Gr 9 MATH: November Mix
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Questions and Answers

What are the numbers that we use to count called?

  • Integers
  • Rational Numbers
  • Natural Numbers (correct)
  • Whole Numbers

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

  • A natural number (correct)
  • A whole number
  • A rational number
  • An integer

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

  • Not always a whole number
  • Always a whole number
  • Always a natural number
  • Not always a natural number (correct)

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

    <p>To write 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

    What is a characteristic of the system of integers?

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

    What is an example of an irrational number?

    <p>\sqrt{2}</p> Signup and view all the answers

    What is the set of numbers that includes both rational and irrational numbers?

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

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

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

    What is the equivalent of adding a negative number?

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

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

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

    What is the purpose of exponents in mathematics?

    <p>To provide a shorthand method for writing repeated multiplication</p> Signup and view all the answers

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

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

    What is the meaning of a negative exponent?

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

    What is the purpose of scientific notation?

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

    What is the rule for writing numbers 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 exponential expressions</p> Signup and view all the answers

    What is the goal of investigating and extending geometric patterns?

    <p>To analyze and describe the patterns in the arrangements</p> Signup and view all the answers

    What is a relationship between two variables where each input has exactly one output?

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

    What represents the calculations needed to find the output number that corresponds to a given input number?

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

    What is a method to visually represent the relationship between variables?

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

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

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

    What is the term for a quantity that can change?

    <p>Variable</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 shows the calculations needed to transform input into output?

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

    What is a method to list input values and their corresponding output values?

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

    What is a characteristic of a function?

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

    What is the purpose of a graph in representing relationships?

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

    What is the distributive property of multiplication?

    <p>a(b + c) = ab + bc</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 convention for writing a known number in a product?

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

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

    <p>Transversal</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 result of subtracting a larger number from a smaller number?

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

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

    <p>Regular polygon</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 sum of the interior angles of a quadrilateral?

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

    What is the formula for evaluating the square of a monomial?

    <p>(2x)^2 = 4x^2</p> Signup and view all the answers

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

    <p>The result is equivalent to subtracting the corresponding positive number</p> Signup and view all the answers

    What is the name of a triangle with one angle equal to 90°?

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

    How is addition performed in columns?

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

    What is the additive inverse of a positive number?

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

    What is the rule for simplifying an expression?

    <p>Combine like terms and apply the distributive property</p> Signup and view all the answers

    What is the name of a shape where all points are equidistant from the center?

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

    What is the result of dividing the number step-by-step in long division?

    <p>The remainder is always less than the divisor</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 formula for the distributive property of division?

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

    What is the lowest common multiple of two or more numbers?

    <p>The smallest number that is a multiple of each of them</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 general form for squaring a binomial?

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

    What is the name of angles that are equal when the lines are parallel?

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

    What is the relationship between distance, speed, and time?

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

    What is the name of angles that are on the same side of the transversal and inside the parallel lines?

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

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

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

    What is the 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 square root of a number?

    <p>The positive square root of the number</p> Signup and view all the answers

    What is the formula for calculating simple interest?

    <p>Simple interest = Principal × Rate × Time</p> Signup and view all the answers

    What is the name of 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 purpose of brackets in algebraic expressions?

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

    What is the difference between the HP price and the cash price?

    <p>Interest</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 purpose of negative numbers?

    <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 convention for writing algebraic expressions?

    <p>Omit the multiplication sign</p> Signup and view all the answers

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

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

    What is the ratio of flour to oatmeal in a biscuit recipe?

    <p>5:2</p> Signup and view all the answers

    How is the highest common factor of two or more numbers found?

    <p>By multiplying the common prime factors of the numbers</p> Signup and view all the answers

    What is the rule for subtracting a negative number?

    <p>Subtracting a negative number is the same as adding the corresponding positive number</p> Signup and view all the answers

    What is the purpose of compensating for errors in calculations?

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

    What is the formula to calculate the 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 key characteristic of a function?

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

    What does the slope of a graph indicate?

    <p>The rate of change of the output 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 two angles whose sum is 180° called?

    <p>Supplementary angles</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 straight lines intersect?

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

    What is the purpose of a table when drawing graphs of functions?

    <p>To choose a range of input values and calculate the corresponding output values</p> Signup and view all the answers

    What does the continuity of a graph indicate?

    <p>The graph is a continuous curve</p> Signup and view all the answers

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

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

    What is the correct order of operations when there are no brackets in an algebraic expression?

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

    What is the term for an expression with three terms?

    <p>Trinomial</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 purpose of brackets in algebraic expressions?

    <p>To perform calculations first</p> Signup and view all the answers

    What is an algebraic expression that has different sequences of operations but the same numerical value?

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

    What is the term for an expression with one term?

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

    What is the convention for writing algebraic expressions when multiplying a number and a variable?

    <p>Write the number first</p> Signup and view all the answers

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

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

    What do flow diagrams sometimes represent in algebraic language?

    <p>Sequences of operations</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 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 formula for 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 for constructing a perpendicular line through a point on a line segment?

    <p>Draw two circles with centers at the ends of the line segment and pass through the point</p> Signup and view all the answers

    What is the method for bisecting an angle?

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

    What is the method for constructing a 45° angle?

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

    What is the property of 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 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 criterion for two triangles to be congruent?

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

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

    <p>One side and two angles</p> Signup and view all the answers

    Which formula is used to calculate the area of a triangle?

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

    What is the formula for the perimeter of a rectangle?

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

    Which of the following is a type of transformation?

    <p>All of the above</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 regular polygon?

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

    What is the method of constructing a triangle with 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 definition of translation?

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

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

    What is the formula for translating a point by a vector (a, b)?

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

    What is the formula for the area of a triangle?

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

    What is the formula for rotating a point 90 degrees counterclockwise about the origin?

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

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

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

    What is the formula for reflecting a point over the x-axis?

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

    What is the formula for dilating a point 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 volume of a cylinder?

    <p>V = πr^2h</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 area of a kite?

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

    What is the formula for the perimeter of a rectangle?

    <p>P = 2(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 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 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 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 volume of a sphere?

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

    What is the purpose of converting between units of measurement?

    <p>To compare quantities</p> Signup and view all the answers

    What is the closure property of natural numbers under addition?

    <p>The result is always a natural number.</p> Signup and view all the answers

    Which of the following statements about integers is true?

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

    What is the defining characteristic of rational numbers?

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

    What is the difference between whole numbers and natural numbers?

    <p>Whole numbers include zero, while natural numbers do not.</p> Signup and view all the answers

    What is a characteristic of irrational numbers?

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

    What is the set of real numbers composed of?

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

    What is the purpose of the system of whole numbers?

    <p>To extend the natural numbers to include zero.</p> Signup and view all the answers

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

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

    What is the purpose of estimating in calculations?

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

    How is addition performed in columns?

    <p>By adding each digit from right to left</p> Signup and view all the answers

    What is the lowest common multiple of two or more numbers?

    <p>The smallest number that is a multiple of each of them</p> Signup and view all the answers

    What is the formula for calculating distance?

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

    What is the purpose of compensating for errors in calculations?

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

    What is the ratio used for in Moeneba's apple collection?

    <p>To compare the number of apples collected by different people</p> Signup and view all the answers

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

    <p>It is equivalent to adding the corresponding positive 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>The result is zero</p> Signup and view all the answers

    How is multiplication performed in columns?

    <p>By multiplying each digit from right to left</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 formula for calculating average speed?

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

    What is the additive inverse of a positive number?

    <p>A negative number with the same magnitude</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 formula for calculating time?

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

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

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

    What is the distributive property of multiplication?

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

    What is the equivalent of subtracting a positive number from another positive number?

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

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

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

    What is the purpose of negative numbers in mathematics?

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

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

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

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

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

    What is the equivalent of adding a negative number?

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

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

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

    What is the purpose of exponents in mathematics?

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

    What is the rule for writing numbers 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 exponential expressions</p> Signup and view all the answers

    What is the meaning of a negative exponent?

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

    What is the goal of investigating and extending geometric patterns?

    <p>To analyze and extend patterns</p> Signup and view all the answers

    What is the 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 multiplying a number in exponent form by another number in exponent form with the same base?

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

    What is the purpose of brackets in algebraic expressions?

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

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

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

    What is the equivalent expression for $(x + 2)^2$?

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

    What is the result of dividing $x^2 + 3x - 2$ by $x + 1$?

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

    What is the purpose of the distributive property in algebra?

    <p>To multiply polynomials by monomials</p> Signup and view all the answers

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

    <p>$9x^2$</p> Signup and view all the answers

    What is the purpose of substituting values into algebraic expressions?

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

    What is the equivalent expression for $x - 1000$ when applied to natural numbers smaller than 1000?

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

    What is the purpose of the rule in functions and relationships?

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

    What is the result of simplifying $2x^2 + 3x + 2x + 1$?

    <p>$2x^2 + 5x + 1$</p> Signup and view all the answers

    What is a sequence of operations that can also be described in words or flow diagrams?

    <p>An algebraic expression</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 rule for calculating expressions without brackets?

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

    What is the term for a symbol, often x, representing the unknown value?

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

    What is the purpose of identifying constants and variables in patterns?

    <p>To understand the relationships between the terms</p> Signup and view all the answers

    What is the term for expressions that have different sequences of operations but the same numerical value?

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

    What is the convention for writing a known number in a product?

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

    What is the purpose of expanding and simplifying algebraic expressions?

    <p>To make the expression easier to understand</p> Signup and view all the answers

    What is the rule for performing calculations within brackets?

    <p>Perform the calculations within brackets first</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 key concept in functions that refers to the specific output corresponding to a given input?

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

    What type of angles are formed when two lines intersect to form equal angles of 90°?

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

    What is the term for the value substituted into a function to produce an output?

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

    What is the characteristic of a graph that indicates how rapidly the output changes with respect to the input?

    <p>Slope/Gradient</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 term for the quantity that can change in a function?

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

    What is the formula for calculating 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 method used to visually represent the relationship between variables?

    <p>Graph</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 purpose of identifying the function in drawing graphs of functions?

    <p>To determine the formula or rule that defines the function</p> Signup and view all the answers

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

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

    Which of the following is a characteristic of a function?

    <p>Each input has exactly one 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 purpose of a graph in representing relationships?

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

    What is the formula for calculating the gradient of a line passing through two points?

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

    Which of the following representations of a function shows the calculations needed to transform input into output?

    <p>Flow diagram</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 purpose of a table in representing functions?

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

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

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

    What is the key feature to consider when interpreting graphs?

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

    What is the minimum condition required to prove congruency in two triangles?

    <p>Three sides (SSS)</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 name of the formula used to calculate the area of a triangle when the length of all three sides are known?

    <p>Heron's Formula</p> Signup and view all the answers

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

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

    What is the name of the 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 minimum condition required to construct a triangle?

    <p>Three sides</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 sum of the interior angles in a triangle?

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

    What is the name of the polygon with four sides of equal length?

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

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

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

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

    <p>A = π × radius²</p> Signup and view all the answers

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

    <p>Formula for the Sum of Angles of a Polygon</p> Signup and view all the answers

    What is the relationship between the angles on opposite sides of a transversal and inside the parallel lines?

    <p>They 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 name of a triangle with 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 name of a line that intersects two or more other lines?

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

    What is the sum of the interior angles in a quadrilateral?

    <p>360°</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 name of a polygon with all sides equal?

    <p>Rhombus</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 formula for the sum of interior angles of a polygon?

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

    What is the formula for the perimeter of a polygon?

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

    What is the formula for 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 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 method to bisect an angle using circles?

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

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

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

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

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

    What is the criteria for congruency of two triangles?

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

    What is the purpose of constructing special angles without a protractor?

    <p>To construct angles that are multiples of 30, 45, or 60 degrees.</p> Signup and view all the answers

    What is the formula for translating a point by vector (a, b)?

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

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

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

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

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

    What is the formula for dilating a point 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 formula for the perimeter of a rectangle?

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

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

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

    What is the formula for converting between units of length?

    <p>1 cm = 10 mm</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 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 rectangular prism?

    <p>SA = 2lw + 2lh + 2wh</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 kite?

    <p>A = 1/2 × d_1 × d_2</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 surface area of a cone?

    <p>SA = πr(l + r)</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 formula for evaluating the average speed?

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

    What is the highest common factor of two or more numbers?

    <p>The largest number that divides each of them without leaving a remainder</p> Signup and view all the answers

    What is the method used to simplify the calculation of multiplying two large numbers?

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

    What is the purpose of compensating for errors in calculations?

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

    What is the formula for calculating the distance travelled?

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

    What is the method used to find the lowest common multiple of two or more numbers?

    <p>Multiplying the prime factors of the numbers</p> Signup and view all the answers

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

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

    What is the method used to subtract one large number from another?

    <p>Column subtraction</p> Signup and view all the answers

    What is the term for the ratio of the number of apples collected by different people?

    <p>Ratio of collection</p> Signup and view all the answers

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

    <p>Equivalent to adding the corresponding positive number</p> Signup and view all the answers

    What is the product of two negative integers?

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

    What is the additive inverse of a positive number?

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

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

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

    What is the purpose of negative numbers?

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

    What is the distributive property of multiplication?

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

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

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

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

    <p>It has the same effect as subtracting a positive number</p> Signup and view all the answers

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

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

    What is the purpose of the exchange rate in currency exchange?

    <p>To convert one currency to another</p> Signup and view all the answers

    What is the property of natural numbers when you subtract one natural number from another?

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

    What is the relationship between the system of whole numbers and the system of natural numbers?

    <p>The system of natural numbers is a subset of the system of whole numbers.</p> Signup and view all the answers

    What is the characteristic of integers that is not true for whole numbers?

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

    What is the definition of rational numbers?

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

    What is the difference between rational and irrational numbers?

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

    What is the set of real numbers comprised of?

    <p>Both rational and irrational numbers.</p> Signup and view all the answers

    What is a characteristic of the system of natural numbers when you add two or more natural numbers?

    <p>The result is always a natural number.</p> Signup and view all the answers

    What is the property of the system of integers that is not true for the system of natural numbers?

    <p>The system of integers is closed under subtraction.</p> Signup and view all the answers

    What is the term for an expression with one term only in algebraic expressions?

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

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

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

    What is the rule for calculating expressions with brackets?

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

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

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

    What is the order of operations when calculating expressions without brackets?

    <p>Multiplication and division, then 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 term for a fixed value in an algebraic expression?

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

    What is the convention for writing a known number in a product?

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

    What is the purpose of algebraic expressions?

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

    What is the term for equivalent expressions that have different sequences of operations but the same numerical value?

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

    When a larger number is subtracted from a smaller number, what is the result?

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

    What is the equivalent of adding a negative number?

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

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

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

    What is the purpose of exponents in mathematics?

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

    What is the rule for writing numbers in scientific notation?

    <p>Move the decimal point to the left for large numbers and to the right for small numbers</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 result of multiplying a negative number by a negative number?

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

    What is the purpose of investigating and extending geometric patterns?

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

    What is the relationship between the number of yellow tiles and the number of blue tiles in a geometric pattern?

    <p>The number of yellow tiles is a variable</p> Signup and view all the answers

    What is the purpose of solving exponential equations?

    <p>To equate the exponents on both sides of the equation</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 the distributive property of division?

    <p>To divide a polynomial by a monomial or an integer</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 general form for squaring a binomial?

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

    What is the result of evaluating the square of a monomial?

    <p>The monomial is squared</p> Signup and view all the answers

    What is the purpose of substituting specific values for variables in algebraic expressions?

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

    What is the convention for writing a known number in a product?

    <p>Write the known number first</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 a set of natural numbers smaller than 10?

    <p>A set of positive numbers</p> Signup and view all the answers

    What is the purpose of expanding the product of two binomials?

    <p>To find the product of two polynomials</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

    Which of the following is a characteristic of a function?

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

    What is the purpose of a graph in representing relationships?

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

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

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

    What is the term for a quantity that can change?

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

    What is the purpose of a flow diagram?

    <p>To illustrate the calculations needed to produce the output numbers</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 a method to visually represent the relationship between variables?

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

    What is the characteristic of a function that describes a relationship between two variables?

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

    What is the purpose of a table in representing relationships?

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

    What is the result of applying the rule ( \frac{x}{10} + 10 ) to natural numbers smaller than 10?

    <p>Positive numbers between 10 and 11</p> Signup and view all the answers

    What is the gradient of a line that passes through the points (2, 3) and (4, 5)?

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

    Which of the following is a characteristic of a function?

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

    What is the purpose of a graph in representing relationships?

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

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

    <p>The rate at which the output changes with respect to the input</p> Signup and view all the answers

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

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

    What is the name of the angles formed when two lines intersect, and the sum of these angles is 180°?

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

    When a transversal intersects two parallel lines, what can be said about the corresponding angles?

    <p>They are equal</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 purpose of drawing graphs of functions?

    <p>To visualize the relationship between variables</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 sum of the interior angles of an equilateral triangle?

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

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

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

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

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

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

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

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

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

    What is the purpose of identifying corresponding angles?

    <p>To determine the properties of a transversal</p> Signup and view all the answers

    What is the name of angles that are equal when the lines are parallel?

    <p>Corresponding angles</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 purpose of identifying alternate angles?

    <p>To identify parallel lines</p> Signup and view all the answers

    What is the name of a shape where 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 sector?

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

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

    <p>$(n - 2) imes 180^\circ$</p> Signup and view all the answers

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

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

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

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

    How can 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 passing through the given point.</p> Signup and view all the answers

    How can you bisect an angle using circles?

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

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

    <p>The angle bisector is always equidistant from each side of the triangle.</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 criterion for two triangles to be congruent?

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

    Which of the following conditions is not a minimum condition for congruency?

    <p>One Side and One Angle</p> Signup and view all the answers

    What is the formula for 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 for the perimeter of a rectangle?

    <p>P = 2(l + w)</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

    How do you construct a triangle using the SSS method?

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

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

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

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

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

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

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

    What is the definition of a translation in transformation geometry?

    <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 for a dilation from the origin with a scale factor of k?

    <p>(x, y) -&gt; (kx, ky)</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 rectangle?

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

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

    <p>360°</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 formula for the area of a sector?

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

    What is the effect of doubling the dimensions of a shape?

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

    What is the formula for the circumference of a circle?

    <p>C = 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 converting from kilometers to meters?

    <p>1 km = 1000 m</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 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 perimeter of a rectangle?

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

    What is the formula for 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 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 cone?

    <p>V = 1/3πr^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

    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 main difference between the system of whole numbers and the system of natural numbers?

    <p>The presence of 0 in the system of whole numbers.</p> Signup and view all the answers

    Which of the following types of numbers is not a rational number?

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

    What is the main characteristic of the system of integers?

    <p>It includes negative numbers.</p> Signup and view all the answers

    What is the main difference between rational and irrational numbers?

    <p>Rational numbers can be expressed as fractions, while irrational numbers cannot.</p> Signup and view all the answers

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

    <p>It includes both rational and irrational numbers.</p> Signup and view all the answers

    What is the additive inverse of a natural number?

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

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

    <p>The sum of two natural numbers is always a natural number.</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 product of two negative integers?

    <p>Always positive</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 with the same magnitude?

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

    What is the purpose of negative numbers in the number system?

    <p>To extend the number system for practical purposes</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 dividing a negative number by a positive number?

    <p>Always negative</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 equivalent of subtracting a negative number?

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

    What is the square root of a number?

    <p>A value that when multiplied by itself gives the original 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 in mathematics?

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

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

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

    What is the result of raising a number to a negative exponent?

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

    What is the purpose of exchange rates in currency exchange?

    <p>To convert one currency to another</p> Signup and view all the answers

    What is the purpose of scientific notation in mathematics?

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

    What is the rule for writing numbers in scientific notation?

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

    What is the goal of investigating and extending geometric patterns?

    <p>To identify and extend geometric patterns</p> Signup and view all the answers

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

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

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

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

    What is the primary purpose of estimating in calculations?

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

    In the process of long division, what is the remainder when the division is complete?

    <p>Less than the divisor</p> Signup and view all the answers

    What is the formula to calculate the highest common factor (HCF) of two numbers?

    <p>Multiply the common prime factors of the numbers</p> Signup and view all the answers

    What is the purpose of compensating for errors in estimation?

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

    What is the formula to calculate the lowest common multiple (LCM) of two numbers?

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

    In the context of ratio and rate problems, what does the ratio of collected apples represent?

    <p>The comparison of collection rates between different people</p> Signup and view all the answers

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

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

    What is the purpose of prime factorization in determining 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 total HP price in a hire purchase agreement?

    <p>Deposit + Total instalments + Interest</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 interest</p> Signup and view all the answers

    What is the purpose of brackets in an algebraic expression?

    <p>To perform the operations within the brackets first</p> Signup and view all the answers

    What is the difference between a monomial, binomial, and trinomial?

    <p>The number of terms in the expression</p> Signup and view all the answers

    What is the convention for writing a known number in a product?

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

    What is the purpose of equivalent algebraic expressions?

    <p>To show different forms of the same expression</p> Signup and view all the answers

    What is the rule for simplifying an algebraic expression?

    <p>Combine like terms and remove any brackets</p> Signup and view all the answers

    What is the purpose of the order of operations?

    <p>To evaluate expressions with multiple operations</p> Signup and view all the answers

    What is the difference between a variable and a constant in an algebraic expression?

    <p>A variable is an unknown value, while a constant is known</p> Signup and view all the answers

    What is the purpose of algebraic expressions?

    <p>To represent relationships between variables</p> Signup and view all the answers

    What is the convention for writing algebraic expressions?

    <p>Omit the multiplication sign in products</p> Signup and view all the answers

    What is the purpose of expanding and simplifying algebraic expressions?

    <p>To evaluate the expressions more easily</p> Signup and view all the answers

    Which of the following is NOT a convention for writing algebraic expressions?

    <p>Write the multiplication sign in all expressions.</p> Signup and view all the answers

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

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

    What is the result of expanding the binomial $(x + 2)^2?$

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

    What is the result of evaluating the expression $x^2 - 4x + 4$ when $x = 2?$

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

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

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

    What is the result of finding the square root of $16x^2?$

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

    What is the result of applying the rule 'multiply by 5 and subtract the result from 50' to the input number $4?$

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

    What is the result of finding the output number for the input number $8$ using the rule 'multiply by 2 and add 1'?

    <p>$17$</p> Signup and view all the answers

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

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

    What is the result of simplifying the expression $rac{x^2 + 3x - 2}{x + 1}?$

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

    What is the common property of all representations of a function?

    <p>They all have a unique output for each input</p> Signup and view all the answers

    Which of the following is not a way to represent a function?

    <p>Histogram</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 produce output values</p> Signup and view all the answers

    What is the formula for 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 graph in representing a function?

    <p>To visualize the relationship between variables</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 term for a quantity that can change?

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

    What represents the value substituted into a function?

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

    What is the formula for the function ( rac{x}{10} + 10 ) when applied to natural numbers smaller than 10?

    <p>Positive numbers between 10 and 11</p> Signup and view all the answers

    What is the formula for the function ( 30x + 2 ) when applied to positive fractions with denominators 2, 3, and 5?

    <p>Positive numbers greater than 2</p> Signup and view all the answers

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

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

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

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

    What is the method used to construct perpendicular lines?

    <p>Using circles</p> Signup and view all the answers

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

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

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

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

    What is the method used to bisect an angle?

    <p>Using circles</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 name of a line that intersects two or more other lines?

    <p>Transversal</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 × tan(π/n))</p> Signup and view all the answers

    What is the method used to construct a 45° angle?

    <p>Bisecting a 90° angle</p> Signup and view all the answers

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

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

    What is the name of a triangle with 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 rhombus?

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

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

    <p>Transversal</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 name of a polygon with all sides and angles equal?

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

    What is the formula for the perimeter of a rectangle?

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

    What is the name of a shape where all points are equidistant from the center?

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

    What is the formula for the area of a parallelogram?

    <p>A = b × h</p> Signup and view all the answers

    What is the name of a triangle with all three sides and angles equal?

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

    What is the purpose of identifying the function value in a given input-output pair?

    <p>To understand the input-output behavior of the function</p> Signup and view all the answers

    When interpreting graphs, what does the continuity of the graph indicate?

    <p>Whether the function is continuous or has breaks</p> Signup and view all the answers

    What is the purpose of creating a table of values when drawing a graph of a function?

    <p>To choose a range of input values and calculate the corresponding output values</p> Signup and view all the answers

    What is the term for the angle formed when two lines intersect, and the vertically opposite angles are equal?

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

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

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

    What is the purpose of identifying the supplementary angles when two lines intersect?

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

    What is the term for the line that intersects two or more other lines, and forms corresponding angles that are equal?

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

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

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

    What is the term for the angles formed when two lines intersect, and the sum of the angles is 180°?

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

    What is the purpose of identifying the input and output numbers in a function?

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

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

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

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

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

    What is the name of the formula used to find the area of a triangle, given the lengths of all three sides?

    <p>Heron's Formula</p> Signup and view all the answers

    What is the name of the theorem used to find the length of the hypotenuse of a right-angled triangle?

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

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

    <p>C = 2 × π × radius</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 find the area of a sector of a circle?

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

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

    <p>P = n × side length</p> Signup and view all the answers

    What is the name of the process used to construct a triangle, given three sides?

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

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

    <p>Sum = (n - 2) × 180°</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 perimeter of a rectangle?

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

    What is the formula for the area of a rhombus?

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

    What is the formula for the 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 cone?

    <p>V = (1/3)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 diameter of a circle?

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

    What is the effect of a 90° counterclockwise rotation on a point (x, y)?

    <p>It becomes (-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 area of a kite with diagonals of 10 cm and 15 cm?

    <p>37.5 cm²</p> Signup and view all the answers

    What is the perimeter of a rectangle with a length of 8 cm and a width of 5 cm?

    <p>26 cm</p> Signup and view all the answers

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

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

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

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

    What is the area of a circle with a radius of 4 cm?

    <p>16π cm²</p> Signup and view all the answers

    What is the result of a 180° rotation on a point (x, y)?

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

    What is the perimeter of a square with a side length of 6 cm?

    <p>24 cm</p> Signup and view all the answers

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

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

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