Gr 10 Math Nov P2 Easy
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Gr 10 Math Nov P2 Easy

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Questions and Answers

What is the fundamental principle of similar triangles?

  • Their sides are always equal in length
  • Their corresponding sides are proportional (correct)
  • Their corresponding angles are equal
  • Their perimeters are always equal

    • What is the key observation about similar triangles?

  • The lengths of corresponding sides are equal
  • The angles of corresponding sides are always different
  • The ratios of corresponding sides are equal (correct)
  • The ratios of corresponding sides are always different

    • What is the relationship between corresponding sides of similar triangles?

  • They are always equal in length
  • They are not related
  • They are proportional (correct)
  • They are always different

    • What is true about the angles of similar triangles?

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

    What is the importance of corresponding order in similar triangles?

    <p>It is crucial for labeling similar triangles</p> Signup and view all the answers

    What are the trigonometric ratios defined in terms of?

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

    What is the relationship between (\Delta ABC) and (\Delta DEF) if they are similar?

    <p>Their corresponding sides are proportional</p> Signup and view all the answers

    What is the significance of the ratios of similar triangles in trigonometry?

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

    What is the value of sin 0°?

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

    What is the classification of a triangle with two sides equal in length and the angles opposite the equal sides also equal?

    <p>Isosceles</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

    What is the definition of tan θ in terms of x, y, and r?

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

    What is the trigonometric ratio that is equal to the sine of an angle?

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

    What is the angle of elevation formed by?

    <p>The line of sight and the horizontal plane for an object above the horizontal plane</p> Signup and view all the answers

    Which of the following triangles is classified as one with all three interior angles less than 90°?

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

    What is the value of cos 90°?

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

    What is the notation for congruency of triangles?

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

    What is the definition of cot θ in terms of x and y?

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

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

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

    What does the gradient of a line describe?

    <p>The steepness of the line</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 product of the gradients of two perpendicular lines?

    <p>-1</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 formula to calculate the mid-point of a line between two points (x₁, y₁) and (x₂, y₂)?

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

    What is data?

    <p>A collection of pieces of information</p> Signup and view all the answers

    What is the plural form of the word 'datum'?

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

    What is the formula for the area of a triangle?

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

    What is the formula for the area of a circle?

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

    What is 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 formula for the volume of a cylinder?

    <p>π × r² × h</p> Signup and view all the answers

    What is the definition of surface area?

    <p>The total area of the exposed or outer surfaces of a prism.</p> Signup and view all the answers

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

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

    What is a right 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 is the formula for the volume of a triangular prism?

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

    What is the formula to find the rank of the pth percentile in an ordered data set with n values?

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

    What is the median also known as?

    <p>Second quartile</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 interquartile range a measure of?

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

    What is the semi-interquartile range?

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

    What does the box in a box-and-whisker plot represent?

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

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

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

    What is the purpose of finding the rank of the pth percentile?

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

    What is the definition of deciles?

    <p>The nine data values that divide an ordered data set into ten groups</p> Signup and view all the answers

    What is the definition of area?

    <p>The two-dimensional space inside the boundary of a flat object</p> Signup and view all the answers

    Which criterion is used to prove that two triangles are congruent if two sides and the included angle of one triangle are equal to those of the other triangle?

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

    What is a property of a rhombus that distinguishes it from other parallelograms?

    <p>Diagonals bisect each pair of angles</p> Signup and view all the answers

    Which of the following defines similarity between two triangles?

    <p>Corresponding angles are equal and 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 characteristic feature of a rectangle compared to other quadrilaterals?

    <p>All angles are right angles</p> Signup and view all the answers

    Which classification includes a kite?

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

    Which of the following is true about the diagonals of a square?

    <p>They are equal in length and intersect at 90°</p> Signup and view all the answers

    In the context of quadrilaterals, what defines a parallelogram?

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

    What establishes triangle congruence under the AAS criterion?

    <p>Two angles and a non-included side are equal</p> Signup and view all the answers

    Which shape is a type of quadrilateral that has only one pair of opposite sides parallel?

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

    Which type of quantitative data is characterized by integer values and typically involves counts?

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

    How is the mean of a data set defined?

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

    What is true about the median in a data set with an even number of values?

    <p>It is the mean of the two central values</p> Signup and view all the answers

    In the context of data sets, what does the term 'outlier' refer to?

    <p>A value that is significantly different from others</p> Signup and view all the answers

    Which measure of central tendency is defined as the most frequently occurring value in a data set?

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

    What is the first step to calculate the median of a quantitative data set?

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

    Which type of qualitative data includes data from a limited number of possibilities?

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

    What calculation can yield more than one mode in a data set?

    <p>Identifying the most frequently occurring values</p> Signup and view all the answers

    What would be the mode of a data set where every value occurs exactly once?

    <p>No mode</p> Signup and view all the answers

    What is another term used for the mean?

    <p>Arithmetic average</p> Signup and view all the answers

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

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

    What is the purpose of grouping continuous data?

    <p>To subdivide the full range of values into sub-ranges.</p> Signup and view all the answers

    What is the formula for 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 modal group in a data set?

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

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

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

    What is the 50th percentile in a data set?

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

    What is the purpose of percentiles in a data set?

    <p>To divide a data set into two parts.</p> Signup and view all the answers

    What is the difference between the value and rank of a datum?

    <p>The value is the measurement, and the rank is the position.</p> Signup and view all the answers

    Why is the range sensitive to outliers?

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

    What is the median group in a data set?

    <p>The central group when the groups are arranged in order.</p> Signup and view all the answers

    If the radius of a cylinder is multiplied by k, what happens to its surface area?

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

    If the height of a cylinder is multiplied by k, what happens to its surface area?

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

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

    What is the definition of a rhombus?

    <p>A special type of parallelogram with equal sides</p> Signup and view all the answers

    What is the mid-point theorem?

    <p>A 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 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 a kite?

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

    What is the purpose of the mid-point theorem in geometric proofs?

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

    What is the name of the theorem used to derive the formula for the distance between two points?

    <p>The theorem of Pythagoras</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 importance of the order of letters when naming a figure in analytical geometry?

    <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 the property of a parallelogram that is used to prove that MNOP is a parallelogram?

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

    What is the hypotenuse of a 30°-60°-90° triangle?

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

    What is the value of cos(60°)?

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

    What is the first step in solving trigonometric equations?

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

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

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

    What can be used to define trigonometric ratios for any angle in the Cartesian plane?

    <p>The angle between the positive x-axis and a line drawn from the origin</p> Signup and view all the answers

    What is the tangent of angle A in the point P(2, 3) in the Cartesian plane?

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

    What is the angle B formed between line OQ and the positive x-axis for the point Q(-2, 3) in the Cartesian plane?

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

    What is the length from the origin to point P in the Cartesian plane, denoted by?

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

    What is the purpose of plotting a point on the Cartesian plane and drawing a line from the origin to that point?

    <p>To work out the angle between the positive x-axis and that line</p> Signup and view all the answers

    What can be formed using the coordinates of a point in the Cartesian plane?

    <p>A right-angled triangle with the x-axis</p> Signup and view all the answers

    What is the hypotenuse in a right-angled triangle?

    <p>The side opposite to the right-angle.</p> Signup and view all the answers

    What is the trigonometric ratio of sine?

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

    What is the mnemonic for remembering the trigonometric ratios?

    <p>Soh Cah Toa</p> Signup and view all the answers

    What is the reciprocal of cosine?

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

    What is the relationship between sine and cosecant?

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

    What mode should your calculator be in to calculate trigonometric ratios?

    <p>degree mode</p> Signup and view all the answers

    What is the formula to calculate cosecant?

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

    What is the square of the hypotenuse equal to in a right-angled triangle?

    <p>the sum of the squares of the two other sides</p> Signup and view all the answers

    What is the trigonometric ratio of tangent?

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

    What is the surface area of a square pyramid with a base side length of "b" and slant height "h_s"?

    <p>b(b + 2h_s)</p> Signup and view all the answers

    What is the volume of a triangular pyramid with a base area of "bh"/2, height "H", and base length "b"?

    <p>(1/3)bhH</p> Signup and view all the answers

    What is the surface area of a sphere with radius "r"?

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

    If one dimension of a rectangular prism is multiplied by a factor of k, what happens to its volume?

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

    If all three dimensions of a rectangular prism are multiplied by a factor of k, what happens to its surface area?

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

    What is the volume of a cone with radius "r" and height "H"?

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

    What is the surface area of a triangular pyramid with a base area of "bh"/2 and three slant heights of "h_s"?

    <p>(1/2)b(h_b + 3h_s)</p> Signup and view all the answers

    What happens to the volume of a rectangular prism when one of its dimensions is multiplied by a factor of 5?

    <p>It increases by a factor of 5</p> Signup and view all the answers

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

    <p>πr(r + h)</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 reciprocal of sine?

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

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

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

    What is the mnemonic used to remember the trigonometric ratios?

    <p>SOH CAH TOA</p> Signup and view all the answers

    What is the product of sin θ and cosec θ?

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

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

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

    When using a calculator to find trigonometric ratios, what mode should the calculator be in?

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

    What is the reciprocal of cosine?

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

    What is the trigonometric ratio that is equal to the ratio of the adjacent side to the opposite side?

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

    What is the definition of tan θ in terms of sin θ and cos θ?

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

    What is the property that distinguishes a rhombus from other parallelograms?

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

    What is the mid-point theorem used for?

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

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

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

    What is the line segment joining the mid-points of two sides of a triangle parallel to?

    <p>The third side</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 purpose of the mid-point theorem in coordinate geometry?

    <p>To calculate mid-points and distances</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 can be used to prove a particular quadrilateral is one of the special quadrilaterals?

    <p>Geometric proofs</p> Signup and view all the answers

    What is the line segment joining the mid-points of two sides of a triangle equal to?

    <p>Half the length of the third side</p> Signup and view all the answers

    What is the process of drawing a figure on the Cartesian plane called?

    <p>Drawing figures on the Cartesian plane</p> Signup and view all the answers

    What is the formula to calculate the distance between two points (x, y) and (x, y)?

    <p>$\sqrt{(x - x)^2 + (y - y)^2}$</p> Signup and view all the answers

    What is the gradient of a line that runs parallel to the y-axis?

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

    What is the purpose of the gradient of a line?

    <p>To describe the slope or steepness of the line</p> Signup and view all the answers

    What is the formula to calculate the mid-point of a line between two points (x, y) and (x, y)?

    <p>$( rac{x + x}{2}, rac{y + y}{2})$</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 type of data can be written as numbers?

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

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

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

    What is the definition of a straight line?

    <p>A set of points with a constant gradient</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 formula for the gradient of a line?

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

    What type of data cannot be written as numbers?

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

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

    <p>(x_1 + x_2 + ...+ x_n)/n</p> Signup and view all the answers

    What is the value in the central position when the data set has been arranged from the lowest to the highest value?

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

    What is the definition of outlier?

    <p>A value that is not typical of the rest of the set</p> Signup and view all the answers

    What is the mode of a data set?

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

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

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

    What is the purpose of calculating the median?

    <p>To find the central value of a data 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 is the difference between the mean and the median?

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

    What is an example of continuous data?

    <p>The height of a person</p> Signup and view all the answers

    What is the mode of a data set?

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

    What happens when a continuous data set is grouped?

    <p>It changes from continuous to discrete</p> Signup and view all the answers

    What is used to visualize grouped data?

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

    What is the formula to calculate 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 modal group?

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

    What is 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 pth percentile?

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

    Why is the range sensitive to outliers?

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

    What is the purpose of measuring dispersion?

    <p>To describe how values are distributed around the centre</p> Signup and view all the answers

    What is the condition for two triangles to be similar?

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

    What is the notation for congruency of triangles?

    <p>≡</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 definition of a parallelogram?

    <p>A quadrilateral with both pairs of opposite sides parallel</p> Signup and view all the answers

    What is the converse of the Theorem of Pythagoras?

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

    What is a property of a rectangle?

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

    What is a property of a rhombus?

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

    What is a square?

    <p>A rhombus with all four interior angles equal to 90°</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 hierarchy of quadrilaterals?

    <p>Quadrilateral &gt; Parallelogram &gt; Rectangle &gt; Rhombus &gt; Square</p> Signup and view all the answers

    If the radius of a cylinder is multiplied by k, what happens to its volume?

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

    If the height of a cylinder is multiplied by k, what happens to its surface area?

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

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

    <p>It increases by 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 and its height is kept constant?

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

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

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

    What is the purpose of finding the rank of the pth percentile?

    <p>To identify the value of the pth percentile.</p> Signup and view all the answers

    What is the 50th percentile also known as?

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

    What does the box in a box-and-whisker plot represent?

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

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

    <p>The 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 interquartile range, IQR, a measure of?

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

    What is the semi-interquartile range?

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

    What are the three parts that divide an ordered data set into four groups of equal size?

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

    What are the nine divisions that divide an ordered data set into ten groups of equal size?

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

    What is the definition of area?

    <p>The two-dimensional space inside the boundary of a flat object</p> Signup and view all the answers

    What is the formula for the surface area of a square pyramid?

    <p>b(b + 2h_s)</p> Signup and view all the answers

    What is the formula for the volume of a triangular pyramid?

    <p>1/3 * b * h * H</p> Signup and view all the answers

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

    <p>4 * * r^2</p> Signup and view all the answers

    What is the effect of multiplying one dimension of a rectangular prism by a factor of k on its volume?

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

    What is the effect of multiplying all three dimensions of a rectangular prism by a factor of k on its surface area?

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

    What is the formula for the volume of a right cone?

    <p>1/3 * * r^2 * H</p> Signup and view all the answers

    What is the formula for the surface area of a triangular pyramid?

    <p>1/2 * b * (h_b + 3h_s)</p> Signup and view all the answers

    What is the effect of multiplying two dimensions of a rectangular prism by a factor of k on its volume?

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

    What is the formula for the volume of a sphere?

    <p>4/3 * * r^3</p> Signup and view all the answers

    What is the effect of multiplying one dimension of a rectangular prism by a factor of k on its surface area?

    <p>The surface area is increased by a factor that includes k</p> Signup and view all the answers

    If two triangles have the same angles, what can be said about their sides?

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

    What is the relationship between the ratios of corresponding sides in similar triangles?

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

    If $\Delta ABC \sim \Delta DEF$, what is the relationship between $\angle A$ and $\angle D$?

    <p>$\angle A$ is equal to $\angle D$.</p> Signup and view all the answers

    What is the importance of corresponding order in similar triangles?

    <p>It is used to match corresponding sides and angles.</p> Signup and view all the answers

    What are the trigonometric ratios defined in terms of?

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

    If two triangles are similar, what can be said about their corresponding angles?

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

    What is the relationship between the sides of $\Delta ABC$ and $\Delta DEF$ if they are similar?

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

    What is the basis of many trigonometric concepts?

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

    What is the value of cos 45°?

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

    What is the name of the diagram that divides the Cartesian plane into four quadrants?

    <p>CAST diagram</p> Signup and view all the answers

    What is the definition of tan θ in terms of opposite and adjacent sides?

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

    What is the angle of elevation formed by?

    <p>the line of sight and the horizontal plane for an object above the horizontal plane</p> Signup and view all the answers

    What is the classification of a triangle with all three sides equal in length and all three angles equal?

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

    What is the definition of sin θ in terms of x, y, and r?

    <p>y / r</p> Signup and view all the answers

    What is the value of tan 0°?

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

    What is the name of the triangle that has one interior angle greater than 90°?

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

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

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

    What is the definition of cosec θ in terms of x, y, and r?

    <p>r / y</p> Signup and view all the answers

    What is the cosine of 30°?

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

    What is the first step in solving a trigonometric equation?

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

    What is the relationship between the angle of elevation and the angle of depression?

    <p>The angle of elevation is equal to the angle of depression</p> Signup and view all the answers

    What is the formula for the area of a square?

    <p>A = s²</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

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

    <p>2 × (area of triangle) + 2 × (area of rectangle)</p> Signup and view all the answers

    How can we find the angles in a Cartesian plane?

    <p>By plotting a point and drawing a line from the origin to that point</p> Signup and view all the answers

    What is the formula for the volume of a cylinder?

    <p>V = π × r² × h</p> Signup and view all the answers

    What is the value of the sine of 60°?

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

    What is the definition of a right 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 is the purpose of using inverse trigonometric functions in solving trigonometric equations?

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

    What is the formula for the area of a trapezium?

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

    What is the value of the cosine of 45°?

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

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

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

    What is the condition for no solution in a trigonometric equation?

    <p>If the values are outside the domain of the trigonometric functions</p> Signup and view all the answers

    What is the importance of using the correct trigonometric ratio in solving a trigonometric equation?

    <p>It is important to ensure that the solution is accurate</p> Signup and view all the answers

    What is the formula for the area of a circle?

    <p>A = π × r²</p> Signup and view all the answers

    What is the definition of surface area?

    <p>The total area of the exposed or outer surfaces of a prism.</p> Signup and view all the answers

    What is true about the ratios of corresponding sides in similar triangles?

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

    If ΔABC ∼ ΔDEF, what is true about ∠A and ∠D?

    <p>∠A is equal to ∠D</p> Signup and view all the answers

    What is the importance of the order of vertices when labeling similar triangles?

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

    What is the basis of many trigonometric concepts?

    <p>Similar triangles</p> Signup and view all the answers

    What is true about the angles of similar triangles?

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

    What is the relationship between the ratios of corresponding sides in similar triangles?

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

    What is used to define the trigonometric ratios?

    <p>Similar triangles</p> Signup and view all the answers

    What is true about two similar triangles ΔABC and ΔDEF?

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

    What is the length of the hypotenuse in a 30°-60°-90° triangle?

    <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

    What is the first step in solving trigonometric equations?

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

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

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

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

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

    What is the tangent ratio of an angle A in a right-angled triangle with opposite side 3 and adjacent side 2?

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

    What is the angle formed between the line OQ and the negative x-axis in the Cartesian plane?

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

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

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

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

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

    What is the definition of the radius in a circle centered on the origin in the Cartesian plane?

    <p>The length from the origin to a point on the circle.</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 corresponding to a given ratio.</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 reciprocal of the cosine of an angle θ?

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

    What is the importance of considering the domain of trigonometric functions when solving trigonometric equations?

    <p>To avoid solutions that are outside the domain of the functions.</p> Signup and view all the answers

    What is the formula for the cotangent of an angle θ in a right-angled triangle?

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

    What is the trigonometric ratio that is equal to the opposite side over the adjacent side in a right-angled triangle?

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

    What is the importance of using the correct trigonometric ratio when solving problems involving right-angled triangles?

    <p>To find the unknown length or angle.</p> Signup and view all the answers

    What is the importance of ensuring your calculator is in 'degrees' mode when calculating trigonometric ratios?

    <p>To ensure accuracy in calculations</p> Signup and view all the answers

    What is the term for the ratios of the sides of a right-angled triangle that are not trigonometric ratios?

    <p>Reciprocal ratios</p> Signup and view all the answers

    Why are some angles called 'special angles' in trigonometry?

    <p>Because they have simple ratios</p> Signup and view all the answers

    What can be used to prove parallelism and segment proportions in geometric figures?

    <p>The Mid-Point Theorem</p> Signup and view all the answers

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

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

    What is the line segment joining the mid-points of two sides of a triangle equal to?

    <p>Half the length of the third side</p> Signup and view all the answers

    What can be used to draw a figure on the Cartesian plane?

    <p>The coordinates of the vertices</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 definition of a parallelogram?

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

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

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

    What is the result of the investigation in the Mid-Point Theorem?

    <p>The line segment joining the mid-points of two sides of a triangle is half the length of the third side</p> Signup and view all the answers

    What is the application of the Mid-Point Theorem in coordinate geometry?

    <p>Calculating mid-points</p> Signup and view all the answers

    What is the property of a rhombus that distinguishes it from other parallelograms?

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

    Which trigonometric ratio is defined as the adjacent side over the hypotenuse?

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

    In which quadrant are only cosine and secant positive?

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

    What is the value of $ an 30^ ext{o}$?

    <p>$\frac{1}{\sqrt{3}}$</p> Signup and view all the answers

    What does the angle of depression refer to?

    <p>Angle below the horizontal</p> Signup and view all the answers

    Which type of triangle has all three sides of different lengths?

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

    What is the ratio of opposite side to adjacent side in the definition of tangent?

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

    Which of the following angles is associated with the sine value of 1?

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

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

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

    What is the definition of cosecant in terms of sides of a triangle?

    <p>Hypotenuse over opposite</p> Signup and view all the answers

    What does congruency in triangles mean?

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

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

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

    If the height of a cylinder is multiplied by k, how does that affect the surface area?

    <p>The surface area changes proportionally to k</p> Signup and view all the answers

    What is the relationship between the change in radius and its effect on both volume and surface area?

    <p>Both volume and surface area are multiplied by k^2</p> Signup and view all the answers

    What is the formula for the volume of a cylinder?

    <p>$ ext{Base Area} imes ext{Height}$</p> Signup and view all the answers

    How does the surface area of a cylinder change when its radius is doubled?

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

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

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

    When all three dimensions of a rectangular prism are multiplied by a factor of 5, how is the volume affected?

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

    What is the correct surface area formula for a square pyramid?

    <p>$b(b + 2h_s)$</p> Signup and view all the answers

    For a sphere, what is the formula used to calculate its surface area?

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

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

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

    Which formula represents 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 of the following formulas calculates the volume of a sphere?

    <p>$ rac{4}{3} ext{pi} r^3$</p> Signup and view all the answers

    What is the surface area formula for a triangular pyramid?

    <p>$ rac{1}{3} b (h_b + 3h_s)$</p> Signup and view all the answers

    If the base area of a cone is $ ext{pi} r^2$ and its height is H, what is the volume of the cone?

    <p>$ rac{1}{3} ext{pi} r^2 H$</p> Signup and view all the answers

    What does the formula for finding the rank of the pth percentile depend on?

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

    What is considered the first quartile (Q1) in terms of percentiles?

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

    What does the box in a box-and-whisker plot represent?

    <p>The interquartile range (IQR)</p> Signup and view all the answers

    How is the semi-interquartile range calculated?

    <p>Subtracting Q1 from Q3 and then dividing by two</p> Signup and view all the answers

    What is indicated by the rank, r, that is not an integer?

    <p>The pth percentile equals the average of two values in the data set</p> Signup and view all the answers

    In the context of percentiles, how are deciles defined?

    <p>Nine data values dividing the data into ten equal parts</p> Signup and view all the answers

    What are the main components of the five number summary?

    <p>Minimum, maximum, first quartile, median, and third quartile</p> Signup and view all the answers

    What does the interquartile range measure?

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

    What does the 100th percentile represent in a data set?

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

    What does a box-and-whisker plot visually represent?

    <p>Five key data points: minimum, Q1, median, Q3, and maximum</p> Signup and view all the answers

    What does the theorem of Pythagoras state?

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

    What is a necessary condition for two triangles to be similar?

    <p>They have proportional corresponding sides</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 property of a parallelogram?

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

    What is the notation for congruent triangles?

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

    What is a kite in geometry?

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

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

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

    What is a property of a rhombus?

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

    What is a property of a square?

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

    What is a trapezium?

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

    What is the formula for the area of a square?

    <p>side length (s) squared (s²)</p> Signup and view all the answers

    What is the formula for the volume of a cylinder?

    <p>π × r² × h</p> Signup and view all the answers

    What is the formula for the area of a triangle?

    <p>½ × base (b) × height (h)</p> Signup and view all the answers

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

    <p>2 × π × r × h + 2 × π × r²</p> Signup and view all the answers

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

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

    What is the formula for the area of a trapezium?

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

    What is a right pyramid?

    <p>A pyramid with an apex that is perpendicular to the center of the base</p> Signup and view all the answers

    What is the formula for the area of a circle?

    <p>π × r²</p> Signup and view all the answers

    What type of data is represented by integers?

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

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

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

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

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

    What does the gradient of a line describe?

    <p>The slope or steepness of the line</p> Signup and view all the answers

    What is the median of a data set?

    <p>The value in the central position when the data is arranged from lowest to highest</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 an outlier in a data set?

    <p>A value that is much greater or less than the rest of the 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 product of the gradients of two perpendicular lines?

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

    What is the mode of a data set?

    <p>The value that occurs most often</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 type of data is represented by real numbers?

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

    What is the purpose of calculating the mean of a data set?

    <p>To summarize the central tendency of the data</p> Signup and view all the answers

    What is the formula to calculate the mid-point of a line between two points (x₁, y₁) and (x₂, y₂)?

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

    What is the difference between the median and the mode?

    <p>The median is the middle value, and the mode is the most frequent value</p> Signup and view all the answers

    What type of data can be written as numbers?

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

    What is the purpose of identifying outliers in a data set?

    <p>To understand the data better and make informed decisions</p> Signup and view all the answers

    What is the plural form of the word 'datum'?

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

    What is true about two lines that run parallel to each other?

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

    What type of data is categorized into a limited number of possibilities?

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

    What is the mode of a data set?

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

    Which statement correctly describes an outlier?

    <p>A value that is significantly different from the other values</p> Signup and view all the answers

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

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

    How is the mean of grouped data calculated?

    <p>Assume all values are at the midpoint of each interval</p> Signup and view all the answers

    What is the purpose of grouping continuous data?

    <p>To simplify the data into discrete categories</p> Signup and view all the answers

    In statistics, what does 'percentile' refer to?

    <p>The specific value where a certain percentage of data lies below it</p> Signup and view all the answers

    What is the modal group in a grouped data set?

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

    Why is the mode not typically computable for continuous data sets?

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

    What happens to data information when values are grouped?

    <p>Information is lost because values are approximated</p> Signup and view all the answers

    What does the median group contain in a data set?

    <p>The class that is at the halfway point of ordered data</p> Signup and view all the answers

    What is the definition of cosecant?

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

    What is the mnemonic used to remember the trigonometric ratios?

    <p>Soh Cah Toa</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

    What is the definition of secant?

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

    What is the purpose of using a calculator in trigonometry?

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

    What is the definition of sine?

    <p>opposite side over hypotenuse</p> Signup and view all the answers

    What is the relationship between sin θ and cosec θ?

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

    What is the definition of tangent?

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

    What are the three trigonometric ratios?

    <p>sine, cosine, and tangent</p> Signup and view all the answers

    What is the reciprocal of cotangent?

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

    What happens to the ratios of corresponding sides of similar triangles when their sizes change?

    <p>The ratios remain constant.</p> Signup and view all the answers

    In triangles \Delta ABC and \Delta DEF, if \Delta ABC is similar to \Delta DEF, which of the following statements is true?

    <p>The angles of both triangles are equal.</p> Signup and view all the answers

    What is the value of tan 90°?

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

    Which angles are present in the mentioned similar triangles?

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

    What quadrant is tan θ and cot θ positive?

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

    What ratio remains constant among similar triangles regardless of their sizes?

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

    What is the sine of 30°?

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

    What can be inferred if the corresponding angles of two triangles are equal?

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

    Which of the following describes the importance of the order of vertices in similar triangles?

    <p>It shows which angles correspond to each other.</p> Signup and view all the answers

    Which angle has a sine of 1?

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

    What is the cosine of 60°?

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

    How is the relationship between the sides of similar triangles typically expressed?

    <p>By ratios.</p> Signup and view all the answers

    If two triangles are similar, which of the following relationships hold true for their corresponding sides?

    <p>The lengths are in a fixed ratio.</p> Signup and view all the answers

    In which quadrant is sin θ and cosec θ positive?

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

    What is the tangent of 45°?

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

    What is the definition of the angle of elevation?

    <p>The angle formed by the line of sight and the horizontal plane for an object above the horizontal plane.</p> Signup and view all the answers

    What is the trigonometric ratio equal to the opposite over the hypotenuse?

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

    What type of triangle has two sides equal in length and the angles opposite the equal sides also equal?

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

    What is the rule for congruent triangles if three sides of a triangle are equal to the corresponding sides of another triangle?

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

    What is the notation for similarity between two triangles?

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

    What is the formula for the Pythagoras theorem in a right-angled triangle?

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

    What is the definition of a quadrilateral?

    <p>A closed shape with four sides</p> Signup and view all the answers

    What is a 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 rectangle?

    <p>A parallelogram with all four angles equal to 90°</p> Signup and view all the answers

    What is a rhombus?

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

    What is a property of a kite?

    <p>Two pairs of adjacent sides are equal</p> Signup and view all the answers

    What is the hierarchy of quadrilaterals?

    <p>A square is a type of rectangle, and a rectangle is a type of parallelogram</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 definition of a kite?

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

    What is the mid-point theorem?

    <p>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 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 a property of the mid-point theorem?

    <p>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 the application of the mid-point theorem in geometric proofs?

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

    What is the order of naming a figure in the Cartesian plane?

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

    What is the formula to derive 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 definition of a rhombus?

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

    What is the purpose of proving MNOP is a parallelogram?

    <p>To show that both pairs of opposite angles of MNOP are equal</p> Signup and view all the answers

    What is the length of the hypotenuse in a 30°-60°-90° triangle?

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

    What is the sine of 60°?

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

    How can you find an angle if two sides of a right-angled triangle are known?

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

    What is the tangent of 45°?

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

    What does the inverse sine function (sin^-1) calculate?

    <p>The angle corresponding to a given sine value</p> Signup and view all the answers

    If an heta = 3/2, what is the corresponding angle?

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

    For a 45°-45°-90° triangle, what is the relationship between the lengths of the legs?

    <p>The legs are each 1</p> Signup and view all the answers

    What must be true for there to be no solution in a trigonometric equation?

    <p>|sin θ| or |cos θ| exceeds 1</p> Signup and view all the answers

    When finding an angle in the Cartesian plane using point P(2, 3), what ratio is used?

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

    What is the cosine of 30°?

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

    If the radius of a cylinder is multiplied by k, what happens to the surface area?

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

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

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

    If the radius of a cylinder is multiplied by k, what happens to the volume?

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

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

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

    What is the general observation about multiplying the radius and height of a cylinder by k?

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

    What is the formula for the area of a square?

    <p>A = s²</p> Signup and view all the answers

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

    <p>Two circles and a rectangle</p> Signup and view all the answers

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

    <p>V = length × width × height</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 formula for the area of a trapezium?

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

    What is the definition of surface area?

    <p>The total area of the exposed or outer surfaces of a prism.</p> Signup and view all the answers

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

    <p>V = ½ × base × height of triangle × height of prism</p> Signup and view all the answers

    What is the definition of a right 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 is the formula for the surface area of a square pyramid?

    <p>b(b + 2hs)</p> Signup and view all the answers

    What is the formula for the volume of a triangular pyramid?

    <p>(1/3)(1/2)bhH</p> Signup and view all the answers

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

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

    What is the formula for the volume of a sphere?

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

    If the dimensions of a rectangular prism are multiplied by 5, what is the effect on the volume?

    <p>The volume is multiplied by 125</p> Signup and view all the answers

    If the dimensions of a rectangular prism are multiplied by k, what is the effect on the surface area?

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

    If one dimension of a rectangular prism is multiplied by 5, what is the effect on the volume?

    <p>The volume is multiplied by 5</p> Signup and view all the answers

    If two dimensions of a rectangular prism are multiplied by 5, what is the effect on the volume?

    <p>The volume is multiplied by 25</p> Signup and view all the answers

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

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

    What is the formula for the volume of a right cone?

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

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

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

    Which of the following statements about the mode is true?

    <p>A data set can have multiple modes.</p> Signup and view all the answers

    What is the term used for a value that is significantly different from the others in a data set?

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

    What does the median group represent?

    <p>The class interval that contains the median value.</p> Signup and view all the answers

    How is the mean of grouped data calculated?

    <p>By using the midpoint of each interval and the frequency.</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 a percentile?

    <p>A measure that divides a data set into equal parts.</p> Signup and view all the answers

    Which statement correctly describes percentiles?

    <p>Percentiles divide the data into parts based on ranks.</p> Signup and view all the answers

    What happens to the accuracy of central tendency measures when data is grouped?

    <p>It decreases due to loss of specific value information.</p> Signup and view all the answers

    In a histogram, what does the height of a rectangle represent?

    <p>The count of values in that range.</p> Signup and view all the answers

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

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

    What does the gradient of a line describe?

    <p>The slope or steepness of the line</p> Signup and view all the answers

    What is the formula to find the equation of a straight line?

    <p>y - y₁ = m(x - x₁)</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 gradient of a horizontal line?

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

    What is the formula to calculate the mid-point of a line between two points (x₁, y₁) and (x₂, y₂)?

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

    What type of data is quantitative data?

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

    What is the plural form of the word 'datum'?

    <p>Data</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 are parallel lines?

    <p>Lines that run parallel to each other and have equal gradients</p> Signup and view all the answers

    What type of data involves counts and is typically represented by integers?

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

    What is the median of a data set?

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

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

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

    What is the value that occurs most often in a data set?

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

    What is a value in a data set that is not typical of the rest of the set?

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

    What type of data cannot be written as numbers?

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

    What is categorical data?

    <p>Data coming from a limited number of possibilities</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 notation for the mean of a set of values?

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

    What is the median of a data set with an even number of values?

    <p>Halfway between two values</p> Signup and view all the answers

    What is the purpose of finding the rank of the pth percentile?

    <p>To determine the value of the pth percentile</p> Signup and view all the answers

    What does the five number summary consist of?

    <p>Minimum, maximum, and three quartiles</p> Signup and view all the answers

    What is the interquartile range a measure of?

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

    What is the semi-interquartile range?

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

    What does the box in a box-and-whisker plot represent?

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

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

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

    What is the definition of deciles?

    <p>The nine data values that divide an ordered data set into ten groups</p> Signup and view all the answers

    What is the formula to find the rank of the pth percentile in an ordered data set with n values?

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

    What is the purpose of the five number summary and the box-and-whisker plot?

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

    What is the definition of area?

    <p>The two-dimensional space inside the boundary of a flat object</p> Signup and view all the answers

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