Gr 9 MATH: November Hard
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Questions and Answers

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

  • Multiplication
  • Division (correct)
  • Subtraction (correct)
  • Addition

    • What is the purpose of the number 0 in the system of whole numbers?

  • To represent the presence of quantity
  • To write fractions
  • To represent the absence of quantity (correct)
  • To make subtraction possible

    • Which of the following statements is true about the system of integers?

  • The system of integers is closed under subtraction
  • The sum of two integers can be zero (correct)
  • The sum of two integers is always an integer
  • Each integer does not have an additive inverse

    • What is the definition of a rational number?

    <p>A number that can be expressed as the quotient of two integers</p> Signup and view all the answers

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

    <p>√2</p> Signup and view all the answers

    What is the set of real numbers composed of?

    <p>Rational and irrational numbers</p> Signup and view all the answers

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

    <p>0</p> Signup and view all the answers

    Which of the following is a property of natural numbers?

    <p>When you add two or more natural numbers, you get a natural number again</p> Signup and view all the answers

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

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

    What is the additive inverse of a positive number?

    <p>Its corresponding negative number</p> Signup and view all the answers

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

    <p>Depends on the magnitudes of the numbers involved</p> Signup and view all the answers

    What is the product of two negative numbers?

    <p>Positive</p> Signup and view all the answers

    What is the distributive property of multiplication over addition?

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

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

    <p>Negative</p> Signup and view all the answers

    What is the square root of a number?

    <p>The positive or negative number that, when multiplied by itself, gives the original number</p> Signup and view all the answers

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

    <p>Zero</p> Signup and view all the answers

    What is the result of subtracting an additive inverse from a number?

    <p>The additive inverse of the number</p> Signup and view all the answers

    What is the purpose of negative numbers in real-world applications?

    <p>Both a and b</p> Signup and view all the answers

    What is the primary purpose of estimating in calculations?

    <p>To get close to an answer without performing precise calculations</p> Signup and view all the answers

    When performing addition in columns, what is the correct order of operation?

    <p>Add each digit starting from the rightmost digit</p> Signup and view all the answers

    What is the process of expressing a number as a product of its prime factors called?

    <p>Prime factorization</p> Signup and view all the answers

    What is the formula to calculate the average speed of an object?

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

    What is the term for the largest number that divides each of two or more numbers without leaving a remainder?

    <p>Highest common factor</p> Signup and view all the answers

    What is the purpose of compensating for errors in calculations?

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

    What is the formula to calculate the distance traveled by an object?

    <p>Distance = Average speed × Time</p> Signup and view all the answers

    What is the term for the process of dividing a number step-by-step, subtracting multiples of the divisor from the dividend, and continuing the process until the remainder is less than the divisor?

    <p>Long division</p> Signup and view all the answers

    What is the formula to calculate the time taken to travel a certain distance?

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

    What is the term for the process of paying a deposit and then making monthly instalments?

    <p>Hire purchase</p> Signup and view all the answers

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

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

    What is the equivalent of adding a negative number?

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

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

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

    What is the order of operations when calculating expressions involving exponents?

    <p>Parentheses, exponents, multiplication, division, addition, subtraction</p> Signup and view all the answers

    What is the value of a^-n in exponential notation?

    <p>1/a^n</p> Signup and view all the answers

    What is the purpose of scientific notation?

    <p>To express very large or very small numbers</p> Signup and view all the answers

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

    <p>Zero</p> Signup and view all the answers

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

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

    What is the purpose of the laws of exponents?

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

    What is the purpose of investigating and extending geometric patterns?

    <p>To analyze arrangements consisting of different shapes and colors</p> Signup and view all the answers

    What is the primary purpose of an algebraic expression?

    <p>To indicate a sequence of operations that can be described in words or diagrams.</p> Signup and view all the answers

    Which of the following is a convention for writing algebraic expressions?

    <p>Write a known number first in a product.</p> Signup and view all the answers

    What is the correct order of operations in an algebraic expression without brackets?

    <p>Multiplication and division, then addition and subtraction.</p> Signup and view all the answers

    What is an expression with one term only?

    <p>Monomial</p> Signup and view all the answers

    What is the symbol often used to represent the variable in an algebraic expression?

    <p>x</p> Signup and view all the answers

    What is the purpose of brackets in an algebraic expression?

    <p>To indicate that the expression should be evaluated first.</p> Signup and view all the answers

    What is an equivalent expression?

    <p>An expression with the same numerical value for any given value of the variable.</p> Signup and view all the answers

    What is the term for the number multiplying the variable in an algebraic expression?

    <p>Coefficient</p> Signup and view all the answers

    What is the purpose of forming sequences and identifying patterns?

    <p>To extend sequences and describe how they are formed.</p> Signup and view all the answers

    What is the term for a fixed value in an algebraic expression?

    <p>Constant</p> Signup and view all the answers

    What is the term for the sum of interior angles of a polygon?

    <p>Dependent on the number of sides</p> Signup and view all the answers

    What is the primary purpose of a flow diagram in representing a function?

    <p>To determine the output value for a given input</p> Signup and view all the answers

    What is the condition for two lines to be perpendicular?

    <p>They intersect at a right angle</p> Signup and view all the answers

    What is the key feature of a graph that indicates the rate of change between variables?

    <p>Slope/Gradient</p> Signup and view all the answers

    What is the result of multiplying the polynomial 2x^2 + 3x - 1 by the monomial 5x?

    <p>10x^3 + 15x^2 - 5x^2</p> Signup and view all the answers

    What is the term for a polygon with all sides and angles equal?

    <p>Regular polygon</p> Signup and view all the answers

    Which of the following representations of a function shows the values of input and corresponding output?

    <p>Table</p> Signup and view all the answers

    What is the formula to calculate the area of a rectangle?

    <p>A = l × w</p> Signup and view all the answers

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

    <p>9x^2 + 12x + 4</p> Signup and view all the answers

    What is the term for the line that intersects two or more other lines?

    <p>Transversal</p> Signup and view all the answers

    What is the result of evaluating the expression 2x^2 + 5x - 1 when x = 3?

    <p>25</p> Signup and view all the answers

    What is the formula to calculate the gradient of a line passing through two points?

    <p>Gradient = (y2 - y1) / (x2 - x1)</p> Signup and view all the answers

    What is the sum of the interior angles of a triangle?

    <p>180°</p> Signup and view all the answers

    What is the result of dividing the polynomial 4x^2 + 2x - 3 by the monomial 2x?

    <p>2x + 1 - 3/2x</p> Signup and view all the answers

    What is the definition of a function in terms of variables?

    <p>A relationship between two variables where each input has exactly one output</p> Signup and view all the answers

    What is the primary purpose of a graph in representing a function?

    <p>To provide a visual representation of the relationship</p> Signup and view all the answers

    What is the term for the angles formed when two lines intersect?

    <p>Vertically opposite angles</p> Signup and view all the answers

    What is the result of applying the rule 2n + 1 to the even number 4?

    <p>9</p> Signup and view all the answers

    What are the key features to consider when interpreting graphs?

    <p>Slope/Gradient, Intercepts, and Continuity</p> Signup and view all the answers

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

    <p>x^2 - x - 6</p> Signup and view all the answers

    What is the formula to calculate the perimeter of a square?

    <p>P = 4s</p> Signup and view all the answers

    What is the term for the angles formed when a transversal intersects parallel lines?

    <p>Corresponding angles</p> Signup and view all the answers

    What is the purpose of a formula in representing a function?

    <p>To describe the algebraic expression that defines the function</p> Signup and view all the answers

    What is the result of evaluating the expression x^2 + 2x - 5 when x = -2?

    <p>-1</p> Signup and view all the answers

    What is the result of multiplying the polynomial x^2 - 2x + 1 by the monomial 3x?

    <p>3x^3 - 6x^2 + 3x</p> Signup and view all the answers

    What is the term for the process of drawing and interpreting graphs of angles and lines?

    <p>Drawing and interpreting graphs of angles and lines</p> Signup and view all the answers

    What is the relationship between the input and output values in a function?

    <p>Each input has exactly one output</p> Signup and view all the answers

    What is the purpose of a table in representing a function?

    <p>To display values of input and corresponding output</p> Signup and view all the answers

    What is the result of simplifying the expression (x + 1)(x - 2) + 3x?

    <p>x^2 - x + 1</p> Signup and view all the answers

    What is the result of applying the rule x - 1000 to the natural number 800?

    <p>-200</p> Signup and view all the answers

    What is the primary purpose of using tables to represent functions?

    <p>To identify the input and output values</p> Signup and view all the answers

    What is the sum of the angles on a straight line?

    <p>180°</p> Signup and view all the answers

    What is the term for angles whose sum is 180°?

    <p>Supplementary angles</p> Signup and view all the answers

    What is the purpose of drawing graphs of functions?

    <p>To visualize the relationship between variables</p> Signup and view all the answers

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

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

    What is the term for lines that intersect to form equal angles of 90°?

    <p>Perpendicular lines</p> Signup and view all the answers

    What is the purpose of identifying the gradient of a line?

    <p>To identify the slope of a line</p> Signup and view all the answers

    What is the term for a line that intersects two or more other lines?

    <p>Transversal</p> Signup and view all the answers

    What is the term for angles formed when two straight lines intersect?

    <p>Vertically opposite angles</p> Signup and view all the answers

    What is the purpose of measuring angles in degrees?

    <p>To describe the size of angles</p> Signup and view all the answers

    What is the formula for the surface area of a cylinder?

    <p>SA = 2πr(h + r)</p> Signup and view all the answers

    What is the formula for the volume of a rectangular prism?

    <p>V = lwh</p> Signup and view all the answers

    What is the formula for the area of a trapezium?

    <p>A = 1/2 × (side1 + side2) × height</p> Signup and view all the answers

    What is the formula for the perimeter of a rectangle?

    <p>P = 2l + 2w</p> Signup and view all the answers

    What is the formula for the surface area of a sphere?

    <p>SA = 4πr^2</p> Signup and view all the answers

    What is the formula for the volume of a cone?

    <p>V = 1/3πr^2h</p> Signup and view all the answers

    What is the formula for the area of a rhombus?

    <p>A = 1/2 × d1 × d2</p> Signup and view all the answers

    What is the formula for the circumference of a circle?

    <p>C = 2πr</p> Signup and view all the answers

    What is the formula to calculate the area of a sector?

    <p>A = (θ/360) × πr^2</p> Signup and view all the answers

    What is the formula to calculate the sum of interior angles in a polygon?

    <p>(n - 2) × 180°</p> Signup and view all the answers

    What is the formula to calculate the perimeter of a polygon?

    <p>P = ns</p> Signup and view all the answers

    What is the method to construct a perpendicular line through a point on a line segment?

    <p>Draw a circle with the point as the center and the radius smaller than the distance to one end of the segment.</p> Signup and view all the answers

    What is the formula to calculate the arc length of a sector?

    <p>L = (θ/360) × 2πr</p> Signup and view all the answers

    What is the method to bisect an angle?

    <p>Draw a circle with the vertex of the angle as the center and marking off equal lengths on both arms of the angle.</p> Signup and view all the answers

    What is the property of the angle bisectors of a triangle?

    <p>The three angle bisectors of a triangle intersect at one point, equidistant from each side of the triangle.</p> Signup and view all the answers

    What is the formula to calculate the area of a regular polygon?

    <p>A = 1/4ns^2cot(π/n)</p> Signup and view all the answers

    What is the method to construct a 45° angle?

    <p>Draw a 90° angle using the method for constructing perpendicular lines and then bisect it.</p> Signup and view all the answers

    What is the property of the exterior angle of a triangle?

    <p>The exterior angle of a triangle is equal to the sum of the interior opposite angles.</p> Signup and view all the answers

    What is the formula to translate a point by a vector (a, b)?

    <p>(x, y) -&gt; (x + a, y + b)</p> Signup and view all the answers

    What is the formula to rotate a point 90 degrees counterclockwise about the origin?

    <p>(x, y) -&gt; (-y, x)</p> Signup and view all the answers

    What is the formula to reflect a point over the line y = x?

    <p>(x, y) -&gt; (y, x)</p> Signup and view all the answers

    What is the formula to dilate a point from the origin by a scale factor k?

    <p>(x, y) -&gt; (kx, ky)</p> Signup and view all the answers

    What is the formula for the area of a parallelogram?

    <p>A = base * height</p> Signup and view all the answers

    What is the formula for the perimeter of a kite?

    <p>P = 2a + 2b</p> Signup and view all the answers

    What is the effect of doubling the dimensions of a shape on its perimeter?

    <p>The perimeter doubles</p> Signup and view all the answers

    What is the effect of doubling the dimensions of a shape on its area?

    <p>The area quadruples</p> Signup and view all the answers

    What is the conversion factor from meters to kilometers?

    <p>1 km = 1000 m</p> Signup and view all the answers

    What is the formula for the circumference of a circle?

    <p>C = 2pi r</p> Signup and view all the answers

    What is the minimum condition required to prove congruency of two triangles using the SAS method?

    <p>Two sides and the included angle</p> Signup and view all the answers

    What is the formula to calculate the area of a triangle using Heron's Formula?

    <p>A = √(s(s - a)(s - b)(s - c))</p> Signup and view all the answers

    What is the formula to calculate the perimeter of a rectangle?

    <p>P = 2(l + w)</p> Signup and view all the answers

    What is the formula to calculate the area of a circle?

    <p>A = πr^2</p> Signup and view all the answers

    What is the formula to calculate the sum of interior angles of a regular polygon?

    <p>Sum = (n - 2) × 180°</p> Signup and view all the answers

    What is the method of constructing a triangle using the SSS method?

    <p>Use a compass to draw arcs from each endpoint of the base to intersect and form the other vertices</p> Signup and view all the answers

    What is the type of transformation that moves every point of a shape the same distance in the same direction?

    <p>Translation</p> Signup and view all the answers

    What is the formula to calculate the arc length of a circle?

    <p>L = θ/360 × 2πr</p> Signup and view all the answers

    What is the method of constructing a parallelogram?

    <p>Draw the base, use a set square to draw the height, and then draw the parallel opposite sides</p> Signup and view all the answers

    What is the formula to calculate the area of a sector of a circle?

    <p>A = θ/360 × πr^2</p> Signup and view all the answers

    Which property of natural numbers is also true for integers?

    <p>When you multiply two or more, you get an integer again.</p> Signup and view all the answers

    What is a characteristic of rational numbers that distinguishes them from integers?

    <p>They can be expressed as the quotient of two integers.</p> Signup and view all the answers

    What is the primary reason for extending whole numbers to integers?

    <p>To include negative numbers.</p> Signup and view all the answers

    Which set of numbers includes both rational and irrational numbers?

    <p>Real numbers.</p> Signup and view all the answers

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

    <p>Zero.</p> Signup and view all the answers

    What is a characteristic of natural numbers under subtraction?

    <p>The answer is not always a natural number.</p> Signup and view all the answers

    Which property of natural numbers is not true for whole numbers?

    <p>Closed under division.</p> Signup and view all the answers

    What is a characteristic of irrational numbers?

    <p>They cannot be expressed as a fraction of two integers.</p> Signup and view all the answers

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

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

    What is the purpose of the laws of exponents?

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

    What is the value of a^0 in exponential notation?

    <p>1</p> Signup and view all the answers

    What is the correct order of operations when calculating expressions involving exponents?

    <p>Parentheses, Exponents, Multiplication and Division, Addition and Subtraction</p> Signup and view all the answers

    What is the purpose of scientific notation?

    <p>To express very large or very small numbers in a compact form</p> Signup and view all the answers

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

    <p>Sometimes positive, sometimes negative</p> Signup and view all the answers

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

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

    What is the purpose of investigating and extending geometric patterns?

    <p>To identify and extend patterns in shapes and arrangements</p> Signup and view all the answers

    What is the value of a^-n in exponential notation?

    <p>1/a^n</p> Signup and view all the answers

    What is the major difference between estimating and rounding off numbers?

    <p>Rounding off is used for precise calculations, while estimating is used for approximate calculations.</p> Signup and view all the answers

    What is the purpose of negative numbers in real-world applications?

    <p>To represent debts or losses</p> Signup and view all the answers

    What is the purpose of finding the lowest common multiple of two numbers?

    <p>To find the common denominator of two fractions.</p> Signup and view all the answers

    What is the formula to calculate the average speed of an object?

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

    What is the term for the process of dividing a number step-by-step, subtracting multiples of the divisor from the dividend, and continuing the process until the remainder is less than the divisor?

    <p>Long division</p> Signup and view all the answers

    What is the purpose of calculating the highest common factor of two numbers?

    <p>To simplify fractions.</p> Signup and view all the answers

    What is the formula to calculate the distance traveled by an object?

    <p>Distance = Average speed × Time</p> Signup and view all the answers

    What is the term for the process of paying a deposit and then making monthly instalments?

    <p>Hire purchase</p> Signup and view all the answers

    What is the purpose of calculating the ratio of two numbers?

    <p>To compare the rates of two people collecting apples.</p> Signup and view all the answers

    What is the formula to calculate the time taken to travel a certain distance?

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

    What is the purpose of finding the prime factorization of a number?

    <p>To find the highest common factor of two numbers.</p> Signup and view all the answers

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

    <p>Zero</p> Signup and view all the answers

    What is the additive inverse of a negative number?

    <p>A positive number with the same magnitude</p> Signup and view all the answers

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

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

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

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

    What is the distributive property of multiplication over addition?

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

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

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

    What is the purpose of negative numbers in real-world applications?

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

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

    <p>Zero</p> Signup and view all the answers

    What is the product of two negative numbers?

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

    What is the result of subtracting an additive inverse from a number?

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

    What is the primary purpose of algebraic expressions?

    <p>To describe a sequence of operations</p> Signup and view all the answers

    What is the correct order of operations in an algebraic expression without brackets?

    <p>Multiplication and division first, then addition and subtraction</p> Signup and view all the answers

    What is the term for an expression with one term only?

    <p>Monomial</p> Signup and view all the answers

    What is the purpose of brackets in an algebraic expression?

    <p>To indicate the order of operations</p> Signup and view all the answers

    What is the term for a fixed value in an algebraic expression?

    <p>Constant</p> Signup and view all the answers

    What is the symbol often used to represent the variable in an algebraic expression?

    <p>x</p> Signup and view all the answers

    What is an equivalent expression?

    <p>An expression with different sequences of operations but the same numerical value</p> Signup and view all the answers

    What is the term for the number multiplying the variable in an algebraic expression?

    <p>Coefficient</p> Signup and view all the answers

    What is the purpose of forming sequences and identifying patterns?

    <p>To describe the relationship between terms and their positions in sequences</p> Signup and view all the answers

    What is the convention for writing algebraic expressions?

    <p>Write the known number first in a product</p> Signup and view all the answers

    What is the result of squaring the binomial (a + b)?

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

    Which of the following expressions is equivalent to 2x^2 + 5x + 3?

    <p>2(x^2 + 2.5x + 1.5)</p> Signup and view all the answers

    What is the result of dividing the polynomial x^2 + 4x + 4 by the monomial x + 2?

    <p>x + 2</p> Signup and view all the answers

    What is the result of applying the rule 2n + 1 to the even number 4?

    <p>9</p> Signup and view all the answers

    What is the result of evaluating the expression (x + 1)^2 when x = 2?

    <p>13</p> Signup and view all the answers

    What is the result of multiplying the polynomial 2x^2 + 3x - 1 by the monomial 3x?

    <p>6x^3 + 9x^2 - 3x</p> Signup and view all the answers

    What is the result of simplifying the expression (3x + 2)(x - 1)?

    <p>3x^2 - x - 2</p> Signup and view all the answers

    What is the result of dividing the polynomial 2x^2 + 5x + 3 by the integer 2?

    <p>x^2 + 2.5x + 1.5</p> Signup and view all the answers

    What is the result of applying the rule x - 1000 to the natural number 800?

    <p>-200</p> Signup and view all the answers

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

    <p>50</p> Signup and view all the answers

    What is the minimum condition for congruency in a triangle with three sides given?

    <p>SSS</p> Signup and view all the answers

    What is the formula to calculate the area of a triangle given the base and height?

    <p>A = 1/2 * base * height</p> Signup and view all the answers

    What is the condition for two triangles to be congruent by SAS?

    <p>Two sides and an included angle</p> Signup and view all the answers

    What is the formula to calculate the perimeter of a rectangle?

    <p>P = 2(l + w)</p> Signup and view all the answers

    What is the condition for constructing a triangle with two sides and an included angle?

    <p>SAS</p> Signup and view all the answers

    What is the formula to calculate the area of a circle?

    <p>A = π * r^2</p> Signup and view all the answers

    What is the type of transformation that moves every point of a shape the same distance in the same direction?

    <p>Translation</p> Signup and view all the answers

    What is the primary characteristic of a function that distinguishes it from other relationships between variables?

    <p>Each input has exactly one output</p> Signup and view all the answers

    What is the advantage of using a flow diagram to represent a function?

    <p>It clearly shows the calculations needed to determine the output value</p> Signup and view all the answers

    What is the formula to calculate the sum of interior angles of a polygon?

    <p>Sum = (n - 2) * 180°</p> Signup and view all the answers

    What is the condition for constructing a parallelogram?

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

    What is the formula used to calculate the gradient of a line passing through two points (x1, y1) and (x2, y2)?

    <p>Gradient = (y2 - y1) / (x2 - x1)</p> Signup and view all the answers

    What is the formula to calculate the area of a regular polygon?

    <p>A = 1/2 * n * s^2 * cot(π/n)</p> Signup and view all the answers

    What is the purpose of interpreting graphs in the context of functions?

    <p>To visualize the relationship between variables and identify key features</p> Signup and view all the answers

    What is the term for a quantity that can change in a function?

    <p>Variable</p> Signup and view all the answers

    What is the purpose of tables in the context of functions?

    <p>To display the input values and their corresponding output values</p> Signup and view all the answers

    What is the term for the result of applying a function to an input value?

    <p>Function value</p> Signup and view all the answers

    What is the purpose of formulas in the context of functions?

    <p>To describe the calculations needed to determine the output value</p> Signup and view all the answers

    What is the term for the rate of change between variables in a graph?

    <p>Gradient</p> Signup and view all the answers

    What is the purpose of drawing graphs in the context of functions?

    <p>To visualize the relationship between variables and identify key features</p> Signup and view all the answers

    What is the sum of interior angles of a quadrilateral?

    <p>360°</p> Signup and view all the answers

    Which of the following angles are equal when two lines intersect?

    <p>Vertically opposite angles</p> Signup and view all the answers

    What is the term for a polygon with all sides and angles equal?

    <p>Regular polygon</p> Signup and view all the answers

    What is the formula to calculate the area of a rhombus?

    <p>A = ½ × d1 × d2</p> Signup and view all the answers

    Which of the following is a property of parallel lines and transversals?

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

    What is the term for a triangle with two sides and two angles equal?

    <p>Isosceles triangle</p> Signup and view all the answers

    What is the sum of interior angles of a triangle?

    <p>180°</p> Signup and view all the answers

    Which of the following is a property of a circle?

    <p>All points are equidistant from the center</p> Signup and view all the answers

    What is the formula to calculate the perimeter of a rectangle?

    <p>P = 2(l + w)</p> Signup and view all the answers

    Which of the following angles are equal when a transversal intersects parallel lines?

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

    What is the formula to calculate the gradient of a line passing through two points (x_1, y_1) and (x_2, y_2)?

    <p>Gradient = (y_2 - y_1) / (x_2 - x_1)</p> Signup and view all the answers

    What is the term for the relationship between two variables where each input corresponds to exactly one output?

    <p>Function</p> Signup and view all the answers

    When interpreting graphs, what does the slope/gradient indicate?

    <p>How rapidly the output changes with respect to the input</p> Signup and view all the answers

    What is the formula to calculate the surface area of a rectangular prism?

    <p>SA = 2lw + 2lh + 2wh</p> Signup and view all the answers

    What is the sum of angles on a straight line?

    <p>180°</p> Signup and view all the answers

    What is the formula to calculate the volume of a cylinder?

    <p>V = πr^2h</p> Signup and view all the answers

    What is the term for two angles whose sum is 180°?

    <p>Supplementary angles</p> Signup and view all the answers

    What is the formula to calculate the surface area of a sphere?

    <p>SA = 4πr^2</p> Signup and view all the answers

    When two lines intersect, what is the relationship between the vertically opposite angles?

    <p>They are equal</p> Signup and view all the answers

    What is the term for a line that intersects two or more other lines?

    <p>Transversal</p> Signup and view all the answers

    What is the formula to calculate the volume of a cone?

    <p>V = (1/3)πr^2h</p> Signup and view all the answers

    What is the term for the angles on opposite sides of the transversal but inside the two intersected lines?

    <p>Alternate angles</p> Signup and view all the answers

    What is the formula to calculate the perimeter of a rectangle?

    <p>P = 2(l + w)</p> Signup and view all the answers

    When drawing graphs of functions, what is the first step?

    <p>Identify the function</p> Signup and view all the answers

    What is the formula to calculate the area of a triangle?

    <p>A = (1/2)base × height</p> Signup and view all the answers

    What is the formula to calculate the surface area of a cube?

    <p>SA = 6s^2</p> Signup and view all the answers

    What is the term for the output value corresponding to a given input?

    <p>Function value</p> Signup and view all the answers

    What is the formula to calculate the volume of a rectangular pyramid?

    <p>V = (1/3)lwh</p> Signup and view all the answers

    What is the formula to calculate the area of a sector?

    <p>A = θ/360 × πr^2</p> Signup and view all the answers

    What is the formula to calculate the arc length of a sector?

    <p>L = θ/360 × 2πr</p> Signup and view all the answers

    What is the sum of interior angles of a regular polygon with n sides?

    <p>(n - 2) × 180°</p> Signup and view all the answers

    What is the formula to calculate the area of a regular polygon with n sides and side length s?

    <p>A = (1/4) × n × s^2 × cot(π/n)</p> Signup and view all the answers

    What is the method to construct a perpendicular line through a point not on the line segment?

    <p>Draw a circle with one end point of the line segment as the center and passing through the given point.</p> Signup and view all the answers

    What is the method to bisect an angle using circles?

    <p>Draw a circle with the vertex of the angle as the center and marking off equal lengths on both arms of the angle.</p> Signup and view all the answers

    What is the method to construct a 45° angle?

    <p>Draw a 90° angle using the method for constructing perpendicular lines and then bisect it.</p> Signup and view all the answers

    What is the property of angle bisectors in a triangle?

    <p>They intersect at one point, equidistant from each side of the triangle.</p> Signup and view all the answers

    What is the relationship between an exterior angle and its interior opposite angles?

    <p>The exterior angle is equal to the sum of its interior opposite angles.</p> Signup and view all the answers

    What is the formula for the reflection of a point over the line y = x?

    <p>(x, y) → (y, x)</p> Signup and view all the answers

    What is the result of a 90° counterclockwise rotation about the origin of a point (x, y)?

    <p>(x, y) → (y, -x)</p> Signup and view all the answers

    What is the formula for the area of a parallelogram?

    <p>A = base × height</p> Signup and view all the answers

    What is the result of doubling the dimensions of a rectangle?

    <p>The area is quadrupled and the perimeter is doubled.</p> Signup and view all the answers

    What is the formula for the circumference of a circle?

    <p>C = 2 × π × radius</p> Signup and view all the answers

    What is the effect of a 180° rotation about the origin of a point (x, y)?

    <p>The point is reflected over the x-axis.</p> Signup and view all the answers

    What is the formula for the area of a kite?

    <p>A = 1/2 × d1 × d2</p> Signup and view all the answers

    What is the result of a translation of a point (x, y) by a vector (a, b)?

    <p>(x, y) → (x + a, y + b)</p> Signup and view all the answers

    What is the formula for the dilation of a point (x, y) with scale factor k?

    <p>(x, y) → (kx, ky)</p> Signup and view all the answers

    What is the result of a reflection of a point (x, y) over the y-axis?

    <p>(x, y) → (-x, y)</p> Signup and view all the answers

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