504 Questions
What are the numbers that we use to count called?
Natural Numbers
What is the result of adding two or more natural numbers?
A natural number
What is the result of subtracting a natural number from another natural number?
Not always a natural number
What is the purpose of 0 in the system of whole numbers?
To write numbers
What is the identity element for addition in the system of whole numbers?
0
What is a characteristic of the system of integers?
The sum of two integers can be zero
What is an example of an irrational number?
\sqrt{2}
What is the set of numbers that includes both rational and irrational numbers?
The set of real numbers
What is the result of subtracting a larger number from a smaller number?
A negative number
What is the equivalent of adding a negative number?
Subtracting a positive number
What is the result of the product of a positive and a negative number?
A negative number
What is the purpose of exponents in mathematics?
To provide a shorthand method for writing repeated multiplication
What is the order of operations when calculating expressions involving exponents?
Parentheses, exponents, multiplication, and division, then addition and subtraction
What is the meaning of a negative exponent?
The reciprocal of the base raised to the positive exponent
What is the purpose of scientific notation?
To express very large or very small numbers in a compact form
What is the rule for writing numbers in scientific notation?
Move the decimal point to the left, and the exponent is positive
What is the purpose of the laws of exponents?
To simplify exponential expressions
What is the goal of investigating and extending geometric patterns?
To analyze and describe the patterns in the arrangements
What is a relationship between two variables where each input has exactly one output?
Function
What represents the calculations needed to find the output number that corresponds to a given input number?
Formula
What is a method to visually represent the relationship between variables?
Graph
What is the formula to calculate the gradient of a line passing through two points?
Gradient = (y2 - y1) / (x2 - x1)
What is the term for a quantity that can change?
Variable
What is the term for the value substituted into a function?
Input Number
What shows the calculations needed to transform input into output?
Flow Diagram
What is a method to list input values and their corresponding output values?
Table
What is a characteristic of a function?
Each input has exactly one output
What is the purpose of a graph in representing relationships?
To provide a visual representation of the relationship
What is the distributive property of multiplication?
a(b + c) = ab + bc
What is the sum of the interior angles of a triangle?
180°
What is the convention for writing a known number in a product?
Write the known number first
What is the name of a line that intersects two or more other lines?
Transversal
What is the result of multiplying a polynomial by a monomial?
Each term in the polynomial is multiplied by the monomial
What is the result of subtracting a larger number from a smaller number?
A negative number
What is the name of a polygon with all sides and angles equal?
Regular polygon
What is the purpose of estimating in calculations?
To get close to an answer without performing precise calculations
What is the sum of the interior angles of a quadrilateral?
360°
What is the formula for evaluating the square of a monomial?
(2x)^2 = 4x^2
What is the effect of adding a negative number to a positive number?
The result is equivalent to subtracting the corresponding positive number
What is the name of a triangle with one angle equal to 90°?
Right triangle
How is addition performed in columns?
By adding each digit starting from the rightmost digit
What is the additive inverse of a positive number?
A negative number with the same magnitude
What is the rule for simplifying an expression?
Combine like terms and apply the distributive property
What is the name of a shape where all points are equidistant from the center?
Circle
What is the result of dividing the number step-by-step in long division?
The remainder is always less than the divisor
What is the result of multiplying a positive number and a negative number?
A negative number
What is the formula for the distributive property of division?
(x + y)/z = x/z + y/z
What is the lowest common multiple of two or more numbers?
The smallest number that is a multiple of each of them
What is the distributive property of multiplication over addition?
a(b + c) = ab + ac
What is the general form for squaring a binomial?
(a + b)^2 = a^2 + 2ab + b^2
What is the name of angles that are equal when the lines are parallel?
Corresponding angles
What is the relationship between distance, speed, and time?
Distance = Speed × Time
What is the name of angles that are on the same side of the transversal and inside the parallel lines?
Co-interior angles
What is the result of dividing a positive number by a negative number?
A negative number
What is the result of applying the rule x - 1000 to natural numbers smaller than 1000?
Negative numbers
What is the square root of a number?
The positive square root of the number
What is the formula for calculating simple interest?
Simple interest = Principal × Rate × Time
What is the name of angles that are on opposite sides of the transversal and inside the parallel lines?
Alternate angles
What is the purpose of brackets in algebraic expressions?
To indicate the order of operations
What is the difference between the HP price and the cash price?
Interest
What is the formula for the area of a rectangle?
A = l × w
What is the purpose of negative numbers?
To provide solutions for equations and to extend the number system for practical purposes
What is the convention for writing algebraic expressions?
Omit the multiplication sign
What is the result of adding a positive number and its additive inverse?
Zero
What is the ratio of flour to oatmeal in a biscuit recipe?
5:2
How is the highest common factor of two or more numbers found?
By multiplying the common prime factors of the numbers
What is the rule for subtracting a negative number?
Subtracting a negative number is the same as adding the corresponding positive number
What is the purpose of compensating for errors in calculations?
To correct errors introduced by rounding
What is the formula to calculate the gradient of a line passing through two points (x₁, y₁) and (x₂, y₂)?
Gradient = y₂ - y₁ / x₂ - x₁
What is the key characteristic of a function?
Each input corresponds to exactly one output
What does the slope of a graph indicate?
The rate of change of the output with respect to the input
What is the sum of angles on a straight line?
180°
What are two angles whose sum is 180° called?
Supplementary angles
What is the name of the line that intersects two or more other lines?
Transversal
What is the name of the angles formed when two straight lines intersect?
Vertically opposite angles
What is the purpose of a table when drawing graphs of functions?
To choose a range of input values and calculate the corresponding output values
What does the continuity of a graph indicate?
The graph is a continuous curve
What is the name of the angles on opposite sides of the transversal but inside the two intersected lines?
Co-interior angles
What is the correct order of operations when there are no brackets in an algebraic expression?
Multiplication and division, then addition and subtraction
What is the term for an expression with three terms?
Trinomial
What is the symbol often used to represent the variable in an algebraic expression?
x
What is the term for a fixed value in an algebraic expression?
Constant
What is the purpose of brackets in algebraic expressions?
To perform calculations first
What is an algebraic expression that has different sequences of operations but the same numerical value?
Equivalent expression
What is the term for an expression with one term?
Monomial
What is the convention for writing algebraic expressions when multiplying a number and a variable?
Write the number first
What is the term for the number multiplying the variable in an algebraic expression?
Coefficient
What do flow diagrams sometimes represent in algebraic language?
Sequences of operations
What is the formula for the circumference of a circle?
C = 2πr
What is the area of a sector?
A = θ/360 × πr^2
What is the sum of the interior angles of a regular polygon?
(n - 2) × 180°
What is the formula for the area of a regular polygon?
A = 1/4 n s^2 cot(π/n)
What is the method for constructing a perpendicular line through a point on a line segment?
Draw two circles with centers at the ends of the line segment and pass through the point
What is the method for bisecting an angle?
Draw a circle with the vertex as the center and mark off equal lengths on both arms of the angle
What is the method for constructing a 45° angle?
Draw a 90° angle and bisect it
What is the property of the three angle bisectors of a triangle?
They intersect at one point, equidistant from each side of the triangle
What is the relationship between the exterior angle of a triangle and the interior opposite angles?
The exterior angle is equal to the sum of the interior opposite angles
What is the criterion for two triangles to be congruent?
They have the same shape and size
What is the minimum condition required to prove congruency of two triangles?
One side and two angles
Which formula is used to calculate the area of a triangle?
A = 1/2 * base * height
What is the formula for the perimeter of a rectangle?
P = 2(l + w)
Which of the following is a type of transformation?
All of the above
What is the formula for the circumference of a circle?
C = 2 * pi * r
What is the formula for the area of a regular polygon?
A = 1/4 * n * s^2 * cot(pi/n)
What is the method of constructing a triangle with two sides and an included angle?
Draw the base, use a protractor to measure the given angle, then draw the other side and connect the vertices
What is the definition of translation?
Moves every point of a shape the same distance in the same direction
What is the formula for the area of a circle?
A = pi * r^2
What is the formula for the sum of interior angles of a regular polygon?
Sum = (n - 2) * 180
What is the formula for translating a point by a vector (a, b)?
(x, y) -> (x + a, y + b)
What is the formula for the area of a triangle?
A = 1/2 × base × height
What is the formula for rotating a point 90 degrees counterclockwise about the origin?
(x, y) -> (-y, x)
What is the formula for the surface area of a cube?
SA = 6s^2
What is the formula for reflecting a point over the x-axis?
(x, y) -> (x, -y)
What is the formula for dilating a point by a scale factor of k from the origin?
(x, y) -> (kx, ky)
What is the formula for the volume of a cylinder?
V = πr^2h
What is the formula for the area of a rectangle?
A = l * w
What is the formula for the area of a kite?
A = 1/2 × d1 × d2
What is the formula for the perimeter of a rectangle?
P = 2(l + w)
What is the formula for the perimeter of a square?
P = 4s
What is the formula for the circumference of a circle?
C = 2 * pi * r
What is the formula for the area of a circle?
A = πr^2
What is the formula for the surface area of a rectangular prism?
SA = 2lw + 2lh + 2wh
What is the effect of doubling the dimensions of a shape on its perimeter?
The perimeter doubles
What is the effect of doubling the dimensions of a shape on its area?
The area quadruples
What is the formula for the volume of a sphere?
V = 4/3πr^3
What is the purpose of converting between units of measurement?
To compare quantities
What is the closure property of natural numbers under addition?
The result is always a natural number.
Which of the following statements about integers is true?
Each integer has an additive inverse.
What is the defining characteristic of rational numbers?
They can be expressed as the quotient of two integers.
What is the difference between whole numbers and natural numbers?
Whole numbers include zero, while natural numbers do not.
What is a characteristic of irrational numbers?
They cannot be expressed as a fraction of two integers.
What is the set of real numbers composed of?
Rational and irrational numbers.
What is the purpose of the system of whole numbers?
To extend the natural numbers to include zero.
Which of the following statements is true about the system of integers?
It is closed under addition and subtraction.
What is the purpose of estimating in calculations?
To get a close approximate answer
How is addition performed in columns?
By adding each digit from right to left
What is the lowest common multiple of two or more numbers?
The smallest number that is a multiple of each of them
What is the formula for calculating distance?
Distance = Average speed × Time
What is the purpose of compensating for errors in calculations?
To correct errors introduced by rounding
What is the ratio used for in Moeneba's apple collection?
To compare the number of apples collected by different people
What is the effect of subtracting a negative number from a positive number?
It is equivalent to adding the corresponding positive number
What is the result of adding a positive and a negative number with the same magnitude?
The result is zero
How is multiplication performed in columns?
By multiplying each digit from right to left
What is the product of two negative numbers?
Positive
What is the formula for calculating average speed?
Average speed = Distance / Time
What is the additive inverse of a positive number?
A negative number with the same magnitude
What is the purpose of prime factorization?
To express a number as a product of its prime factors
What is the formula for calculating time?
Time = Distance / Average speed
What is the result of dividing a positive number by a negative number?
The result is negative
What is the distributive property of multiplication?
a(b + c) = ab + ac
What is the equivalent of subtracting a positive number from another positive number?
Adding the corresponding negative number
What is the result of adding a negative number to its additive inverse?
The result is zero
What is the purpose of negative numbers in mathematics?
To extend the number system for practical purposes
What is the result of multiplying a positive number and a negative number?
The result is negative
What is the result of subtracting a larger number from a smaller number?
A negative number
What is the equivalent of adding a negative number?
Subtracting a positive number
What is the result of the product of a positive and a negative number?
A negative number
What is the purpose of exponents in mathematics?
To simplify multiplication
What is the rule for writing numbers in scientific notation?
Move the decimal point to the left, and the exponent is positive
What is the purpose of the laws of exponents?
To simplify exponential expressions
What is the meaning of a negative exponent?
The reciprocal of the base raised to the positive exponent
What is the goal of investigating and extending geometric patterns?
To analyze and extend patterns
What is the order of operations when calculating expressions involving exponents?
Parentheses, Exponents, Multiplication and Division, Addition and Subtraction
What is the result of multiplying a number in exponent form by another number in exponent form with the same base?
The sum of the exponents
What is the purpose of brackets in algebraic expressions?
To indicate the order of operations
What is the result of multiplying $(2x + 3)(x - 2)$?
$2x^2 - x - 6$
What is the equivalent expression for $(x + 2)^2$?
$x^2 + 4x + 4$
What is the result of dividing $x^2 + 3x - 2$ by $x + 1$?
$x - 2$
What is the purpose of the distributive property in algebra?
To multiply polynomials by monomials
What is the result of evaluating $(3x)^2$?
$9x^2$
What is the purpose of substituting values into algebraic expressions?
To evaluate the expression
What is the equivalent expression for $x - 1000$ when applied to natural numbers smaller than 1000?
A negative number
What is the purpose of the rule in functions and relationships?
To multiply a number by 5 and subtract the result from 50
What is the result of simplifying $2x^2 + 3x + 2x + 1$?
$2x^2 + 5x + 1$
What is a sequence of operations that can also be described in words or flow diagrams?
An algebraic expression
What is the term for an expression with one term only?
Monomial
What is the rule for calculating expressions without brackets?
Perform multiplication and division first, then addition and subtraction
What is the term for a symbol, often x, representing the unknown value?
Variable
What is the purpose of identifying constants and variables in patterns?
To understand the relationships between the terms
What is the term for expressions that have different sequences of operations but the same numerical value?
Equivalent expressions
What is the convention for writing a known number in a product?
Write the known number first
What is the purpose of expanding and simplifying algebraic expressions?
To make the expression easier to understand
What is the rule for performing calculations within brackets?
Perform the calculations within brackets first
What is the term for an expression which is a sum of three terms?
Trinomial
What is the key concept in functions that refers to the specific output corresponding to a given input?
Function Value
What type of angles are formed when two lines intersect to form equal angles of 90°?
Perpendicular Lines
What is the term for the value substituted into a function to produce an output?
Input Number
What is the characteristic of a graph that indicates how rapidly the output changes with respect to the input?
Slope/Gradient
What is the name of the line that intersects two or more other lines?
Transversal
What is the term for the quantity that can change in a function?
Variable
What is the formula for calculating the gradient of a line passing through two points (x1, y1) and (x2, y2)?
Gradient = y2 - y1 / x2 - x1
What is the method used to visually represent the relationship between variables?
Graph
What is the term for the angles formed when two straight lines intersect?
Vertically Opposite Angles
What is the purpose of identifying the function in drawing graphs of functions?
To determine the formula or rule that defines the function
What is the primary purpose of a flow diagram in representing functions?
To illustrate the calculations needed to determine the output number
Which of the following is a characteristic of a function?
Each input has exactly one output
What is the term for the value substituted into a function?
Input number
What is the purpose of a graph in representing relationships?
To provide a visual representation of the relationship between variables
What is the formula for calculating the gradient of a line passing through two points?
(y2 - y1) / (x2 - x1)
Which of the following representations of a function shows the calculations needed to transform input into output?
Flow diagram
What is the term for a quantity that can change?
Variable
What is the purpose of a table in representing functions?
To list input values and their corresponding output values
What is the role of the formula in representing a function?
To describe the calculations needed to determine the output number
What is the key feature to consider when interpreting graphs?
All of the above
What is the minimum condition required to prove congruency in two triangles?
Three sides (SSS)
What is the formula to calculate the area of a triangle?
A = (1/2) × base × height
What is the name of the formula used to calculate the area of a triangle when the length of all three sides are known?
Heron's Formula
What is the formula to calculate the circumference of a circle?
C = 2 × π × radius
What is the name of the transformation that moves every point of a shape the same distance in the same direction?
Translation
What is the minimum condition required to construct a triangle?
Three sides
What is the formula to calculate the perimeter of a triangle?
P = a + b + c
What is the sum of the interior angles in a triangle?
180°
What is the name of the polygon with four sides of equal length?
Rhombus
What is the name of a shape with all sides and angles equal?
Regular Polygon
What is the formula to calculate the area of a circle?
A = π × radius²
What is the name of the formula used to calculate the sum of interior angles of a polygon?
Formula for the Sum of Angles of a Polygon
What is the relationship between the angles on opposite sides of a transversal and inside the parallel lines?
They are equal
What is the sum of co-interior angles?
180°
What is the name of a triangle with two sides and two angles equal?
Isosceles Triangle
What is the formula for the area of a rectangle?
A = l × w
What is the name of a line that intersects two or more other lines?
Transversal
What is the sum of the interior angles in a quadrilateral?
360°
What is the formula for the area of a circle?
A = πr^2
What is the name of a polygon with all sides equal?
Rhombus
What is the formula for the area of a sector?
A = θ/360 × πr^2
What is the formula for the sum of interior angles of a polygon?
(n - 2) × 180°
What is the formula for the perimeter of a polygon?
P = n × s
What is the formula for the area of a regular polygon?
A = 1/4 × n × s^2 × cot(π/n)
What is the method to construct a perpendicular line through a point not on the line segment?
Draw two circles with each end point of the line segment as the center and passing through the point.
What is the method to bisect an angle using circles?
Draw a circle with the vertex of the angle as the center, marking off equal lengths on both arms of the angle.
What is the characteristic of an angle bisector in a triangle?
It is a line that cuts an angle in half.
What is the relationship between the exterior angle and interior opposite angles of a triangle?
The exterior angle is equal to the sum of the interior opposite angles.
What is the criteria for congruency of two triangles?
They have the same shape and size.
What is the purpose of constructing special angles without a protractor?
To construct angles that are multiples of 30, 45, or 60 degrees.
What is the formula for translating a point by vector (a, b)?
(x, y) → (x + a, y + b)
What is the formula for rotating a point 90° counterclockwise about the origin?
(x, y) → (-y, x)
What is the formula for reflecting a point over the line y = x?
(x, y) → (y, x)
What is the formula for dilating a point by a scale factor of k from the origin?
(x, y) → (kx, ky)
What is the formula for the area of a parallelogram?
A = base × height
What is the formula for the perimeter of a rectangle?
P = 2(l + w)
What is the effect of doubling the dimensions of a shape on its area?
The area is quadrupled
What is the formula for converting between units of length?
1 cm = 10 mm
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 formula for the surface area of a cube?
SA = 6s^2
What is the formula for the volume of a cylinder?
V = πr^2h
What is the formula for the area of a triangle?
A = 1/2 × base × height
What is the formula for the surface area of a rectangular prism?
SA = 2lw + 2lh + 2wh
What is the formula for the circumference of a circle?
C = 2πr
What is the formula for the area of a kite?
A = 1/2 × d_1 × d_2
What is the formula for the volume of a sphere?
V = 4/3πr^3
What is the formula for the surface area of a cone?
SA = πr(l + r)
What is the purpose of estimating in calculations?
To get close to an answer without performing precise calculations
What is the formula for evaluating the average speed?
Distance / Time
What is the highest common factor of two or more numbers?
The largest number that divides each of them without leaving a remainder
What is the method used to simplify the calculation of multiplying two large numbers?
Expanded notation
What is the purpose of compensating for errors in calculations?
To correct errors introduced by rounding
What is the formula for calculating the distance travelled?
Distance = Average speed × Time
What is the method used to find the lowest common multiple of two or more numbers?
Multiplying the prime factors of the numbers
What is the term for a type of interest that is calculated on the principal amount without adding the interest to the principal each year?
Simple interest
What is the method used to subtract one large number from another?
Column subtraction
What is the term for the ratio of the number of apples collected by different people?
Ratio of collection
What is the result of subtracting a negative number from a positive number?
Equivalent to adding the corresponding positive number
What is the product of two negative integers?
Always positive
What is the additive inverse of a positive number?
The corresponding negative number
What is the result of adding a positive and a negative number?
Depends on the magnitudes of the numbers involved
What is the purpose of negative numbers?
To provide solutions for equations and extend the number system for practical purposes
What is the distributive property of multiplication?
a(b + c) = ab + bc
What is the result of adding a negative number to its additive inverse?
Zero
What is the effect of adding a negative number to a positive number?
It has the same effect as subtracting a positive number
What is the result of multiplying a positive number and a negative number?
Always negative
What is the purpose of the exchange rate in currency exchange?
To convert one currency to another
What is the property of natural numbers when you subtract one natural number from another?
The answer is not always a natural number.
What is the relationship between the system of whole numbers and the system of natural numbers?
The system of natural numbers is a subset of the system of whole numbers.
What is the characteristic of integers that is not true for whole numbers?
The sum of two integers can be zero.
What is the definition of rational numbers?
Numbers that can be expressed as the quotient of two integers.
What is the difference between rational and irrational numbers?
Rational numbers can be expressed as a fraction, and irrational numbers cannot.
What is the set of real numbers comprised of?
Both rational and irrational numbers.
What is a characteristic of the system of natural numbers when you add two or more natural numbers?
The result is always a natural number.
What is the property of the system of integers that is not true for the system of natural numbers?
The system of integers is closed under subtraction.
What is the term for an expression with one term only in algebraic expressions?
Monomial
What is the symbol often used to represent the variable in an algebraic expression?
x
What is the rule for calculating expressions with brackets?
Perform the calculations within the brackets first
What is the term for the number multiplying the variable in an algebraic expression?
Coefficient
What is the order of operations when calculating expressions without brackets?
Multiplication and division, then addition and subtraction
What is the term for an expression which is a sum of two terms?
Binomial
What is the term for a fixed value in an algebraic expression?
Constant
What is the convention for writing a known number in a product?
Write the known number first
What is the purpose of algebraic expressions?
To represent a sequence of operations
What is the term for equivalent expressions that have different sequences of operations but the same numerical value?
Equivalent expressions
When a larger number is subtracted from a smaller number, what is the result?
A negative number
What is the equivalent of adding a negative number?
Subtracting a positive number
What is the result of the product of a positive and a negative number?
A negative number
What is the purpose of exponents in mathematics?
To represent repeated multiplication
What is the rule for writing numbers in scientific notation?
Move the decimal point to the left for large numbers and to the right for small numbers
What is the purpose of the laws of exponents?
To simplify exponential expressions
What is the result of multiplying a negative number by a negative number?
A positive number
What is the purpose of investigating and extending geometric patterns?
To identify and extend patterns in arrangements of tiles
What is the relationship between the number of yellow tiles and the number of blue tiles in a geometric pattern?
The number of yellow tiles is a variable
What is the purpose of solving exponential equations?
To equate the exponents on both sides of the equation
What is the result of multiplying a polynomial by a monomial?
Each term in the polynomial is multiplied by the monomial
What is the purpose of the distributive property of division?
To divide a polynomial by a monomial or an integer
What is the result of applying the rule x - 1000 to natural numbers smaller than 1000?
Negative numbers
What is the general form for squaring a binomial?
(a + b)^2 = a^2 + 2ab + b^2
What is the result of evaluating the square of a monomial?
The monomial is squared
What is the purpose of substituting specific values for variables in algebraic expressions?
To check for equivalence and simplification
What is the convention for writing a known number in a product?
Write the known number first
What is the result of applying the rule 'multiply a number by 5 and subtract the result from 50' to a set of natural numbers smaller than 10?
A set of positive numbers
What is the purpose of expanding the product of two binomials?
To find the product of two polynomials
What is the result of dividing a polynomial by a monomial?
Each term in the polynomial is divided by the monomial
Which of the following is a characteristic of a function?
Each input has exactly one output
What is the purpose of a graph in representing relationships?
To provide a visual representation of the relationship
What is the formula to calculate the gradient of a line passing through two points?
Gradient = (y2 - y1) / (x2 - x1)
What is the term for a quantity that can change?
Variable
What is the purpose of a flow diagram?
To illustrate the calculations needed to produce the output numbers
What is the term for the value substituted into a function?
Input number
What is a method to visually represent the relationship between variables?
Graph
What is the characteristic of a function that describes a relationship between two variables?
Each input has exactly one output
What is the purpose of a table in representing relationships?
To list input values and their corresponding output values
What is the result of applying the rule ( \frac{x}{10} + 10 ) to natural numbers smaller than 10?
Positive numbers between 10 and 11
What is the gradient of a line that passes through the points (2, 3) and (4, 5)?
2/3
Which of the following is a characteristic of a function?
Each input has exactly one output
What is the purpose of a graph in representing relationships?
To visualize the relationship between variables
When interpreting graphs, what does the slope or gradient indicate?
The rate at which the output changes with respect to the input
What is the sum of the interior angles of a straight line?
180°
What is the name of the angles formed when two lines intersect, and the sum of these angles is 180°?
Supplementary angles
When a transversal intersects two parallel lines, what can be said about the corresponding angles?
They are equal
What is the term for the value substituted into a function?
Input number
What is the purpose of drawing graphs of functions?
To visualize the relationship between variables
What is the term for a line that intersects two or more other lines?
Transversal
What is the sum of the interior angles of an equilateral triangle?
180°
What is the name of a line that intersects two or more other lines?
Transversal
What is the sum of the interior angles of a quadrilateral?
360°
What is the name of a polygon with all sides and angles equal?
Regular polygon
What is the result of multiplying a positive number and a negative number?
Always negative
What is the purpose of identifying corresponding angles?
To determine the properties of a transversal
What is the name of angles that are equal when the lines are parallel?
Corresponding angles
What is the formula for the area of a rectangle?
A = l × w
What is the purpose of identifying alternate angles?
To identify parallel lines
What is the name of a shape where all points are equidistant from the center?
Circle
What is the formula to calculate the area of a sector?
$A = rac{ heta}{360} imes \pi r^2$
What is the formula to calculate the arc length of a sector?
$L = rac{ heta}{360} imes 2 \pi r$
What is the sum of the interior angles of a polygon with n sides?
$(n - 2) imes 180^\circ$
What is the formula to calculate the area of a regular polygon with n sides and side length s?
$A = rac{1}{2} n s^2 \cot(rac{\pi}{n})$
What is the formula to calculate the diagonal of a rectangle with length l and width w?
$d = \sqrt{l^2 + w^2}$
How can you construct a perpendicular line through a point not on the line segment?
Draw a circle with one end point of the line segment as the center and passing through the given point.
How can you bisect an angle using circles?
Draw a circle with the vertex of the angle as the center, marking off equal lengths on both arms of the angle.
What is the characteristic of an angle bisector in a triangle?
The angle bisector is always equidistant from each side of the triangle.
What is the relationship between the exterior angle of a triangle and the interior opposite angles?
The exterior angle is equal to the sum of the interior opposite angles.
What is the criterion for two triangles to be congruent?
Two triangles are congruent if they have the same shape and size.
Which of the following conditions is not a minimum condition for congruency?
One Side and One Angle
What is the formula for the area of a triangle using Heron's Formula?
A = √(s(s - a)(s - b)(s - c))
What is the formula for the perimeter of a rectangle?
P = 2(l + w)
What is the formula for the area of a circle?
A = πr^2
How do you construct a triangle using the SSS method?
Use a compass to draw arcs from each endpoint of the base to intersect and form the other vertices.
What is the formula for a translation by a vector (a, b)?
(x, y) -> (x + a, y + b)
What is the formula for the area of a regular polygon?
A = 1/4 n s^2 cot(π/n)
What is the formula for a 90° counterclockwise rotation about the origin?
(x, y) -> (-y, x)
What is the formula for a reflection over the line y = x?
(x, y) -> (y, x)
What is the definition of a translation in transformation geometry?
A transformation that moves every point of a shape the same distance in the same direction.
What is the formula for a dilation from the origin with a scale factor of k?
(x, y) -> (kx, ky)
What is the formula for the circumference of a circle?
C = 2πr
What is the formula for the area of a rectangle?
A = l * w
What is the sum of the interior angles of a quadrilateral?
360°
What is the formula for the perimeter of a triangle?
P = a + b + c
What is the formula for the area of a sector?
A = θ/360 × πr^2
What is the effect of doubling the dimensions of a shape?
The area is quadrupled, and the perimeter is doubled.
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 formula for converting from kilometers to meters?
1 km = 1000 m
What is the formula for the area of a rectangle?
A = l × w
What is the formula for the surface area of a cylinder?
SA = 2πr(h + r)
What is the formula for the volume of a sphere?
V = 4/3πr^3
What is the formula for the perimeter of a rectangle?
P = 2(l + w)
What is the formula for the area of a trapezium?
A = 1/2 (side_1 + side_2) × height
What is the formula for the surface area of a cube?
SA = 6s^2
What is the formula for the volume of a cone?
V = 1/3πr^2h
What is the formula for the circumference of a circle?
C = 2πr
Which of the following statements is true about the system of natural numbers?
It is closed under addition and multiplication.
What is the main difference between the system of whole numbers and the system of natural numbers?
The presence of 0 in the system of whole numbers.
Which of the following types of numbers is not a rational number?
Irrational number
What is the main characteristic of the system of integers?
It includes negative numbers.
What is the main difference between rational and irrational numbers?
Rational numbers can be expressed as fractions, while irrational numbers cannot.
Which of the following statements is true about the system of real numbers?
It includes both rational and irrational numbers.
What is the additive inverse of a natural number?
A negative number
Which of the following is a property of the system of natural numbers?
The sum of two natural numbers is always a natural number.
What is the result of subtracting a negative number from a positive number?
Always positive
What is the product of two negative integers?
Always positive
What is the additive inverse of a number?
The opposite of the number
What is the result of adding a positive and a negative number with the same magnitude?
Zero
What is the purpose of negative numbers in the number system?
To extend the number system for practical purposes
What is the result of subtracting a larger number from a smaller number?
A negative number
What is the result of dividing a negative number by a positive number?
Always negative
What is the distributive property of multiplication over addition?
a(b + c) = ab + ac
What is the equivalent of subtracting a negative number?
Adding a positive number
What is the square root of a number?
A value that when multiplied by itself gives the original number
What is the product of a positive and a negative number?
A negative number
What is the purpose of the laws of exponents in mathematics?
All of the above
What is the result of adding a positive number to its additive inverse?
Zero
What is the result of raising a number to a negative exponent?
The reciprocal of the base raised to the positive exponent
What is the purpose of exchange rates in currency exchange?
To convert one currency to another
What is the purpose of scientific notation in mathematics?
To express very large or very small numbers
What is the rule for writing numbers in scientific notation?
Move the decimal point to the left and the exponent is negative
What is the goal of investigating and extending geometric patterns?
To identify and extend geometric patterns
What is the result of multiplying a negative number and a positive number?
A negative number
What is the result of adding a negative number to a positive number?
A negative number
What is the primary purpose of estimating in calculations?
To simplify complex calculations
In the process of long division, what is the remainder when the division is complete?
Less than the divisor
What is the formula to calculate the highest common factor (HCF) of two numbers?
Multiply the common prime factors of the numbers
What is the purpose of compensating for errors in estimation?
To correct for errors introduced by rounding
What is the formula to calculate the lowest common multiple (LCM) of two numbers?
Multiply all the prime factors of both numbers without repeating any factors
In the context of ratio and rate problems, what does the ratio of collected apples represent?
The comparison of collection rates between different people
What is the formula to calculate the average speed of an object?
Distance / Time
What is the purpose of prime factorization in determining the LCM and HCF of two numbers?
To express a number as a product of its prime factors
What is the total HP price in a hire purchase agreement?
Deposit + Total instalments + Interest
What is the difference between simple interest and compound interest?
Simple interest is calculated on the principal amount, while compound interest is calculated on the principal amount and interest
What is the purpose of brackets in an algebraic expression?
To perform the operations within the brackets first
What is the difference between a monomial, binomial, and trinomial?
The number of terms in the expression
What is the convention for writing a known number in a product?
Write the known number first in the product
What is the purpose of equivalent algebraic expressions?
To show different forms of the same expression
What is the rule for simplifying an algebraic expression?
Combine like terms and remove any brackets
What is the purpose of the order of operations?
To evaluate expressions with multiple operations
What is the difference between a variable and a constant in an algebraic expression?
A variable is an unknown value, while a constant is known
What is the purpose of algebraic expressions?
To represent relationships between variables
What is the convention for writing algebraic expressions?
Omit the multiplication sign in products
What is the purpose of expanding and simplifying algebraic expressions?
To evaluate the expressions more easily
Which of the following is NOT a convention for writing algebraic expressions?
Write the multiplication sign in all expressions.
What is the result of simplifying the expression $(2x^2 + 3x) + (x^2 - 2x)?]
$3x^2 + x$
What is the result of expanding the binomial $(x + 2)^2?$
$x^2 + 4x + 4$
What is the result of evaluating the expression $x^2 - 4x + 4$ when $x = 2?$
$0$
What is the result of dividing the polynomial $x^2 + 2x$ by the monomial $x?$
$x + 2$
What is the result of finding the square root of $16x^2?$
$4x$
What is the result of applying the rule 'multiply by 5 and subtract the result from 50' to the input number $4?$
$30$
What is the result of finding the output number for the input number $8$ using the rule 'multiply by 2 and add 1'?
$17$
What is the result of evaluating the expression $(2x^2 - 3x)(x + 2)?$
$2x^3 + x^2 - 6x - 6$
What is the result of simplifying the expression $rac{x^2 + 3x - 2}{x + 1}?$
$x - 2$
What is the common property of all representations of a function?
They all have a unique output for each input
Which of the following is not a way to represent a function?
Histogram
What is the purpose of a flow diagram in representing a function?
To illustrate the calculations needed to produce output values
What is the formula for the gradient of a line passing through two points (x1, y1) and (x2, y2)?
Gradient = (y2 - y1) / (x2 - x1)
What is the purpose of a graph in representing a function?
To visualize the relationship between variables
Which of the following is a key feature to consider when interpreting graphs?
All of the above
What is the term for a quantity that can change?
Variable
What represents the value substituted into a function?
Input number
What is the formula for the function ( rac{x}{10} + 10 ) when applied to natural numbers smaller than 10?
Positive numbers between 10 and 11
What is the formula for the function ( 30x + 2 ) when applied to positive fractions with denominators 2, 3, and 5?
Positive numbers greater than 2
What is the formula to find the area of a sector of a circle?
A = θ/360 × πr^2
What is the sum of the interior angles of a polygon with n sides?
(n - 2) × 180°
What is the method used to construct perpendicular lines?
Using circles
What is the name of a triangle with all sides and angles equal?
Equilateral triangle
What is the formula to find the diagonal of a rectangle?
d = √(l^2 + w^2)
What is the method used to bisect an angle?
Using circles
What is the sum of the interior angles of a triangle?
180°
What is the name of a line that intersects two or more other lines?
Transversal
What is the formula to find the area of a regular polygon?
A = (n × s^2) / (4 × tan(π/n))
What is the method used to construct a 45° angle?
Bisecting a 90° angle
What is the sum of the interior angles of a quadrilateral?
360°
What is the name of a triangle with two sides and two angles equal?
Isosceles Triangle
What is the formula for the area of a rhombus?
A = (1/2) × d1 × d2
What is the name of a line that intersects two or more other lines?
Transversal
What is the sum of the interior angles of a triangle?
180°
What is the name of a polygon with all sides and angles equal?
Regular Polygon
What is the formula for the perimeter of a rectangle?
P = 2(l + w)
What is the name of a shape where all points are equidistant from the center?
Circle
What is the formula for the area of a parallelogram?
A = b × h
What is the name of a triangle with all three sides and angles equal?
Equilateral Triangle
What is the purpose of identifying the function value in a given input-output pair?
To understand the input-output behavior of the function
When interpreting graphs, what does the continuity of the graph indicate?
Whether the function is continuous or has breaks
What is the purpose of creating a table of values when drawing a graph of a function?
To choose a range of input values and calculate the corresponding output values
What is the term for the angle formed when two lines intersect, and the vertically opposite angles are equal?
Vertically opposite angle
What is the sum of the co-interior angles when a transversal intersects two parallel lines?
180°
What is the purpose of identifying the supplementary angles when two lines intersect?
To verify that the sum of the angles is 180°
What is the term for the line that intersects two or more other lines, and forms corresponding angles that are equal?
Transversal
What is the purpose of using a flow diagram to represent a function?
To illustrate the steps to compute outputs from inputs
What is the term for the angles formed when two lines intersect, and the sum of the angles is 180°?
Supplementary angles
What is the purpose of identifying the input and output numbers in a function?
To understand the relationship between variables
What is the minimum condition required to prove congruency of two triangles?
All of the above
What is the formula to find the area of a triangle, given the base and height?
A = 1/2 × base × height
What is the name of the formula used to find the area of a triangle, given the lengths of all three sides?
Heron's Formula
What is the name of the theorem used to find the length of the hypotenuse of a right-angled triangle?
Pythagorean Theorem
What is the formula to find the circumference of a circle?
C = 2 × π × radius
What is the type of transformation that moves every point of a shape the same distance in the same direction?
Translation
What is the formula to find the area of a sector of a circle?
A = θ/360 × π × radius^2
What is the formula to find the perimeter of a regular polygon?
P = n × side length
What is the name of the process used to construct a triangle, given three sides?
SSS Construction
What is the formula to find the sum of the interior angles of a polygon?
Sum = (n - 2) × 180°
What is the formula for the surface area of a rectangular prism?
SA = 2lw + 2lh + 2wh
What is the formula for the volume of a sphere?
V = (4/3)πr^3
What is the formula for the perimeter of a rectangle?
P = 2l + 2w
What is the formula for the area of a rhombus?
A = (1/2)d1 × d2
What is the formula for the surface area of a cylinder?
SA = 2πr(h + r)
What is the formula for the volume of a cone?
V = (1/3)πr^2h
What is the formula for the area of a triangle?
A = (1/2)base × height
What is the formula for the diameter of a circle?
d = 2r
What is the effect of a 90° counterclockwise rotation on a point (x, y)?
It becomes (-y, x).
What is the formula for a reflection over the line y = x?
(x, y) → (y, x)
What is the area of a kite with diagonals of 10 cm and 15 cm?
37.5 cm²
What is the perimeter of a rectangle with a length of 8 cm and a width of 5 cm?
26 cm
What is the result of doubling both dimensions of a rectangle?
The perimeter doubles and the area quadruples.
What is the formula for a translation of (a, b)?
(x, y) → (x + a, y + b)
What is the area of a circle with a radius of 4 cm?
16π cm²
What is the result of a 180° rotation on a point (x, y)?
(x, y) → (-x, -y)
What is the perimeter of a square with a side length of 6 cm?
24 cm
What is the formula for a dilation with a scale factor of k?
(x, y) → (kx, ky)
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