Gr 10 Math Nov P2 Mix

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

$rac{ ext{opposite}}{ ext{hypotenuse}}$ (correct)

$rac{ ext{hypotenuse}}{ ext{opposite}}$

$rac{ ext{adjacent}}{ ext{hypotenuse}}$

$rac{ ext{opposite}}{ ext{adjacent}}$

Which mnemonic can help remember the trigonometric ratios for sine, cosine, and tangent?

Ratios of Angles

Soh Cah Toa (correct)

Right Triangle Rules

Sin Cos Tan

What is the definition of cosecant for angle theta?

$rac{ ext{hypotenuse}}{ ext{adjacent}}$

$rac{ ext{hypotenuse}}{ ext{opposite}}$ (correct)

$rac{1}{ an heta}$

$rac{1}{ ext{cos } heta}$

Which relationship correctly represents the tangent of angle theta?

$rac{ ext{opposite}}{ ext{adjacent}}$ Signup and view all the answers

What is the reciprocal of cosine for angle theta called?

Secant Signup and view all the answers

What condition is necessary to use trigonometric ratios in a triangle?

The triangle must be right-angled. Signup and view all the answers

Which of the following statements about special angles is true?

Some angles can be determined without a calculator. Signup and view all the answers

What is the value of the reciprocal of sine multiplied by sine?

1 Signup and view all the answers

If a calculator is needed to find the values of sine for most angles, what must the calculator be set to?

Degrees mode Signup and view all the answers

Which ratio defines cotangent in relation to angle theta?

$rac{ ext{adjacent}}{ ext{opposite}}$ Signup and view all the answers

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

2 Signup and view all the answers

Which of the following ratios corresponds to sin 45°?

√2/2 Signup and view all the answers

If the length of the opposite side is 3 and the adjacent side is 2, what is tan A?

3/2 Signup and view all the answers

What is the angle associated with a cosine ratio of 1/2?

60° Signup and view all the answers

Which of the following values is possible for the sine of an angle?

0.8 Signup and view all the answers

In a 45°-45°-90° triangle, what is the length of the opposite side if the hypotenuse is √2?

1 Signup and view all the answers

What angle is formed if the tangent ratio is 56.3°?

123.7° Signup and view all the answers

If a circle is centered at the origin and passes through point P(2, 3), what is the radius of the circle?

√13 Signup and view all the answers

Which trigonometric function would be used to find an angle if the sine value is known?

sin^-1 Signup and view all the answers

For a point Q(-2, 3), what is the relationship between angles B and α based on their definitions?

B + α = 180° Signup and view all the answers

In which quadrant are all trigonometric ratios positive?

Quadrant I Signup and view all the answers

What is the value of $ an 90^ heta$?

undefined Signup and view all the answers

Which of the following represents the sine ratio in terms of a right triangle's sides?

$rac{ ext{opposite}}{ ext{hypotenuse}}$ Signup and view all the answers

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

180° Signup and view all the answers

In terms of the CAST diagram, which trigonometric ratios are positive in Quadrant II?

$ an heta$ and $ an^{-1} heta$ Signup and view all the answers

What is the angle of elevation?

The angle formed by the line of sight to an object above the horizontal plane Signup and view all the answers

What type of triangle has all sides and angles different?

Scalene Signup and view all the answers

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

The angle of elevation from one point equals the angle of depression from the corresponding point Signup and view all the answers

What does SSS stand for in the context of triangle congruence?

Side-Side-Side Signup and view all the answers

Which condition demonstrates that two triangles are similar?

All three pairs of corresponding angles are equal Signup and view all the answers

What is a defining characteristic of a parallelogram?

Both pairs of opposite sides are parallel Signup and view all the answers

Which property is exclusive to a square compared to other quadrilaterals?

All sides are equal in length Signup and view all the answers

What is true about the interior angles of a quadrilateral?

They add up to 360° Signup and view all the answers

In a right-angled triangle, which equation reflects the Pythagorean Theorem?

b^2 = c^2 - a^2 Signup and view all the answers

Which of the following is NOT a property of a rhombus?

All angles are equal to 90° Signup and view all the answers

A trapezium is defined as having how many pairs of opposite sides that are parallel?

One pair Signup and view all the answers

What distinguishes a rectangle from other types of quadrilaterals?

It has all four angles equal to 90° Signup and view all the answers

Which quadrilateral always has at least one pair of adjacent sides equal?

Kite Signup and view all the answers

What defines a trapezium?

A quadrilateral with one pair of parallel sides. Signup and view all the answers

What does the Mid-Point Theorem state?

The line segment joining the mid-points of two sides of a triangle is parallel to the third side and half of its length. Signup and view all the answers

Which statement is true regarding the properties of the Mid-Point Theorem?

The mid-segment is parallel to the third side. Signup and view all the answers

What is the conclusion drawn when proving that MNOP is a parallelogram?

Both pairs of opposite angles of MNOP are equal. Signup and view all the answers

In analytical geometry, what is crucial when naming a quadrilateral?

The order of the points indicates how to connect them. Signup and view all the answers

What is a characteristic of a kite, based on its definition?

A kite has two pairs of adjacent sides that are equal. Signup and view all the answers

When drawing figures on the Cartesian plane, what should be avoided?

Connecting points in the incorrect order. Signup and view all the answers

How is distance between two points A(x₁, y₁) and B(x₂, y₂) typically derived?

Using the Pythagorean theorem. Signup and view all the answers

Which of the following statements is true about proving similarity in triangles?

Similarity requires proportional sides and equal angles. Signup and view all the answers

What is the definition of mean?

The sum of a set of values divided by the number of values in the set. Signup and view all the answers

How is the median determined in a data set?

By sorting the data and finding the central value. Signup and view all the answers

What describes a mode in a data set?

The value that occurs most often. Signup and view all the answers

What is an outlier?

A value that is significantly different from other values. Signup and view all the answers

What is qualitative data?

Data that cannot be expressed as numerical values. Signup and view all the answers

What is the relationship between mode and outlier?

An outlier can skew the perception of the mode. Signup and view all the answers

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

It is the average of the two central values. Signup and view all the answers

Which of the following options is classified as categorical data?

Favorite color. Signup and view all the answers

What determines if a data set has more than one mode?

If two values are equally common. Signup and view all the answers

Which statement about mean is accurate?

It is sensitive to extreme values in the data set. Signup and view all the answers

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

d = |x₁ - x₂| + |y₁ - y₂| Signup and view all the answers

How is the gradient of a line defined?

The ratio of horizontal change to vertical change. Signup and view all the answers

What is the equation of a straight line in slope-intercept form?

y = mx + b Signup and view all the answers

Which statement is true about parallel lines?

They are always the same distance apart. Signup and view all the answers

What is the mid-point formula for the coordinates M(x, y) between points A(x₁, y₁) and B(x₂, y₂)?

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

What characterizes a horizontal line?

It has a gradient of zero. Signup and view all the answers

What condition must be met for two lines to be perpendicular?

The product of their gradients must be equal to -1. Signup and view all the answers

Which type of data can be represented by numbers?

Quantitative data Signup and view all the answers

Which of the following can be a characteristic of a vertical line?

It has a gradient that is undefined. Signup and view all the answers

In the notation of lines, what does 'c' represent in the equation y = mx + c?

The y-intercept. Signup and view all the answers

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

V = l imes b imes h Signup and view all the answers

If the height of a rectangular prism is multiplied by 5, what is the new volume in relation to the original volume?

V_1 = 5V Signup and view all the answers

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

Surface area is multiplied by 25 Signup and view all the answers

When the radius of a cylinder is multiplied by a factor of k, how is the volume affected?

The volume is multiplied by k^2 Signup and view all the answers

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

A = ext{base area} + 2 imes ext{lateral surface area} Signup and view all the answers

If the height of a cylinder is multiplied by k, how does the volume change?

The volume is multiplied by k Signup and view all the answers

What occurs to the volume of a rectangular prism if all dimensions are multiplied by a factor of k?

Volume is multiplied by k^3 Signup and view all the answers

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

Surface area changes to k^2A Signup and view all the answers

What is the base shape of a triangular prism?

Triangle Signup and view all the answers

What is the surface area formula for a cylinder?

$ ext{Area} = ext{Area of base} + ext{Area of walls}$ Signup and view all the answers

To calculate the volume of a rectangular prism, which formula is used?

$ ext{Volume} = ext{length} imes ext{width} imes ext{height}$ Signup and view all the answers

What shape is the base of a right cone?

Circle Signup and view all the answers

How is the volume of a sphere calculated?

$rac{4}{3} imes ext{r}^3$ Signup and view all the answers

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

Both are multiplied by k Signup and view all the answers

What is the key characteristic of a cube in relation to a rectangular prism?

All sides are of equal length. Signup and view all the answers

Which formula represents the surface area of a square pyramid?

$ ext{Area} = b^2 + 4 imes rac{1}{2} b h_s$ Signup and view all the answers

How is the surface area of a triangular pyramid calculated?

$ ext{Area} = b^2 + 3 imes rac{1}{2} b h_s$ Signup and view all the answers

What is the definition of the first quartile (Q1)?

The 25th percentile of the data set. Signup and view all the answers

Which of the following correctly defines the interquartile range (IQR)?

The difference between the third and first quartiles. Signup and view all the answers

What does the term 'deciles' refer to?

Nine data values that divide the data set into ten equal groups. Signup and view all the answers

In a box-and-whisker plot, which feature represents the median?

The line inside the box. Signup and view all the answers

How is the semi-interquartile range defined?

Half of the interquartile range. Signup and view all the answers

What are included in the five number summary?

Minimum, maximum, Q1, Q2, Q3. Signup and view all the answers

Which statement about percentiles is true for grouped data?

Percentiles lie within a specified range in the data. Signup and view all the answers

What is a characteristic of a right prism?

It has a polygon as its base with vertical faces perpendicular to the base. Signup and view all the answers

How is the area of a rectangle calculated?

Area = base × height Signup and view all the answers

What is the area formula for a triangle?

Area = ½ × base × height Signup and view all the answers

What is the mode of a data set?

The most frequently occurring value in the data set. Signup and view all the answers

If all values in a data set occur with equal frequency, how is the data set described?

It is considered to have no mode. Signup and view all the answers

Which statement about outliers is correct?

An outlier is a value that deviates significantly from other values. Signup and view all the answers

What is the purpose of grouping continuous data into ranges?

To convert continuous data into discrete data for analysis. Signup and view all the answers

How is the mean of grouped data calculated?

By assuming values are located at the midpoints of intervals. Signup and view all the answers

What does the median group represent in grouped data?

The class interval that contains the median value. Signup and view all the answers

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

The difference between the maximum and minimum values. Signup and view all the answers

What is a percentile in a data set?

A value that divides the data into two parts. Signup and view all the answers

Which formula is used to find the rank of the pth percentile?

$ r = rac{p}{100} (n - 1) $ Signup and view all the answers

What happens to the information when data values are grouped?

Some information is lost leading to less accuracy. Signup and view all the answers

What property is true about the sides of similar triangles?

Their lengths are proportional. Signup and view all the answers

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

They are equal. Signup and view all the answers

What is the significance of the order in labeling vertices of similar triangles?

It shows which angles correspond to each other. Signup and view all the answers

Using the properties of similar triangles, if $AB = 3$, $DE = 9$, and $BC = 6$, what is the value of $EF$?

18 Signup and view all the answers

In the statement $ riangle ABC ext{ is similar to } riangle DEF $, what can be concluded about angle A?

It is equal to angle D. Signup and view all the answers

What is NOT a key ratio property of similar triangles?

$ rac{AC}{DF} = rac{BC}{EF} $ Signup and view all the answers

Which of the following ratios represents the sides of the similar triangles $ riangle ABC$, $ riangle DEF$, and $ riangle GHK$?

$ rac{AB}{BC} = rac{GH}{HK} $ Signup and view all the answers

Which trigonometric ratios are defined based on similar triangles?

Ratios that remain consistent among similar triangles. Signup and view all the answers

What condition must be met for two triangles to be considered similar?

They must have the same corresponding angles. Signup and view all the answers

In similar triangles, the ratios of their corresponding sides remain consistent regardless of what?

The size of the triangles. Signup and view all the answers

Which statement correctly describes the angle relationships in similar triangles?

Corresponding angles are equal. Signup and view all the answers

How are the sides of similar triangles related if triangles have angles of 30°, 60°, and 90°?

The sides are proportional based on angle relationships. Signup and view all the answers

What does the notation Δ ABC ∼ Δ DEF signify in terms of triangle similarity?

Triangles ABC and DEF are similar with corresponding angles equal. Signup and view all the answers

Which of the following accurately describes the significance of the order of labeling in similar triangles?

It indicates which sides are proportional. Signup and view all the answers

In the context of similar triangles, if the sides of triangles ABC and DEF are proportional, what can be concluded about their angles?

They must be equal. Signup and view all the answers

If triangle ABC is similar to triangle DEF, which of the following ratios is correct?

$rac{AB}{DE} = rac{BC}{EF}$ Signup and view all the answers

In which quadrant are only sine and cosecant positive according to the CAST diagram?

Quadrant II Signup and view all the answers

What is the value of sin 30°?

1/2 Signup and view all the answers

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

The angle of elevation from one point is equal to the angle of depression from the other point. Signup and view all the answers

What type of triangle has all sides of different lengths?

Scalene Signup and view all the answers

If a right-angled triangle has an opposite side of length 4 and an adjacent side of length 3, what is the value of tan θ?

4/3 Signup and view all the answers

In a right-angled triangle, what must be true about the sum of the interior angles?

It is always equal to 180°. Signup and view all the answers

Which trigonometric ratio is defined as the opposite side divided by the hypotenuse?

sin θ Signup and view all the answers

What does it mean for two triangles to be congruent?

They must have the same size and shape. Signup and view all the answers

For angle θ, if the cosecant value is equal to 2, what is the sin θ?

1/2 Signup and view all the answers

Which statement is true regarding the properties of isosceles triangles?

Two sides are equal in length, and the angles opposite those sides are equal. Signup and view all the answers

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

1 Signup and view all the answers

Which is the correct value of cos 60°?

1/2 Signup and view all the answers

What is the hypotenuse length of a 45°-45°-90° triangle when each leg measures 1?

√2 Signup and view all the answers

What is the relationship between angles B and α for point Q(-2, 3)?

B + α = 180° Signup and view all the answers

When solving a trigonometric equation, what is one necessary step to find the angle?

Isolate the trigonometric ratio. Signup and view all the answers

What value does tan 45° equal?

1 Signup and view all the answers

Which statement is true regarding the sine value for the angle θ in any triangle?

|sin θ| < 1 Signup and view all the answers

In the Cartesian plane, if the coordinates of point P are (2, 3), what is the tangent of the angle A formed?

1.5 Signup and view all the answers

What is the length of the hypotenuse in a 30°-60°-90° triangle when the side opposite the 60° angle is √3?

2 Signup and view all the answers

What angle corresponds to a tangent ratio of √3?

60° Signup and view all the answers

Which statement accurately describes the role of the hypotenuse in a right-angled triangle?

It is the longest side of the triangle. Signup and view all the answers

What does the mnemonic 'Soh Cah Toa' help with?

Recalling the definitions of trigonometric ratios. Signup and view all the answers

Which expression correctly represents the value of secant?

$rac{ ext{hypotenuse}}{ ext{adjacent}}$ Signup and view all the answers

Which of the following is true about the trigonometric ratios defined in a right-angled triangle?

Sine is the ratio of the opposite side to the hypotenuse. Signup and view all the answers

What is the reciprocal of the tangent function known as?

Cotangent Signup and view all the answers

In terms of relationships among trigonometric ratios, which is a true statement?

Cosine multiplied by secant equals 1. Signup and view all the answers

If a calculator needs to be set to a specific mode to find trigonometric ratios, which mode is essential?

Degree mode Signup and view all the answers

Which of the following correctly defines the relationship of sine squared to sine?

sin² $θ$ = (sin $θ$)² Signup and view all the answers

Which of the following angles can typically be calculated easily without a calculator?

30 degrees Signup and view all the answers

What defines the cosecant function in relation to sine?

It equals the reciprocal of sine. Signup and view all the answers

How are two triangles proven to be similar using corresponding sides?

By showing that the ratios of all three pairs of corresponding sides are equal. Signup and view all the answers

What is a defining characteristic of a square compared to other quadrilaterals?

All four interior angles are equal to 90° and all sides are equal in length. Signup and view all the answers

Which property is associated with all types of parallelograms?

Opposite sides are parallel and equal in length. Signup and view all the answers

What does the acronym AAA stand for in similarity rules?

Angle-Angle-Angle. Signup and view all the answers

What defines a rhombus in relation to other quadrilaterals?

All sides are equal in length and opposite angles are equal. Signup and view all the answers

In a right-angled triangle, what does the Pythagorean Theorem state?

$ a^2 + b^2 = c^2 $ where c is the longest side. Signup and view all the answers

What is a unique property of a kite compared to other quadrilaterals?

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

What condition must be met for triangles to be congruent using the SSS rule?

All three sides of one triangle are equal to all three sides of another triangle. Signup and view all the answers

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

360° Signup and view all the answers

Which statement accurately describes a trapezium?

It is defined by having only one pair of opposite sides that are parallel. Signup and view all the answers

What is the primary difference between qualitative data and quantitative data?

Qualitative data cannot be expressed in numbers, while quantitative data can. Signup and view all the answers

How is the median of a dataset determined when there is an even number of values?

It is the average of the two middle values. Signup and view all the answers

Which of the following statements accurately describes the mode of a dataset?

The mode is the value that appears most frequently in the dataset. Signup and view all the answers

What defines an outlier in a dataset?

An outlier is a value that significantly differs from the other values. Signup and view all the answers

What is the formula for calculating the mean of a dataset?

ar{x} = rac{1}{n} imes ext{sum of values} Signup and view all the answers

When sorting data to find the median, what is the first step?

Sort the data from lowest to highest value. Signup and view all the answers

How can a dataset have more than one mode?

If two or more values occur with the same highest frequency. Signup and view all the answers

What can be concluded about the relationship between the segment joining the mid-points of two sides of a triangle and the third side?

It is parallel to the third side and equal to half its length. Signup and view all the answers

In which scenario would the Mid-Point Theorem not hold true?

When the triangle is obtuse. Signup and view all the answers

Which statistical measure is determined by the position of data in a sorted list?

Median Signup and view all the answers

In a dataset where every value occurs with equal frequency, how is the mode described?

It does not exist. Signup and view all the answers

Which property is NOT true about kites?

They are a type of parallelogram. Signup and view all the answers

What is a common example of qualitative data?

Favorite movie genres. Signup and view all the answers

What is required to prove that a quadrilateral is a parallelogram based on its properties?

The diagonals must bisect each other. Signup and view all the answers

Which statement best describes the process of proving similarity in triangles?

It requires showing that corresponding side lengths are proportional. Signup and view all the answers

Which of the following is an application of the Mid-Point Theorem?

Proving segment ratios in geometric figures. Signup and view all the answers

When plot points on the Cartesian plane, which statement is essential?

Points must be connected in the order they are listed. Signup and view all the answers

When calculating distance between two points A(x₁, y₁) and B(x₂, y₂), what geometrical principle is applied?

Pythagorean Theorem. Signup and view all the answers

How is the bisector of an angle in a parallelogram characterized?

It remains parallel to the opposite side. Signup and view all the answers

How is the value of a percentile determined when the rank is not an integer?

It is interpolated between the two surrounding values. Signup and view all the answers

What values are included in the five number summary of a data set?

Minimum, Maximum, Q1, Q2, Q3 Signup and view all the answers

What is the definition of the interquartile range?

The difference between the first and third quartiles. Signup and view all the answers

How many groups does a decile divide an ordered data set into?

Ten groups Signup and view all the answers

In a box-and-whisker plot, what does the line inside the box represent?

The median value of the data set Signup and view all the answers

What does the semi-interquartile range represent?

Half of the interquartile range Signup and view all the answers

What is the primary purpose of calculating percentiles in grouped data?

To identify the ranges within which percentiles lie Signup and view all the answers

Which of the following geometric solids is defined as having perpendicular vertical faces to its base?

Right prism Signup and view all the answers

What defines the lower quartile (Q1)?

The median of the lower half of the data Signup and view all the answers

What does the interquartile range measure?

Middle fifty percent of the data Signup and view all the answers

What is the primary method for calculating the mode of a data set?

Count how many times each value appears and find the most frequent. Signup and view all the answers

Which scenario would likely result in a data set having no mode?

A set where all values are distinct. Signup and view all the answers

In a histogram, what do the heights of the rectangles represent?

The number of values that fall into each sub-range. Signup and view all the answers

What effect do outliers have on measures of dispersion, such as the range?

They can significantly distort the calculation of dispersion. Signup and view all the answers

How is the mean of grouped data typically calculated?

By using the frequency of each class interval and its midpoint. Signup and view all the answers

What defines the modal group in a data set?

The class interval that has the highest frequency of data values. Signup and view all the answers

What is the correct formula for finding the rank of the pth percentile in a dataset?

$r = rac{p}{100} (n - 1) + 1$ Signup and view all the answers

Which of the following best describes the range of a dataset?

The maximum value minus the minimum value. Signup and view all the answers

When dealing with grouped data, what loss in accuracy occurs?

Loss of specific value details but retention of overall pattern. Signup and view all the answers

What distinguishes a percentile from other measures of central tendency?

It indicates the position of data in relation to the whole set. Signup and view all the answers

What is the surface area formula for a triangular prism?

2 * Area of triangles + 3 * Area of rectangles Signup and view all the answers

How do you calculate the volume of a cylinder?

$ ext{Volume} = heta imes r^2 imes h$ Signup and view all the answers

Which of the following describes a right pyramid?

It has a polygon as its base with an apex that is perpendicular to the center of the base. Signup and view all the answers

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

It is multiplied by 125. Signup and view all the answers

What is the surface area of a right cone?

πr^2 + πrh Signup and view all the answers

How does the surface area change when one dimension of a rectangular prism is increased by a factor of k?

It is multiplied by k. Signup and view all the answers

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

Volume is multiplied by k and surface area is multiplied by k^2. Signup and view all the answers

Which formula represents the volume of a triangular pyramid?

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

Which shape is described as having the same properties in all directions?

Sphere Signup and view all the answers

If the radius of a cylinder is multiplied by a factor of k, how do the volume and surface area change?

Volume is multiplied by k^2 and surface area is multiplied by k^2. Signup and view all the answers

If one dimension of a prism is multiplied by a factor of k, how does the surface area change?

It multiplies by $k^2$. Signup and view all the answers

What is the effect on the volume when two dimensions of a rectangular prism are each multiplied by 5?

The volume increases by a factor of 25. Signup and view all the answers

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

It is multiplied by k. Signup and view all the answers

What distinguishes a cube from a rectangular prism?

All its sides are of equal length. Signup and view all the answers

What is the general effect on the surface area of a rectangular prism when all dimensions are multiplied by k?

Surface area is multiplied by k^2. Signup and view all the answers

What is the correct formula for the volume of a sphere?

$4rac{1}{3} ext{π} r^3$ Signup and view all the answers

If the dimensions of a rectangular prism are scaled by a factor of k, what is the relationship between the original volume V and the new volume V_k?

V_k = k^3V Signup and view all the answers

How is the surface area of a square pyramid calculated?

$b(b + 2h_s)$ Signup and view all the answers

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

$ ext{distance}(d) = ext{sqrt}((x₁ - x₂)^2 + (y₁ - y₂)^2)$ Signup and view all the answers

What does the gradient of a line represent?

The slope of the line measured by vertical change over horizontal change Signup and view all the answers

In the context of straight lines, what represents the y-intercept in the equation $y = mx + c$?

The point where the line intersects the y-axis Signup and view all the answers

Which condition must be satisfied for two lines to be classified as perpendicular?

The product of their gradients equals -1 Signup and view all the answers

What is the gradient of a horizontal line?

0 Signup and view all the answers

How can the coordinates of the mid-point M(x, y) be calculated between two points A(x₁, y₁) and B(x₂, y₂)?

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

What type of data is classified as quantitative?

Data that can be counted or measured numerically Signup and view all the answers

Which statement about collinear points is true?

Collinear points lie on the same straight line Signup and view all the answers

What is the general equation used to express a straight line in standard form?

$y - y₁ = m(x - x₁)$ Signup and view all the answers

What type of quantitative data can be represented by integers?

Discrete data Signup and view all the answers

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

√3 Signup and view all the answers

What is the cosine of 45°?

√2/2 Signup and view all the answers

Which angle corresponds to a sine value of √3/2?

60° Signup and view all the answers

If you know the opposite side measures 4 and the adjacent side measures 3 in a right triangle, what is the value of tan A?

4/3 Signup and view all the answers

What is the length of the hypotenuse in a 45°-45°-90° triangle if the length of each leg is 1?

√2 Signup and view all the answers

How would you find the angle associated with a tangent ratio of 3/2?

Use tangent inverse Signup and view all the answers

For the point P(2, 3) in the Cartesian plane, which expression represents tan A?

3/2 Signup and view all the answers

What will happen if you try to compute sin θ with a value greater than 1?

It will have no solution. Signup and view all the answers

Using the coordinates (x,y), what does the radius 'r' represent in relation to the origin?

The distance from the point to the origin Signup and view all the answers

What is the measure of angle B for point Q(-2, 3) given that tan α = 3/2?

123.7° Signup and view all the answers

If the opposite side of angle theta measures 4 units and the hypotenuse measures 5 units, what is the value of sin theta?

0.8 Signup and view all the answers

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

Cosine Signup and view all the answers

What is the reciprocal of the tangent function?

Cotangent Signup and view all the answers

If sin theta equals 0.5, which of the following is the angle theta?

30° Signup and view all the answers

Which relationship correctly reflects the reciprocal nature of sine and cosecant?

sin theta × cosec theta = 1 Signup and view all the answers

In which scenario would you calculate the secant of an angle?

To find the ratio of hypotenuse to adjacent Signup and view all the answers

What value does tan of 45° equal?

1 Signup and view all the answers

When angle theta approaches 90°, which of the following statements is true about tan theta?

tan theta approaches infinity Signup and view all the answers

For which of the following angles would you NOT need a calculator to find the sine value?

45° Signup and view all the answers

In which quadrant of the Cartesian plane does an heta become positive?

Quadrant III Signup and view all the answers

Which of the following correctly expresses the relationship between sine and cosecant?

<pre><code>ext{cosecant} = rac{r}{y} </code></pre> Signup and view all the answers

What is the sine value for a 60° angle according to special angles?

rac{ ext{ ext{√3}}}{2} Signup and view all the answers

If the angle of elevation is 45°, what can be said about the relationship between opposite and adjacent sides in a right triangle?

The opposite and adjacent sides are equal. Signup and view all the answers

What property defines an isosceles triangle based on its sides?

Two sides are of equal length. Signup and view all the answers

In which quadrant are both sine and cosine negative?

Quadrant III Signup and view all the answers

How can two triangles be classified as congruent?

They have equal corresponding angles and sides. Signup and view all the answers

What is the sine of an angle if the opposite side is 4 and the hypotenuse is 5?

rac{4}{5} Signup and view all the answers

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

180° Signup and view all the answers

If an angle of depression is formed, what can be inferred about the angle of elevation from the corresponding point?

It is equal to the angle of depression. Signup and view all the answers

What characteristic defines a trapezium?

One pair of parallel sides Signup and view all the answers

What does the converse of the Mid-Point Theorem state?

If a line is drawn parallel to one side, it will bisect the other side. Signup and view all the answers

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

It is parallel to the third side. Signup and view all the answers

In quadrilateral ABCD with vertices A(1, 1), B(3, 1), C(3, 3), and D(1, 3), which statement is true?

The figure is closed and represents a rectangle. Signup and view all the answers

What conclusion can be drawn about quadrilateral MNOP when both pairs of opposite angles are equal?

MNOP is a parallelogram. Signup and view all the answers

When applying the Mid-Point Theorem, what is the length relationship of DE to the length of BC?

DE is half the length of BC. Signup and view all the answers

In trying to prove quadrilateral MNOP is a parallelogram, which step is essential in proving triangle congruence?

Demonstrating two triangles are congruent by AAS. Signup and view all the answers

What is a key application of the Mid-Point Theorem in geometric proofs?

Proving parallelism in geometric figures. Signup and view all the answers

Which statement correctly describes a kite in relation to its sides?

It has two pairs of adjacent sides equal. Signup and view all the answers

Which of the following statements about triangle congruence is true?

Two triangles are congruent if all three sides of one triangle are equal to the three sides of the other triangle. Signup and view all the answers

Which condition does NOT determine the similarity of two triangles?

If two triangles have two equal angles and an unequal side. Signup and view all the answers

What is a defining property of a rhombus?

All sides are equal in length. Signup and view all the answers

Which statement accurately describes the relationship between different types of quadrilaterals?

A square is a type of rhombus and also a type of rectangle. Signup and view all the answers

In a right-angled triangle, which equation represents the Pythagorean Theorem?

$b^2 = a^2 + c^2$ Signup and view all the answers

What unique property does a square have compared to other quadrilaterals?

All angles are equal to 90° and all sides are equal. Signup and view all the answers

Which property is exclusive to a kite among quadrilaterals?

It has one pair of opposite angles equal. Signup and view all the answers

What is a characteristic of a trapezium?

It has at least one pair of opposite sides parallel. Signup and view all the answers

What is true about the angles in a quadrilateral?

The sum of the interior angles is 360°. Signup and view all the answers

Which of the following describes a property of a rectangle that is not true for all parallelograms?

All angles are equal. Signup and view all the answers

What property must be true for triangles to be classified as similar?

Their corresponding sides must be proportional. Signup and view all the answers

When comparing two similar triangles, which of the following statements is correct?

The ratios of their heights are equal to the ratios of their corresponding bases. Signup and view all the answers

If triangles ΔABC and ΔDEF are similar, what can be determined about the angles?

Angle B is equal to Angle E. Signup and view all the answers

Which of the following ratios related to similar triangles is incorrect?

$rac{AC}{DF} = rac{AB + BC}{DE + EF}$ Signup and view all the answers

In the context of similar triangles, what does the notation ΔABC ∼ ΔDEF indicate?

They have equal angles and proportional sides. Signup and view all the answers

What can be concluded about the ratio of sides in a triangle with angles of 30°, 60°, and 90°?

The side opposite the 30° angle is half the length of the hypotenuse. Signup and view all the answers

How is the distance between two points calculated?

Using the formula d = \sqrt{(x₁ - x₂)² + (y₁ - y₂)²} Signup and view all the answers

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

It defines the orientation of the triangles. Signup and view all the answers

What is the formula for calculating the gradient of a line?

m = \frac{y₂ - y₁}{x₂ - x₁} Signup and view all the answers

In similar triangles, if the corresponding angles are equal, what can be inferred about the side lengths?

Their lengths can vary but maintain specific ratios. Signup and view all the answers

What characterizes a horizontal line in terms of gradient?

It has a gradient of 0. Signup and view all the answers

How is the mid-point of a line segment defined?

M(x, y) = \left( \frac{x₁ + x₂}{2}, \frac{y₁ + y₂}{2} ight) Signup and view all the answers

What must be true for two lines to be considered parallel?

They must have equal gradients. Signup and view all the answers

What is true about the gradients of perpendicular lines?

Their gradients multiply to equal -1. Signup and view all the answers

Which is the standard form of the equation of a straight line?

y = mx + b Signup and view all the answers

What does collinear mean in relation to points?

Points that lie on the same line. Signup and view all the answers

Which of the following statements about quantitative data is correct?

It can be expressed numerically. Signup and view all the answers

Which of the following explains why a vertical line has an undefined gradient?

There is no horizontal change in x-values. Signup and view all the answers

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

$ar{x} = ext{sum of all values} / n$ Signup and view all the answers

What defines the mode in a data set?

The value that occurs most frequently Signup and view all the answers

In how many ways can a median be determined from a data set with an odd number of values?

By selecting the middle value directly Signup and view all the answers

What is an outlier in a data set?

A value that is significantly higher or lower than other values Signup and view all the answers

Which of the following statements about the median is correct?

It is the middle value when data is sorted in order Signup and view all the answers

Which type of data consists of a limited number of categories?

Qualitative data Signup and view all the answers

If a data set has two values appearing most frequently, what is it called?

Bimodal Signup and view all the answers

Which of these is NOT a characteristic of the median?

It can be influenced by extreme values Signup and view all the answers

When trying to find a mode, what must be counted?

The amount of times each value appears Signup and view all the answers

Which type of data involves numeric representations such as height or mass?

Continuous data Signup and view all the answers

What is the mode of a data set?

The value that occurs most frequently. Signup and view all the answers

Which statement best describes an outlier?

A value significantly different from other values. Signup and view all the answers

How does the process of grouping continuous data change the nature of the data?

It turns continuous data into discrete data. Signup and view all the answers

What is the purpose of a histogram?

To visualize the distribution of grouped data. Signup and view all the answers

What does the term 'modal group' refer to?

The group that has the highest frequency of data values. Signup and view all the answers

In data analysis, how is the range defined?

The difference between the maximum and minimum values. Signup and view all the answers

What is the definition of a percentile?

A value that divides the data set into two parts such that a specific percent is lower. Signup and view all the answers

What is a key limitation of calculating the mode for continuous data sets?

Any particular value in a continuous set rarely repeats. Signup and view all the answers

Which formula is used to find the mean of grouped data?

$ar{x} = rac{ extstyle oldsymbol{ ext{f}}_i oldsymbol{ ext{x}}_i}{ ext{sum of } oldsymbol{ ext{f}}_i}$ Signup and view all the answers

To find the rank of the $p$th percentile, which formula is used?

$r = rac{p}{100} (n - 1) + 1$ Signup and view all the answers

What happens to the volume when only one dimension of a rectangular prism is multiplied by 5?

It is multiplied by 5 Signup and view all the answers

When all dimensions of a rectangular prism are multiplied by a constant k, how is the surface area affected?

It is multiplied by k^2 Signup and view all the answers

If the height of a cylinder is increased by a factor of k, what is the effect on the cylinder's volume?

The volume is multiplied by k Signup and view all the answers

Which equation correctly describes how to find the volume of a cylinder when the radius is multiplied by k?

$V_k = k^2 au r^2 h$ Signup and view all the answers

How does the surface area of a cylinder change if the radius is multiplied by k?

It is multiplied by k^2 Signup and view all the answers

What factor does the volume increase by when two dimensions of a rectangular prism are multiplied by 5?

25 Signup and view all the answers

If the surface area of a rectangular prism changes to 25A after all dimensions are multiplied by a factor of 5, what does A represent?

The original surface area Signup and view all the answers

When only the height of a cylinder is multiplied by k, how does the surface area change?

It is multiplied by k Signup and view all the answers

How is the value of the 25th percentile, or Q1, determined in an ordered data set?

It divides the data set into four equal parts. Signup and view all the answers

What does the interquartile range (IQR) measure?

The spread of the middle half of the data set. Signup and view all the answers

When calculating percentiles for grouped data, what is a significant challenge?

Percentiles can fall within a range rather than at a specific value. Signup and view all the answers

What does the five number summary include?

Minimum, maximum, and the three quartiles. Signup and view all the answers

What primarily distinguishes a right prism from other prisms?

The faces are perpendicular to the base. Signup and view all the answers

In terms of visualization, what do box-and-whisker plots aim to represent?

The spread and central tendency of the data. Signup and view all the answers

How is the semi-interquartile range defined?

It is half of the interquartile range. Signup and view all the answers

What is a defining property of quartiles in a data set?

They divide the data into four equal parts. Signup and view all the answers

Which formula correctly calculates the area of a circle?

Area = πr² Signup and view all the answers

What does the height refer to in the context of area formulas for polygons?

The distance from the baseline to the top vertex. Signup and view all the answers

What describes the surface area of a cube?

The total area of six identical squares Signup and view all the answers

Which formula represents the volume of a triangular prism?

$rac{1}{2} imes ext{base} imes ext{height of triangle} imes ext{height of prism}$ Signup and view all the answers

What distinguishes a sphere from other geometric solids?

It is perfectly round and looks the same from any direction. Signup and view all the answers

How does the volume of a right cone correlate to its dimensions?

It is calculated as $rac{1}{3} imes ext{Area of base} imes ext{Height of cone}$ Signup and view all the answers

Which statement is correct regarding the surface area of a cylinder?

It consists of two circles and a rectangle. Signup and view all the answers

When dimensions of a prism are multiplied by a factor of k, what happens to the surface area?

It increases by a factor of k squared. Signup and view all the answers

What is the volume formula for a sphere?

$rac{4}{3} imes ext{pi} imes r^3$ Signup and view all the answers

How is the surface area of a square pyramid calculated?

$b^2 + 4 imes rac{1}{2} b h_s$ Signup and view all the answers

What does multiplying a dimension of a solid by a constant k do to its volume?

It increases the volume by a factor of k cubed. Signup and view all the answers

What is the value of tan 60°?

√3 Signup and view all the answers

For a right triangle with an opposite side of 4 and an adjacent side of 3, which trigonometric function would yield the angle closest to 53°?

tan Signup and view all the answers

If the sine of an angle θ is equal to 0.5, what is the principal value of θ in degrees?

30° Signup and view all the answers

Given the angles A and B, with A = 45°, what is the value of angle B if tan A = 1?

45° Signup and view all the answers

In a 30°-60°-90° triangle, if the hypotenuse is 10, what is the length of the side opposite the 30° angle?

5 Signup and view all the answers

What is the relationship between angles A and B in the context of point Q(-2, 3) when defined through the tangent ratio?

A + B = 180° Signup and view all the answers

Which of the following statements is false for the tangent function in a right triangle?

tan θ is always positive in Quadrant II Signup and view all the answers

Using inverse functions, which operation would be performed to find an angle given tan θ = 2?

tan^-1(2) Signup and view all the answers

In a triangle where the lengths of the sides are known, which method can be used to find the angle opposite to a given side?

Law of Sines Signup and view all the answers

What is the maximum value that the cosine function can take for any angle?

1 Signup and view all the answers

What can be concluded about the sides of similar triangles?

The ratios of corresponding sides remain constant. Signup and view all the answers

Which set of angles is characteristic of a type of similar triangles used in defining trigonometric ratios?

30°, 60°, 90° Signup and view all the answers

In the context of similarity, what does the notation ΔABC ∼ ΔDEF imply?

The corresponding angles of the triangles are equal. Signup and view all the answers

How are the ratios of similar triangles related to their corresponding angles?

Ratios remain constant as long as the triangle angles are consistent. Signup and view all the answers

Which of the following represents a true property of similar triangles?

The ratio of their areas is proportional to the square of their sides' ratios. Signup and view all the answers

What is essential in determining the labeling of similar triangles?

The order of the vertices. Signup and view all the answers

Which statement is true about the proportionality of sides in triangle similarity?

The ratios of the sides are equal for any triangle configuration. Signup and view all the answers

If triangles have angles measuring 30°, 90°, and 60°, what can be determined about their side lengths?

Their side ratios will be 1:2:√3. Signup and view all the answers

In which quadrant is the cosecant of an angle positive?

Quadrant I Signup and view all the answers

What is the value of tan 30° expressed as a fraction?

$rac{1}{ ext{√3}}$ Signup and view all the answers

If the angle of depression from a point is 45°, what is the corresponding angle of elevation?

45° Signup and view all the answers

What is the sine of 60° in its simplest radical form?

$rac{ ext{√3}}{2}$ Signup and view all the answers

Which of the following statements about triangles is true regarding isosceles triangles?

They have two sides of equal length. Signup and view all the answers

The exterior angle of a triangle is equal to which of the following?

The sum of the two adjacent interior angles Signup and view all the answers

If the hypotenuse of a right-angled triangle is 10 units and one side is 6 units, what is the length of the other side?

8 units Signup and view all the answers

Which of these describes an acute triangle?

All angles are less than 90° Signup and view all the answers

Which condition characterizes the RHS congruency rule for triangles?

Equal hypotenuse and one leg of a right triangle Signup and view all the answers

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

180° Signup and view all the answers

What is the cosecant of angle theta in a right triangle, given that the opposite side has a length of 4 and the hypotenuse has a length of 5?

$\frac{5}{4}$ Signup and view all the answers

Which expression correctly represents the relationship between sine and cosecant?

$\sin \theta \times \text{cosec } \theta = 1$ Signup and view all the answers

What is the value of cosine for angle theta if the adjacent side measures 3 and the hypotenuse measures 6?

$\frac{1}{2}$ Signup and view all the answers

For a right triangle with an angle of 60 degrees, what is the tangent ratio?

$\sqrt{3}$ Signup and view all the answers

Which of the following defines cotangent in terms of angle theta?

$\frac{ ext{adjacent}}{ ext{opposite}}$ Signup and view all the answers

If sin theta equals $\frac{3}{5}$, what is the value of cosec theta?

$\frac{5}{3}$ Signup and view all the answers

How do the sine and cosecant ratios relate mathematically for any angle theta?

$\sin \theta \times ext{cosec } \theta = 1$ Signup and view all the answers

If the angle theta has a tangent ratio of 2, which of the following can be concluded about the triangle's sides?

The opposite side is twice the length of the adjacent side. Signup and view all the answers

In a right-angled triangle, if angle theta is 30 degrees, what is the value of sin theta?

$\frac{1}{2}$ Signup and view all the answers

Which statement is true regarding the tangent function for an angle of 45 degrees?

tan 45° is equal to 1. Signup and view all the answers

What must be true for two triangles to be congruent based on the SSS congruence criterion?

All three sides of one triangle are equal to the corresponding sides of the other. Signup and view all the answers

Which of these properties is unique to a rhombus compared to other quadrilaterals?

All sides are equal in length. Signup and view all the answers

What is the primary condition for two triangles to be considered similar under the SSS similarity criterion?

The corresponding sides must be proportional. Signup and view all the answers

Which statement correctly describes the relationship between squares and other quadrilaterals?

A square is a type of rectangle and also a type of rhombus. Signup and view all the answers

What can be concluded from the theorem of Pythagoras regarding a triangle with sides a, b, and hypotenuse c?

The triangle must have at least one angle that measures 90°. Signup and view all the answers

Which statement regarding a kite is true?

The diagonal connecting equal sides bisects the other diagonal. Signup and view all the answers

For a quadrilateral to be classified as a trapezium, which property must it have?

Only one pair of opposite sides is parallel. Signup and view all the answers

Which property is NOT true for rectangles?

All sides are of equal length. Signup and view all the answers

What defines the angle relationship in similar triangles based on the AAA similarity criterion?

All three pairs of corresponding angles must be equal. Signup and view all the answers

Which characteristic defines a parallelogram?

Both pairs of opposite sides are equal and parallel. Signup and view all the answers

What specific property does the Mid-Point Theorem guarantee about the line connecting the mid-points of two sides of a triangle?

It is parallel to the third side and is equal to half its length. Signup and view all the answers

Which characteristic of a kite distinguishes it from other quadrilaterals?

Adjacent sides are equal in length. Signup and view all the answers

When applying the Mid-Point Theorem in geometric proofs, how is it utilized regarding parallelograms?

To establish that opposite sides are equal. Signup and view all the answers

In a scalene triangle, if the mid-points of two sides are connected and the third side is known to be $BC$, what conclusion can be drawn about the segment connecting the midpoints?

It is half the length of $BC$ and parallel to it. Signup and view all the answers

How does the converse of the Mid-Point Theorem relate to the sides of a triangle?

If a line is drawn parallel to one side from the midpoint of another, it will bisect the remaining side. Signup and view all the answers

What essential property applies to the diagonals of a parallelogram formed from the angles and sides of another parallelogram?

The diagonals bisect each other only if the angles are equal. Signup and view all the answers

How is analytical geometry used in relation to drawing figures on the Cartesian plane?

It provides a method to connect points based on a specific order. Signup and view all the answers

In the context of proving the properties of quadrilaterals, what role does the bisector of an angle play?

It aids in establishing congruence between triangles formed. Signup and view all the answers

When deriving the distance formula for points on a Cartesian plane, which theorem is primarily referenced?

The Pythagorean Theorem. Signup and view all the answers

Which aspect of a trapezium is critical for identifying its classification in relation to other quadrilaterals?

Only one pair of sides is parallel while the other pair is not. Signup and view all the answers

What can be concluded about a data set when all values occur with equal frequency?

It has no mode. Signup and view all the answers

When calculating the mean of grouped data, what assumption is made regarding the individual data values within a class interval?

They are averaged to the midpoint of the interval. Signup and view all the answers

What is a characteristic of an outlier in a data set?

It lies significantly outside the range of other values. Signup and view all the answers

How does the range of a data set behave when outliers are present?

It is significantly affected. Signup and view all the answers

Which statement best describes the role of percentiles in a data set?

They indicate the position of a value in relation to the entire dataset. Signup and view all the answers

When grouping continuous data into class intervals, what is a requirement for the sub-ranges?

They must cover the entire dataset without any gaps. Signup and view all the answers

What is the formula for calculating the rank of the $p$th percentile in an ordered dataset?

$r = rac{p}{100} (n - 1) + 1$ Signup and view all the answers

Which group best represents the modal group in a given data set?

The group that has the highest number of data values. Signup and view all the answers

How is data typically visualized when dealing with grouped continuous data?

As a histogram. Signup and view all the answers

What is the primary purpose of the five number summary in data analysis?

To provide a concise numerical representation of the data. Signup and view all the answers

What happens to the volume of a rectangular prism when all its dimensions are multiplied by 3?

The volume is multiplied by 27. Signup and view all the answers

How do you compute the interquartile range (IQR) from a data set?

Subtract the first quartile (Q1) from the third quartile (Q3). Signup and view all the answers

In the context of grouped data, how is a percentile typically determined?

By identifying the range within which the rank for that percentile lies. Signup and view all the answers

If the height of a cylinder is doubled, how is the surface area affected?

The surface area is doubled. Signup and view all the answers

When two dimensions of a rectangular prism are multiplied by 2, what is the relationship between the new and original surface areas?

The surface area is multiplied by 4. Signup and view all the answers

Which statement correctly defines a right prism?

A solid where the base and top are congruent polygons with parallel vertical sides. Signup and view all the answers

What is the significance of the quartiles in a statistical data set?

They divide the data into equal parts, allowing insights into data distribution. Signup and view all the answers

For a cylinder, what happens to the volume when the radius is halved?

The volume is reduced to a quarter. Signup and view all the answers

What does the semi-interquartile range represent?

Half of the interquartile range, indicating dispersion of the middle half of the data. Signup and view all the answers

What is the formula for the new surface area of a rectangular prism if two dimensions are multiplied by 5?

$25A$ Signup and view all the answers

When one dimension of a cylinder is multiplied by 3, what factor does the volume increase by?

The volume increases by a factor of 3. Signup and view all the answers

In a box-and-whisker plot, what do the whiskers represent?

The minimum and maximum values of the dataset. Signup and view all the answers

Which of the following best describes the relationship between percentiles and quartiles?

Quartiles are a specific type of percentile that divides data into four parts. Signup and view all the answers

If the volume of a cylinder is calculated using the formula $V = ext{π}r^2h$, what happens to the volume if the radius is multiplied by 4?

The volume is multiplied by 16. Signup and view all the answers

If the volume of a rectangular prism is initially $V$, what will be the new surface area when all three dimensions are multiplied by 2?

The new surface area will be $4A$. Signup and view all the answers

What distinguishes the deciles from quartiles in data analysis?

Deciles involve nine divisions while quartiles involve three, leading to more detailed insights. Signup and view all the answers

What is the main characteristic of continuous data?

It can take any value within a given range. Signup and view all the answers

How is the mode of a dataset determined?

By counting the frequency of each unique value. Signup and view all the answers

When determining the median of a data set with an even number of values, what step must be taken?

Calculate the average of the two central values. Signup and view all the answers

Which statement best defines an outlier in a dataset?

A value that lies significantly outside the overall range. Signup and view all the answers

What symbol denotes the mean of a set of values?

𝑥̄ Signup and view all the answers

Which type of data is described as non-numerical and includes preferences or categories?

Qualitative Data Signup and view all the answers

If a dataset has values of {2, 4, 4, 6, 7}, what is the median?

4 Signup and view all the answers

What is the relationship between the number of modes in a dataset and the frequency of values?

It can be one, more than one, or none at all. Signup and view all the answers

In quantitative analysis, what does 'mean' imply about the dataset?

It is always affected by outliers. Signup and view all the answers

In the context of measures of central tendency, which aspect distinctly separates the median from the mean?

The median does not consider extreme values in its calculation. Signup and view all the answers

What does the formula for gradient represent in the context of two points on a line?

The ratio of vertical change to horizontal change between two points Signup and view all the answers

Which statement accurately describes horizontal and vertical lines in terms of their gradients?

Horizontal lines have a gradient of zero, while vertical lines have an undefined gradient Signup and view all the answers

How is the distance between two points calculated using their coordinates?

By taking the square root of the sum of the squares of the differences in x and y coordinates Signup and view all the answers

What relationship holds true for the product of gradients of lines that are perpendicular to each other?

Their product equals negative one Signup and view all the answers

In the equation of a straight line, what does the term 'c' represent in standard form?

The y-coordinate where the line crosses the x-axis Signup and view all the answers

When applying the mid-point formula for a line segment between two points, what does the resulting point represent?

The average x and y coordinates of the two points Signup and view all the answers

Which of the following statements about collinear points is true?

A straight line can pass through any two points that are collinear Signup and view all the answers

What best defines quantitative data in the context of types of data?

Data that can be expressed in numerical form Signup and view all the answers

What does the distance formula calculate between any two points in the coordinate plane?

The euclidean distance which measures the straight line between the points Signup and view all the answers

What is the primary characteristic that distinguishes a cube from a rectangular prism?

A cube has all sides of equal length while a rectangular prism can have unequal sides. Signup and view all the answers

To find the volume of a triangular prism, which formula should be used?

$rac{1}{2} imes base imes height of triangle imes height of prism$ Signup and view all the answers

What is included in the surface area calculation of a cylinder?

Two circles and a rectangle whose length equals the circumference of the circles. Signup and view all the answers

Which formula accurately represents the surface area of a square pyramid?

$b^2 + 4 imes rac{1}{2} b h_s$ Signup and view all the answers

What defines the volume of a cone?

Half the volume of a cylinder with the same base and height. Signup and view all the answers

When dimensions of a prism are multiplied by a factor of $k$, how does the surface area change?

It multiplies by the factor $k^2$. Signup and view all the answers

Which of the following solids has a volume formula that includes $rac{4}{3} imes ext{pi} imes r^3$?

Sphere Signup and view all the answers

For a triangular pyramid, the correct formula for volume is?

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

Which statement correctly describes the apex of a pyramid?

It is the highest point, where all triangular faces meet. Signup and view all the answers

The area of which shape is NOT included when calculating the total surface area of a triangle prism?

Orientation of the prism's height. Signup and view all the answers

Gr 10 Math Nov P2 Mix

Questions and Answers

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

Which mnemonic can help remember the trigonometric ratios for sine, cosine, and tangent?

What is the definition of cosecant for angle theta?

Which relationship correctly represents the tangent of angle theta?

What is the reciprocal of cosine for angle theta called?

What condition is necessary to use trigonometric ratios in a triangle?

Which of the following statements about special angles is true?

What is the value of the reciprocal of sine multiplied by sine?

If a calculator is needed to find the values of sine for most angles, what must the calculator be set to?

Which ratio defines cotangent in relation to angle theta?

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

Which of the following ratios corresponds to sin 45°?

If the length of the opposite side is 3 and the adjacent side is 2, what is tan A?

What is the angle associated with a cosine ratio of 1/2?

Which of the following values is possible for the sine of an angle?

In a 45°-45°-90° triangle, what is the length of the opposite side if the hypotenuse is √2?

What angle is formed if the tangent ratio is 56.3°?

If a circle is centered at the origin and passes through point P(2, 3), what is the radius of the circle?

Which trigonometric function would be used to find an angle if the sine value is known?

For a point Q(-2, 3), what is the relationship between angles B and α based on their definitions?

In which quadrant are all trigonometric ratios positive?

What is the value of $ an 90^ heta$?

Which of the following represents the sine ratio in terms of a right triangle's sides?

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

In terms of the CAST diagram, which trigonometric ratios are positive in Quadrant II?

What is the angle of elevation?

What type of triangle has all sides and angles different?

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

What does SSS stand for in the context of triangle congruence?

Which condition demonstrates that two triangles are similar?

What is a defining characteristic of a parallelogram?

Which property is exclusive to a square compared to other quadrilaterals?

What is true about the interior angles of a quadrilateral?

In a right-angled triangle, which equation reflects the Pythagorean Theorem?

Which of the following is NOT a property of a rhombus?

A trapezium is defined as having how many pairs of opposite sides that are parallel?

What distinguishes a rectangle from other types of quadrilaterals?

Which quadrilateral always has at least one pair of adjacent sides equal?

What defines a trapezium?

What does the Mid-Point Theorem state?

Which statement is true regarding the properties of the Mid-Point Theorem?

What is the conclusion drawn when proving that MNOP is a parallelogram?

In analytical geometry, what is crucial when naming a quadrilateral?

What is a characteristic of a kite, based on its definition?

When drawing figures on the Cartesian plane, what should be avoided?

How is distance between two points A(x₁, y₁) and B(x₂, y₂) typically derived?

Which of the following statements is true about proving similarity in triangles?

What is the definition of mean?

How is the median determined in a data set?

What describes a mode in a data set?

What is an outlier?

What is qualitative data?

What is the relationship between mode and outlier?

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

Which of the following options is classified as categorical data?

What determines if a data set has more than one mode?

Which statement about mean is accurate?

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

How is the gradient of a line defined?

What is the equation of a straight line in slope-intercept form?

Which statement is true about parallel lines?

What is the mid-point formula for the coordinates M(x, y) between points A(x₁, y₁) and B(x₂, y₂)?

What characterizes a horizontal line?

What condition must be met for two lines to be perpendicular?

Which type of data can be represented by numbers?

Which of the following can be a characteristic of a vertical line?

In the notation of lines, what does 'c' represent in the equation y = mx + c?

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

If the height of a rectangular prism is multiplied by 5, what is the new volume in relation to the original volume?

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

When the radius of a cylinder is multiplied by a factor of k, how is the volume affected?

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

If the height of a cylinder is multiplied by k, how does the volume change?

What occurs to the volume of a rectangular prism if all dimensions are multiplied by a factor of k?

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

What is the base shape of a triangular prism?

What is the surface area formula for a cylinder?

To calculate the volume of a rectangular prism, which formula is used?