Gr 10 Math Term 2 Test

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What does the sign of the coefficient 'a' indicate in a quadratic function?

The position of the x-intercept

The direction and shape of the graph (correct)

The steepness of the graph

The vertical shift of the graph

What is the effect of a positive value for 'q' in the equation of a parabola?

It increases the x-intercept

It shifts the entire graph vertically upwards (correct)

It stretches the graph horizontally

It reflects the graph over the x-axis

How do you calculate the x-intercept of a function of the form $y = ax^2 + q$?

Use the value of 'q' directly

Set $y = 0$ and solve for $x$ (correct)

Identify the maximum point on the graph

Set $x = 0$ and solve for $y$

In the equation $y = mx + c$, what does 'm' represent?

The slope of the line Signup and view all the answers

What describes the turning point of a parabola when $a < 0$?

It is the highest point on the graph Signup and view all the answers

Which of the following correctly states the domain of the function $y = ax^2 + q$?

${x : x \in \mathbb{R}}$ Signup and view all the answers

What is the range of a quadratic function $y = ax^2 + q$ when $a > 0$?

[q; \infty)$ Signup and view all the answers

How can you determine the y-intercept of the quadratic function $y = ax^2 + q$?

Evaluate the function at $x = 0$ Signup and view all the answers

Which statement is true regarding the axis of symmetry for a quadratic function?

It is always at $x = 0$ Signup and view all the answers

What happens to the graph as 'a' approaches zero but remains positive, $0 < a < 1$?

The graph widens Signup and view all the answers

What is the domain of the function $y = \frac{a}{x} + q$?

{x : x \in \mathbb{R}, x \neq 0} Signup and view all the answers

What determines the direction of a parabola?

The sign of coefficient $a$ Signup and view all the answers

What is the range of the function $y = \frac{a}{x} + q$ when $q < 0$?

{y : y \in \mathbb{R}, y \neq q} Signup and view all the answers

What effect does the parameter $q$ have on the graph of $y = \frac{a}{x} + q$?

It shifts the graph vertically. Signup and view all the answers

How can you determine the value of $q$ for a parabola?

By using the y-intercept point Signup and view all the answers

What is the first step in determining the equation of a hyperbola?

Examine the quadrants where the curves lie to find $a$ Signup and view all the answers

How do you find the x-intercept of the function $y = \frac{a}{x} + q$?

Set $y = 0$. Signup and view all the answers

What affects the amplitude of trigonometric functions like sine and cosine?

The coefficient $a$ Signup and view all the answers

Which of the following describe the asymptotes of $y = \frac{a}{x} + q$?

Horizontal asymptote is $y = q$, vertical asymptote is $x = 0$. Signup and view all the answers

What method is used to find points of intersection between two graphs?

Equate the expressions of the two graphs Signup and view all the answers

What is the y-intercept of the function $y = \frac{a}{x} + q$?

There is no y-intercept. Signup and view all the answers

For the function $y = b^x$ with $a < 0$, what can be said about its range?

The range is $ ext{all values less than } q$. Signup and view all the answers

In terms of triangle classification, which of the following describes a triangle with all sides of different lengths?

Scalene Signup and view all the answers

What determines the direction in which the graph of $y = ab^x + q$ curves?

The sign of $a$. Signup and view all the answers

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

180° Signup and view all the answers

Which statement correctly describes the relationship between exterior and interior angles of a triangle?

An exterior angle equals the sum of the two opposite interior angles Signup and view all the answers

Which lines represent the axes of symmetry for the function $y = \frac{a}{x} + q$?

$y = x + q$ and $y = -x + q$. Signup and view all the answers

What determines the vertical shift of the graph of a hyperbola?

The coefficient $q$ in the equation Signup and view all the answers

What is the range of an exponential function $y = ab^x + q$ if $a > 0$?

{f(x) : f(x) > q} Signup and view all the answers

What happens to the graph of a function when the gradient, represented by $m$, increases?

The graph slopes upwards more steeply. Signup and view all the answers

Which of these characteristics does NOT relate to parabolas?

Determining the amplitude Signup and view all the answers

If $c < 0$ in the equation $y = mx + c$, how will the graph shift vertically?

It shifts vertically downwards. Signup and view all the answers

What is the effect of a negative gradient ($m < 0$) on the graph?

The graph slopes downwards from left to right. Signup and view all the answers

Which statement is true about the intercepts of the function $y = mx + c$?

The graph does not have an x-intercept if $m = 0$. Signup and view all the answers

Which of the following describes the domain of the function $f(x) = mx + c$?

All real numbers. Signup and view all the answers

If $m = 0$ in the equation $y = mx + c$, what can be said about the graph?

The graph is a horizontal line. Signup and view all the answers

What will happen to the y-intercept if $c$ increases?

It will move upwards on the graph. Signup and view all the answers

How is the x-intercept determined for the function $y = mx + c$?

By setting $y = mx + c$ equal to 0. Signup and view all the answers

What does the value of $b$ in the function $y = ab^x + q$ determine when $b > 1$?

The rate of growth Signup and view all the answers

Which point represents the maximum turning point of the sine function $y = a ext{sin} heta + q$ when $a > 0$?

(90°, 1) Signup and view all the answers

For the cosine function $y = a ext{cos} heta + q$, what happens if $|a| < 1$?

The function has a vertical compression Signup and view all the answers

What is the range of the function $y = a ext{sin} heta + q$ when $a < 0$?

[q - |a|, q] Signup and view all the answers

Which of the following characteristics is NOT true for the tangent function $y = a ext{tan} heta + q$?

The domain includes all angles between $0°$ and $360°$ Signup and view all the answers

Which characteristic of the sine and cosine functions is TRUE?

Both functions can be shifted to overlap each other Signup and view all the answers

What effect does a positive $q$ value have on the graph of $y = a ext{sin} heta + q$?

It translates the graph vertically upwards Signup and view all the answers

If the value of $a$ is negative in the function $y = a ext{tan} heta + q$, what is the impact on the graph?

The entire graph is reflected about the x-axis Signup and view all the answers

Which of the following statements about the y-intercept of the cosine function $y = a ext{cos} heta + q$ is true?

The y-intercept is at $(0°, a + q)$ Signup and view all the answers

If $b$ is between 0 and 1 in the function $y = ab^x + q$, what does this indicate about the graph?

The graph represents exponential decay Signup and view all the answers

What denotes congruency between two triangles?

≡ Signup and view all the answers

Which congruency rule can be applied only to right-angled triangles?

RHS Signup and view all the answers

What is a key characteristic of similar triangles?

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

Which property is NOT true for a rectangle?

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

Which quadrilateral has all four sides of equal length?

Square Signup and view all the answers

What is true about the interior angles of any quadrilateral?

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

In a rhombus, how do the diagonals behave?

They bisect each other at 90°. Signup and view all the answers

Which quadrilateral is defined as having one pair of opposite sides parallel?

Trapezium Signup and view all the answers

What property distinguishes a kite from other quadrilaterals?

Diagonals intersect at 90°. Signup and view all the answers

Which statement is true regarding the hierarchy of quadrilaterals?

All squares are rectangles. Signup and view all the answers

What is a characteristic that differentiates a trapezium from a kite?

A trapezium has one pair of parallel sides. Signup and view all the answers

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

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

Which property is true for a rectangle that distinguishes it from other types of quadrilaterals?

It has four right angles. Signup and view all the answers

When using the mid-point theorem, if line DE connects the mid-points of sides AB and AC, what can be concluded about side BC?

Line DE is parallel to BC and equal to half its length. Signup and view all the answers

In a scalene triangle, which aspect remains constant when connecting mid-points of two sides?

The segment connecting the mid-points remains parallel to the third side. Signup and view all the answers

What is the result of applying the converse of the mid-point theorem?

A line through the mid-point of one side parallel to another will divide the third side into two equal parts. Signup and view all the answers

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

All angles are right angles. Signup and view all the answers

How does a square relate to a rectangle and a rhombus?

Both A and B. Signup and view all the answers

What can you determine about the properties of quadrilateral ABCD if AB is parallel to CD and AD is parallel to BC?

ABCD is a parallelogram. Signup and view all the answers

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

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

Which of the following statements is true regarding congruent triangles in the context of parallelograms?

Congruent triangles have exactly the same size and shape. Signup and view all the answers

Which of the following statements correctly describes the gradient of a line?

The gradient is calculated as the difference in y-values divided by the difference in x-values. Signup and view all the answers

What does it mean for two lines to be perpendicular?

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

Which equation represents the standard form of a straight line?

$y = mx + c$ Signup and view all the answers

What is the characteristic of a horizontal line regarding its gradient?

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

If two points are collinear, what can be implied about them?

They have a constant gradient between them. Signup and view all the answers

How is the mid-point M(x, y) of a line segment determined?

$M(x, y) = rac{x_1 + x_2}{2} , rac{y_1 + y_2}{2}$ Signup and view all the answers

What can be said about vertical lines in terms of their gradient?

Their gradient is undefined. Signup and view all the answers

Which of the following statements is false regarding straight lines?

Two parallel lines have different gradients. Signup and view all the answers

Given points A(3, 4) and B(7, 8), what is the gradient of the line joining them?

$2$ Signup and view all the answers

What is the primary effect of increasing the value of 'q' in the equation of a parabola?

It shifts the graph vertically upwards. Signup and view all the answers

How is the gradient 'm' defined in the context of linear functions?

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

What does a negative value for 'a' indicate in the function of a parabola?

The graph will open downwards. Signup and view all the answers

Which of the following correctly describes the x-intercept of a function?

It is found by solving $y = 0$. Signup and view all the answers

What is the domain of the quadratic function $y = ax^2 + q$?

$ ext{all real numbers}$ Signup and view all the answers

What additional characteristic must be determined when sketching the graph of $y = ax^2 + q$?

The x-intercept. Signup and view all the answers

When $a < 0$ for the quadratic function $y = ax^2 + q$, what is the nature of the graph?

It has a maximum point. Signup and view all the answers

If the gradient $m$ is 0 in the function $y = mx + c$, what will the graph look like?

A horizontal line along y = c. Signup and view all the answers

In the context of the y-intercept of a graph, how is it determined for a linear function $y = mx + c$?

By letting $x = 0$. Signup and view all the answers

What does the term 'turning point' refer to in a parabolic graph?

The maximum or minimum point of the graph. Signup and view all the answers

What effect does a negative value of 'a' have in the sine function $y = a \sin \theta + q$?

It reflects the graph below the x-axis. Signup and view all the answers

Which of the following statements correctly describes the x-intercepts of the function $y = \tan \theta$?

They occur at 0°, 180°, and 360°. Signup and view all the answers

For which values of 'b' does the function represent exponential decay?

$0 Signup and view all the answers

What is the range of the cosine function $y = a \cos \theta + q$ when $a < 0$?

[q + |a|, q - |a|] Signup and view all the answers

What is the period of the tangent function $y = a \tan \theta + q$?

180° Signup and view all the answers

What describes the y-intercept of the sine function $y = a \sin \theta + q$?

It is at (0, q). Signup and view all the answers

If $b > 1$ in the function $y = ab^x + q$, what does this indicate about the graph?

The graph curves upward. Signup and view all the answers

In the cosine function $y = a \cos \theta + q$, what effect does $|a| > 1$ have?

It stretches the graph vertically. Signup and view all the answers

Which point corresponds to the maximum turning point of the cosine function $y = a \cos \theta + q$ when $a > 0$?

(0°, 1) Signup and view all the answers

What role does the constant 'c' play in the equation of a straight line $y = mx + c$?

Identifies the y-intercept Signup and view all the answers

How does a positive value of 'm' influence the graph of a function?

The graph slopes upwards from left to right. Signup and view all the answers

What is the effect of increasing the value of 'm' in the equation $y = mx + c$?

It increases the steepness of the slope. Signup and view all the answers

What describes the domain of the function $f(x) = mx + c$?

All real numbers Signup and view all the answers

If 'c' is less than zero in the equation $y = mx + c$, how does it affect the position of the graph?

The graph shifts vertically downwards. Signup and view all the answers

To find the y-intercept of the function $y = mx + c$, what value should be substituted for 'x'?

0 Signup and view all the answers

What characteristic describes the x-intercept of the function $y = mx + c$?

Value of 'x' when 'y' is equal to 0 Signup and view all the answers

What happens to the graph of a function $y = mx + c$ if 'm' equals zero?

The graph remains a straight line with a slope of 0. Signup and view all the answers

What is the domain of the hyperbolic function of the form $y = \frac{a}{x} + q$?

{x : x \in \mathbb{R}, x \neq 0} Signup and view all the answers

Which statement about the range of the hyperbolic function $y = \frac{a}{x} + q$ is correct when $q < 0$?

The range is $(q; \infty)$ Signup and view all the answers

What identifies the y-intercept in an exponential function of the form $y = ab^x + q$?

It is found by letting $x = 0$ Signup and view all the answers

What does the term 'asymptotes' refer to in the context of the hyperbolic function $y = \frac{a}{x} + q$?

Lines that the graph approaches as $x$ or $y$ approach infinity Signup and view all the answers

Which property does NOT characterize the graph of the hyperbolic function?

It contains a y-intercept Signup and view all the answers

For the exponential function $y = ab^x + q$, what indicates that the graph curves upward?

When $a > 0$ and $b > 1$ Signup and view all the answers

What happens to the horizontal asymptote of an exponential function when $q < 0$?

It moves downwards below the x-axis by $|q|$ units Signup and view all the answers

Which of the following describes the x-intercept for the hyperbolic function $y = \frac{a}{x} + q$?

It is calculated by setting $y = 0$ Signup and view all the answers

What effect does a negative value of $a$ have on the graph of the function $y = \frac{a}{x} + q$?

The graph is reflected in the x-axis Signup and view all the answers

Which characteristic is true for the function $y = ab^x + q$ when $a < 0$?

The range is ${y : y \in \mathbb{R}, y < q}$ Signup and view all the answers

Which of the following statements is true about congruent triangles?

Their corresponding angles must be equal. Signup and view all the answers

Which property is true for a parallelogram?

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

What distinguishes a rectangle from other parallelograms?

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

Which of the following best describes a rhombus?

All sides are of equal length and diagonals intersect at 90°. Signup and view all the answers

What does the value of 'a' determine in the equation of a hyperbola?

The curvature and shape of the hyperbola Signup and view all the answers

Which statement about similar triangles is true?

Their sides are proportional and angles are equal. Signup and view all the answers

Which of the following best describes the vertical shift in the equation of a sine function?

It is determined by the value of 'q'. Signup and view all the answers

What is a defining property of a kite?

Diagonals intersect at 90° and one diagonal bisects the other. Signup and view all the answers

What is the significance of the x-intercepts when analyzing the graph of a quadratic function?

They represent the solutions to the equation. Signup and view all the answers

According to the rules of similarity, which condition satisfies the AAA criterion?

All corresponding angles are equal. Signup and view all the answers

In which scenario is the Pythagorean theorem applicable?

Exclusively in right-angled triangles. Signup and view all the answers

How should one find the value of 'q' in a hyperbola represented as $y = \frac{a}{x} + q$?

By identifying the y-intercept of the graph. Signup and view all the answers

In which scenario would the interior angles of a triangle sum to more than 180°?

In any type of triangle being drawn on a sphere. Signup and view all the answers

What characteristic is unique to squares compared to other quadrilaterals?

All sides are equal, and all angles are right angles. Signup and view all the answers

Which characteristic is true for a rectangle compared to other quadrilaterals?

It has right angles. Signup and view all the answers

Which of the following properties is specific to trapeziums?

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

When solving for 'a' and 'q' in a trigonometric function like $y = a \sin \theta + q$, what should be done first?

Examine the type of trigonometric graph. Signup and view all the answers

What does the Mid-Point Theorem state about a triangle?

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

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

The exterior angle is equal to the sum of the two opposite interior angles. Signup and view all the answers

Which of the following statements is NOT true about trapeziums?

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

Which characteristic is true about the graph of a tangent function?

It has asymptotes where the function is undefined. Signup and view all the answers

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

Proving line parallelism. Signup and view all the answers

What determines the shape of the graph for a sine function with respect to its parameter 'a'?

The amplitude and possible reflection across the x-axis. Signup and view all the answers

Which describes a kite in comparison to other quadrilaterals?

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

In the context of triangles, what does the term 'scalene' refer to?

Triangles where all sides have different lengths. Signup and view all the answers

Which conclusion can be drawn about the angles in a parallelogram?

Opposite angles are equal. Signup and view all the answers

If two sides of a triangle are extended, what can be said about the angles formed outside the triangle?

They are supplementary to the interior angles. Signup and view all the answers

In a scalene triangle, how many sides and angles are equal?

No sides and angles are equal. Signup and view all the answers

What happens when you draw a line segment parallel to one side of a triangle through its mid-point?

The segment creates two similar triangles. Signup and view all the answers

Which property distinguishes a square from other rectangles?

A square has equal side lengths. Signup and view all the answers

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

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

How is the gradient of a line determined?

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

What characterizes a straight line in terms of gradient?

The gradient is constant between any two points. Signup and view all the answers

Which statement about parallel lines is correct?

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

What is the mid-point of a line segment defined by points A(x₁, y₁) and B(x₂, y₂)?

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

What is true about a vertical line's gradient?

It has an undefined gradient. Signup and view all the answers

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

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

What can be deduced about horizontal lines?

They maintain a constant zero gradient. Signup and view all the answers

How can you determine if three points are collinear?

Compare the gradients between pairs of points. Signup and view all the answers

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

$y = mx + c$ Signup and view all the answers

How does the graph of a function with a negative slope value ( $m < 0$) behave?

It slopes downwards from left to right. Signup and view all the answers

In the equation of a straight line, if the y-intercept ( $c$) is negative, what effect does it have on the graph?

The graph shifts vertically downwards. Signup and view all the answers

What describes the impact of increasing the slope ( $m$) of the line in the equation $y = mx + c$?

The graph becomes steeper and rises more sharply. Signup and view all the answers

What can be concluded about the range of the function $f(x) = mx + c$?

It can take any real number value. Signup and view all the answers

Which statement accurately represents the impact of a zero slope ( $m = 0$) in the equation $y = mx + c$?

The graph remains horizontal and equal to the y-intercept. Signup and view all the answers

How do you determine the x-intercept of the function $y = mx + c$?

Set $y$ equal to zero and solve for $x$. Signup and view all the answers

If both $m$ and $c$ are positive, how does this affect the overall behavior of the graph?

The graph will slope upwards and start above the x-axis. Signup and view all the answers

What occurs to the graphs of functions when the parameter 'b' is between 0 and 1?

The function exhibits exponential decay. Signup and view all the answers

Which of the following describes the range of the function $y = a \sin \theta + q$ for $a < 0$?

[q - |a|, q + |a|] Signup and view all the answers

In the context of trigonometric functions, what is the impact of a positive 'q' in the equation $y = a \cos \theta + q$?

It shifts the graph up by 'q' units. Signup and view all the answers

What characterizes the period of the tangent function $y = a \tan \theta + q$?

180° Signup and view all the answers

For a function of the form $y = a \tan \theta + q$, how is the steepness of the graph branches affected?

Increasing 'a' makes the branches steeper. Signup and view all the answers

What type of shift occurs if $q < 0$ in the function $y = a \sin \theta + q$?

Vertical shift down by 'q' units. Signup and view all the answers

In the situation where $a < 0$, what is the orientation of the graph for $y = a \cos \theta + q$?

The graph reflects about the x-axis. Signup and view all the answers

What is the x-intercept of the function $y = a \tan \theta + q$ if $q = 0$?

0° Signup and view all the answers

What does the presence of asymptotes at $ heta = 90°$ and $ heta = 270°$ indicate for the function $y = a \tan \theta + q$?

The function approaches infinity at those angles. Signup and view all the answers

For the sine function $y = \sin \theta$, where does the maximum turning point occur?

At (90°, 1) Signup and view all the answers

How does a positive value for 'a' affect the shape of the graph of a quadratic function?

It produces a parabolic 'smile' with a minimum turning point. Signup and view all the answers

What happens to the graph of a quadratic function as the value of 'a' approaches zero but remains positive?

The graph becomes wider. Signup and view all the answers

Which characteristic does NOT influence the vertical shift of a quadratic function graph?

The x-intercept location. Signup and view all the answers

What is the range of the quadratic function $y = ax^2 + q$ when $a < 0$?

$(- p> f q]$ Signup and view all the answers

Which statement best describes the effect of a negative value of 'q' on the graph of a quadratic function?

The graph is shifted vertically downwards by 'q' units. Signup and view all the answers

What defines the axis of symmetry for the quadratic function $y = ax^2 + q$?

The line $x = a$. Signup and view all the answers

When determining the y-intercept of the function $f(x) = mx + c$, what should be set to find this characteristic?

Set $x=0$. Signup and view all the answers

What impact does a decreasing value of 'a' (where $-1 < a < 0$) have on the graph's shape?

The graph widens significantly. Signup and view all the answers

What denotes the vertical position of the turning point of the graph for $y = ax^2 + q$?

The value of 'q'. Signup and view all the answers

In the context of a quadratic function, if the turning point is located at (0, q) and $a < 0$, what can be inferred about the graph?

The graph has a maximum turning point. Signup and view all the answers

What determines the specific shape and orientation of a hyperbola's curves?

The sign and magnitude of a Signup and view all the answers

In the classification of triangles by angles, which combination correctly identifies a triangle with one angle greater than 90°?

Obtuse Scalene Signup and view all the answers

When solving the system of equations to find a and q for trigonometric functions, what is the first step necessary?

Substitute one point into the equation Signup and view all the answers

What is true regarding the asymptotes of the hyperbola defined by the equation y = a/x + q?

Asymptotes are horizontal and equal to q Signup and view all the answers

Which of the following best describes the role of the variable q in the equations of trigonometric functions?

It causes a vertical shift in the graph Signup and view all the answers

What happens to the graph of a parabola when the value of a is negative?

The graph maintains its shape but reflects across the x-axis Signup and view all the answers

When calculating the distance between two points on the Cartesian plane, which formula is generally used?

Distance formula: d = √((x2-x1)² + (y2-y1)²) Signup and view all the answers

In the context of parabolas, what does a wider graph indicate about the value of a?

a is between 0 and 1 Signup and view all the answers

What is the significance of the y-intercept when determining equations for parabolas and hyperbolas?

It helps determine the value of q in the equations Signup and view all the answers

Which type of triangle has one angle equal to 90° and also meets the criteria of having two equal sides?

Right-angled Isosceles Triangle Signup and view all the answers

What happens to the graph of the function $y = ax^2 + q$ when $a < 0$?

The graph opens downwards and reaches a maximum at $(0, q)$. Signup and view all the answers

Which statement about the asymptotes of the hyperbolic function $y = rac{a}{x} + q$ is false?

The graph intersects the horizontal asymptote at $(0, q)$. Signup and view all the answers

For the exponential function $y = ab^x + q$, if $a < 0$ and $b > 1$, what can be said about the horizontal asymptote?

The horizontal asymptote is at $y = q$. Signup and view all the answers

In the function $y = rac{a}{x} + q$, how does a negative value of 'a' affect the quadrants in which the graph resides?

The graph lies in both the second and fourth quadrants. Signup and view all the answers

Which of the following accurately describes the y-intercept of the hyperbolic function $y = rac{a}{x} + q$?

Since the function is undefined at $x = 0$, there is no y-intercept. Signup and view all the answers

Which characteristic is true for an exponential function when $0 < a < 1$?

The graph approaches the x-axis as $x$ approaches negative infinity. Signup and view all the answers

When graphing $y = rac{a}{x} + q$, what effect does increasing the value of $q$ have?

It shifts the entire graph vertically upwards by $q$ units. Signup and view all the answers

What is the effect of the parameter 'b' when $b > 1$ in the exponential function $y = ab^x + q$?

The graph curves upwards as $x$ increases. Signup and view all the answers

Which of the following statements is true regarding the intercepts of the function $y = ab^x + q$?

The x-intercept occurs when $y = 0$. Signup and view all the answers

For the function $y = rac{a}{x} + q$, which axis of symmetry is represented?

The y-axis is the axis of symmetry. Signup and view all the answers

What signifies that two triangles are congruent?

All corresponding angles and sides are equal. Signup and view all the answers

Which rule is NOT applicable for establishing the congruency of triangles?

SSA (Side-Side-Angle) Signup and view all the answers

What is the primary characteristic of similar triangles?

Their corresponding angles are equal and sides are proportional. Signup and view all the answers

Which property does NOT apply to all parallelograms?

They have one pair of opposite sides parallel. Signup and view all the answers

In a rhombus, which property is exclusively unique compared to other quadrilaterals?

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

Which statement is correct regarding the properties of a rectangle?

All interior angles are equal to 90 degrees. Signup and view all the answers

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

360° Signup and view all the answers

Which quadrilateral has diagonals that bisect each other at right angles?

Kite Signup and view all the answers

In proving triangles are congruent, which of the following rules is valid only for right-angled triangles?

RHS (Right angle-Hypotenuse-Side) Signup and view all the answers

How can one determine if a triangle is right-angled based on the Pythagorean Theorem?

If $b^2 = a^2 + c^2$ holds true. Signup and view all the answers

Which statement accurately describes a trapezium?

A trapezium can exist without any equal sides. Signup and view all the answers

What does the Mid-Point Theorem indicate about the line segment joining the midpoints of two sides of a triangle?

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

In the context of a parallelogram, what can be inferred if the angles are congruent?

The sides opposite the angles are parallel. Signup and view all the answers

Which geometric property is crucial in proving that MNOP is a parallelogram?

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

What geometric relationship is defined by the converse of the Mid-Point Theorem?

If a line is drawn through the midpoint of a triangle side parallel to another side, it will create two equal segments on the third side. Signup and view all the answers

What characteristic differentiates a kite from other quadrilaterals?

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

How does one prove that a given quadrilateral is a special type of parallelogram?

By establishing that one pair of opposite sides is both equal and parallel. Signup and view all the answers

Which sequence correctly identifies the special quadrilaterals within the classification of parallelograms?

Rectangle, Rhombus, Square. Signup and view all the answers

When given coordinates, what does the order of letters define in constructing a quadrilateral?

The order in which the vertices must be connected. Signup and view all the answers

Which aspect is crucial in the investigation of the mid-point theorem using a triangle?

Cutting the triangle and observing the properties. Signup and view all the answers

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

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

When two lines are said to be perpendicular, what mathematical relationship do their gradients share?

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

How is the gradient of a line determined between two points A(x₁, y₁) and B(x₂, y₂)?

Gradient (m) = $rac{y₂ - y₁}{x₂ - x₁}$ Signup and view all the answers

What is the mid-point M(x, y) of a line segment defined by 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

Which of the following accurately describes a characteristic of horizontal lines?

They have a gradient of 0. Signup and view all the answers

When determining if two points are collinear, what method can be employed?

The gradient method. Signup and view all the answers

What is the general form of the equation for a straight line?

$y = mx + c$ Signup and view all the answers

If the gradient of a line is negative, what does this imply about its direction?

The line moves downwards from left to right. Signup and view all the answers

For a line that runs parallel to the y-axis, what can be said about its gradient?

Its gradient is undefined. Signup and view all the answers

How can the concept of gradient be represented in the context of a right-angled triangle formed by points A and B?

Gradient is the ratio of the vertical side over the horizontal side. Signup and view all the answers

What can be concluded about the slope of the graph when the value of the gradient 'm' is negative?

The graph slopes downwards from left to right. Signup and view all the answers

If the y-intercept 'c' is set to zero in the equation of a straight line, which of the following statements is true regarding the graph?

The graph will pass through the origin. Signup and view all the answers

How does the graph behave if both 'm > 0' and 'c < 0' are true in the equation 'y = mx + c'?

The graph has a positive slope and intersects the y-axis below the origin. Signup and view all the answers

If the slope 'm' of a linear function is increased, what characteristic of the graph is affected?

The graph's slope becomes steeper. Signup and view all the answers

What is the effect on the graph of a linear function if 'c' is a large positive number?

The graph will shift vertically upwards. Signup and view all the answers

How does the domain of a function of the form 'y = mx + c' differ from that of other types of functions?

It includes all real numbers. Signup and view all the answers

In the equation 'y = mx + c', which statement accurately describes the function when 'm = 0'?

The graph will be a horizontal line. Signup and view all the answers

If the graph of 'y = mx + c' has an x-intercept, what does it imply about the linear function?

The function can take on a value of zero. Signup and view all the answers

What characteristic is determined by the value of 'm' in the linear equation of the form $y = mx + c$?

The steepness and direction of the line Signup and view all the answers

How does the sign of 'a' in the quadratic function $y = ax^2 + q$ affect the turning point?

It determines if the turning point is a minimum or maximum Signup and view all the answers

Which scenario best describes the effect of increasing 'q' in the quadratic equation $y = ax^2 + q$ where 'a' is positive?

The graph shifts upwards maintaining its shape Signup and view all the answers

What is the range of the quadratic function $y = ax^2 + q$ when 'a' is negative?

(- infty; q) Signup and view all the answers

In which condition does the quadratic graph become wider as 'a' approaches zero but remains positive?

When $0 < a < 1$ Signup and view all the answers

What is the axis of symmetry for the quadratic function $y = ax^2 + q$?

The line $x = 0$ Signup and view all the answers

Which statement accurately describes how to find the x-intercepts of a parabola represented by $y = ax^2 + q$?

Set $y = 0$ and solve for $x$ Signup and view all the answers

How does the graph of $y = ax^2 + q$ behave if $a > 0$?

The graph opens upwards with a minimum turning point at $(0; q)$ Signup and view all the answers

Which characteristic is NOT true for the linear function $f(x) = mx + c$?

Linear functions can have multiple x-intercepts Signup and view all the answers

What will occur to the whole graph of the function $y = ax^2 + q$ if 'q' is decreased?

The graph shifts downwards Signup and view all the answers

What is a characteristic of hyperbolic functions when the coefficient 'a' is less than zero?

The graph lies in the second and fourth quadrants. Signup and view all the answers

In the function of the form $y = ab^x + q$, how does a negative value of 'a' affect the graph?

The graph curves downwards for all values of x. Signup and view all the answers

Which statement accurately describes the domain of hyperbolic functions?

The function is defined for all real numbers except x equals zero. Signup and view all the answers

What describes the x-intercept of the hyperbolic function $y = rac{a}{x} + q$?

It is determined by setting 'y = 0'. Signup and view all the answers

What is the effect of the parameter 'q' in the graph of $y = rac{a}{x} + q$?

It affects the horizontal asymptote of the graph. Signup and view all the answers

When analyzing the range of the function $y = ab^x + q$ with $a < 0$, which statement is true?

The range is bounded above by q. Signup and view all the answers

Which characteristic is true regarding the turning point of hyperbolic functions?

It does not exist in a hyperbolic function. Signup and view all the answers

In sketching the graph of the function $y = rac{a}{x} + q$, which factor must be primarily considered to determine the general shape?

The sign of 'a'. Signup and view all the answers

What is a distinguishing feature of the vertical asymptote in hyperbolic functions?

It occurs at x = 0. Signup and view all the answers

When the function is in the form $y = b^x$ and demonstrates exponential growth, what can be said about the value of 'b'?

It should be greater than one. Signup and view all the answers

What signifies that two triangles are similar?

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

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

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

What is a defining characteristic of a parallelogram?

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

Which statement concerning the angles of a quadrilateral is accurate?

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

Which pair of triangles can be proven congruent using the SSS rule?

A triangle with sides 3, 4, 5 and another with sides 5, 4, 3. Signup and view all the answers

What is a core property of a kite?

The diagonals intersect at a right angle. Signup and view all the answers

What does the term AAS imply about two triangles?

They have two angles and one non-included side equal. Signup and view all the answers

How would you classify a quadrilateral with one pair of opposite sides that are parallel?

Trapezium Signup and view all the answers

In the context of triangle congruence, what does RHS stand for?

Right-angle Hypotenuse Side Signup and view all the answers

What effect does the sign of 'a' have on the shape of a hyperbola?

It determines which quadrants the hyperbola curves will belong to. Signup and view all the answers

How can the vertical shift of a sine function be determined?

By examining the coefficient 'q' in the equation. Signup and view all the answers

In the context of hyperbolas, how is the value of 'q' significant?

It determines the vertical positioning of the hyperbola. Signup and view all the answers

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

Each exterior angle equals the sum of the adjacent interior angles. Signup and view all the answers

Which property is characteristic of a right-angled triangle?

One angle measures 90°. Signup and view all the answers

Which aspect describes how to determine the intercepts of the function $y = a \sin \theta + q$?

Set $y$ equal to zero and solve for $\theta$. Signup and view all the answers

What determines the direction of a parabola?

The sign of the coefficient 'a'. Signup and view all the answers

Which characteristic is true for all trapeziums?

They have one pair of parallel sides. Signup and view all the answers

What does the Mid-Point Theorem assert about a line segment connecting two mid-points of a triangle?

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

How can distances between points on a graph be calculated?

By simple subtraction when points are aligned either vertically or horizontally. Signup and view all the answers

What is true about the range of a function $y = \frac{a}{x} + q$?

It is unbounded as 'y' approaches infinity. Signup and view all the answers

Which is a requirement for a quadrilateral to be classified as a kite?

Two pairs of adjacent sides must be equal. Signup and view all the answers

In the proof that MNOP is a parallelogram, which congruency rule is primarily used?

SAS (Side-Angle-Side) Signup and view all the answers

What condition must be met for two triangles to be similar using the Mid-Point Theorem?

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

Which of the following statements about parallelograms is false?

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

When applying the Mid-Point Theorem in coordinate geometry, what is the significance of the mid-point coordinates?

They provide the basis for paralleling the third side. Signup and view all the answers

Which definition correctly describes the characteristics of a square?

A rhombus with right angles. Signup and view all the answers

Which of the following is NOT an application of the Mid-Point Theorem?

Calculating the area of triangles. Signup and view all the answers

Which property must be true for the diagonals of a kite?

They bisect each other at right angles. Signup and view all the answers

What is the distance between the points A(2, 3) and B(5, 7)?

$5$ Signup and view all the answers

If two lines are perpendicular, which of the following products of their gradients is true?

$m_{1} imes m_{2} = -1$ Signup and view all the answers

What are the coordinates of the mid-point M of the line segment between A(-2, 4) and B(4, -6)?

(3, -1) Signup and view all the answers

Which of the following statements is true regarding horizontal and vertical lines?

A horizontal line has a gradient of 0. Signup and view all the answers

Given the points A(1, 2) and B(3, 4), what is the gradient of the line connecting these points?

$1$ Signup and view all the answers

Which equation represents the equation of a line with gradient $-3$ that passes through the point (2, 1)?

$y - 1 = -3(x - 2)$ Signup and view all the answers

To prove that points A(2, 3), B(4, 5), and C(6, 7) are collinear, what must be true about the gradients?

Gradients between any two pairs must be equal. Signup and view all the answers

If the distances between the points A(x₁, y₁) and B(x₂, y₂) is calculated using $(y₁ - y₂)^2 + (x₂ - x₁)^2$, what is the possibility of error?

It incorrectly applies the Pythagorean theorem. Signup and view all the answers

What is the significance of the negative gradient in the equation of a line?

It signifies a downward slope. Signup and view all the answers

For the function of the form $y = a \sin \theta + q$, what is the effect of a negative amplitude ($a < 0$) on the graph?

The graph reflects about the x-axis. Signup and view all the answers

What effect does a coefficient of $|a| > 1$ have on the cosine function $y = a \cos \theta + q$?

It stretches the graph vertically. Signup and view all the answers

In the function $y = a \tan \theta + q$, if $q < 0$, what is the effect on the y-intercept?

The y-intercept shifts down by $|q|$ units. Signup and view all the answers

What characteristic distinguishes the range of the tangent function $y = a \tan \theta + q$?

The range is all real numbers. Signup and view all the answers

For the sine function $y = \sin \theta$, where is the maximum turning point located?

At $(90°, 1)$. Signup and view all the answers

What is the period of the cosine function $y = a \cos \theta + q$?

360° Signup and view all the answers

In the graph of $y = ab^x + q$, what happens when $b < 1$?

The graph exhibits exponential decay. Signup and view all the answers

Which points indicate the x-intercepts of the sine function $y = a \sin \theta + q$?

$(0°, 0)$ and $(180°, 0)$. Signup and view all the answers

Where are the asymptotes located in the tangent function $y = a \tan \theta + q$?

$\theta = 90°$ and $\theta = 270°$. Signup and view all the answers

What occurs when $0 < |a| < 1$ in the cosine function $y = a \cos \theta + q$?

The graph is compressed vertically. Signup and view all the answers

Gr 10 Math Term 2 Test

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Questions and Answers

What does the sign of the coefficient 'a' indicate in a quadratic function?

What is the effect of a positive value for 'q' in the equation of a parabola?

How do you calculate the x-intercept of a function of the form $y = ax^2 + q$?

In the equation $y = mx + c$, what does 'm' represent?

What describes the turning point of a parabola when $a < 0$?

Which of the following correctly states the domain of the function $y = ax^2 + q$?

What is the range of a quadratic function $y = ax^2 + q$ when $a > 0$?

How can you determine the y-intercept of the quadratic function $y = ax^2 + q$?

Which statement is true regarding the axis of symmetry for a quadratic function?

What happens to the graph as 'a' approaches zero but remains positive, $0 < a < 1$?

What is the domain of the function $y = \frac{a}{x} + q$?

What determines the direction of a parabola?

What is the range of the function $y = \frac{a}{x} + q$ when $q < 0$?

What effect does the parameter $q$ have on the graph of $y = \frac{a}{x} + q$?

How can you determine the value of $q$ for a parabola?

What is the first step in determining the equation of a hyperbola?

How do you find the x-intercept of the function $y = \frac{a}{x} + q$?

What affects the amplitude of trigonometric functions like sine and cosine?

Which of the following describe the asymptotes of $y = \frac{a}{x} + q$?

What method is used to find points of intersection between two graphs?

What is the y-intercept of the function $y = \frac{a}{x} + q$?

For the function $y = b^x$ with $a < 0$, what can be said about its range?

In terms of triangle classification, which of the following describes a triangle with all sides of different lengths?

What determines the direction in which the graph of $y = ab^x + q$ curves?

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

Which statement correctly describes the relationship between exterior and interior angles of a triangle?

Which lines represent the axes of symmetry for the function $y = \frac{a}{x} + q$?

What determines the vertical shift of the graph of a hyperbola?

What is the range of an exponential function $y = ab^x + q$ if $a > 0$?

What happens to the graph of a function when the gradient, represented by $m$, increases?

Which of these characteristics does NOT relate to parabolas?

If $c < 0$ in the equation $y = mx + c$, how will the graph shift vertically?

What is the effect of a negative gradient ($m < 0$) on the graph?

Which statement is true about the intercepts of the function $y = mx + c$?

Which of the following describes the domain of the function $f(x) = mx + c$?

If $m = 0$ in the equation $y = mx + c$, what can be said about the graph?

What will happen to the y-intercept if $c$ increases?

How is the x-intercept determined for the function $y = mx + c$?

What does the value of $b$ in the function $y = ab^x + q$ determine when $b > 1$?

Which point represents the maximum turning point of the sine function $y = a ext{sin} heta + q$ when $a > 0$?

For the cosine function $y = a ext{cos} heta + q$, what happens if $|a| < 1$?

What is the range of the function $y = a ext{sin} heta + q$ when $a < 0$?

Which of the following characteristics is NOT true for the tangent function $y = a ext{tan} heta + q$?

Which characteristic of the sine and cosine functions is TRUE?

What effect does a positive $q$ value have on the graph of $y = a ext{sin} heta + q$?

If the value of $a$ is negative in the function $y = a ext{tan} heta + q$, what is the impact on the graph?

Which of the following statements about the y-intercept of the cosine function $y = a ext{cos} heta + q$ is true?

If $b$ is between 0 and 1 in the function $y = ab^x + q$, what does this indicate about the graph?

What denotes congruency between two triangles?

Which congruency rule can be applied only to right-angled triangles?

What is a key characteristic of similar triangles?

Which property is NOT true for a rectangle?

Which quadrilateral has all four sides of equal length?

What is true about the interior angles of any quadrilateral?

In a rhombus, how do the diagonals behave?

Which quadrilateral is defined as having one pair of opposite sides parallel?

What property distinguishes a kite from other quadrilaterals?

Which statement is true regarding the hierarchy of quadrilaterals?

What is a characteristic that differentiates a trapezium from a kite?

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

Which property is true for a rectangle that distinguishes it from other types of quadrilaterals?

When using the mid-point theorem, if line DE connects the mid-points of sides AB and AC, what can be concluded about side BC?

In a scalene triangle, which aspect remains constant when connecting mid-points of two sides?

What is the result of applying the converse of the mid-point theorem?

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

How does a square relate to a rectangle and a rhombus?

What can you determine about the properties of quadrilateral ABCD if AB is parallel to CD and AD is parallel to BC?

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

Which of the following statements is true regarding congruent triangles in the context of parallelograms?

Which of the following statements correctly describes the gradient of a line?

What does it mean for two lines to be perpendicular?

Which equation represents the standard form of a straight line?

What is the characteristic of a horizontal line regarding its gradient?

If two points are collinear, what can be implied about them?

How is the mid-point M(x, y) of a line segment determined?

What can be said about vertical lines in terms of their gradient?