Gr 10 Math Nov P2 Medium
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Questions and Answers

What is the definition of the sine of an angle θ in a right-angled triangle?

  • opposite / hypotenuse (correct)
  • hypotenuse / opposite
  • opposite / adjacent
  • adjacent / hypotenuse

    • What is the reciprocal of the tangent of an angle θ?

  • secant
  • cosine
  • cotangent (correct)
  • cosecant

    • What is the relationship between sin θ and cosec θ?

  • sin θ - cosec θ = 1
  • sin θ / cosec θ = 1
  • sin θ × cosec θ = 1 (correct)
  • sin θ + cosec θ = 1

    • What is the label given to the side next to angle θ in a right-angled triangle?

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

    What is the purpose of the mnemonic 'Soh Cah Toa'?

    <p>To remember the definition of sine, cosine and tangent</p> Signup and view all the answers

    What is the definition of the secant of an angle θ?

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

    What is the importance of ensuring the calculator is in 'degrees' mode?

    <p>To ensure the calculator calculates the values of trigonometric ratios correctly</p> Signup and view all the answers

    What is the relationship between tan θ and cot θ?

    <p>tan θ × cot θ = 1</p> Signup and view all the answers

    Which of the following is a special angle that can be calculated without a calculator?

    <p>60°</p> Signup and view all the answers

    What is the label given to the side opposite the right-angle in a right-angled triangle?

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

    What property remains constant for similar triangles regardless of their size?

    <p>The ratios of their corresponding sides are equal.</p> Signup and view all the answers

    Which set of angles indicates that two triangles are similar?

    <p>30°, 60°, 90°</p> Signup and view all the answers

    Which statement is true regarding the corresponding angles of similar triangles?

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

    If triangles ΔABC and ΔDEF are similar, which relationship holds true?

    <p>AB/DE = BC/EF = AC/DF</p> Signup and view all the answers

    What does the notation ΔABC ∼ ΔDEF signify?

    <p>The triangles are similar.</p> Signup and view all the answers

    Why is the order of vertices crucial when labeling similar triangles?

    <p>It indicates corresponding angles.</p> Signup and view all the answers

    If triangle ΔABC has sides 3, 4, and 5, what can be inferred about triangle ΔDEF if it is similar?

    <p>Its sides will be in the ratio of 3:4:5.</p> Signup and view all the answers

    Which of the following statements about similar triangles is incorrect?

    <p>The triangles have the same perimeter.</p> Signup and view all the answers

    What is the length of the side opposite the 60° angle in a 30°-60°-90° triangle with a hypotenuse of 2?

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

    In a 45°-45°-90° triangle, what is the length of each leg if the hypotenuse measures √2?

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

    What is the value of an 45°?

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

    Which trigonometric ratio would be used to find the angle in a right triangle given the opposite and adjacent sides?

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

    When solving for an angle using trigonometric ratios, what range should the sine value fall within?

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

    For the point P(2, 3) on the Cartesian plane, what is the value for an A?

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

    What is the angle B in degrees if an B = 3/2 and lies in the second quadrant?

    <p>123.7°</p> Signup and view all the answers

    What should be the calculated angle when using an^-1(√3)?

    <p>60°</p> Signup and view all the answers

    If the hypotenuse of a 30°-60°-90° triangle is doubled, what happens to the lengths of the sides?

    <p>They double</p> Signup and view all the answers

    What is the sine value for a 60° angle?

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

    What is a trapezium?

    <p>A quadrilateral with one pair of parallel sides</p> Signup and view all the answers

    What is the mid-point theorem?

    <p>A theorem that states the line segment joining the mid-points of two sides of a triangle is parallel to the third side and is equal to half the length of the third side</p> Signup and view all the answers

    What is an application of the mid-point theorem?

    <p>To prove parallelism and segment proportions in geometric figures</p> Signup and view all the answers

    What is a kite?

    <p>A quadrilateral with two pairs of adjacent sides equal</p> Signup and view all the answers

    What is the converse of the mid-point theorem?

    <p>If a line is drawn through the mid-point of a side of a triangle parallel to the second side, it will bisect the third side</p> Signup and view all the answers

    What is the shape of the figure MNOP in the given diagram?

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

    What is the method used to prove that MNOP is a parallelogram?

    <p>Using the properties of the parallelogram ABCD</p> Signup and view all the answers

    What is the significance of the order of the letters in naming a figure?

    <p>It indicates the order in which points must be joined</p> Signup and view all the answers

    What is the formula for the distance between two points A(x₁, y₁) and B(x₂, y₂)?

    <p>√((x₂ - x₁)² + (y₂ - y₁)²)</p> Signup and view all the answers

    What is a point in analytical geometry?

    <p>An ordered pair of numbers written as (x, y)</p> Signup and view all the answers

    What is the 50th percentile also known as?

    <p>Second quartile</p> Signup and view all the answers

    What is the range of values in a data set that includes the median, first quartile, and third quartile?

    <p>Middle half of the data set</p> Signup and view all the answers

    What is the five number summary used to represent?

    <p>The entire data set</p> Signup and view all the answers

    What is the purpose of the box-and-whisker plot?

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

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

    <p>½ × b × h</p> Signup and view all the answers

    What is the definition of a right prism?

    <p>A geometric solid with a polygon as its base</p> Signup and view all the answers

    What is the difference between the 100th and 0th percentile?

    <p>Full data range</p> Signup and view all the answers

    What is the purpose of the five number summary?

    <p>To provide a concise numerical representation of the data</p> Signup and view all the answers

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

    <p>πr²</p> Signup and view all the answers

    What is the range of values in which a percentile lies in grouped data?

    <p>A range within which the rank is</p> Signup and view all the answers

    What type of data cannot be written as numbers?

    <p>Qualitative data</p> Signup and view all the answers

    What is the formula for the mean of a data set?

    <p>$\frac{x_1 + x_2 + ...+ x_n}{n}$</p> Signup and view all the answers

    What is the median of a data set when it has an even number of values?

    <p>The value halfway between the two middle values</p> Signup and view all the answers

    What is the mode of a data set?

    <p>The value that occurs most often in the data set</p> Signup and view all the answers

    What is an outlier in a data set?

    <p>A value that is much greater or much less than the other values</p> Signup and view all the answers

    What type of data is represented by real numbers, such as the height or mass of a person?

    <p>Continuous data</p> Signup and view all the answers

    What is the notation for the mean of a set of values?

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

    What is a categorical data?

    <p>Data coming from a limited number of possibilities</p> Signup and view all the answers

    What is the median of a data set when it has an odd number of values?

    <p>The value in the middle</p> Signup and view all the answers

    What is anecdotal data?

    <p>Data in the form of stories or interviews</p> Signup and view all the answers

    What is the condition for two triangles to be similar?

    <p>If all three pairs of corresponding sides are in proportion.</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 a parallelogram with all four angles equal to 90° called?

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

    What is the condition for two triangles to be congruent?

    <p>If three sides of a triangle are equal to the corresponding sides of another triangle.</p> Signup and view all the answers

    What is the name of the theorem that states b^2 = a^2 + c^2 in a right-angled triangle?

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

    What is the name of the quadrilateral with two pairs of adjacent sides equal?

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

    What is the property of a rhombus that is not true for a rectangle?

    <p>All interior angles are equal to 90°.</p> Signup and view all the answers

    What is the hierarchy of quadrilaterals?

    <p>Square is a type of rectangle, and rectangle is a type of parallelogram.</p> Signup and view all the answers

    What is the property of a parallelogram?

    <p>Both pairs of opposite sides are parallel.</p> Signup and view all the answers

    What is the condition for a triangle to be right-angled?

    <p>If the square of the length of the longest side is equal to the sum of the squares of the lengths of the other two sides.</p> Signup and view all the answers

    What happens to the volume of a rectangular prism when one dimension is multiplied by k?

    <p>It is multiplied by k</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 happens to the surface area of a rectangular prism when all three dimensions are multiplied by k?

    <p>It is multiplied by k^2</p> Signup and view all the answers

    What is the effect on the volume of a cylinder when the radius is multiplied by k?

    <p>It is multiplied by k^2</p> Signup and view all the answers

    What happens to the surface area of a cylinder when the height is multiplied by k?

    <p>It is multiplied by k</p> Signup and view all the answers

    What is the general formula for the volume of a rectangular prism when all three dimensions are multiplied by k?

    <p>V_k = k^3V</p> Signup and view all the answers

    What is the general formula for the surface area of a rectangular prism when all three dimensions are multiplied by k?

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

    What happens to the volume of a cylinder when the height is multiplied by k?

    <p>It is multiplied by k</p> Signup and view all the answers

    What is the correct formula to calculate the distance between two points (x₁, y₁) and (x₂, y₂)?

    <p>$d = rac{(x₁ - x₂)^2 + (y₁ - y₂)^2}{2}$</p> Signup and view all the answers

    What does the gradient (m) of a line represent?

    <p>The vertical change divided by the horizontal change</p> Signup and view all the answers

    Which equation represents a straight line in slope-intercept form?

    <p>$y = mx + b$</p> Signup and view all the answers

    What is the relationship between two parallel lines?

    <p>They maintain a constant distance apart and have equal gradients.</p> Signup and view all the answers

    How is the gradient of a horizontal line defined?

    <p>Gradient is equal to 0.</p> Signup and view all the answers

    The mid-point of a line between points A(x₁, y₁) and B(x₂, y₂) is calculated using which formula?

    <p>M(x, y) = $ rac{x₁ + x₂}{2}, rac{y₁ + y₂}{2}$</p> Signup and view all the answers

    What is the condition for two lines to be perpendicular?

    <p>The product of their gradients is equal to -1.</p> Signup and view all the answers

    What is true about vertical lines?

    <p>Their gradient is undefined.</p> Signup and view all the answers

    How can you prove that two points are collinear?

    <p>Using the gradient method or the distance formula.</p> Signup and view all the answers

    When calculating quantitative data, which characteristic is correct?

    <p>It is expressed as numbers representing counts or measurements.</p> Signup and view all the answers

    In which quadrant are all trigonometric ratios positive?

    <p>Quadrant I</p> Signup and view all the answers

    What is the value of $ an 45^ heta$?

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

    Which of the following statements about the angles of elevation and depression is true?

    <p>They are equal at corresponding points.</p> Signup and view all the answers

    Given a right triangle, which ratio correctly represents $ an heta$?

    <p>$ rac{ ext{opposite}}{ ext{adjacent}}$</p> Signup and view all the answers

    Which trigonometric ratio is defined as $ rac{r}{x}$?

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

    How can triangles be classified by angle?

    <p>Acute, Obtuse, Right-angled</p> Signup and view all the answers

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

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

    Which of the following statements about congruent triangles is false?

    <p>Congruent triangles have different corresponding angles.</p> Signup and view all the answers

    Which special angle has a sine of $ rac{ ext{sqrt{3}}}{2}$?

    <p>60°</p> Signup and view all the answers

    What is the definition of cosecant in terms of its sine?

    <p>$ rac{r}{y}$</p> Signup and view all the answers

    What is the surface area calculation for a triangular prism?

    <p>Area of two triangles plus area of three rectangles</p> Signup and view all the answers

    How is the volume of a cylindrical shape calculated?

    <p>$ ext{π}r^2h$</p> Signup and view all the answers

    What distinguishes a cube from other rectangular prisms?

    <p>It has equal lengths for all sides.</p> Signup and view all the answers

    Which formula correctly represents the surface area of a right cone?

    <p>$ ext{Area of base} + ext{Area of walls}$</p> Signup and view all the answers

    What effect does multiplying a dimension of a prism by a factor of k have on volume?

    <p>Volume increases by a factor of k cubed.</p> Signup and view all the answers

    What is the base shape of a right pyramid?

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

    Which formula is used for calculating the volume of a triangular pyramid?

    <p>$ rac{1}{3} imes ext{Area of base} imes H$</p> Signup and view all the answers

    Which statement correctly applies to spheres?

    <p>They are perfectly round and look the same from any direction.</p> Signup and view all the answers

    What is the sum of the surface areas of the two circular bases and the rectangular wrap of a cylinder?

    <p>Total surface area</p> Signup and view all the answers

    How is the surface area of a square pyramid calculated?

    <p>$ ext{Area of base} + ext{Area of triangular sides}$</p> Signup and view all the answers

    What does the mode of a data set represent?

    <p>The value that appears most frequently</p> Signup and view all the answers

    In continuous data sets, why is the mode often considered not computable?

    <p>Values in continuous data rarely repeat</p> Signup and view all the answers

    What distinguishes an outlier in a data set?

    <p>It is a value discordant with the rest of the data</p> Signup and view all the answers

    How is the mean of grouped data calculated?

    <p>Using the midpoints of each class interval</p> Signup and view all the answers

    What represents the modal group in a data set?

    <p>The group that has the highest frequency</p> Signup and view all the answers

    What does the range of a data set measure?

    <p>The difference between maximum and minimum values</p> Signup and view all the answers

    What is a percentile in the context of a data set?

    <p>A position that indicates a percentage of values below it</p> Signup and view all the answers

    In the percentile formula, what does the variable 'n' represent?

    <p>The total number of distinct values in the data set</p> Signup and view all the answers

    What is a consequence of grouping continuous data into intervals?

    <p>Loss of detailed information about individual values</p> Signup and view all the answers

    Which of the following is true regarding measures of dispersion?

    <p>Dispersion indicates how much data values are concentrated around the mean</p> Signup and view all the answers

    In a right-angled triangle with angles 30°, 60°, and 90°, what is the ratio of the length of the hypotenuse to the length of the side opposite the 30° angle?

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

    What is the value of cos(45°)?

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

    If sin(A) = 2/3, what is the value of tan(A)?

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

    In the Cartesian plane, what is the angle formed between the line OP and the negative x-axis if tan(α) = 3/2?

    <p>123.7°</p> Signup and view all the answers

    What is the first step to solve a trigonometric equation?

    <p>Identify the trigonometric ratio involved</p> Signup and view all the answers

    What is the length of the side opposite the 45° angle in a 45°-45°-90° triangle with a hypotenuse of √2?

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

    What is the value of sin(30°) in a right-angled triangle?

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

    If tan(A) = 1, what is the value of A in degrees?

    <p>45°</p> Signup and view all the answers

    What is the ratio of the length of the side opposite the 60° angle to the length of the side opposite the 30° angle in a 30°-60°-90° triangle?

    <p>√3:1</p> Signup and view all the answers

    If cos(A) = 1/2, what is the value of tan(A)?

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

    What condition must be met for triangles to be similar?

    <p>The triangles must have equal corresponding angles.</p> Signup and view all the answers

    If triangles have been determined to be similar, what can be said about the ratios of their corresponding sides?

    <p>They are equal regardless of the size of the triangles.</p> Signup and view all the answers

    When labeling similar triangles, why is the order of the vertices important?

    <p>It identifies corresponding angles between the triangles.</p> Signup and view all the answers

    In the context of similar triangles, which of the following statements is true?

    <p>The ratios of the lengths of corresponding sides in similar triangles are equal.</p> Signup and view all the answers

    If triangle ΔABC is similar to triangle ΔDEF, what can be inferred about their angles?

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

    What is the value obtained when the sine of an angle θ is multiplied by the cosecant of the same angle?

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

    Which of the following correctly defines the cosecant of an angle θ?

    <p>The reciprocal of the sine of θ</p> Signup and view all the answers

    Which of the following is a true statement regarding the sides of similar triangles?

    <p>The ratio of any two corresponding sides is constant.</p> Signup and view all the answers

    In a right-angled triangle, what does the tangent of an angle θ represent?

    <p>The ratio of the opposite side to the adjacent side</p> Signup and view all the answers

    Which of the following is true regarding the relationship between angles and ratios in similar triangles?

    <p>Equal angles lead to equal ratios of the corresponding sides.</p> Signup and view all the answers

    If the side opposite angle θ measures 5 units and the hypotenuse measures 10 units, what is the sine of angle θ?

    <p>0.5</p> Signup and view all the answers

    Which represents a correct mathematical expression that can be used to relate the sides of similar triangles ΔABC and ΔDEF?

    <p>$ rac{AB}{DE} = rac{BC}{EF}$</p> Signup and view all the answers

    What is the cotangent of an angle θ in terms of the triangle sides?

    <p>The ratio of the adjacent side to the opposite side</p> Signup and view all the answers

    When resolving trigonometric values on a calculator, why is it essential to set the calculator to degree mode?

    <p>To ensure accurate angle measurements in degrees</p> Signup and view all the answers

    What is the secant of an angle θ when the adjacent side measures 4 units and the hypotenuse measures 5 units?

    <p>1.25</p> Signup and view all the answers

    Which of the following statements about the mnemonic 'Soh Cah Toa' is true?

    <p>It provides relationships for all three basic trigonometric ratios.</p> Signup and view all the answers

    What is the relationship between the sine squared of an angle and the cosecant squared of the same angle?

    <p>sin² θ × cosec² θ = 1.</p> Signup and view all the answers

    How can the reciprocal of the cosine of an angle θ be expressed in terms of the triangle's sides?

    <p>Hypotenuse/adjacent</p> Signup and view all the answers

    What is the value of sin θ in the third quadrant?

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

    What is the angle of elevation if the angle of depression is 30°?

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

    What is the value of cos θ in a 45°-45°-90° triangle?

    <p>1/√2</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 classification of a triangle with two sides of equal length?

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

    What is the value of tan θ in a 30°-60°-90° triangle?

    <p>1/√3</p> Signup and view all the answers

    What is the CAST diagram used to divide the Cartesian plane into?

    <p>Four quadrants</p> Signup and view all the answers

    What is the relationship between the sine and cosine of an angle θ?

    <p>sin² θ + cos² θ = 1</p> Signup and view all the answers

    What is the value of cot θ in a 45°-45°-90° triangle?

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

    What is the property of congruent triangles?

    <p>Equal corresponding angles and sides</p> Signup and view all the answers

    What is the condition for two triangles to be congruent under the SSS rule?

    <p>All three sides are equal</p> Signup and view all the answers

    Which of the following is a property of a rectangle?

    <p>Both diagonals are equal in length</p> Signup and view all the answers

    What is the notation for similarity of triangles?

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

    Which of the following quadrilaterals has one pair of opposite sides parallel?

    <p>Trapezium</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

    Which of the following is a property of a rhombus?

    <p>All sides are equal in length</p> Signup and view all the answers

    What is the relationship between the corresponding angles of similar triangles?

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

    Which of the following is a condition for two triangles to be similar under the AAA rule?

    <p>All three pairs of corresponding angles are equal</p> Signup and view all the answers

    What is the hierarchy of quadrilaterals?

    <p>A square is a type of rhombus and a type of rectangle</p> Signup and view all the answers

    Which of the following is a property of a parallelogram?

    <p>Both pairs of opposite sides are parallel</p> Signup and view all the answers

    What is the mode of a data set?

    <p>The value that appears most often in the data set</p> Signup and view all the answers

    What is the main advantage of grouping continuous data?

    <p>It allows for easier visualization and calculation of central tendency</p> Signup and view all the answers

    What is the formula for calculating the mean of grouped data?

    <p>( \overline{x} = \frac{\sum f_i x_i}{\sum f_i} )</p> Signup and view all the answers

    What is the definition of the range of a data set?

    <p>The difference between the maximum and minimum values in the set</p> Signup and view all the answers

    What is the definition of the pth percentile?

    <p>The value that divides a data set into two parts, such that p percent of the values are less than it and 100-p percent are greater than it</p> Signup and view all the answers

    What is the modal group of a data set?

    <p>The group with the highest number of data values</p> Signup and view all the answers

    What is the disadvantage of using the range to measure dispersion?

    <p>It is sensitive to outliers</p> Signup and view all the answers

    What is the purpose of grouping data?

    <p>To change the data from continuous to discrete</p> Signup and view all the answers

    What is the rank of a datum in a data set?

    <p>Its position in the sorted data set</p> Signup and view all the answers

    What is the formula for finding the pth percentile in an ordered data set?

    <p>( r = \frac{p}{100} (n - 1) + 1 )</p> Signup and view all the answers

    What is the most appropriate way to define an outlier in a data set?

    <p>A value that is much greater or much less than the rest of the values.</p> Signup and view all the answers

    Which of the following statements best describes the median of a data set?

    <p>The median divides the data set into two equal halves.</p> Signup and view all the answers

    In a data set with an even number of observations, how is the median determined?

    <p>It is the average of the two central numbers.</p> Signup and view all the answers

    Which scenario correctly illustrates a measure of central tendency?

    <p>Calculating the mean of distances traveled by cars.</p> Signup and view all the answers

    What does the mean of a data set represent?

    <p>The sum of all values divided by the number of values.</p> Signup and view all the answers

    Which type of data is characterized by specific categories instead of numerical values?

    <p>Categorical data.</p> Signup and view all the answers

    If a data set consists of the values {3, 4, 4, 5, 6}, what is the mode?

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

    Which measure of central tendency is most affected by extreme values in a data set?

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

    What is the main purpose of calculating the mode in a data set?

    <p>To identify the most frequently occurring value.</p> Signup and view all the answers

    Which of these types of data often includes personal experiences or opinions?

    <p>Anecdotal data.</p> Signup and view all the answers

    What is the purpose of the five number summary?

    <p>To represent the overall data set concisely</p> Signup and view all the answers

    What is the definition of the interquartile range?

    <p>The range of the middle half of the data set</p> Signup and view all the answers

    What is the 25th percentile also known as?

    <p>The first quartile</p> Signup and view all the answers

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

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

    What is the purpose of the box-and-whisker plot?

    <p>To represent the overall data set graphically</p> Signup and view all the answers

    What is the definition of a right prism?

    <p>A geometric solid with a polygon as its base and vertical faces perpendicular to the base</p> Signup and view all the answers

    What is the range of values in which a percentile lies in grouped data?

    <p>A range within a group</p> Signup and view all the answers

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

    <p>A = ½ × (a + b) × h</p> Signup and view all the answers

    What is the definition of the semi-interquartile range?

    <p>Half of the interquartile range</p> Signup and view all the answers

    What is the difference between the 100th and 0th percentiles?

    <p>The full data range</p> Signup and view all the answers

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

    <p>Volume = length × width × height</p> Signup and view all the answers

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

    <p>Surface Area = πr² + πrh</p> Signup and view all the answers

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

    <p>Volume = (1/2) × base × height of triangle × height of prism</p> Signup and view all the answers

    What is the formula to calculate the surface area of a triangular pyramid?

    <p>Surface Area = (1/2) × base × height + 3 × (1/2) × base × height of side</p> Signup and view all the answers

    What happens to the surface area and volume of a prism or cylinder when one or more dimensions are multiplied by a factor of k?

    <p>The surface area will increase by a factor of k and the volume will increase by a factor of k²</p> Signup and view all the answers

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

    <p>Volume = (4/3) × πr³</p> Signup and view all the answers

    What is the formula to calculate the surface area of a right cone?

    <p>Surface Area = πr² + πrh</p> Signup and view all the answers

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

    <p>Volume = (1/3) × base² × height</p> Signup and view all the answers

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

    <p>Surface Area = 4πr²</p> Signup and view all the answers

    What is the definition of a pyramid?

    <p>A geometric solid with a polygon as its base and faces that converge at a point</p> Signup and view all the answers

    What happens to the volume of a rectangular prism when all its dimensions are multiplied by 5?

    <p>It increases by a factor of 125</p> Signup and view all the answers

    What happens to the surface area of a rectangular prism when all its dimensions are multiplied by 5?

    <p>It increases by a factor of 25</p> Signup and view all the answers

    What happens to the volume of a cylinder when its radius is multiplied by k?

    <p>It increases by a factor of k^2</p> Signup and view all the answers

    What happens to the surface area of a cylinder when its radius is multiplied by k?

    <p>It increases by a factor of k^2</p> Signup and view all the answers

    What is the relationship between the volume of a rectangular prism and its surface area when all its dimensions are multiplied by k?

    <p>The volume increases by k^3 and the surface area increases by k^2</p> Signup and view all the answers

    What happens to the volume of a cylinder when its height is multiplied by k?

    <p>It increases by a factor of k</p> Signup and view all the answers

    What is the relationship between the volume of a cylinder and its surface area when the radius is multiplied by k?

    <p>The volume increases by k^2 and the surface area increases by k^2</p> Signup and view all the answers

    What happens to the surface area of a cylinder when its height is multiplied by k?

    <p>It increases by a factor of k</p> Signup and view all the answers

    What is the definition of a trapezium?

    <p>A quadrilateral with one pair of parallel sides</p> Signup and view all the answers

    What is the converse of the Mid-Point Theorem?

    <p>If a line is drawn through the mid-point of a side of a triangle parallel to the second side, it will bisect the third side</p> Signup and view all the answers

    What is an application of the Mid-Point Theorem?

    <p>To prove parallelism and segment proportions in geometric figures</p> Signup and view all the answers

    What is the definition of a kite?

    <p>A quadrilateral with two pairs of adjacent sides equal</p> Signup and view all the answers

    What is the shape of the figure MNOP in the given diagram?

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

    What is the method used to prove that MNOP is a parallelogram?

    <p>Using the properties of triangles</p> Signup and view all the answers

    What is the significance of the order of the letters in naming a figure?

    <p>It indicates the order in which points must be joined</p> Signup and view all the answers

    What is the formula for the distance between two points A(x₁, y₁) and B(x₂, y₂)?

    <p>√((x₂ - x₁)² + (y₂ - y₁)²)</p> Signup and view all the answers

    What is a point in analytical geometry?

    <p>An ordered pair of numbers written as (x, y)</p> Signup and view all the answers

    What is the name of the quadrilateral ABCD, with coordinates A(1, 1), B(3, 1), C(3, 3), and D(1, 3)?

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

    How is the distance between two points calculated?

    <p>Distance = $|x_1 - x_2| + |y_1 - y_2|$</p> Signup and view all the answers

    What is the gradient of a line that is horizontal?

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

    Which formula correctly expresses how to find the gradient between points A(x₁, y₁) and B(x₂, y₂)?

    <p>Gradient (m) = $ rac{y_2 - y_1}{x_2 - x_1}$</p> Signup and view all the answers

    What is the result of multiplying the gradients of two perpendicular lines?

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

    Which of the following statements is true about parallel lines?

    <p>They are always the same distance apart.</p> Signup and view all the answers

    To find the mid-point M between points A(x₁, y₁) and B(x₂, y₂), which formula is used?

    <p>M = $ rac{x_1 + x_2}{2}, rac{y_1 + y_2}{2}$</p> Signup and view all the answers

    Which of the following best describes a vertical line?

    <p>m is undefined</p> Signup and view all the answers

    In the context of data, what is quantitative data?

    <p>Data that can be quantified as numbers</p> Signup and view all the answers

    Which equation represents the general form of a straight line?

    <p>$y = mx + c$</p> Signup and view all the answers

    What is the fundamental principle behind the concept of similar triangles?

    <p>The sides of similar triangles are proportional</p> Signup and view all the answers

    What is the condition for two triangles to be similar?

    <p>They have proportional sides and equal angles</p> Signup and view all the answers

    If ΔABC ∼ ΔDEF, what is the relationship between the corresponding sides?

    <p>AB/BC = DE/EF, AB/AC = DE/DF, BC/AC = EF/DF</p> Signup and view all the answers

    Why is the order of vertices crucial when labeling similar triangles?

    <p>To identify the corresponding sides</p> Signup and view all the answers

    What is the importance of similar triangles in trigonometry?

    <p>They are used to define trigonometric ratios</p> Signup and view all the answers

    What can be inferred about two triangles if they are similar?

    <p>They have proportional sides and equal angles</p> Signup and view all the answers

    If ΔABC ∼ ΔDEF, what can be said about ∠A and ∠D?

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

    What is the significance of similar triangles in geometry?

    <p>They form the basis of many geometric concepts</p> Signup and view all the answers

    In which quadrant is the tangent and cotangent of an angle θ positive?

    <p>Quadrant III</p> Signup and view all the answers

    What is the value of sin 45°?

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

    What is the angle of elevation of an object above the horizontal plane?

    <p>The angle formed by the line of sight and the horizontal plane</p> Signup and view all the answers

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

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

    In a 30°-60°-90° triangle, what is the length of the side opposite the 60° angle if the hypotenuse is 2?

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

    What is the definition of an isosceles triangle?

    <p>A triangle with two sides of equal length</p> Signup and view all the answers

    What is the equivalent of the angle of elevation from one point?

    <p>The angle of depression from the corresponding point</p> Signup and view all the answers

    What is the value of the tangent of 45°?

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

    Using the sine function, what is the value of sin 30°?

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

    What is the notation for congruency of two triangles?

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

    What is the condition for two triangles to be congruent using the RHS rule?

    <p>The hypotenuse and one side are equal</p> Signup and view all the answers

    If the length of the two legs of a 45°-45°-90° triangle is 1, what is the length of the hypotenuse?

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

    What is the value of cos 30°?

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

    Which inverse trigonometric function would you use to find an angle when the sine ratio is known?

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

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

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

    What is the cosine of 60°?

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

    For the point Q(-2, 3) on the Cartesian plane, what is the angle B formed between line OQ and the positive x-axis?

    <p>123.7°</p> Signup and view all the answers

    When solving the equation tan θ = 3/2, what should you first do?

    <p>Rearrange to isolate the tangent ratio.</p> Signup and view all the answers

    If the lengths of two sides of a right triangle are known, what can be calculated?

    <p>The angles and the hypotenuse</p> Signup and view all the answers

    If the sine of an angle exceeds 1, what can be inferred about that angle?

    <p>It does not exist in the defined range of sine.</p> Signup and view all the answers

    What is the minimum requirement for two triangles to be similar?

    <p>Three pairs of corresponding angles</p> Signup and view all the answers

    What is the property of a parallelogram?

    <p>Both pairs of opposite sides are parallel</p> Signup and view all the answers

    What is the definition of a rhombus?

    <p>A quadrilateral with all four sides equal</p> Signup and view all the answers

    What is the property of a kite?

    <p>The diagonal between equal sides bisects the other diagonal</p> Signup and view all the answers

    What is the notation for congruent triangles?

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

    What is the hierarchy of quadrilaterals?

    <p>A square is a type of rhombus and a type of rectangle</p> Signup and view all the answers

    What is the converse of the Pythagorean Theorem?

    <p>If a^2 + b^2 = c^2, then the triangle is right-angled</p> Signup and view all the answers

    What is the property of a rectangle?

    <p>All four angles are equal to 90°</p> Signup and view all the answers

    What is the property of a trapezium?

    <p>One pair of opposite sides are parallel</p> Signup and view all the answers

    What is the relationship between a square and a rectangle?

    <p>A square is a type of rectangle with all four sides equal</p> Signup and view all the answers

    What type of data is represented by real numbers?

    <p>Continuous data</p> Signup and view all the answers

    What is the definition of the mean?

    <p>The sum of a set of values, divided by the number of values in the set</p> Signup and view all the answers

    What is the purpose of calculating the median?

    <p>To find the value in the central position when the data set has been arranged from the lowest to the highest value</p> Signup and view all the answers

    What is an outlier?

    <p>A value that is much greater or much less than all the other values in the data set</p> Signup and view all the answers

    What type of data is categorical data?

    <p>Qualitative data</p> Signup and view all the answers

    What is the notation for the mean of a set of values?

    <p>horizontal bar over the variable</p> Signup and view all the answers

    What is the formula for the mean of a data set?

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

    What is the definition of the mode?

    <p>The value that occurs most often in the set</p> Signup and view all the answers

    How do you calculate the median of a quantitative data set?

    <p>Sort the data from the smallest to the largest value and find the value in the middle</p> Signup and view all the answers

    What type of data can be written as numbers?

    <p>Quantitative data</p> Signup and view all the answers

    What is the formula for the gradient of a line?

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

    What is the formula for the distance between two points A(x₁, y₁) and B(x₂, y₂)?

    <p>Distance (d) = √((x₂ - x₁)² + (y₂ - y₁)²)</p> Signup and view all the answers

    What is the definition of a straight line?

    <p>A set of points with a constant gradient between any two of the points</p> Signup and view all the answers

    What is the formula for the mid-point of a line between the points A(x₁, y₁) and B(x₂, y₂)?

    <p>Mid-point M(x, y) = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)</p> Signup and view all the answers

    What is the characteristic of parallel lines?

    <p>They have the same gradient and are always the same distance apart</p> Signup and view all the answers

    What is the characteristic of perpendicular lines?

    <p>They have negative reciprocal gradients and intersect at a point</p> Signup and view all the answers

    What is the definition of data?

    <p>A collection of pieces of information that have been observed and recorded</p> Signup and view all the answers

    What is the difference between quantitative and qualitative data?

    <p>Quantitative data can be written as numbers, qualitative data cannot</p> Signup and view all the answers

    What is the type of data that is represented by integers, typically involving counts?

    <p>Discrete data</p> Signup and view all the answers

    What is the formula for the equation of a straight line in the standard form?

    <p>y = mx + c</p> Signup and view all the answers

    What characteristic defines a trapezium?

    <p>One pair of parallel sides</p> Signup and view all the answers

    According to the mid-point theorem, what does the line segment joining the mid-points of two sides of a triangle represent?

    <p>It is equal to half the length of the third side.</p> Signup and view all the answers

    What does the converse of the mid-point theorem state?

    <p>If a line is drawn through the midpoint, it will parallel the third side.</p> Signup and view all the answers

    In the context of quadrilaterals, which property holds true for a kite?

    <p>It has two pairs of adjacent sides equal.</p> Signup and view all the answers

    Which application of the mid-point theorem involves calculating mid-points and distances?

    <p>Coordinate geometry</p> Signup and view all the answers

    What is the purpose of finding the value of a percentile in a data set?

    <p>To identify the value that lies at a specific percentage of the data</p> Signup and view all the answers

    When proving that MNOP is a parallelogram, which of the following is a necessary condition?

    <p>Both pairs of opposite sides are congruent.</p> Signup and view all the answers

    What conclusion can be drawn about the angles of a parallelogram like ABCD?

    <p>Adjacent angles are supplementary.</p> Signup and view all the answers

    What is the difference between the 100th and 0th percentile?

    <p>The full data range</p> Signup and view all the answers

    Why is the order of letters important when naming a figure in geometry?

    <p>It indicates the sequence of points to be joined.</p> Signup and view all the answers

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

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

    What is the definition of a right prism?

    <p>A geometric solid with a polygon as its base and vertical faces perpendicular to the base</p> Signup and view all the answers

    What is the derived formula for the distance between two points A(x₁, y₁) and B(x₂, y₂)?

    <p>$ ext{Distance} = ext{sqrt}((x₂ - x₁)² + (y₂ - y₁)²)$</p> Signup and view all the answers

    What happens to the line segment when slicing along the mid-points of a triangle?

    <p>It divides the triangle into two equal area triangles.</p> Signup and view all the answers

    What is the purpose of the five number summary?

    <p>To provide a concise numerical representation of the data set</p> Signup and view all the answers

    What is the range of values in which a percentile lies in grouped data?

    <p>A range within which the rank lies</p> Signup and view all the answers

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

    <p>A = ½ × (a + b) × h</p> Signup and view all the answers

    What is the definition of the interquartile range?

    <p>The range of the middle half of the data set</p> Signup and view all the answers

    What is the purpose of the box-and-whisker plot?

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

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

    <p>A = πr²</p> Signup and view all the answers

    If the length, width, and height of a rectangular prism are multiplied by 5, what will happen to the volume?

    <p>It will be multiplied by 125</p> Signup and view all the answers

    If the radius of a cylinder is multiplied by 3, what will happen to the surface area?

    <p>It will be multiplied by 9</p> Signup and view all the answers

    What happens to the volume of a rectangular prism when one of its dimensions is multiplied by k?

    <p>It is multiplied by k</p> Signup and view all the answers

    If the height of a cylinder is multiplied by 2, what will happen to the volume?

    <p>It will be multiplied by 2</p> Signup and view all the answers

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

    <p>2(lh + lb + bh)</p> Signup and view all the answers

    What happens to the surface area of a rectangular prism when all its dimensions are multiplied by k?

    <p>It is multiplied by k^2</p> Signup and view all the answers

    If the length and width of a rectangular prism are multiplied by 2, what will happen to the volume?

    <p>It will be multiplied by 4</p> Signup and view all the answers

    What is the formula for the volume of a cylinder?

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

    Which trigonometric ratio is defined as the ratio of the length of the adjacent side to the length of the hypotenuse?

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

    What is the value of cosecant ($\text{cosec } \theta$) in terms of sine?

    <p>$\frac{1}{\sin \theta}$</p> Signup and view all the answers

    Which of the following ratios correctly represents tangent ($\tan \theta$)?

    <p>$\frac{\text{opposite}}{\text{adjacent}}$</p> Signup and view all the answers

    If $\sin 30^{\circ}$ is known to be equal to a simple ratio, what is that ratio?

    <p>$\frac{1}{2}$</p> Signup and view all the answers

    Which trigonometric function is undefined at $\theta = 90^{\circ}$?

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

    What does the mnemonic 'Soh Cah Toa' represent?

    <p>The definitions of trigonometric ratios</p> Signup and view all the answers

    If $\tan \theta = \frac{2}{3}$, what represents the relationship between the opposite side and adjacent side in triangle?

    <p>Opposite = 2, Adjacent = 3</p> Signup and view all the answers

    What is the reciprocal of secant ($\text{sec } \theta$)?

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

    Which statement is true regarding the important relationships between trigonometric and reciprocal ratios?

    <p>$\tan \theta \times \cot \theta = 1$</p> Signup and view all the answers

    Which of the following ratios relates opposite and hypotenuse in a right triangle?

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

    How do you determine if a data set has more than one mode?

    <p>When two or more values have the same highest frequency.</p> Signup and view all the answers

    What is an outlier in a data set?

    <p>A value that deviates significantly from other values in the set.</p> Signup and view all the answers

    What is the range of a data set?

    <p>The difference between the highest and lowest values.</p> Signup and view all the answers

    When dealing with grouped data, how is the mean calculated?

    <p>By assuming values are concentrated at the midpoints of intervals.</p> Signup and view all the answers

    What does the median group refer to in grouped data?

    <p>The middle-most group when arranged in order.</p> Signup and view all the answers

    What happens to the mean estimation when data is grouped?

    <p>It may lose some accuracy due to information loss.</p> Signup and view all the answers

    What is a percentile?

    <p>A measure that describes how many values are below a certain point.</p> Signup and view all the answers

    In calculating the pth percentile, what does the term 'rank' refer to?

    <p>The position of a datum in a sorted data set.</p> Signup and view all the answers

    What is the typical reason the mode cannot be computed for continuous data sets?

    <p>Continuous values occur with unique frequency.</p> Signup and view all the answers

    What does a histogram visualize?

    <p>The frequency of data points within specified ranges.</p> Signup and view all the answers

    Which shape has a triangular base?

    <p>Triangular prism</p> Signup and view all the answers

    What is the formula for the volume of a cylinder?

    <p>$ rac{1}{3} imes ext{Area of base} imes ext{Height}$</p> Signup and view all the answers

    What element does NOT contribute to the surface area of a rectangular prism?

    <p>The diameter</p> Signup and view all the answers

    What geometric solid has a circular base and converging faces to a point?

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

    How is the surface area of a sphere computed?

    <p>$ ext{Surface Area} = 4 ext{pi}r^2$</p> Signup and view all the answers

    What is a characteristic of a right pyramid?

    <p>The apex is perpendicular to the base</p> Signup and view all the answers

    What is the volume formula for a triangular prism?

    <p>$ ext{Volume} = rac{1}{2} imes ext{base} imes ext{height of triangle} imes ext{height of prism}$</p> Signup and view all the answers

    What happens to the surface area and volume when a dimension is multiplied by a factor of k?

    <p>Surface area increases by $k^2$, volume increases by $k^3$</p> Signup and view all the answers

    Which formula represents the surface area of a right cone?

    <p>$ ext{Surface Area} = ext{Area of base} + ext{Area of walls}$</p> Signup and view all the answers

    What is the side of a right-angled triangle labelled when it is next to the angle θ?

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

    What is the definition of tan θ in a right-angled triangle?

    <p>opposite / adjacent</p> Signup and view all the answers

    What is the value of cos θ when θ is 0°?

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

    What is the reciprocal of the cosecant of an angle θ?

    <p>sin θ</p> Signup and view all the answers

    What is the purpose of the mnemonic 'Soh Cah Toa'?

    <p>To remember the trigonometric ratios</p> Signup and view all the answers

    What is the value of sec θ when θ is 90°?

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

    What is the ratio of the opposite side to the hypotenuse in a right-angled triangle?

    <p>sin θ</p> Signup and view all the answers

    What is the value of sin² θ?

    <p>(sin θ)²</p> Signup and view all the answers

    What is the relationship between the trigonometric ratios of an angle θ?

    <p>sin θ × cos θ = 1</p> Signup and view all the answers

    What is the purpose of ensuring the calculator is in 'degrees' mode?

    <p>To calculate the values of the trigonometric ratios</p> Signup and view all the answers

    What is the ratio of corresponding sides in similar triangles?

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

    If ∆ABC ∼ ∆DEF, which of the following is true?

    <p>∠A = ∠E and BC = EF</p> Signup and view all the answers

    Why is the order of vertices crucial when labeling similar triangles?

    <p>To establish the correct ratios of corresponding sides</p> Signup and view all the answers

    What can be inferred about ∆DEF if it is similar to ∆ABC with sides 3, 4, and 5?

    <p>It has proportional side lengths to ∆ABC</p> Signup and view all the answers

    What is the basis of many trigonometric concepts?

    <p>Properties of similar triangles</p> Signup and view all the answers

    What do the ratios of corresponding sides in similar triangles represent?

    <p>Similarity of triangles</p> Signup and view all the answers

    If ∆ABC and ∆DEF are similar, which of the following statements is true?

    <p>AB/AC = DE/DF and ∠A = ∠E</p> Signup and view all the answers

    What is the relationship between corresponding angles in similar triangles?

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

    What is the value of sin(θ) in a 30°-60°-90° triangle?

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

    If the length of the hypotenuse of a 30°-60°-90° triangle is doubled, what happens to the lengths of the sides?

    <p>All sides are doubled</p> Signup and view all the answers

    What is the value of tan(θ) in a 45°-45°-90° triangle?

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

    To solve a trigonometric equation, what step should be taken first?

    <p>Identify the trigonometric ratio involved</p> Signup and view all the answers

    What is the definition of the cosine of an angle θ in a right-angled triangle?

    <p>Adjacent side divided by the hypotenuse</p> Signup and view all the answers

    What is the purpose of using inverse trigonometric functions when solving trigonometric equations?

    <p>To find the angle that corresponds to a given ratio</p> Signup and view all the answers

    What is the value of cos(θ) in a 30°-60°-90° triangle?

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

    When finding an angle in a right-angled triangle using trigonometric ratios, what should be done to ensure an accurate solution?

    <p>Ensure the calculator is in degrees mode</p> Signup and view all the answers

    What is the definition of the tangent of an angle θ in a right-angled triangle?

    <p>Opposite side divided by the adjacent side</p> Signup and view all the answers

    What is the value of an angle θ in a right-angled triangle if tan(θ) = 3/2?

    <p>56.3°</p> Signup and view all the answers

    What is the formula to calculate the distance between two points A(x₁, y₁) and B(x₂, y₂)?

    <p>√((x₂ - x₁)² + (y₂ - y₁)²)</p> Signup and view all the answers

    What is the gradient of a horizontal line?

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

    What is the product of the gradients of two perpendicular lines?

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

    What is the formula for the mid-point of a line between points A(x₁, y₁) and B(x₂, y₂)?

    <p>((x₁ + x₂)/2, (y₁ + y₂)/2)</p> Signup and view all the answers

    What type of data cannot be written as numbers?

    <p>Qualitative data</p> Signup and view all the answers

    What is the general formula for finding the equation of a straight line?

    <p>y - y₁ = m(x - x₁)</p> Signup and view all the answers

    What is the gradient of a vertical line?

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

    What is the formula for the gradient of a line?

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

    What is the condition for two lines to be parallel?

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

    What is the definition of data?

    <p>Pieces of information that have been observed and recorded</p> Signup and view all the answers

    What is the primary characteristic of a modal group in a data set?

    <p>It is the group with the highest number of data values.</p> Signup and view all the answers

    When dealing with grouped data, what happens to the accuracy of central tendency measures?

    <p>They decrease as some information is lost in grouping.</p> Signup and view all the answers

    How is the mean of grouped data calculated?

    <p>By calculating midpoints for each class interval.</p> Signup and view all the answers

    What defines an outlier in a data set?

    <p>A value much greater or less than typical values.</p> Signup and view all the answers

    In which quadrant are all trigonometric ratios positive?

    <p>Quadrant I</p> Signup and view all the answers

    What does the range of a data set represent?

    <p>The difference between the maximum and minimum values.</p> Signup and view all the answers

    What is the sine of a 30° angle?

    <p>$ rac{1}{2}$</p> Signup and view all the answers

    In calculating the $p$th percentile, what does the variable $n$ represent?

    <p>The number of values in the ordered data set.</p> Signup and view all the answers

    Which trigonometric ratio is defined as the ratio of the opposite side to the hypotenuse in a right-angled triangle?

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

    What is the characteristic of percentiles in a data set?

    <p>They provide an index for comparative ranking.</p> Signup and view all the answers

    Which angle has an undefined tangent value?

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

    What happens when all values in a data set occur with equal frequency?

    <p>The data set will be considered to have no mode.</p> Signup and view all the answers

    If two triangles are congruent, what can be said about their corresponding angles and sides?

    <p>They have equal corresponding angles and sides.</p> Signup and view all the answers

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

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

    Which of the following is true regarding measures of dispersion?

    <p>They show how values are closely clustered around the mean.</p> Signup and view all the answers

    What is the angle of depression equivalent to when looking down from a height?

    <p>The angle of elevation from the ground</p> Signup and view all the answers

    Which type of triangle is classified as having all sides of different lengths?

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

    What is the reciprocal of the sine function?

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

    For the point P(2, 3), if P lies in Quadrant I, what can be determined about the signs of x and y?

    <p>x is positive, y is positive</p> Signup and view all the answers

    What is the purpose of the five number summary?

    <p>To provide a concise numerical representation of a data set</p> Signup and view all the answers

    What is the definition of a right prism?

    <p>A geometric solid with a polygon as its base and vertical faces perpendicular to the base</p> Signup and view all the answers

    What is the main difference between quantitative and qualitative data?

    <p>Quantitative data can be written as numbers, while qualitative data cannot</p> Signup and view all the answers

    What is the range of values in which a percentile lies in grouped data?

    <p>A range</p> Signup and view all the answers

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

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

    What is the definition of the mode of a data set?

    <p>The value that occurs most often in the set</p> Signup and view all the answers

    How is the median of a data set calculated?

    <p>By finding the value in the central position when the data set is arranged from lowest to highest</p> Signup and view all the answers

    Which statement correctly describes a property of a rectangle?

    <p>Opposite sides are equal in length and all angles are 90°.</p> Signup and view all the answers

    What is the 50th percentile also known as?

    <p>The median</p> Signup and view all the answers

    What is an outlier in a data set?

    <p>A value that is much greater or much less than all the other values in the set</p> Signup and view all the answers

    What is the purpose of the box-and-whisker plot?

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

    Which of the following is NOT a method used to prove that two triangles are congruent?

    <p>ASA (Angle-Side-Angle)</p> Signup and view all the answers

    What is the main purpose of measures of central tendency?

    <p>To summarize and describe the distribution of a data set</p> Signup and view all the answers

    What can be concluded if a quadrilateral has both pairs of opposite sides parallel?

    <p>It is a parallelogram.</p> Signup and view all the answers

    What is the definition of the interquartile range?

    <p>The range of the middle half of the data set</p> Signup and view all the answers

    What is the formula for the mean of a data set {x1, x2, ..., xn}?

    <p>(x1 + x2 + ... + xn) / n</p> Signup and view all the answers

    Which statement is true regarding the properties of a rhombus?

    <p>All sides are of equal length.</p> Signup and view all the answers

    What is the five number summary used to represent?

    <p>The entire data set</p> Signup and view all the answers

    What type of data is categorical data an example of?

    <p>Qualitative data</p> Signup and view all the answers

    In which scenario could two triangles be classified as similar?

    <p>All corresponding angles are equal, with sides in proportion.</p> Signup and view all the answers

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

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

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

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

    What is the main difference between the mean and the median?

    <p>The mean is the sum of a set of values, while the median is the value in the central position</p> Signup and view all the answers

    What is the difference between the 100th and 0th percentile?

    <p>The range of the data set</p> Signup and view all the answers

    Which description applies to the angles and sides of similar triangles?

    <p>All corresponding angles are equal, and sides are in proportion.</p> Signup and view all the answers

    What can be inferred about a data set if it has multiple modes?

    <p>The data set is qualitative</p> Signup and view all the answers

    What is the purpose of calculating the mean, median, and mode of a data set?

    <p>To summarize and describe the distribution of the data set</p> Signup and view all the answers

    What distinguishes a square from a rectangle?

    <p>A square has equal sides, while a rectangle can have unequal sides.</p> Signup and view all the answers

    Which characteristic is associated with a kite?

    <p>Diagonals intersect at right angles.</p> Signup and view all the answers

    Which pair of congruence conditions can be used to prove triangles are congruent?

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

    If the dimensions of a rectangular prism are tripled, what happens to its volume?

    <p>It becomes 27 times larger</p> Signup and view all the answers

    What happens to the surface area of a rectangular prism when its length, width, and height are all multiplied by 2?

    <p>It is multiplied by 4</p> Signup and view all the answers

    If the radius of a cylinder is quadrupled, what happens to its volume?

    <p>It becomes 16 times larger</p> Signup and view all the answers

    What happens to the surface area of a cylinder when its radius is tripled?

    <p>It becomes 9 times larger</p> Signup and view all the answers

    If the height of a cylinder is doubled, what happens to its volume?

    <p>It becomes 2 times larger</p> Signup and view all the answers

    What happens to the surface area of a cylinder when its height is quadrupled?

    <p>It becomes 4 times larger</p> Signup and view all the answers

    If the length, width, and height of a rectangular prism are all multiplied by 4, what happens to its surface area?

    <p>It becomes 16 times larger</p> Signup and view all the answers

    What happens to the volume of a rectangular prism when its length is doubled, its width is tripled, and its height is quadrupled?

    <p>It becomes 24 times larger</p> Signup and view all the answers

    What is the surface area of a cube with side length 2 units?

    <p>6 square units</p> Signup and view all the answers

    What is the volume of a triangular prism with a base of 3 units, height of 4 units, and length of 5 units?

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

    What is the surface area of a cylinder with radius 2 units and height 3 units?

    <p>24π square units</p> Signup and view all the answers

    What is the volume of a sphere with radius 3 units?

    <p>72π cubic units</p> Signup and view all the answers

    If the length of a rectangular prism is tripled, what happens to its surface area?

    <p>It increases by 9 times</p> Signup and view all the answers

    What is the surface area of a square pyramid with base side length 4 units and slant height 5 units?

    <p>16 + 40 square units</p> Signup and view all the answers

    What is the volume of a right cone with radius 2 units and height 5 units?

    <p>(1/3) * π * 2^2 * 5 cubic units</p> Signup and view all the answers

    What happens to the volume of a rectangular prism when its height is doubled?

    <p>It doubles</p> Signup and view all the answers

    What is the surface area of a triangular pyramid with base side length 3 units, base height 4 units, and slant height 5 units?

    <p>(1/2) * 3 * 4 + 3 * (1/2) * 3 * 5 square units</p> Signup and view all the answers

    What is the effect on the surface area of a cylinder if its radius is tripled and its height is doubled?

    <p>It increases by 27 times</p> Signup and view all the answers

    What is true about the line segment joining the mid-points of two sides of a triangle?

    <p>It is parallel to the third side and half its length.</p> Signup and view all the answers

    What property distinguishes a kite from other quadrilaterals?

    <p>It has two pairs of adjacent sides that are equal.</p> Signup and view all the answers

    In parallelogram ABCD, if AB = CD and AD = BC, which statement is true?

    <p>Both pairs of opposite angles are equal.</p> Signup and view all the answers

    How is the order of letters important when naming a figure?

    <p>It indicates the direction in which points are to be joined.</p> Signup and view all the answers

    Using the Mid-Point Theorem, what is the relationship between a line drawn through the mid-point of one side and the third side?

    <p>It will be parallel to the side and bisect the other side.</p> Signup and view all the answers

    Which geometric figure is specifically described by having only one pair of parallel sides?

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

    When applying the distance formula, which theorem is utilized?

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

    The result of drawing a line segment connecting the mid-points of two sides of a triangle is what type of geometric relationship to the third side?

    <p>It is parallel to the third side.</p> Signup and view all the answers

    In the context of geometric proofs, which quadrilateral is defined by having opposite angles equal but not all sides equal?

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

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