Gr 9 MATH: November Medium
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Questions and Answers

What is the result of adding two or more natural numbers?

  • You always get an irrational number.
  • You always get a rational number.
  • You always get a natural number. (correct)
  • You always get an integer.

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

  • It is used as a symbol for 10.
  • It is needed to write numbers and represent the concept of nothing or absence. (correct)
  • It is used for counting.
  • It is used to write numbers that are multiples of 10.

    • What is true about the system of integers?

  • It includes only positive numbers.
  • It is closed under addition and multiplication. (correct)
  • It is not closed under subtraction or division.
  • It includes only negative numbers.

    • What is an additive inverse?

    <p>A number that when added to another number results in 0.</p> Signup and view all the answers

    What is the definition of rational numbers?

    <p>Numbers that can be expressed as a fraction of two integers.</p> Signup and view all the answers

    What is an example of an irrational number?

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

    What is the set of real numbers?

    <p>The set of rational and irrational numbers.</p> Signup and view all the answers

    Why is the system of natural numbers not closed under subtraction?

    <p>Because you can always get a negative number.</p> Signup and view all the answers

    What is the purpose of estimating in calculations?

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

    What is the result of compensating for errors introduced by rounding?

    <p>The error is eliminated</p> Signup and view all the answers

    What is the purpose of using column subtraction?

    <p>To subtract large numbers</p> Signup and view all the answers

    What is the term for the smallest common multiple of two or more numbers?

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

    How do you find the LCM of two numbers using prime factorization?

    <p>Multiply all the prime factors of both numbers without repeating any factors</p> Signup and view all the answers

    What is the formula to calculate average speed?

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

    What is the term for a payment method where a deposit is paid and then monthly instalments are made?

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

    What is the difference between simple interest and compound interest?

    <p>Simple interest does not add the interest to the principal each year, while compound interest does</p> Signup and view all the answers

    What is the term for the 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 calculating the ratio of collected apples?

    <p>To compare the rate of collecting apples</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 effect of adding a negative number to a positive number?

    <p>It is the same as subtracting the corresponding positive number</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 result of adding a number to its additive inverse?

    <p>Zero</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 subtracting a negative number from a positive number?

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

    What is the notation for the square root of a number x?

    <p>$\sqrt{x}$</p> Signup and view all the answers

    What is the quotient of a positive number and a negative number?

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

    What is the additive inverse of a number?

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

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

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

    What is the first step in evaluating an algebraic expression with brackets?

    <p>Perform the calculations within the brackets</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 result of subtracting a larger number from a smaller number?

    <p>A negative number</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 term for a fixed value in an algebraic expression?

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

    What is equivalent to subtracting the corresponding positive number?

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

    What is the order of operations when evaluating an algebraic expression without brackets?

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

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

    <p>A negative number</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 term for an expression which is a sum of two terms?

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

    What is the meaning of a negative exponent in exponential notation?

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

    What is the term for an expression which is a sum of three terms?

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

    How do you write a large number in scientific notation?

    <p>Move the decimal point to the left, and the exponent is positive</p> Signup and view all the answers

    What is the purpose of the convention to write a known number first in a product?

    <p>To avoid confusion when reading the expression</p> Signup and view all the answers

    What is the term for an expression that has different sequences of operations but the same numerical value for any given value of the variable?

    <p>Equivalent expression</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 correct formula for $a^m \div a^n$?

    <p>$a^{m-n}$</p> Signup and view all the answers

    What is the purpose of using algebraic expressions to describe a sequence of operations?

    <p>To simplify complex calculations</p> Signup and view all the answers

    What is the purpose of solving exponential equations?

    <p>To find the solution to the equation</p> Signup and view all the answers

    What is the property of exponents that states $a^m imes a^n = a^{m+n}$?

    <p>The product of powers property</p> Signup and view all the answers

    What is the correct way to write an algebraic expression with a product of a known number and a variable?

    <p>Write the known number first, followed by the multiplication sign and the variable.</p> Signup and view all the answers

    What is the purpose of using brackets in algebraic expressions?

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

    What is the result of applying the distributive property to the expression a(b + c)?

    <p>ab + ac</p> Signup and view all the answers

    What is the correct way to simplify the expression 2x + 3x?

    <p>Combine like terms to get 5x.</p> Signup and view all the answers

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

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

    What is the result of dividing the polynomial x^2 + 2x + 1 by the monomial x?

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

    What is the result of applying the rule 'multiply a number by 5 and subtract the result from 50' to the input number 8?

    <p>30</p> Signup and view all the answers

    What is the result of expanding the product of two binomials (x + 2)(x + 3)?

    <p>x^2 + 5x + 6</p> Signup and view all the answers

    What is the result of substituting x = 2 into the expression 2x^2 + 3x - 1?

    <p>15</p> Signup and view all the answers

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

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

    What is the sum of interior angles in a triangle?

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

    Which type of triangle has two sides and two angles equal?

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

    What is the formula for the area of a rectangle?

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

    What is the term for angles in matching corners when a transversal intersects parallel lines?

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

    What is the property of parallel lines and transversals?

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

    What is the sum of co-interior angles?

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

    What is the definition of a polygon?

    <p>A closed figure with straight sides</p> Signup and view all the answers

    What is the formula for the area of a circle?

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

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

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

    What is the definition of a regular polygon?

    <p>A polygon with all sides and angles equal</p> Signup and view all the answers

    What is the name of the representation that shows the calculations needed to determine the output number for a given input variable?

    <p>Flow Diagram</p> Signup and view all the answers

    Which of the following is a characteristic of a function?

    <p>One output for each input</p> Signup and view all the answers

    What is the formula 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 term for a quantity that can change?

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

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

    <p>$\frac{y_2 - y_1}{x_2 - x_1}$</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 purpose of interpreting graphs?

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

    What is the key characteristic of a function?

    <p>Each input corresponds to exactly one output.</p> Signup and view all the answers

    What do intercepts on a graph indicate?

    <p>The points where the graph crosses the axes.</p> Signup and view all the answers

    What type of representation is a visual method to understand the relationship between variables?

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

    What is the term for the result after applying the function to the input?

    <p>Output Number</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 are the angles called when two lines intersect and form equal angles of 90°?

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

    Which of the following is a key feature to consider when interpreting graphs?

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

    What is the purpose of a flow diagram?

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

    When two angles on a straight line sum to 180°, what are they called?

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

    What is the result of measuring the angles formed when a transversal intersects two parallel lines?

    <p>The corresponding angles are equal.</p> Signup and view all the answers

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

    <p>Co-interior angles</p> Signup and view all the answers

    What is the sum of co-interior angles when a transversal intersects two parallel lines?

    <p>180°</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 formula for the area of a sector?

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

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

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

    How do you construct a perpendicular line through a point on a line segment?

    <p>Draw a circle with the given 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 for the circumference of a circle?

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

    What is the diagonal of a rectangle with length l and width w?

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

    How do you construct a 45° angle?

    <p>Draw a 90° angle and bisect it.</p> Signup and view all the answers

    What is the angle bisector of a triangle?

    <p>A line that cuts an angle in half.</p> Signup and view all the answers

    What is the sum of the interior opposite angles of an exterior angle of a triangle?

    <p>Equal to the exterior angle.</p> Signup and view all the answers

    What is the criteria for congruency of two triangles?

    <p>Two triangles are congruent if they have the same shape and size.</p> Signup and view all the answers

    What is the formula for 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 formula for the area of a triangle?

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

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

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

    What is the formula for the volume of a cylinder?

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

    What is the formula for the area of a circle?

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

    What is the formula for the surface area of a rectangular prism?

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

    What is the formula for the volume of a sphere?

    <p>V = (4/3)πr^3</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 for the volume of a cone?

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

    What is the minimum condition for congruency in triangles that results in two different triangles?

    <p>SSA</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 perimeter of a rectangle?

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

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

    <p>C = 2πr</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

    How do you construct a triangle given two sides and an included angle?

    <p>Draw the base, use a protractor to measure the given angle, then draw the other side and connect the vertices.</p> Signup and view all the answers

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

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

    How do you construct a circle?

    <p>Use a compass to draw a circle with a given radius from a central point.</p> Signup and view all the answers

    A shape is translated by the vector (3, 4). What is the new coordinate of the point (2, 5) after the translation?

    <p>(5, 9)</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 for rotating a point (x, y) by 90 degrees counterclockwise about the origin?

    <p>(-y, x)</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

    A shape is reflected over the line y = x. What is the new coordinate of the point (3, 4) after the reflection?

    <p>(4, 3)</p> Signup and view all the answers

    A shape is dilated by a scale factor of 2 from the origin. What is the new coordinate of the point (3, 4) after the dilation?

    <p>(6, 8)</p> Signup and view all the answers

    What is the formula for the area of a rectangle with length l and width w?

    <p>A = l × w</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 kilometers to meters?

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

    What is the formula for the circumference of a circle with radius r?

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

    What is the formula for the area of a circle with radius r?

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

    Which of the following statements is true about the system of natural numbers?

    <p>It is closed under addition and multiplication.</p> Signup and view all the answers

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

    <p>To represent the absence of quantity.</p> Signup and view all the answers

    Which of the following is a characteristic of integers?

    <p>The sum of two integers can be zero.</p> Signup and view all the answers

    What is the main difference between rational and irrational numbers?

    <p>Rational numbers can be expressed as a fraction of two integers, while irrational numbers cannot.</p> Signup and view all the answers

    Which of the following sets includes both rational and irrational numbers?

    <p>The set of real 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 statements is true about the system of natural numbers?

    <p>It is closed under addition and multiplication.</p> Signup and view all the answers

    What is a characteristic of the set of integers?

    <p>Each integer has an additive inverse.</p> Signup and view all the answers

    What is the next term in the sequence 2, 5, 8, 11?

    <p>14</p> Signup and view all the answers

    Which of the following is an example of a trinomial?

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

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

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

    What is the term for an expression that has different sequences of operations but the same numerical value for any given value of the variable?

    <p>Equivalent Expression</p> Signup and view all the answers

    What is the coefficient of the variable term in the expression 3x^2?

    <p>3</p> Signup and view all the answers

    What is the purpose of using algebraic expressions to describe a sequence of operations?

    <p>To provide an alternative to verbal descriptions</p> Signup and view all the answers

    What is the symbolic representation of 'multiply 5 by 3, then add 12'?

    <p>12 + 3x</p> Signup and view all the answers

    Which of the following is an example of a binomial?

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

    What is the purpose of writing a known number first in a product?

    <p>To follow a convention</p> Signup and view all the answers

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

    <p>Variable</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 effect of adding a negative number to a positive number?

    <p>It is equivalent to subtracting the corresponding positive number</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 adding a number to its additive inverse?

    <p>Zero</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 quotient of a positive number and a negative number?

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

    What is the additive inverse of a number?

    <p>The opposite of the 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 notation for the square root of a number x?

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

    What is equivalent to subtracting the corresponding positive number?

    <p>Adding a negative number</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 to a positive number?

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

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

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

    What is the correct order of operations when evaluating an algebraic expression involving exponents?

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

    What is the notation for a number that is expressed as a power of 10?

    <p>Scientific notation</p> Signup and view all the answers

    What is the result of rewriting a number from scientific notation to decimal form?

    <p>The decimal point is moved according to the exponent</p> Signup and view all the answers

    What is the purpose of the laws of exponents?

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

    What is the result of multiplying a number by its additive inverse?

    <p>The result is 0</p> Signup and view all the answers

    What is the correct formula for $a^m imes a^n$?

    <p>$a^{m+n}$</p> Signup and view all the answers

    What is the meaning of a negative exponent in exponential notation?

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

    What is the purpose of estimating in calculations?

    <p>To get a close approximation of the answer</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 difference between the Highest Common Factor (HCF) and the Lowest Common Multiple (LCM) of two numbers?

    <p>HCF is the largest number that divides each of the two numbers, and LCM is the smallest number that is a multiple of each of the two numbers</p> Signup and view all the answers

    What is the formula to calculate the average speed of a journey?

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

    What is the term for a payment method where a deposit is paid and then monthly instalments are made?

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

    What is the result of multiplying all the prime factors of two numbers without repeating any factors unless they appear more than once in one of the numbers?

    <p>The Lowest Common Multiple (LCM) of the two numbers</p> Signup and view all the answers

    What is the purpose of prime factorization?

    <p>To find both the HCF and the LCM of two numbers</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 (HCF)</p> Signup and view all the answers

    What is the purpose of calculating the ratio of collected apples?

    <p>To compare the collection rates of different people</p> Signup and view all the answers

    What is the result of multiplying the common prime factors of two numbers?

    <p>The HCF of the two numbers</p> Signup and view all the answers

    What is the formula 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 purpose of a table in understanding functions?

    <p>To show specific input-output pairs</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 term for two angles whose sum is 180°?

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

    What is a characteristic of a function?

    <p>It can have only one output value for a single input value.</p> Signup and view all the answers

    What is the result of interpreting the slope of a graph?

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

    What is the purpose of drawing a graph of a function?

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

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

    <p>To illustrate the calculations needed to determine the output number.</p> Signup and view all the answers

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

    <p>Co-interior angles</p> Signup and view all the answers

    What is represented by a graph of a function?

    <p>A visual representation of the relationship between the variables.</p> Signup and view all the answers

    What is the result of measuring angles using a protractor when drawing graphs of angles and lines?

    <p>To check their properties</p> Signup and view all the answers

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

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

    What is the purpose of identifying supplementary angles when drawing graphs of angles and lines?

    <p>To verify their sum is 180°</p> Signup and view all the answers

    What is the term for a quantity that can change?

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

    What is the result of interpreting the continuity of a graph?

    <p>It indicates whether the graph is a continuous curve or has breaks</p> Signup and view all the answers

    What is the term for the result after applying a function to the input?

    <p>Output number</p> Signup and view all the answers

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

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

    What is a representation of a relationship between two variables?

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

    What is a key feature to consider when interpreting graphs?

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

    Which of the following is an example of equivalent algebraic expressions?

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

    What is the convention for writing a product of a known number and a variable?

    <p>Write the known number first, then the variable</p> Signup and view all the answers

    What is the result of multiplying a polynomial by a monomial?

    <p>Each term in the polynomial is multiplied by the monomial</p> Signup and view all the answers

    What is the formula for the square of a binomial (a + b)?

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

    What is the result of dividing a polynomial by a monomial?

    <p>Each term in the polynomial is divided by the monomial</p> Signup and view all the answers

    What is the distributive property of division?

    <p>(x + y) / z = (x / z) + (y / z)</p> Signup and view all the answers

    What is the purpose of substituting specific values for variables?

    <p>To evaluate the expression for equivalence and simplification</p> Signup and view all the answers

    What is the rule for calculating the output numbers for a given input number?

    <p>Multiply the number by 5 and subtract the result from 50</p> Signup and view all the answers

    What is the result of applying the rule x - 1000 to natural numbers smaller than 1000?

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

    What is the term for the smallest common multiple of two or more numbers?

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

    What is the formula for the area of a sector?

    <p>$A = rac{ heta}{360} imes \pi r^2$</p> Signup and view all the answers

    What is the sum of the interior angles of a regular polygon with 8 sides?

    <p>$720^\circ$</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 formula for the diagonal of a rectangle?

    <p>$d = \sqrt{l^2 + w^2}$</p> Signup and view all the answers

    What is the name of the angle that measures 90° in a right triangle?

    <p>Right angle</p> Signup and view all the answers

    What is the name of the polygon with all sides and angles equal?

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

    What is the method for constructing 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 intersect it with the given point, then draw another circle with the other end point of the line segment as the center and intersect it with the given point.</p> Signup and view all the answers

    What is the method for bisecting an angle using circles?

    <p>Draw a circle with the vertex of the angle as the center and intersect it with the arms of the angle, then draw two equal circles with centers at the points where the first circle intersects the arms of the angle, and then draw a line from the vertex through the points where the two circles intersect.</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 formula for the area of a regular polygon with side length $s$ and number of sides $n$?

    <p>$A = rac{1}{4} n s^2 \cot(rac{\pi}{n})$</p> Signup and view all the answers

    What is the name of the line that intersects two or more other lines?

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

    What is the name of the angles formed when two lines intersect?

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

    What is the method for constructing 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 sum of the co-interior angles formed when two parallel lines are intersected by a transversal?

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

    What is the property of triangles that states that the three angle bisectors of a triangle intersect at one point, equidistant from each side of the triangle?

    <p>The concurrency of angle bisectors</p> Signup and view all the answers

    What is the formula for the arc length of a sector?

    <p>$L = rac{ heta}{360} imes 2 \pi r$</p> Signup and view all the answers

    What is the name of the angle that is equal to its supplementary angle?

    <p>Right angle</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 definition of a regular polygon?

    <p>A polygon with all sides and angles equal.</p> Signup and view all the answers

    What is the name of the shape that is circular in shape and all points are equidistant from the center?

    <p>Circle</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 formula to calculate the surface area of a cube?

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

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

    <p>V = πr^2 h</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 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 sphere?

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

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

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

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

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

    What is the minimum condition required to prove congruency in triangles using the RHS method?

    <p>A right angle, the hypotenuse, and one other side</p> Signup and view all the answers

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

    <p>A = sqrt(s(s-a)(s-b)(s-c))</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 perimeter of a rectangle?

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

    What is the method to construct a triangle given two sides and an included angle?

    <p>Draw the base, use a protractor to measure the given angle, then draw the other side and connect the vertices</p> Signup and view all the answers

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

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

    What is the type of quadrilateral with all sides equal and opposite angles equal?

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

    What is the method to construct a regular polygon using a protractor?

    <p>Divide 360 degrees by the number of sides to get the angle between vertices</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 degrees</p> Signup and view all the answers

    What is the type of transformation that changes the size of a shape?

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

    What is the formula for rotating a point (x, y) 90 degrees counterclockwise around the origin?

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

    What is the formula for translating a point (x, y) by a horizontal shift of a and a vertical shift of b?

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

    What is the formula for reflecting a point (x, y) over the line y = x?

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

    What is the formula for dilating a point (x, y) by a scale factor of k from the origin?

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

    What is the formula for the area of a rectangle with length l and width w?

    <p>A = lw</p> Signup and view all the answers

    What is the formula for the perimeter of a square with side length s?

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

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

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

    What is the formula for the circumference of a circle with radius r?

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

    What is the formula for the area of a circle with radius r?

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

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

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

    What is the result of subtracting a natural number from another natural number?

    <p>Not always a natural number</p> Signup and view all the answers

    Which of the following is a property of whole numbers?

    <p>0 is the additive identity in whole numbers.</p> Signup and view all the answers

    What is an example of an integer that is not a whole number?

    <p>-3</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

    Which of the following is a true statement about the real numbers?

    <p>The set of real numbers includes both rational and irrational numbers.</p> Signup and view all the answers

    What is the result of multiplying two or more natural numbers?

    <p>Always a natural number</p> Signup and view all the answers

    What is a characteristic of the system of integers?

    <p>The system of integers extends whole numbers to include negative numbers.</p> Signup and view all the answers

    Which of the following is a property of the system of natural numbers?

    <p>The system of natural numbers is closed under addition and multiplication.</p> Signup and view all the answers

    What is the term for an expression that has a sequence of operations but can also be described in words or flow diagrams?

    <p>Algebraic Expression</p> Signup and view all the answers

    Which of the following is a 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 the term for a symbol, often x, representing the unknown value in an algebraic expression?

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

    What is the correct way to evaluate an algebraic expression with brackets?

    <p>Perform the calculations within the brackets first</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 term for a fixed value in an algebraic expression?

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

    What is the purpose of writing a known number first in a product in algebraic expressions?

    <p>To follow a convention</p> Signup and view all the answers

    What is the term for two or more expressions that have different sequences of operations but the same numerical value for any given value of the variable?

    <p>Equivalent Expressions</p> Signup and view all the answers

    What is the correct way to write an algebraic expression with a product of a known number and a variable?

    <p>The known number first, then the variable</p> Signup and view all the answers

    What is the purpose of algebraic expressions in describing sequences of operations?

    <p>To provide a symbolic representation of the sequence of operations</p> Signup and view all the answers

    What is the result of applying the distributive property to the expression 2(x + 3)?

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

    Which of the following expressions is equivalent to (x + 2)^2?

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

    What is the result of dividing the polynomial 2x^2 + 3x - 4 by the monomial x + 1?

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

    What is the result of applying the rule x - 1000 to the natural number 500?

    <p>-500</p> Signup and view all the answers

    Which of the following expressions is equivalent to (x - 2)(x + 3)?

    <p>x^2 + x - 6</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 result of substituting x = 2 into the expression 3x^2 - 2x + 1?

    <p>7</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 effect of adding a negative number to a positive number?

    <p>It results in a negative number</p> Signup and view all the answers

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

    <p>8</p> Signup and view all the answers

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

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

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

    <p>x - 4</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 result of finding the square root of the expression 16x^2?

    <p>4x</p> Signup and view all the answers

    What is the meaning of a negative exponent in exponential notation?

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

    How do you write a large number in scientific notation?

    <p>Move the decimal point to the left, and the exponent is positive</p> Signup and view all the answers

    What is the purpose of the laws of exponents?

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

    What is the correct formula for $a^m \div a^n$?

    <p>$a^{m-n}$</p> Signup and view all the answers

    What is the purpose of solving exponential equations?

    <p>To find the value of the exponent</p> Signup and view all the answers

    What is the property of exponents that states $a^m imes a^n = a^{m+n}$?

    <p>The law of exponents</p> Signup and view all the answers

    What is the benefit of estimating in calculations?

    <p>To simplify the calculation process</p> Signup and view all the answers

    How can you correct errors introduced by rounding?

    <p>By compensating for the errors</p> Signup and view all the answers

    What is the purpose of adding in columns?

    <p>To add numbers digit by digit</p> Signup and view all the answers

    What is the definition of a function?

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

    What is the result of multiplying a number by 1, 2, 3, and so on?

    <p>A sequence of consecutive multiples</p> Signup and view all the answers

    What is the formula to calculate the distance traveled?

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

    What is the purpose of a flow diagram in functions?

    <p>To show the calculations needed to transform input into output.</p> Signup and view all the answers

    What is the purpose of calculating the ratio of collected apples?

    <p>To compare the rates of apple collection</p> Signup and view all the answers

    What is the formula to calculate the gradient of a line?

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

    What is the term for the value substituted into a function?

    <p>Input number</p> Signup and view all the answers

    What is the term for the total amount paid for an item under a hire purchase plan?

    <p>Total HP price</p> Signup and view all the answers

    What is the difference between simple interest and compound interest?

    <p>Simple interest does not add interest to the principal each year</p> Signup and view all the answers

    What is the purpose of graphing a function?

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

    What is the term for the result after applying a function to the input?

    <p>Output number</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 prime factorization?

    <p>To express a number as a product of its prime factors</p> Signup and view all the answers

    What is the term for the relationship between variables represented by a flow diagram?

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

    What is the key feature of a graph to consider when interpreting the relationship between variables?

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

    What is the purpose of representing a function in different ways?

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

    What is the term for a quantity that can change?

    <p>Variable</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

    What is the name of the line that intersects two or more other lines?

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

    What is the name of the angles formed when two lines intersect?

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

    What is the name of the polygon with all sides and angles equal?

    <p>Square</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 name of the angles that are equal when two parallel lines are intersected by a transversal?

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

    What is the name of the theorem that states a^2 + b^2 = c^2?

    <p>Pythagorean Theorem</p> Signup and view all the answers

    What is the name of the shape with all points equidistant from the center?

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

    What is the sum of co-interior angles when a transversal intersects two parallel lines?

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

    What is the name of the angles that are on opposite sides of the transversal and inside the parallel lines?

    <p>Alternate angles</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 a function?

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

    What is the purpose of a flow diagram in understanding functions?

    <p>To illustrate the steps to compute outputs from inputs.</p> Signup and view all the answers

    Which of the following minimum conditions guarantees the congruency of two triangles?

    <p>Three sides (SSS)</p> Signup and view all the answers

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

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

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

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

    What does the slope of a graph indicate?

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

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

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

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

    <p>A = πr^2</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

    How do you construct a triangle given two sides and an included angle (SAS)?

    <p>Draw the base, use a protractor to measure the given angle, then draw the other side and connect the vertices.</p> Signup and view all the answers

    What are two angles called when they sum to 180°?

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

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

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

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

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

    What is the property of parallel lines and transversals?

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

    What is the definition of a translation?

    <p>A transformation that moves every point of a shape the same distance in the same direction.</p> Signup and view all the answers

    What is the formula to find the circumference of a circle?

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

    What is the purpose of drawing graphs of functions?

    <p>To visualize the relationship between input and output.</p> Signup and view all the answers

    How do you construct a parallelogram?

    <p>Draw the base and use a set square to draw the height. Draw the parallel opposite sides, ensuring opposite angles are equal.</p> Signup and view all the answers

    What is the formula to find 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 area of a rectangle?

    <p>A = l × w</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 formula to calculate the volume of a cylinder?

    <p>V = πr^2 h</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

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

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

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

    <p>A = 1/2 × (side_1 + side_2) × height</p> Signup and view all the answers

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

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

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

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

    What is the formula for the area of a circle?

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

    What is the formula for the arc length of a sector?

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

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

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

    How can you construct a perpendicular line to a given line segment through a point not on the line segment?

    <p>Draw two circles with each end point of the line segment as the center and passing through the point</p> Signup and view all the answers

    What is the formula for 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 formula for the diagonal of a rectangle with length l and width w?

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

    What is the angle bisector of a triangle?

    <p>A line that cuts an angle in half</p> Signup and view all the answers

    What is the relationship between the exterior angle of a triangle and the interior opposite angles?

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

    What is the condition for two triangles to be congruent?

    <p>They have the same shape and size</p> Signup and view all the answers

    What is the purpose of constructing congruent triangles?

    <p>To prove that two triangles are congruent</p> Signup and view all the answers

    What is the formula for a 90° counterclockwise rotation about the origin?

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

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

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

    What is the formula for a dilation from the origin with a scale factor of k?

    <p>(x, y) → (kx, ky)</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 effect of doubling the dimensions of a shape?

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

    What is the formula for the circumference of a circle?

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

    What is the formula for the area of a rectangle?

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

    What is the formula for the perimeter of a square?

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

    What is the formula for the area of a trapezium?

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

    What is the formula for the perimeter of a triangle?

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

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

    <p>May be positive or negative</p> Signup and view all the answers

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

    <p>May be positive, negative, or zero</p> Signup and view all the answers

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

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

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

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

    What is the distributive property of multiplication over addition?

    <p>a(b + c) = ab + bc</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 notation for the square root of a number x?

    <p>$\sqrt{x}$</p> Signup and view all the answers

    What is the quotient of a positive number and a negative number?

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

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

    <p>To extend the number system and provide solutions for equations</p> Signup and view all the answers

    What is the result of multiplying two negative numbers?

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

    Which of the following properties is true for the system of natural numbers?

    <p>Closed under addition and multiplication</p> Signup and view all the answers

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

    <p>To write numbers and multiples of 10</p> Signup and view all the answers

    What is true about the system of integers?

    <p>It is closed under addition, subtraction, and multiplication</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?

    <p>The set of rational and irrational numbers</p> Signup and view all the answers

    What is true about the system of whole numbers?

    <p>It is closed under addition and multiplication</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 characteristic of the system of natural numbers?

    <p>It is infinite</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 to a positive number?

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

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

    <p>A negative 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 correct order of operations when calculating expressions involving exponents?

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

    What is the meaning of a negative exponent in exponential notation?

    <p>The reciprocal of the base raised to the positive exponent</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 purpose of writing numbers in scientific notation?

    <p>To express very large or very small numbers</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 result of multiplying a positive and a negative number?

    <p>A negative number</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 formula for $a^m \div a^n$?

    <p>$a^{m-n}$</p> Signup and view all the answers

    What is the additive inverse of a number?

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

    What is the purpose of solving exponential equations?

    <p>To find the value of a variable</p> Signup and view all the answers

    What is the distributive property of multiplication over addition?

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

    What is the result of multiplying two negative numbers?

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

    What is the notation for the square root of a number x?

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

    What is the quotient of a positive number and a negative number?

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

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

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

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

    <p>To provide solutions for equations and to extend the number system for practical purposes</p> Signup and view all the answers

    What is the result of multiplying a polynomial by a monomial?

    <p>Each term in the polynomial is multiplied by the monomial</p> Signup and view all the answers

    What is the correct way to simplify the expression $(x + 3)(x + 2)$?

    <p>Use the distributive property to expand the product</p> Signup and view all the answers

    What is the result of evaluating the expression $(5x)^2$?

    <p>$25x^2$</p> Signup and view all the answers

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

    <p>To divide a polynomial by a monomial</p> Signup and view all the answers

    What is the result of applying the rule 'multiply a number by 5 and subtract the result from 50' to the input 6?

    <p>30</p> Signup and view all the answers

    What is the term for an expression that has different sequences of operations but the same numerical value for any given value of the variable?

    <p>Equivalent expression</p> Signup and view all the answers

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

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

    What is the purpose of using brackets in algebraic expressions?

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

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

    <p>$8x^3$</p> Signup and view all the answers

    What is the correct way to write an algebraic expression with a product of a known number and a variable?

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

    What is the main advantage of using estimating in calculations?

    <p>To simplify calculations and get a close answer</p> Signup and view all the answers

    What is the purpose of prime factorization in finding the LCM and HCF of two numbers?

    <p>To express a number as a product of its prime factors</p> Signup and view all the answers

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

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

    What is the term for the total amount paid in a hire purchase, including the deposit and interest?

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

    What is the purpose of subtracting a multiple of the divisor from the dividend in long division?

    <p>To continue the process until the remainder is less than the divisor</p> Signup and view all the answers

    What is the purpose of calculating the ratio of collected apples?

    <p>To compare the collection rates of different people</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 result of multiplying a number by 1 in the context of consecutive multiples?

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

    What is the purpose of calculating the average speed in a journey?

    <p>To determine the overall journey time</p> Signup and view all the answers

    What is the term for the interest calculated on the principal amount without adding the interest to the principal each year?

    <p>Simple interest</p> Signup and view all the answers

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

    <p>Multiplication and division first, followed by addition and subtraction</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 correct way to write an algebraic expression with a product of a known number and a variable?

    <p>The known number is written first, followed by the variable</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 purpose of using brackets in algebraic expressions?

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

    What is the term for an expression that has different sequences of operations but the same numerical value for any given value of the variable?

    <p>Equivalent expression</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 result of multiplying a positive number and a negative number?

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

    What is the term for an expression which is a sum of three terms?

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

    What is the first step in evaluating an algebraic expression with brackets?

    <p>Perform the calculations within the brackets first</p> Signup and view all the answers

    What is the key feature of a function?

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

    What is a flow diagram used for?

    <p>To illustrate the calculations needed to determine the output number for a given input variable</p> Signup and view all the answers

    What is the formula to calculate the gradient of a line?

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

    What is the purpose of a graph in functions?

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

    What is a table used for in functions?

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

    What is the term for the value substituted into a function?

    <p>Input number</p> Signup and view all the answers

    What is the term for the result after applying the function to the input?

    <p>Output number</p> Signup and view all the answers

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

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

    What is the key concept in functions that describes a relationship between two variables?

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

    What is the term for a quantity that can change?

    <p>Variable</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 a function?

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

    What does the slope of a graph indicate?

    <p>How rapidly the output changes with respect to the input.</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 a supplementary angle?

    <p>One of two angles whose sum is 180°.</p> Signup and view all the answers

    What is a vertically opposite angle?

    <p>An angle that is equal to its opposite angle when two lines intersect.</p> Signup and view all the answers

    What is a transversal?

    <p>A line that intersects two or more other lines.</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 sum of the interior angles of an equilateral triangle?

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

    What is the difference between corresponding angles and alternate angles?

    <p>Corresponding angles are equal, and alternate angles are also equal.</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 sum of co-interior angles?

    <p>180°</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 term for angles in matching corners when a transversal intersects parallel lines?

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

    What is the Pythagorean Theorem for a right triangle?

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

    What is the sum of two supplementary angles?

    <p>180°</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 a circle?

    <p>A closed figure with all points equidistant from the center</p> Signup and view all the answers

    What is the term for 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

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

    <p>Three sides</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 method of constructing a triangle given two sides and an included angle?

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

    What is the definition of a translation in transformation geometry?

    <p>A move of every point of a shape the same distance in the same direction</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 sum of the interior angles of a regular polygon?

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

    What is the method of constructing a rhombus?

    <p>Using a compass to draw four equal sides from a single vertex</p> Signup and view all the answers

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

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

    What is the formula for the translation of a shape by a vector (a, b)?

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

    If a shape is rotated 90 degrees counterclockwise about the origin, what is the resulting coordinate of a point (x, y)?

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

    What is the formula for the dilation of a shape by a scale factor k from the origin?

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

    What is the formula for the area of a rectangle?

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

    What is the formula for the perimeter of a square?

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

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

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

    What is the formula for the reflection of a shape over the x-axis?

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

    What is the formula for the rotation of a shape by 180 degrees about the origin?

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

    What is the formula for the area of a circle?

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

    What is the formula for the circumference of a circle?

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

    What is the formula for the area of a rectangle?

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

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

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

    What is the formula for the volume of a cylinder?

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

    What is the formula for the area of a triangle?

    <p>A = 1/2 × base × height</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 = 1/3 × πr^2h</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 for the surface area of a rectangular prism?

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

    What is the formula for the area of a sector?

    <p>$rac{ heta}{360} imes \pi r^2$</p> Signup and view all the answers

    What is the sum of interior angles of a polygon with 8 sides?

    <p>720</p> Signup and view all the answers

    What is the formula for the perimeter of a polygon?

    <p>Sum of all side lengths</p> Signup and view all the answers

    How do you 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 pass it through the point</p> Signup and view all the answers

    What is the formula for the diagonal of a rectangle?

    <p>$\sqrt{l^2 + w^2}$</p> Signup and view all the answers

    What is the angle bisector of a triangle?

    <p>A line that cuts an angle in half</p> Signup and view all the answers

    What is true about the three angle bisectors of 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 exterior angle of a triangle equal to?

    <p>The sum of the interior opposite angles</p> Signup and view all the answers

    What is the criteria for two triangles to be congruent?

    <p>They have the same shape and size</p> Signup and view all the answers

    What is the purpose of constructing congruent triangles?

    <p>To prove geometric theorems</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 purpose of including 0 in the system of whole numbers?

    <p>To write numbers with multiples of 10</p> Signup and view all the answers

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

    <p>It extends whole numbers to include negative numbers.</p> Signup and view all the answers

    What is a characteristic of rational numbers?

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

    What is a characteristic of irrational numbers?

    <p>They can be expressed as the square root of a rational number.</p> Signup and view all the answers

    What is the relationship between the set of real numbers and the set of rational and irrational numbers?

    <p>The set of real numbers includes both rational and irrational numbers.</p> Signup and view all the answers

    Which of the following is NOT a property of natural numbers?

    <p>When a natural number is divided by another natural number, the answer is always a natural number.</p> Signup and view all the answers

    What is a property of the system of whole numbers?

    <p>It is closed under addition and multiplication but not under subtraction or division.</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>Always negative</p> Signup and view all the answers

    What is the additive inverse of a number?

    <p>The opposite of the 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</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 notation for the square root of a number x?

    <p>√x</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 effect of adding a negative number to a positive number?

    <p>It decreases the number</p> Signup and view all the answers

    What is the result of multiplying two negative numbers?

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

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

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

    What is the purpose of estimating in calculations?

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

    How do you perform addition in columns?

    <p>By adding each digit starting from the rightmost digit</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 (HCF)</p> Signup and view all the answers

    How do you find the Lowest Common Multiple (LCM) of two numbers using prime factorization?

    <p>By multiplying all the prime factors of both numbers without repeating any factors</p> Signup and view all the answers

    What is the formula for calculating average speed?

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

    What is the purpose of compensating for errors introduced by rounding?

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

    What is the term for the payment method where a deposit is paid and then monthly instalments are made?

    <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 to a positive number?

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

    What is the difference between simple interest and compound interest?

    <p>Simple interest is calculated on the principal amount, while compound interest is calculated on the principal amount and the interest</p> Signup and view all the answers

    What is the term for the number that is a multiple of each of two or more numbers?

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

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

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

    What is the purpose of calculating the ratio of collected apples?

    <p>To compare the collection rates of different people</p> Signup and view all the answers

    What is the purpose of exponents in mathematical notation?

    <p>To represent repeated multiplication</p> Signup and view all the answers

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

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

    What is the result of $a^{-n}$ in exponential notation?

    <p>The reciprocal of $a^n$</p> Signup and view all the answers

    What is the purpose of scientific notation in mathematical notation?

    <p>To represent both very small and very large numbers</p> Signup and view all the answers

    What is the first step in solving exponential equations?

    <p>Rewrite both sides of the equation with the same base</p> Signup and view all the answers

    What is the purpose of the laws of exponents in mathematical notation?

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

    What is the formula for $a^m \div a^n$ in exponential notation?

    <p>$a^{m-n}$</p> Signup and view all the answers

    What is the purpose of using algebraic expressions to describe a sequence of operations?

    <p>To represent a sequence of operations in a concise and meaningful way</p> Signup and view all the answers

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

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

    What is the term for an expression that has different sequences of operations but the same numerical value for any given value of the variable?

    <p>Equivalent expression</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 term for a fixed value in an algebraic expression?

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

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

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

    What is the correct way to write an algebraic expression with a product of a known number and a variable?

    <p>3 × 2x</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 first step in evaluating an algebraic expression with brackets?

    <p>Perform the operations within the brackets</p> Signup and view all the answers

    What is the term for an expression which is a sum of two terms?

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

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

    <p>$\frac{y_2 - y_1}{x_2 - x_1}$</p> Signup and view all the answers

    Which of the following is a key representation of a function?

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

    What is the term for the specific output corresponding to a given input in a function?

    <p>Function Value</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 sum of angles on a straight line?

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

    What are the angles called when two lines intersect to form equal angles of 90°?

    <p>Perpendicular Angles</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 are the angles called when the corresponding angles formed by two lines and a transversal are equal?

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

    What is the sum of co-interior angles formed by two lines and a transversal?

    <p>180°</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 result of multiplying a polynomial by a monomial?

    <p>Each term in the polynomial is multiplied by the monomial.</p> Signup and view all the answers

    What is the purpose of using brackets in algebraic expressions?

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

    What is the result of evaluating the expression $(5x)^2$?

    <p>25x^2</p> Signup and view all the answers

    What is the distributive property of division?

    <p>$(x - y) / z = (x / z) - (y / z)$</p> Signup and view all the answers

    What is the result of expanding the product of two binomials $(x + a)(x + b)$?

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

    What is the general form for squaring a binomial $(a + b)$?

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

    What is the result of substituting a specific value for a variable in an algebraic expression?

    <p>The expression evaluates to a numerical value.</p> Signup and view all the answers

    What is the purpose of finding output numbers for given input numbers in a function?

    <p>To analyze the output types and apply different rules.</p> Signup and view all the answers

    What is the result of applying the rule $x - 1000$ to natural numbers smaller than 1000?

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

    What is the term for an algebraic expression that has different sequences of operations but yields the same numerical value for any given value of the variable?

    <p>Equivalent expression.</p> Signup and view all the answers

    What is the sum of the interior angles of an equilateral triangle?

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

    What is the name of the angle formed when two lines intersect to form equal angles of 90°?

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

    What is the definition of a polygon?

    <p>A closed figure with straight sides</p> Signup and view all the answers

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

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

    What is the formula for the area of a rectangle?

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

    What is the name of the angles formed when two lines intersect and the opposite angles are equal?

    <p>Vertically Opposite Angles</p> Signup and view all the answers

    What is the definition of a regular polygon?

    <p>A polygon with all sides and angles equal</p> Signup and view all the answers

    What is the sum of the co-interior angles formed when a transversal intersects two parallel lines?

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

    What is the formula for the area of a square?

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

    What is the name of the angles formed when a transversal intersects two parallel lines and the angles are on opposite sides of the transversal?

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

    What is the main characteristic of a function?

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

    What is the purpose of a flow diagram?

    <p>To illustrate the calculations needed to determine the output number for a given input variable</p> Signup and view all the answers

    What is the formula to calculate the gradient of a line?

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

    What is the purpose of a graph?

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

    What is the term for the value substituted into a function?

    <p>Input number</p> Signup and view all the answers

    What is the term for the result after applying the function to the input?

    <p>Output number</p> Signup and view all the answers

    What is the term for a quantity that can change?

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

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

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

    What is the purpose of a table representation of a function?

    <p>To show the input numbers and their corresponding function values</p> Signup and view all the answers

    What is the term for the rate of change between variables?

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

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

    <p>One side and two angles</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 perimeter of a triangle?

    <p>P = a + b + c</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 condition required to construct a triangle using the SAS method?

    <p>Two sides and one angle</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 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 area of a sector?

    <p>A = (θ/360) × πr^2</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 rhombus?

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

    What is the formula for the rotation of a shape by 90 degrees counterclockwise about the origin?

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

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

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

    What is the formula for the dilation of a shape by a scale factor of k from the origin?

    <p>(x, y) → (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 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 formula for the circumference of a circle?

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

    What is the formula for the area of a circle?

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

    What is the formula for the perimeter of a square?

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

    What is the formula for the area of a square?

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

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

    <p>SA = 6s^2</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 triangle?

    <p>A = 1/2 × base × height</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 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 sphere?

    <p>V = 4/3πr^3</p> Signup and view all the answers

    What is the formula for the area of a trapezium?

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

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

    <p>SA = πr(l + r)</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 in a 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?

    <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 two circles with the end points of the line segment as centers and intersecting 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 intersecting the arms of the angle</p> Signup and view all the answers

    What is the property of an angle bisector in a triangle?

    <p>The angle bisector is 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 in a triangle?

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

    What is the criterion for two triangles to be congruent?

    <p>If they have the same shape and size</p> Signup and view all the answers

    What is the method to construct a 45° angle?

    <p>Draw a 90° angle and bisect it</p> Signup and view all the answers

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