elements in the nth position of a T-shaped number pattern that follows an arithmetic progression?
$T_1 + (n - 1) \cdot d$
When adding or subtracting decimal fractions, what is the first step?
Align the decimal points.
To multiply decimal fractions, what is the first step?
Convert the decimals to whole numbers by multiplying by powers of 10.
What is the purpose of converting the divisor to a whole number in dividing decimal fractions?
To make the division easier.
What is the purpose of dividing the total amount saved by the weekly savings amount?
To determine the duration of saving.
What is the property of integer operations that states that the order of addition does not change the sum?
Commutative Property of Addition.
What is the additive inverse of an integer?
A number that when added to the integer results in zero.
What is the result of multiplying two negative integers?
Always positive
What is the purpose of expressing large numbers in scientific notation?
To make numbers easier to read
What is the symbol used to indicate that one integer is greater than another?
>
What is the rule for multiplying powers with the same base?
Add the exponents
What is the purpose of comparing integers?
To determine the relationship between two integers.
What is the property of multiplication that states that the order of multiplication does not change the product?
Commutative Property of Multiplication.
What is the result of raising a number to the power of zero?
One
What is the purpose of the distributive property of multiplication?
To simplify calculations
What is the result of multiplying two negative integers?
A positive integer.
What happens when a positive integer is added to its additive inverse?
The result is always zero
What is the rule for dividing powers with the same base?
Subtract the exponents
What is the result of squaring a fraction?
A new fraction with the numerator and denominator squared
What is the purpose of exponential form?
To write a product of the same integer
What is the result of cubing a fraction?
A new fraction with the numerator and denominator cubed
To find a fraction of a fraction, what operation do you need to perform?
Multiplication
What is the property that states that the order of multiplication does not change the product?
Commutative Property
What is the formula to simplify a fraction?
$\frac{a}{b} = \frac{a \div \text{GCD}(a, b)}{b \div \text{GCD}(a, b)}$
What is the property that states that changing the order of numbers does not change the sum in addition?
Commutative Property
How do you convert a fraction to a decimal?
Divide the numerator by the denominator
What is the formula to convert a fraction to a percentage?
$\text{Percentage} = \frac{a}{b} \times 100$
What is the formula for the nth term of a sequence with a constant difference?
T_n = T_1 + (n - 1) * d
What is the formula for the nth term of a sequence with a constant ratio?
T_n = T_1 * r^(n-1)
What is the formula to find the percentage of a given number?
$\text{Percentage of a number} = \left( \frac{\text{Percentage}}{100} \right) \times \text{Number}$
What is the formula to find the percentage change?
$\text{Percentage Change} = \left( \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \right) \times 100$
What is the purpose of finding the additive inverse of an integer?
To cancel out the effect of the integer
What is the term for an equation where all the numbers are known?
Closed number sentence
What is the method to increase a number by a percentage?
Calculate the percentage of the number and add it to the original number
What is the symbol used to indicate a greater than relationship between two integers?
>
What is the formula to convert a percentage to a fraction?
$\text{Fraction} = \frac{\text{Percentage}}{100}$
What is the purpose of comparing integers?
To determine the relationship between two integers
What is the method to decrease a number by a percentage?
Calculate the percentage of the number and subtract it from the original number
What is the formula for the nth term of a linear sequence?
T_n = a * n + b
What is the purpose of identifying the rule for a pattern in a sequence?
To apply the rule to determine subsequent terms
What are fractions that have different numerators and denominators but represent the same value?
Equivalent Fractions
What is the process of finding an equivalent fraction in its simplest form?
Simplifying Fractions
What are decimals that represent the same value?
Equivalent Decimals
How do you convert a fraction to a decimal?
Divide the numerator by the denominator
What is the distributive property used for in algebra?
Multiplying a single term by each term within a parenthesis
What is the purpose of combining like terms in algebra?
To simplify an algebraic expression
What is the result of multiplying a fraction by a power of 10?
A decimal
What is the purpose of using the distributive property to remove brackets?
To expand an algebraic expression
What is the purpose of rearranging terms in an algebraic expression?
To combine like terms
What is the purpose of simplifying an algebraic expression?
To make it easier to understand and work with
What is the formula for adding two fractions with different denominators?
$\frac{a}{b} + \frac{c}{d} = \frac{a \times d + b \times c}{b \times d}$
What is the result of multiplying two fractions?
The result is always a fraction.
What is the formula for dividing a fraction by another fraction?
$\frac{a}{b} ÷ \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$
What is the formula for simplifying a fraction?
$\frac{a}{b} = \frac{a ÷ \text{GCD}(a, b)}{b ÷ \text{GCD}(a, b)}$
What is the formula for converting a fraction to a percentage?
$\text{Percentage} = \frac{a}{b} \times 100$
What is the definition of a mixed number?
A mixed number is a fraction with a whole number part and a fractional part.
What is the formula for finding equivalent fractions?
$\frac{a}{b} = \frac{a \times k}{b \times k}$
What is the purpose of simplifying a fraction?
To make the fraction easier to understand and work with.
What is the definition of a unit fraction?
A unit fraction is a fraction with a numerator of 1.
What is the purpose of converting a fraction to a decimal?
To make the fraction easier to work with in calculations.
What is the purpose of estimating in whole numbers?
To simplify calculations and make quick decisions
What is the method of addition that involves breaking down numbers into parts?
Expanded Notation
What is the purpose of compensating in rounding off?
To adjust for errors introduced by rounding
What is the method of subtraction that involves rearranging parts to make subtraction easier?
Borrowing Technique
What is the result of rounding 386 to the nearest hundred?
400
What is the purpose of aligning numbers by their place values in column addition and subtraction?
To ensure accurate calculations
What is the method of multiplication that involves breaking down the multiplication into smaller parts?
Multiplication in Parts
What is the purpose of carrying over in multiplication?
To write down the partial product and carry over extra values
What is the result of rounding 3,435 to the nearest thousand?
3,400
What is the method of division that involves breaking down the division into smaller, manageable steps?
Step-by-Step Division
Which property of whole numbers states that the order of factors does not change the product?
Commutative property
What is the purpose of using the distributive property of multiplication?
To break down complex multiplications into simpler parts
What is the result of applying the additive property of 0 to a number?
The number remains unchanged
What is the main purpose of using a summary table for multiplication?
To practice and reinforce multiplication of various numbers
What is the purpose of estimating in whole number calculations?
To get close to the exact answer without doing precise calculations
What property of whole numbers states that when adding or multiplying three or more numbers, the way in which the numbers are grouped does not affect the result?
Associative property
What is the result of applying the multiplicative property of 1 to a number?
The number remains unchanged
What is the purpose of using the associative property of addition and multiplication?
To group numbers in a way that does not affect the result
What is the purpose of finding the Least Common Multiple (LCM)?
To find the common denominator for adding fractions
What is the purpose of scaling quantities in recipes?
To increase or decrease the quantity of ingredients as needed
What is the definition of a composite number?
A natural number greater than 1 that can be formed by multiplying two smaller natural numbers
How do you calculate the selling price after a discount?
Subtract the discount from the marked price
What is the purpose of prime factorization?
To express a number as the product of its prime factors
What is the definition of a rate?
Describes how one quantity changes in relation to another
What is the result of multiplying a positive integer by a negative integer?
A negative integer
What is the result of adding a positive integer to its square root?
Zero
How do you determine if a number is prime?
By checking if it can be divided evenly by any prime numbers smaller than its square root
What is the purpose of calculating the absolute value of an integer?
To find the distance between the integer and zero on the number line
What is the result of multiplying a positive integer by its additive inverse?
Zero
What is the result of subtracting a negative integer from its additive inverse?
A positive value
How do you calculate the profit percentage?
By finding the difference between the selling price and the cost price, dividing by the cost price, and multiplying by 100
What is the purpose of finding the Highest Common Factor (HCF)?
To simplify fractions to their lowest terms
What is the result of multiplying a positive integer by a negative integer?
A negative value
What is the formula for Distance and Time Calculations?
Distance = Speed × Time
What is the result of subtracting a positive integer from another positive integer?
A positive integer
What is the result of adding a positive integer to a negative integer?
A negative value
What is the purpose of comparing ratios?
To determine which shapes or objects are more similar
What is the definition of a multiple of a number?
The product of a number and an integer
What is the result of dividing a positive integer by a negative integer?
A negative value
What is the purpose of finding the ratio of two or more quantities?
To compare two quantities, showing how many times one value contains or is contained within the other
What is the formula for calculating simple interest?
Interest = Principal x Rate x Time
What is the purpose of calculating the time based on a rate?
To find the time required to complete a task
What is the result of multiplying a negative integer by its additive inverse?
Zero
What is the result of adding a positive integer to its additive inverse?
Zero
What is the purpose of dividing quantities in a ratio?
To allocate a quantity into parts based on a ratio
What is the result of subtracting a positive integer from its additive inverse?
A positive value
What is the result of adding a negative integer to a positive integer?
A positive value
What is the result of multiplying a negative integer by a negative integer?
A positive value
What is the property that states that when adding or multiplying two numbers, the order of the numbers does not change the result?
Commutative Property
What is the property that states that changing the grouping of numbers does not change the sum in addition?
Associative Property
What is the result of multiplying a number by its additive inverse?
0
What is the purpose of the additive inverse property?
To find the negative counterpart of a number
What is the property that states that multiplying a number by 1 does not change the value of that number?
Identity Property of Multiplication
What is the result of multiplying two negative integers?
A positive integer
What is the property that states that adding zero to a number does not change the value of that number?
Identity Property of Addition
What is the purpose of finding equivalent fractions?
To simplify fractions
What is the formula for finding equivalent fractions?
(\frac{a}{b} = \frac{a \times k}{b \times k})
What is the result of adding a positive integer to its additive inverse?
0
What is the first step to add or subtract fractions?
Convert them to have a common denominator
What is the formula for multiplying two fractions?
(a × c) / (b × d)
How do you simplify a fraction?
By dividing both the numerator and denominator by their greatest common divisor
What is the result of dividing a fraction by another fraction?
The product of the fractions
What is the term for fractions that represent the same value?
Equivalent fractions
How do you convert a fraction to a decimal?
By dividing the numerator by the denominator
What is the term for a mixed number that combines a whole number with a fraction?
Mixed fraction
What is the purpose of finding the least common multiple (LCM) of the denominators?
To add or subtract fractions
What is the formula for finding a fraction of a fraction?
(a × c) / (b × d)
What is the purpose of converting a fraction to a percentage?
To make the fraction more understandable
What is the formula to find a fraction of a fraction?
( \frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d} )
What is the formula to convert a fraction to a decimal?
Divide the numerator by the denominator
What is the formula to simplify a fraction?
( \frac{a}{b} = \frac{a \div \text{GCD}(a, b)}{b \div \text{GCD}(a, b)} )
What is the formula to find the percentage of a number?
( \frac{\text{Part}}{\text{Whole}} \times 100 )
What is the formula to find the increased value of a number by a percentage?
( \text{Original Number} + \left( \frac{\text{Percentage}}{100} \times \text{Original Number} \right) )
What is the formula to find the decreased value of a number by a percentage?
( \text{Original Number} - \left( \frac{\text{Percentage}}{100} \times \text{Original Number} \right) )
What is the formula to find the percentage change?
( \left( \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \right) \times 100 )
What is the purpose of converting fractions to decimals?
To make fractions more understandable
What is the purpose of converting percentages to fractions?
To make percentages more understandable
What is the purpose of comparing quantities using percentages?
To express one quantity as a part of another
When adding or subtracting decimal fractions, what should be done first?
Align the decimal points
What is the purpose of multiplying both numbers by a power of 10 in decimal fraction multiplication?
To eliminate the decimals
What is done to the divisor in decimal fraction division?
It is converted to a whole number
What is the result of adding a negative integer to its additive inverse?
Zero
What is the property that states that the order of multiplication does not change the product?
Commutative property
What is the purpose of converting decimal fractions to whole numbers in multiplication?
To eliminate the decimals
What is the result of dividing a decimal fraction by a whole number?
A decimal fraction
What is the purpose of adjusting the result in decimal fraction multiplication?
To adjust the result to the correct decimal place
What is the result of multiplying a decimal fraction by a whole number?
A decimal fraction
What is the purpose of dividing the result by the power of 10 in decimal fraction multiplication?
To adjust the result to the correct decimal place
What is the result of multiplying two integers with the same sign?
Always positive
What is the purpose of using exponential form?
To represent very large or very small numbers
What is the law of exponents that states a^m × a^n = a^(m+n)?
Product of Powers
What is an equivalent fraction?
Fractions that have different numerators and denominators but represent the same value
What is the result of cubing a fraction?
A new fraction where both the numerator and the denominator are cubed
What is the purpose of scientific notation?
To represent very large or very small numbers in a more concise and manageable way
What is the process of finding an equivalent fraction in its simplest form?
Dividing the numerator and denominator by their greatest common divisor
What is the result of adding a positive integer to a negative integer?
Depends on the integers
How do you convert a decimal to a fraction?
Write the decimal as a fraction with a denominator of a power of 10 and then simplify
What are equivalent algebraic expressions?
Different algebraic expressions that simplify to the same value
What is the property that states that when multiplying powers with the same base, add the exponents?
Product of Powers
How do you simplify an algebraic expression?
Combine like terms and use the distributive property
What is the result of dividing a positive integer by a negative integer?
Always negative
What is the distributive property?
A property that allows us to multiply a single term by each term within a parenthesis
What is the purpose of calculating the square root of a fraction?
To find the magnitude of the fraction
What is the result of multiplying a negative integer by a negative integer?
Always positive
What is an algebraic expression?
A sequence of operations that can be written in different forms
What are like terms in an algebraic expression?
Terms with the same variable raised to the same power
What is the purpose of expanding an algebraic expression?
To simplify the expression
How do you simplify a quotient expression?
Divide each term in the numerator by the denominator
What is the formula for the number of elements in the n-th position of square numbers?
Tn = n^2
What is the relationship between the number of calls you make and the airtime left on your cell phone?
The number of calls you make has a direct influence on the airtime left.
What is the formula for the number of elements in the n-th position of triangular numbers?
Tn = n(n+1)/2
What is the relationship between the number of learners at a school and the number of classrooms needed?
The number of learners at a school has a direct influence on the number of classrooms needed.
What is the purpose of flow diagrams in calculations?
To describe the calculation process and the connection between input and output numbers.
What is the term for different expressions that represent the same value or relationship?
Equivalent forms
What is the relationship between the number of identical houses to be built and the number of bricks required?
The number of houses has a direct influence on the number of bricks required.
What is the formula for patterns that follow a geometric progression?
Tn = T1 * r^(n-1)
What is the relationship between the number of matches in each arrangement and the number of triangles in the arrangement?
The number of matches has a direct influence on the number of triangles.
What is the term for a variable quantity that is influenced by another variable?
Dependent variable
What is the purpose of the commutative property of multiplication?
To ensure that the order of multiplication does not change the product
What is the formula for the nth term in a sequence with a constant difference?
Tn = T1 + (n - 1) * d
What is the result of subtracting a positive integer from another positive integer?
A positive integer
What is the purpose of the distributive property of multiplication?
To multiply integers by a sum of integers
What is the result of adding a negative integer to its additive inverse?
Zero
What is the formula for the nth term in a sequence with a constant ratio?
Tn = T1 * r^(n-1)
What is the purpose of the associative property of addition?
To add integers in any order
What is the result of multiplying a positive integer by a negative integer?
A negative integer
What is the purpose of the additive inverse of an integer?
To find the negative counterpart of an integer
What is the formula for the nth term in a linear sequence?
Tn = a * n + b
What is the key characteristic of the commutative property of addition?
The order of numbers does not change the result.
Which property allows you to break down complex multiplications into simpler parts?
Distributive Property
What is the purpose of using a summary table for multiplication?
To practice and reinforce multiplication facts.
What is the main advantage of using the associative property of addition?
It simplifies calculations by reducing the number of steps.
What is the purpose of estimating whole numbers?
To get close to an exact answer without doing precise calculations.
What is the result of applying the multiplicative property of 1?
The result is the same as the original number.
Which property does not apply to subtraction and division?
Commutative Property of Addition and Multiplication
What is the purpose of simplifying calculations using properties?
To reduce the number of steps in calculations.
What is the purpose of scaling quantities in recipes?
To compare the ratio of ingredients to the number of servings
How do you calculate the discount amount?
By multiplying the marked price by the discount rate
What is the purpose of absolute value in integers?
To find the distance between a number and zero on the number line
What is the result of multiplying two negative integers?
A positive integer
What is the purpose of comparing ratios?
To determine which shapes or objects are more similar
How do you subtract a negative integer from another integer?
By adding the two integers
What is the formula for calculating simple interest?
Interest = Principal × Rate × Time
What is the result of adding a positive integer and a negative integer with the same absolute value?
Zero
What is the purpose of finding the cube of an integer?
To find the cube root of an integer
How do you divide quantities in a ratio?
By summing the parts of the ratio and dividing by the number of parts
What is the process of expressing a number as the product of its prime factors called?
Prime factorization
What is the purpose of finding the Least Common Multiple (LCM) of two numbers?
To add fractions with different denominators
What is a characteristic of a prime number?
It has exactly two distinct positive divisors
What is the formula used to calculate distance?
Distance = Speed × Time
What is the purpose of finding the Highest Common Factor (HCF) of two numbers?
To simplify fractions to their lowest terms
What is a multiple of a number?
The product of a number and an integer
What is the purpose of rate and ratio calculations?
To compare quantities and describe patterns
What is a characteristic of a composite number?
It has more than two factors
How do you determine if a number is prime?
By checking if it can be divided evenly by any prime number
What is the purpose of expressing a ratio?
To compare quantities and describe patterns
What is the result of adding a positive integer to its square root?
0
What is the result of subtracting a negative integer from a positive integer?
A positive integer
What is the product of two positive integers?
A positive integer
What is the main purpose of rounding off numbers in calculations?
To simplify calculations and make them easier
What is the result of adding an integer to its additive inverse?
0
What is the method of addition that involves breaking down numbers into parts?
Expanded Notation
What is the purpose of compensating in rounding off?
To correct for errors introduced by rounding
What is the quotient of a positive integer and a negative integer?
A negative integer
What is the method of subtraction that involves borrowing from the next column?
Column Subtraction
What is the result of multiplying a positive integer by its additive inverse?
0
What is the result of subtracting a positive integer from its additive inverse?
A negative integer
What is the purpose of multiplying each part separately in multiplication in parts?
To break down the multiplication into smaller parts
What is the result of adding a negative integer to its additive inverse?
0
What is the purpose of carrying over in multiplication?
To write down the partial product and carry over extra values
What is the result of multiplying a number by its additive inverse?
Always zero
What is the main advantage of using multiples of a thousand for estimation?
To make quick and approximate calculations
What is the property that states that the order of multiplication does not change the product?
Commutative Property
What is the result of multiplying a negative integer by its additive inverse?
0
Which property states that multiplication distributes over addition?
Distributive Property
What is the purpose of step-by-step division?
To divide the number step-by-step
What is the purpose of finding the additive inverse of a number?
To find the number that, when added, results in zero
Why is it important to align numbers by their place values in column addition and subtraction?
To ensure correct calculation of the sum or difference
What is the result of long division when you can't go any further?
The leftover value is the remainder
What is the result of adding two negative integers?
Depends on the absolute values of the integers
What is the property that states that the order of numbers does not change the product in multiplication?
Commutative Property
What is the result of multiplying a positive integer by a negative integer?
Always negative
What is the purpose of the identity property of addition?
To show that adding zero to a number does not change its value
What is the result of adding a positive integer and a negative integer?
Depends on the absolute values of the integers
Which property states that the order of numbers does not change the sum in addition?
Commutative Property
What is the purpose of the distributive property of multiplication over subtraction?
To show that multiplication distributes over subtraction
When adding or subtracting fractions, what must be found first?
The least common multiple (LCM)
What is the result of multiplying the numerators and denominators of two fractions?
An equivalent fraction
What is the reciprocal of a fraction?
A fraction with its numerator and denominator swapped
What is the purpose of simplifying a fraction?
To reduce the fraction to its simplest form
How is a fraction converted to a decimal?
By dividing the numerator by the denominator
What is a mixed number?
A whole number and a fraction combined
What is the least common multiple (LCM) used for?
To find a common denominator
What is the result of dividing a fraction by its reciprocal?
A fraction with a value of 1
What is the purpose of equivalent fractions?
To represent the same value in different forms
What is the result of multiplying two fractions?
A fraction with a numerator and denominator multiplied together
When adding or subtracting decimal fractions, what is the first step?
Align decimal points and add or subtract as with whole numbers
What is the purpose of multiplying both numbers by a power of 10 in the multiplication of decimal fractions?
To eliminate the decimals
When dividing a total amount by a certain number of people, what should you do first?
Convert the total amount to a decimal
What is the purpose of converting the divisor to a whole number in the division of decimal fractions?
To make the divisor a whole number
What is the result of applying the commutative property of addition?
The order of addition does not change the result
What is the additive inverse of an integer?
The negative counterpart of the integer
When comparing integers, what symbol is used to indicate that one integer is greater than another?
What is the result of multiplying two integers with the same sign?
The result is always positive
What is the purpose of using exponential form to represent numbers?
To make the numbers easier to multiply and divide
What is the result of adding a positive integer to its additive inverse?
The result is always zero
What happens when you add a positive integer to another positive integer?
The value increases
What is the purpose of finding the additive inverse of an integer?
To find the integer that when added results in zero
What is the formula for the nth term in a sequence with a constant ratio?
Tn = T1 * r^(n-1)
What is the purpose of using the commutative property of addition?
To add integers in any order
What is the formula for the nth term in a linear sequence?
Tn = a * n + b
What happens when you subtract a positive integer from another positive integer?
The value decreases
What is the purpose of finding the difference between two temperatures?
To find the change in temperature
What is the formula for the nth term in a sequence with a constant difference?
Tn = T1 + (n - 1) * d
What is the purpose of using the distributive property of multiplication?
To expand the product of a sum
What happens when you subtract a negative integer from its additive inverse?
The value increases
What is the result of multiplying two integers with the same signs?
Always positive
What is the purpose of the distributive property of multiplication?
To distribute multiplication over addition and subtraction
What is the result of raising a number to the power of zero?
One
What is the law of exponents that states that when multiplying powers with the same base, add the exponents?
Product of Powers
What is the result of squaring a fraction?
A new fraction where the numerator and denominator are squared
What is the purpose of scientific notation?
To express large numbers in a compact form
What is the result of subtracting a negative integer from its additive inverse?
A positive integer
What is the rule for multiplying a positive integer and a negative integer?
The product is always negative
What is the result of adding a positive integer and a negative integer?
Positive or negative depending on the numbers
What is the purpose of exponents in exponential form?
To represent the product of the same integer
What is the formula to find a fraction of a fraction?
$\frac{a}{b} \times \frac{c}{d}$
What is the formula to simplify a fraction?
$\frac{a \div \text{GCD}(a, b)}{b \div \text{GCD}(a, b)}$
What is the formula to convert a fraction to a percentage?
$\frac{a}{b} \times 100$
What is the formula to find the percentage of a given number?
$\left(\frac{a}{b} \right) \times \text{Number}$
How do you increase a number by a percentage?
Add the percentage of the number to the original number
What is the formula to find the percentage change?
$\left(\frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \right) \times 100$
What is the formula to convert a percentage to a fraction?
$\frac{\text{Percentage}}{100}$
How do you decrease a number by a percentage?
Subtract the percentage of the number from the original number
What is the formula to compare quantities using percentages?
$\left(\frac{\text{Part}}{\text{Whole}} \right) \times 100$
What is the formula to find the reciprocal of a fraction?
$\frac{b}{a}$
What is the formula for the nth triangular number?
Tn = n(n+1)/2
What is the name of the sequence where each term is obtained by adding a fixed constant to the previous term?
Arithmetic sequence
What is the relationship between the number of calls you make and the airtime left on your cell phone?
The more calls you make, the less airtime you have left.
What is the type of diagram that shows the calculations needed to produce output numbers from input numbers and the relationships between these numbers?
Flow diagram
What is the term for different expressions that represent the same value or relationship?
Equivalent forms
What is the type of sequence where each term is obtained by multiplying the previous term by a fixed constant?
Geometric sequence
What is the relationship between the number of identical houses to be built and the number of bricks required?
The number of houses determines the number of bricks required.
What is an equivalent fraction?
A fraction that has different numerators and denominators but represents the same value.
What is the formula for the nth square number?
Tn = n^2
What is the term for a variable quantity that is influenced by another variable quantity?
Dependent variable
What is the process of finding an equivalent fraction in its simplest form?
Dividing the numerator and the denominator by their greatest common divisor (GCD).
How can you convert a decimal to a fraction?
By writing the decimal as a fraction with a denominator of a power of 10 and then simplifying.
What is the relationship between the number of learners at a school and the number of classrooms needed?
The number of learners determines the number of classrooms needed.
What are equivalent algebraic expressions?
Different expressions that simplify to the same value.
How can you identify equivalent fractions?
By multiplying both the numerator and the denominator by the same number.
What is the distributive property of multiplication?
The property that states that a single term can be multiplied by each term within a parenthesis.
What is the purpose of combining like terms in algebra?
To simplify expressions by combining terms that have the same variable raised to the same power.
What is the purpose of expanding algebraic expressions?
To multiply a single term by each term within a parenthesis.
What is the purpose of simplifying quotient expressions?
To divide each term in the numerator by the denominator.
What is the purpose of rearranging terms in algebra?
To group like terms together for simplification.
What is the definition of an equation?
A mathematical statement that asserts the equality of two expressions.
What is the purpose of solving an equation?
To find the value(s) of the variable(s) that make the equation true.
What is the term for two or more equations that have the same solution?
Equivalent equations
What is the term for evaluating an expression by substituting a variable with a value?
Doing
What is the term for finding the original value of the variable that produces a given result?
Undoing
What is the sum of angles that form on a straight line?
180°
What is the term for numbers that add up to zero?
Additive inverses
What is the term for numbers that multiply to give one?
Multiplicative inverses
What is the sum of the interior angles of a triangle?
180°
What type of quadrilateral has all sides equal and opposite angles equal?
Rhombus
What is the angle subtended by an arc at the center of a circle?
Twice the angle subtended at any point on the circumference
What is the sum of the interior angles of a quadrilateral?
360°
What type of triangle has two equal sides?
Isosceles triangle
What is the purpose of using geometric tools to construct shapes accurately?
To validate theoretical findings
What is the result of applying the Pythagorean theorem to a right triangle?
The sum of the squares of the two sides is equal to the square of the hypotenuse
What is the purpose of applying theorems and properties in geometry?
To solve problems involving unknown measurements
What is the result of applying the properties of parallelograms to a quadrilateral?
Opposite sides are equal and parallel
What is the purpose of using transformations in geometry?
To affect the properties of shapes
What is the definition of vertically opposite angles?
Angles that are opposite each other when two lines intersect.
What is the key property of vertically opposite angles?
They are always equal.
What is the formula for vertically opposite angles?
$\angle a = \angle c$ and $\angle b = \angle d$
What is a transversal in geometry?
A line that intersects at least two other lines.
What is the key property of corresponding angles?
They are always equal.
What is the formula for corresponding angles?
$\angle a = \angle e$ and $\angle b = \angle f$
What is the definition of a quadrilateral?
A two-dimensional shape with four sides.
What is the sum of the interior angles of a quadrilateral?
360°
What is the definition of a square?
A quadrilateral with four equal sides and four right angles.
What is the definition of a rectangle?
A quadrilateral with opposite sides equal and four right angles.
What is the formula to find the perimeter of a rectangle?
P = 2l + 2b
What is the formula to find the area of a square?
A = s^2
What is the formula to find the circumference of a circle?
C = 2πr
What is the formula to find the area of a circle?
A = πr^2
What is the formula to find the area of a triangle?
A = 1/2 × base × height
What is the formula to find the perimeter of a square?
P = 4s
What is the formula to find the area of a rectangle?
A = l × b
What is the formula to find the perimeter of a rectangle when only the length and breadth are given?
P = 2l + 2b
What is the relationship between the sides of a right-angled triangle?
a^2 + b^2 = c^2
What is the formula to find the length of the hypotenuse in a right-angled triangle?
c = √(a^2 + b^2)
How do you determine if a triangle is right-angled?
If the sum of the squares of two sides is equal to the square of the third side
What is the formula for the perimeter of a rectangle?
P = 2l + 2b
What is the formula for the area of a circle?
A = πr^2
What is the purpose of converting between square units?
To understand the relationship between units
What is the formula for the circumference of a circle?
C = 2πd
What is the relationship between the diameter and radius of a circle?
d = 2r
What is the purpose of calculating the perimeter of a shape?
To measure the boundary length of the shape
What is the formula for the area of a square?
A = s^2
What is the characteristic of a rhombus?
All sides are equal with opposite equal angles
What is the term for a line segment within a circle that touches two points?
Chord
What is the primary focus of constructing 2D shapes?
Creating accurate shapes, angles, and lines
What is the term for a polygon with all sides and angles equal?
Regular polygon
What is the technique used to divide an angle into two equal parts?
Bisecting an angle
What is the term for a region bounded by two radii and an arc?
Sector
What is the primary tool used for constructing angles?
Compass
What is the term for a quadrilateral with two pairs of adjacent sides equal?
Kite
What is the purpose of investigating properties of geometric figures?
To examine the attributes, relationships, and characteristics of various shapes
What is the term for a distance from the center of a circle to any point on the circle?
Radius
What is the definition of similar shapes?
Shapes with the same shape but not necessarily the same size
What is the purpose of identifying similar shapes?
To determine the proportionality of corresponding sides
What is a scale factor?
A ratio of corresponding sides
What is the purpose of using similar shapes in real-world applications?
To solve problems involving map reading and creating scale models
What is a composite figure?
A figure that includes both similar and congruent shapes
What is the purpose of geometric proofs?
To develop logical arguments to show relationships between different parts of geometric figures
What is the purpose of interpreting graphs?
To understand relationships between variables and make predictions
What does the x-axis typically represent in a line graph?
Time
What is the purpose of analyzing bar graphs?
To compare the heights of different bars to analyze data
What should you check at the beginning when analyzing data?
The scale to understand the range and intervals of data
What is the purpose of interpreting scatter plots?
To determine if there is a positive, negative, or no correlation between variables
Which type of graph is used to show the relationship between two variables?
Scatter plot
What is the purpose of drawing a line of best fit in a scatter plot?
To display the trend or correlation between variables
What is the Pythagorean Theorem used for?
To calculate the square of the length of the hypotenuse
What should you ensure when drawing a bar graph?
The bars are separated by equal spacing
What is the purpose of a title in a graph?
To provide a clear and descriptive title
What is the purpose of labeling the axes in a graph?
To label the axes appropriately
What should you do when drawing a histogram?
Draw the bars touching each other
What is an outlier in a dataset?
A value that is significantly higher or lower than the rest of the data
What is the purpose of identifying trends in a line graph?
To predict future values
What is the main difference between congruent and similar shapes?
Congruent shapes have equal corresponding sides, while similar shapes have equal corresponding angles and proportional sides.
What is the purpose of using the SSS criterion in congruent shapes?
To determine if two shapes are congruent.
What is the result of applying the properties of congruent shapes?
Corresponding angles and sides are equal.
What is the purpose of solving problems with congruent 2D shapes?
To solve practical problems involving congruent shapes, such as designing patterns and creating tiling designs.
What is the definition of similar shapes?
Two shapes are similar if they have the same shape but not necessarily the same size.
What is the AA criterion used for in similar shapes?
To determine if two shapes are similar.
What is the purpose of using the problem-solving steps in geometry?
To solve problems involving congruent and similar shapes.
What is the result of applying the properties of similar shapes?
Corresponding angles are equal, but corresponding sides are not equal.
What is the purpose of using the RHS criterion in congruent shapes?
To determine if two right-angled triangles are congruent.
What is the main advantage of using the problem-solving steps in geometry?
It helps to solve problems accurately.
What is a characteristic of a kite?
Two pairs of adjacent sides are equal with one pair of opposite equal angles
What is the main focus of constructing 2D shapes?
Creating accurate shapes, angles, and lines
What is a characteristic of a parallelogram?
Opposite sides are equal and parallel with opposite equal angles
What is the term for a line segment within a circle that touches two points?
Chord
What is the purpose of bisecting an angle?
To divide an angle into two equal parts
What is the definition of vertically opposite angles?
Angles opposite each other when two lines intersect
What type of angles are formed when a transversal intersects two parallel lines?
Alternate interior angles, alternate exterior angles, and co-interior angles
What is the term for a region bounded by two radii and an arc?
Sector
What is the formula for co-interior angles?
Co-interior angles are supplementary (180)
What is the term for a polygon with all sides and angles equal?
Regular Polygon
What is the process of creating precise figures using specific tools and methods?
Construction in geometry
What is the sum of interior angles of any quadrilateral?
360
What is the definition of an isosceles triangle?
A triangle with two equal sides and two equal angles
What is the term for the distance from the center of a circle to any point on the circle?
Radius
What is the process of examining the attributes, relationships, and characteristics of various shapes?
Investigating geometric figures
What is the definition of a rectangle?
A quadrilateral with opposite sides equal and four right angles
What is the formula for alternate interior angles?
Alternate interior angles are equal
What is the definition of a scalene triangle?
A triangle with all sides and angles different
What is an equation?
A mathematical statement that asserts the equality of two expressions.
What is the purpose of solving an equation?
To find the value of a variable.
What is the definition of a transversal?
A line that intersects at least two other lines
What is the definition of corresponding angles?
Angles in the same position at each intersection
What is the definition of additive inverses?
Numbers that add up to zero.
What is the sum of angles on a straight line?
180°
What is the definition of supplementary angles?
Angles that add up to 180°.
What is the purpose of doing and undoing?
To solve equations by finding the original value of the variable.
What is the formula for angles on a straight line?
∠1 + ∠2 + ∠3 = 180°
What is the purpose of using inverses to solve equations?
To use multiplicative inverses to solve for the variable.
What is the sum of the interior angles of a triangle?
180°
What type of quadrilateral has all sides equal and opposite angles equal?
Rhombus
What is the sum of the interior angles of any quadrilateral?
360°
What is the angle subtended by an arc at the center of a circle?
Twice the angle subtended at any point on the circumference
What is the process of applying theorems to prove properties of geometric figures?
Using Theorems and Proofs
What is the term for a quadrilateral inscribed in a circle?
Cyclic Quadrilateral
What is the term for the line that divides a shape into two identical halves?
Line of Symmetry
What is the process of using geometric tools to construct shapes accurately?
Construction and Measurement
What is the term for a shape that has rotational symmetry?
Regular Polygon
What is the term for the point where two lines intersect?
Vertex
What is the primary goal of understanding congruent and similar shapes in geometry?
To compare and analyze geometric figures
What is the main difference between congruent and similar shapes?
Congruent shapes have the same size and shape, while similar shapes have the same shape but not necessarily the same size
What is the Side-Side-Side (SSS) congruence criterion for triangles?
If all three sides of one triangle are equal to all three sides of another triangle
What is the Angle-Angle (AA) similarity criterion for triangles?
If two angles of one triangle are equal to two angles of another triangle
What is the Right Angle-Hypotenuse-Side (RHS) congruence criterion for triangles?
If the hypotenuse and one other side of one right-angled triangle are equal to the hypotenuse and one other side of another right-angled triangle
What is the primary step in solving problems involving congruent and similar shapes?
Draw diagrams to visualize the problem
What is the purpose of using congruent shapes in real-world applications?
To design patterns and create tiling designs
What is the property of congruent shapes that allows them to be superimposed on each other perfectly?
Corresponding sides are equal in length
What is the definition of similar shapes?
Two shapes that have the same shape but not necessarily the same size
What is the purpose of understanding the concepts of similarity and congruence in geometry?
To compare and analyze geometric figures
What is the purpose of a scale in a graph?
To understand the range and intervals of the data
Which type of graph is used to show the proportion of each category?
Pie chart
What is the formula for the Pythagorean Theorem?
c^2 = a^2 + b^2
What is the purpose of a title in a graph?
To provide a clear and descriptive title
What is the longest side in a right-angled triangle?
Hypotenuse
Which type of graph is used to show the relationship between two variables?
Scatter plot
What is the purpose of identifying outliers in a graph?
To identify anomalies or unusual data points
What is the purpose of using a legend in a graph?
To include multiple datasets or colors
What is the purpose of using histograms?
To show the frequency of continuous data
What is the purpose of using trends in line graphs?
To predict future values
What is the formula for the perimeter of a square?
P = 4s
What is the formula for the area of a rectangle?
A = l * b
What is the formula for the circumference of a circle?
C = 2πr
How do you find the area of a composite shape?
Break it down into simpler shapes and calculate their areas separately
What is the formula for the area of a triangle?
A = 1/2 * base * height
What is the diameter of a circle?
The line segment passing through the center, joining two points on the circle
What is the formula for the area of a circle?
A = πr^2
When converting between units, how do you convert square units?
By squaring the conversion factor
What is the definition of similar shapes?
Shapes that have the same shape but not necessarily the same size
What is the purpose of using scale factors in similar shapes?
To determine the scale factor between similar shapes and scale shapes up or down
What is the main purpose of using graphs in real-world applications?
To show the relationships between variables and make predictions
What is the purpose of the axis labels in a graph?
To understand what each axis represents
What is the purpose of using histograms in graphing?
To analyze the shape of the distribution of continuous data
What is the purpose of using scatter plots in graphing?
To determine if there is a positive, negative, or no correlation between variables
What is the purpose of using composite figures in geometry?
To solve problems involving both similar and congruent shapes
What is the purpose of using geometric proofs in geometry?
To develop proofs that combine congruence and similarity to establish relationships between different parts of geometric figures
What is the purpose of using pie charts in graphing?
To display proportions and percentages as segments of a circle
What is the purpose of using bar graphs in graphing?
To represent categorical data with rectangular bars
In a right-angled triangle, what is the relationship between the squares of the sides?
a^2 + b^2 = c^2
What is the formula to find the length of the hypotenuse of a right-angled triangle?
c = √(a^2 + b^2)
What is the perimeter of a rectangle with a length of 6 cm and a breadth of 4 cm?
20 cm
What is the area of a circle with a radius of 4 cm?
16π cm^2
What is the formula to find the circumference of a circle?
C = 2πr
What is the relationship between the sides of an acute-angled triangle?
a^2 + b^2 > c^2
What is the area of a square with a side length of 5 cm?
25 cm^2
What is the perimeter of a square with a side length of 6 cm?
24 cm
What is the converse of the Pythagorean theorem?
If a^2 + b^2 = c^2, then the triangle is right-angled
What is the formula to find the area of a triangle?
A = 1/2bh
What is an equation according to the key concepts?
A mathematical statement that asserts the equality of two expressions
What is the purpose of solving an equation?
To find the value(s) of the variable(s) that make the equation true
What are additive inverses?
Numbers that add up to zero
What are multiplicative inverses?
Numbers that multiply to give one
What is the sum of angles that form on a straight line?
180°
What are supplementary angles?
Angles that add up to 180°
What is the definition of vertically opposite angles?
Angles opposite each other when two lines intersect.
What is a transversal?
A line that intersects at least two other lines.
What is the formula for angles on a straight line?
∠1 + ∠2 + ∠3 = 180°
What is doing and undoing in solving equations?
Evaluating an expression by substituting a variable with a value, and solving an equation by finding the original value of the variable
What type of angles are formed when a transversal intersects two lines?
Corresponding, alternate interior, alternate exterior, and co-interior angles
What is the formula for co-interior angles?
Angle c + Angle f = 180°
What is the sum of the interior angles of any quadrilateral?
360°
What type of triangle has all sides and angles equal?
Equilateral triangle
What is a square?
A quadrilateral with four equal sides and four right angles
What is a property of alternate interior angles?
They are equal if the lines are parallel
What is a property of corresponding angles?
They are equal if the lines are parallel
What type of angles are alternate exterior angles?
Angles on opposite sides of the transversal but outside the two lines
Which quadrilateral has opposite sides of equal length?
Rhombus
What is the name of the line segment that divides an angle into two equal parts?
Bisector
What is the term for a polygon with all sides and angles equal?
Regular Polygon
What is the name of the tool used to draw a circle with a given radius?
Compass
What is the term for a figure with four right angles and opposite sides of equal length?
Rectangle
What is the name of the line that bisects a line segment at a right angle?
Perpendicular Bisector
What is the term for a shape with two pairs of adjacent sides of equal length?
Kite
What is the name of the region bounded by two radii and an arc of a circle?
Sector
What is the term for a figure with four sides and all angles equal?
Square
What is the name of the process of creating precise figures using specific tools and methods?
Construction
What is the definition of congruent shapes?
Two shapes with the same shape and size
What is the purpose of using the Side-Side-Side (SSS) criterion?
To determine if two triangles are congruent
What is the definition of similar shapes?
Two shapes with the same shape but different sizes
What is the definition of similar shapes?
Two shapes that have the same shape but not necessarily the same size
What is the purpose of using scale factors in similar shapes?
To calculate unknown side lengths or to scale shapes up or down
What is the purpose of using the Angle-Angle (AA) criterion?
To determine if two triangles are similar
What is a common application of similar shapes in real-world problems?
All of the above
What is the first step in solving problems with congruent 2D shapes?
Identify congruent shapes
What is the property of congruent shapes that states corresponding angles are equal?
Corresponding angles are equal
What type of graph is used to show trends over time?
Line graph
What is the purpose of a histogram?
To display continuous data divided into intervals
What is the purpose of using congruent shapes in real-world applications?
To design patterns and create tiling designs
What is the result of using the Right Angle-Hypotenuse-Side (RHS) criterion?
Determining if two triangles are congruent
What is the purpose of analyzing a graph?
To understand relationships between variables and make predictions
What is the purpose of using the Angle-Angle-Side (AAS) criterion?
To determine if two triangles are congruent
What is the purpose of a scatter plot?
To show relationships between two variables
What is the result of using the Side-Angle-Side (SAS) criterion?
Determining if two triangles are congruent
What is the purpose of interpreting a bar graph?
To compare the heights of different bars to analyze data
What is the purpose of a composite figure?
To solve problems involving both similar and congruent shapes
What is the purpose of using similarity in real-world applications?
To resize images and create proportional models and structures
What is the sum of the interior angles of a triangle?
180°
What is the sum of the interior angles of any quadrilateral?
360°
What is the name of the line that divides a circle into two equal parts?
Diameter
What is the name of the shape formed by a quadrilateral inscribed in a circle?
Cyclic Quadrilateral
What is the purpose of using theorems and proofs in geometry?
To prove properties of geometric figures
What is the name of the transformation that changes the size of a shape?
Enlargement
What is the name of the line that touches a circle at a single point?
Tangent
What is the name of the quadrilateral with all sides equal?
Square
What is the purpose of using geometric tools to construct shapes?
To construct shapes accurately
What is the name of the angle formed by a vertex of a triangle and a point on the circumference of a circle?
Inscribed Angle
What is the purpose of identifying outliers in a graph?
To recognize unusual data points that do not fit the pattern
What type of graph is used to show the relationship between two variables?
Scatter plot
What is the Pythagorean theorem used for?
To find the length of the hypotenuse of a right-angled triangle
What is the purpose of drawing a line of best fit in a scatter plot?
To show the trend of the data
What is the purpose of labeling the axes in a graph?
To show the units of the data
What type of graph is used to show categorical data?
Bar graph
What is the purpose of using different colors or patterns in a pie chart?
To differentiate between the categories
What is the purpose of checking the scale of a graph?
To ensure that all data points are included
What is the purpose of using a title in a graph?
To provide a clear and descriptive title
In a right-angled triangle, what is the relationship between the sides?
a^2 + b^2 = c^2
What is the formula to find the length of the hypotenuse in a right-angled triangle?
c = √(a^2 + b^2)
What is the purpose of using a legend in a graph?
To differentiate between multiple datasets
What is the converse of the Pythagorean theorem used for?
To verify if a triangle is right-angled
What is the formula to find the perimeter of a rectangle?
P = 2(l + b)
What is the formula to find the area of a square?
A = s^2
What is the formula to find the circumference of a circle?
C = 2πr
What is the formula to find the area of a circle?
A = πr^2
What is the purpose of converting between square units?
To understand the relationship between units
What is the formula to find the perimeter of a square?
P = 4s
What is the purpose of finding the perimeter of a shape?
To measure the distance around the shape
What is the formula for the perimeter of a square?
P = 4s
What is the formula for the area of a rectangle?
A = l × b
What is the formula for the area of a triangle?
A = 1/2 × base × height
What is the formula for the circumference of a circle?
C = 2πr
What is the formula for the area of a circle?
A = πr^2
How do you find the area of a composite shape?
Break down the shape into simpler shapes, calculate their areas separately, and then sum them up
What is the purpose of converting between units when finding perimeters and areas?
To convert between lengths and square units
What is the formula for the perimeter of a rectangle?
P = 2(l + b)
What is the defining feature of a rhombus?
All sides are equal
What is the term for a line segment within a circle that touches two points?
Chord
What is the purpose of constructing a 60° angle?
To create an equilateral triangle
What is the primary tool used to divide an angle into two equal parts?
Compass
What is the term for a polygon with all sides and angles equal?
Regular polygon
What is the purpose of identifying lines of symmetry in a shape?
To identify the shape's properties
What is the sum of the interior angles of a triangle?
180°
What is the term for a region bounded by two radii and an arc?
Sector
What is the purpose of constructing perpendicular lines?
To create a right angle
What is the name of the theorem that states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides?
Pythagorean Theorem
What is the term for a polygon with at least one interior angle greater than 180 degrees?
Concave polygon
What is the sum of the interior angles of any quadrilateral?
360°
What is the term for a quadrilateral with opposite sides equal and parallel, opposite angles equal, and diagonals bisecting each other?
Parallelogram
What is the primary focus of constructing 2D shapes?
Creating accurate shapes and angles
What is an equation?
A mathematical statement that asserts the equality of two expressions.
What is the angle subtended by an arc at the center of a circle?
Twice the angle subtended at any point on the circumference
What is the term for a line that just touches a circle at a single point?
Tangent
What is the purpose of solving an equation?
To find the value of the variable that makes the equation true.
What is the definition of additive inverses?
Numbers that add up to zero.
What is the term for a quadrilateral inscribed in a circle?
Cyclic Quadrilateral
What is the sum of angles that form on a straight line?
180°
What is the process of using theorems to prove properties of geometric figures?
Using Theorems and Proofs
What is the formula for angles on a straight line?
∠1 + ∠2 + ∠3 = 180°
What is the term for a transformation that changes the size of a shape but not its shape?
Enlargement
What is the purpose of doing and undoing in solving equations?
To solve an equation by finding the original value of the variable that produces a given result.
What is the purpose of identifying geometric figures?
To classify shapes
What is the purpose of isolating the variable in solving equations?
To use additive inverses to move constants to the other side of the equation.
What is the definition of supplementary adjacent angles?
Adjacent angles that sum to 180°.
What is the key property of vertically opposite angles?
They are equal
What is the type of angle formed by a transversal intersecting two lines, where the angles are on the same side of the transversal and inside the two lines?
Alternate interior angles
What is the sum of the interior angles of a quadrilateral?
360°
What is the type of triangle with all sides and angles equal?
Equilateral triangle
What is the formula for co-interior angles when two lines are parallel?
∠a + ∠c = 180°
What is the type of angle formed by a transversal intersecting two lines, where the angles are on opposite sides of the transversal and inside the two lines?
Alternate interior angles
What is the definition of a 2D shape?
A shape with length and width but no depth
What is the type of quadrilateral with four equal sides and four right angles?
Square
What is the formula for alternate interior angles when two lines are parallel?
∠a = ∠c
What is the key property of corresponding angles when two lines are parallel?
They are equal
What is the main goal of the problem-solving steps in geometry?
To understand and solve geometric problems
What is the definition of congruent shapes?
Shapes with the same shape and size
What is the Side-Side-Side (SSS) criterion for congruent triangles?
If all three sides of one triangle are equal to all three sides of another triangle
What is the definition of similar shapes?
Shapes with the same shape but not necessarily the same size
What is the purpose of using the Angle-Angle (AA) criterion for similar triangles?
To determine if two triangles are similar
What is the result of applying the properties of congruent shapes?
Corresponding angles and sides are equal
What is the purpose of using congruent shapes in real-world applications?
To design patterns and create tiling designs
What is the first step in the problem-solving steps for geometry?
Understand the problem
What is the purpose of verifying solutions in the problem-solving steps for geometry?
To check if the solution satisfies all given constraints
What is the result of using the properties of similar shapes?
Corresponding angles are equal, and corresponding sides are proportional
What is the definition of similar shapes?
Two shapes with the same shape but not necessarily the same size
What is the purpose of using scale factors?
To determine the scale factor between similar shapes
What is the purpose of breaking down composite figures into simpler components?
To solve problems involving similar and congruent shapes
What is the purpose of using geometric proofs?
To develop logical arguments to show relationships between different parts of geometric figures
What is the purpose of using bar graphs?
To represent categorical data with rectangular bars
What is the purpose of interpreting line graphs?
To look for upward, downward, or constant trends
What is the purpose of using pie charts?
To display proportions and percentages as segments of a circle
What is the purpose of interpreting histograms?
To analyze the shape of the distribution
What is the purpose of interpreting scatter plots?
To determine if there is a positive, negative, or no correlation between variables
What is the purpose of analyzing graphs?
To understand the relationships between variables
What is the main purpose of checking the scale of a graph?
To understand the range and intervals of data
Which type of graph is used to show the relationship between two variables?
Scatter plot
What is the formula for the Pythagorean Theorem?
c^2 = a^2 + b^2
What is the purpose of drawing a line of best fit in a scatter plot?
To show the trend in the data
What is the longest side in a right-angled triangle?
Hypotenuse
What is the purpose of title in a graph?
To provide a clear and descriptive title
What is the purpose of using different colors or patterns in a pie chart?
To differentiate between sectors
What is the purpose of histogram?
To display continuous data divided into intervals
What is the purpose of drawing a graph?
To illustrate relationships between variables
What is the purpose of labeling the axes in a graph?
To identify the variables being plotted
What is the formula to find the length of the hypotenuse in a right-angled triangle?
c = √(a^2 + b^2)
Which of the following is true about a right-angled triangle?
The sum of the squares of two sides is equal to the square of the third side
What is the formula to find the area of a rectangle?
A = l × b
What is the perimeter of a square with a side length of 5cm?
20cm
What is the formula to find the circumference of a circle?
C = 2πr
What is the formula to find the area of a circle?
A = πr^2
What is the purpose of the Pythagorean theorem?
To find the length of a side in a right-angled triangle
What is the relationship between the sides of an acute-angled triangle?
a^2 + b^2 > c^2
What is the formula to find the perimeter of a rectangle?
P = 2l + 2b
What is the purpose of converting between square units?
To understand the relationship between units
What is the formula for the perimeter of a square?
P = 4s
What is the formula for the area of a rectangle?
A = l × b
What is the formula for the circumference of a circle?
C = 2πr
What is the formula for the area of a circle?
A = πr^2
What is the method used to calculate the area of a composite shape?
Breaking down into simpler shapes and calculating their areas separately
What is the definition of the radius of a circle?
A line segment from the center to any point on the circle
What is the formula for the perimeter of a rectangle?
P = 2l + 2b
What is the definition of the area of a shape?
The size of a flat surface, measured in square units
What is an equation?
A mathematical statement that asserts the equality of two expressions.
What is the purpose of solving an equation?
To find the value(s) of the variable(s) that make the equation true.
What are two or more equations that have the same solution called?
Equivalent equations
What is the definition of additive inverses?
Numbers that add up to zero.
What is the definition of multiplicative inverses?
Numbers that multiply to give one.
What is the formula for angles on a straight line?
( \angle 1 + \angle 2 + \angle 3 = 180 )
What is the sum of angles that form on a straight line?
180
What are two angles that add up to 180 called?
Supplementary angles
What is the key property of vertically opposite angles?
They are always equal.
What type of angles are formed when a transversal intersects two parallel lines and lie on the same side of the transversal?
Co-interior angles
What is the sum of the interior angles of any quadrilateral?
360°
What type of triangle has all sides and angles equal?
Equilateral triangle
What is the formula for vertically opposite angles?
∠a = ∠c and ∠b = ∠d
What type of angle is formed when a transversal intersects two parallel lines and lies outside the two lines?
Alternate exterior angle
What is the key property of corresponding angles?
They are always equal.
What is the definition of a quadrilateral?
A two-dimensional shape with four sides and four angles.
What is the key property of alternate interior angles?
They are always equal.
What is the key property of co-interior angles?
They are always supplementary.
What is the definition of a rhombus?
A quadrilateral with all sides equal and opposite equal angles
What is the name of a polygon with all sides and angles equal?
Regular polygon
What is the distance from the center to any point on a circle?
Radius
What is the purpose of constructing shapes in geometry?
To create precise figures using specific tools and methods
How do you construct a 60° angle?
Drawing an equilateral triangle and using its properties
What is the purpose of identifying shapes in geometry?
To name shapes using their properties
What is the method of constructing a triangle given three sides?
Using a compass to measure and draw the sides
What is the purpose of constructing perpendicular lines?
To create a right angle
What is the method of constructing a quadrilateral given specific properties?
Using a combination of techniques for constructing angles, sides, and parallel lines
What is the purpose of investigating properties of geometric figures?
To examine the attributes, relationships, and characteristics of various shapes
What is the sum of the interior angles of a triangle?
180°
Which type of quadrilateral has all sides equal and opposite angles equal?
Rhombus
What is the angle subtended by an arc at the center of a circle?
Twice the angle subtended at any point on the circumference
What is the result of applying the Pythagorean theorem to a right triangle?
The sum of the squares of the two sides is equal to the square of the hypotenuse
What is the purpose of identifying lines of symmetry in geometric figures?
To investigate the properties of the figure
What is the sum of the interior angles of a quadrilateral?
360°
What is the purpose of using theorems in geometry?
To prove properties of geometric figures
What is the result of translating a geometric figure?
The figure is moved to a new position
What is the purpose of using geometric tools to construct shapes?
To validate theoretical findings
What is the purpose of solving problems involving geometric figures?
To enhance critical thinking and spatial reasoning skills
What is a necessary condition for two shapes to be similar?
They have the same shape and proportional corresponding sides
What is the purpose of using a scale factor in similar shapes?
To determine the scale factor between similar shapes
What type of graph is used to display categorical data with rectangular bars?
Bar graph
What does the axis label on a line graph typically represent?
The x-axis represents time and the y-axis represents the variable being measured
What is the purpose of analyzing a graph?
To understand the relationship between variables and make predictions
What is the definition of a similar shape?
A shape with the same shape but not necessarily the same size
What is the purpose of using similar shapes in real-world applications?
To create scale models and resize images
What is the purpose of using a scatter plot?
To show the relationship between two variables
What is the purpose of using a histogram?
To show the distribution of continuous data
What is the purpose of using a pie chart?
To display proportions and percentages as segments of a circle
What is the primary step in solving a problem involving geometric figures?
Understand the problem
What is the definition of congruent shapes?
Shapes with the same shape and size
What is the property of congruent shapes that states corresponding sides are equal?
Corresponding sides are equal in length
What is the criterion for congruent triangles that states if all three sides of one triangle are equal to all three sides of another triangle, the triangles are congruent?
Side-Side-Side (SSS)
What is the definition of similar shapes?
Shapes with the same shape but not necessarily the same size
What is the property of similar shapes that states corresponding angles are equal?
Corresponding angles are equal
What is the criterion for similar triangles that states if two angles of one triangle are equal to two angles of another triangle, the triangles are similar?
Angle-Angle (AA)
What is the purpose of identifying congruent shapes in problem-solving?
To compare corresponding sides and angles
What is the application of congruent shapes in real-world problems?
Designing patterns and creating tiling designs
What is the purpose of using the properties of congruent shapes in problem-solving?
To apply the properties of corresponding sides and angles
What is the purpose of checking the scale in a graph?
To understand the range and intervals of data
Which type of graph is used to show the relationship between two variables?
Scatter plot
What is the purpose of drawing a line of best fit in a scatter plot?
To show the correlation between variables
What is the formula for the Pythagorean Theorem?
c^2 = a^2 + b^2
What is the condition for a triangle to be right-angled?
a^2 + b^2 = c^2
What is the purpose of using a title in a graph?
To provide a clear and descriptive title
What is the definition of a right-angled triangle?
A triangle with one angle equal to 90 degrees
What is the formula to find the length of the hypotenuse of a right-angled triangle?
c = √(a^2 + b^2)
What is the perimeter of a rectangle with length 5 cm and breadth 3 cm?
16 cm
What is the purpose of using a legend in a graph?
To include multiple datasets or colors
What is the purpose of identifying outliers in a graph?
To identify anomalies or unusual data points
What is the area of a square with side 4 cm?
16 cm²
What is the circumference of a circle with radius 7 cm?
42 cm
What is the purpose of using histograms?
To divide continuous data into intervals
What is the purpose of using trends in line graphs?
To predict future values
What is the area of a circle with radius 5 cm?
78.5 cm²
What is the process of converting between square units?
Multiplication
What is the formula for the perimeter of a square?
P = 4s
What is the formula for the area of a rectangle?
A = l × b
What is the purpose of the Pythagorean theorem?
To find the length of a side in a right-angled triangle
What is the formula for the perimeter of a square?
P = 4s
What is the formula for the area of a rectangle?
A = l × b
What is the formula for the circumference of a circle?
C = 2πr
What is the formula for the area of a circle?
A = πr^2
How do you find the perimeter of a composite shape?
Break down the shape into simpler shapes and calculate their perimeters separately
What is the unit of measurement for area?
Square meters
What is the purpose of converting between units of length?
To solve problems involving different units of measurement
How do you find the area of a triangle?
Use the formula A = (1/2) × base × height
Make Your Own Quizzes and Flashcards
Convert your notes into interactive study material.
Get started for free
