Gr 10 Math June P2 Medium

What is the value of the sine function for an angle theta in a right-angled triangle?

Opposite divided by hypotenuse (correct)

Adjacent divided by hypotenuse

Hypotenuse divided by adjacent

Opposite divided by adjacent

Which of the following statements about trigonometric ratios is false?

Cotangent is the reciprocal of tangent.

Secant is the ratio of opposite to hypotenuse. (correct)

Cosecant is the reciprocal of sine.

Tangent is the ratio of opposite to adjacent.

What does the mnemonic 'Soh Cah Toa' help to remember?

Types of angles in trigonometry

Trigonometric ratios of sine, cosine, and tangent (correct)

Pythagorean theorem applications

Reciprocal relationships of trigonometric functions

What is the reciprocal of the sine function?

Cosecant Signup and view all the answers

If angle theta is known, how can you find the value of cosine theta?

By dividing the length of the adjacent side by the hypotenuse Signup and view all the answers

What must be true about triangles for them to be considered similar?

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

Which of the following statements about the ratios of similar triangles is correct?

The ratios are equal if corresponding angles are equal. Signup and view all the answers

Which relationship correctly describes the tangent of angle theta?

Tan theta equals opposite divided by adjacent Signup and view all the answers

To calculate trigonometric ratios using a calculator, which mode should it be set to for angle measurements in degrees?

Degrees mode Signup and view all the answers

If two triangles are similar, which property regarding their angles holds true?

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

What is the primary use of the Pythagorean theorem in relation to trigonometric functions?

To relate the sides of a right triangle to the angles Signup and view all the answers

In similar triangles, how is the order of the vertices important?

It indicates the correspondence of sides. Signup and view all the answers

Which of the following is a characteristic of the ratios in similar triangles with angles of 30°, 60°, and 90°?

They maintain the same proportion regardless of size. Signup and view all the answers

Which trigonometric function relates the opposite side to the adjacent side in a right triangle?

Tangent Signup and view all the answers

For triangles ΔABC and ΔDEF where ΔABC ∼ ΔDEF, what can be deduced about the relationship between side lengths?

AC is proportional to DF. Signup and view all the answers

Which of the following reciprocal identities is correct?

Cosec theta equals 1 over sin theta Signup and view all the answers

When comparing the sides of similar triangles, which ratio is commonly used to express the relationship between the sides?

The ratio of the lengths of corresponding sides. Signup and view all the answers

Which of the following constitutes a valid comparison between the angles in two similar triangles?

Each angle in one triangle matches the corresponding angle in the other triangle. Signup and view all the answers

What are the positive trigonometric ratios in Quadrant II?

sin θ and cosec θ Signup and view all the answers

What is the sine of 90 degrees?

1 Signup and view all the answers

Which of the following is true regarding the tangent function?

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

In the case of the function y = a sin θ + q, what effect does a < 0 have?

Reflection about the x-axis Signup and view all the answers

Which angle corresponds to a sine value of 1/2?

60 degrees Signup and view all the answers

What is the range of the cosine function over one complete cycle?

[-1, 1] Signup and view all the answers

What is the equivalent of the angle of elevation concerning the angle of depression?

They are always equal in measurement. Signup and view all the answers

What is the x-intercept of the function y = cos θ?

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

Which of the following ratios is NOT a definition of a trigonometric ratio for a right triangle?

tan θ = adjacent / hypotenuse Signup and view all the answers

What is the maximum turning point of the sine function?

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

How does the value of $q$ in the function $y = a an heta + q$ affect the graph?

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

What is the range of the function $y = a an heta + q$?

All real numbers. Signup and view all the answers

Which classification applies to a triangle with one angle greater than 90° and two unequal sides?

Obtuse scalene. Signup and view all the answers

What type of triangle is defined by having all three sides equal in length?

Equilateral. Signup and view all the answers

According to congruency rules, which condition is sufficient to prove two triangles are congruent?

The hypotenuse and one side of a right-angled triangle are equal. Signup and view all the answers

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

180°. Signup and view all the answers

Which statement is true regarding the cosine graph compared to the sine graph?

The cosine graph is shifted to the left by 90° to overlap with the sine graph. Signup and view all the answers

What is the period of the tangent function $y = an heta$?

180°. Signup and view all the answers

What occurs when $|a| > 1$ in the function $y = a an heta + q$?

The graph stretches vertically. Signup and view all the answers

Which congruency rule is applicable if two angles and the included side of one triangle are equal to two angles and the included side of another triangle?

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

In a 30°-60°-90° triangle, what is the length of the hypotenuse if the length of the side opposite the 30° angle is 1?

2 Signup and view all the answers

What is the tangent value of a 45° angle?

1 Signup and view all the answers

If the sine of angle θ is 1/2, what is the possible value of θ?

Both B and C Signup and view all the answers

For a right triangle with an opposite side of length 3 and an adjacent side of length 4, what is the angle corresponding to the tangent ratio?

53.13° Signup and view all the answers

What is the cosine value of a 60° angle?

1/2 Signup and view all the answers

If the angle B corresponds to the point Q(-2, 3) in the Cartesian plane, what is the value of B?

123.7° Signup and view all the answers

What is the relationship between the sine and cosine of a 45° angle?

sin 45° = cos 45° Signup and view all the answers

What value does tan θ equal when the opposite side is 5 and the adjacent side is 0?

Undefined Signup and view all the answers

In general, what is the maximum value of sin θ?

1 Signup and view all the answers

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

360° Signup and view all the answers

Which of the following quadrilaterals has all sides of equal length?

Rhombus Signup and view all the answers

Which statement about a rectangle is true?

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

What does the Mid-Point Theorem state?

The segment joining the midpoints of two sides is parallel to the third side. Signup and view all the answers

Which of the following shapes is a trapezium?

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

Which quadrilateral is classified as both a rhombus and a rectangle?

Square Signup and view all the answers

In which of the following quadrilaterals do the diagonals bisect each other at right angles?

Kite Signup and view all the answers

What are the properties of a parallelogram?

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

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

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

What is the converse of the Mid-Point Theorem?

If a line is drawn through the midpoint of a triangle parallel to a side, it bisects the third side. Signup and view all the answers

What is the gradient of a horizontal line?

0 Signup and view all the answers

Which of the following describes the relationship of gradients between two perpendicular lines?

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

Which formula represents the equation of a straight line in standard form?

y = mx + c Signup and view all the answers

How do you calculate the mid-point M(x, y) between the 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

When given two points, how can we determine if they are collinear?

By using the gradient method. Signup and view all the answers

What determines the steepness of a straight line in the gradient formula?

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

If line WX has a gradient of 3, what must be the gradient of line YZ for them to be perpendicular?

-1/3 Signup and view all the answers

Which statement is true about the gradients of parallel lines?

They have equal values. Signup and view all the answers

What is the relationship between the line segment joining the mid-points of two sides of a triangle and the third side?

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

How does the length of the line segment joining the mid-points of a triangle's sides compare to the length of the third side?

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

In the proof of parallelogram MNOP from parallelogram ABCD, which property is utilized to prove congruency between triangles?

Angle-Angle-Side (AAS) criterion. Signup and view all the answers

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

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

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

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

Which application of the Mid-Point Theorem is focused on calculating distances in the Cartesian plane?

Coordinate Geometry Signup and view all the answers

In parallelogram ABCD, which property is NOT true?

Adjacent angles are equal. Signup and view all the answers

When constructing a figure on the Cartesian plane, which order must the points be joined?

In alphabetical order as defined. Signup and view all the answers

What can be concluded if both pairs of opposite angles in quadrilateral MNOP are equal?

MNOP is a parallelogram. Signup and view all the answers

What is one major use of the Mid-Point Theorem in geometric proofs?

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

What can be concluded about the side lengths of similar triangles?

They are proportional to each other. Signup and view all the answers

Which of the following is a property of corresponding angles in similar triangles?

They must be congruent. Signup and view all the answers

If triangles ΔABC and ΔDEF are similar, what does the notation ΔABC ∼ ΔDEF specifically indicate?

The triangles share the same angles and proportional sides. Signup and view all the answers

What happens to the ratios of the sides in similar triangles when their angles are scaled uniformly?

The ratios remain constant. Signup and view all the answers

For similar triangles, which statement regarding the lengths of their corresponding sides is incorrect?

The ratio varies between each pair of corresponding sides. Signup and view all the answers

Why are the specific angles in 30°, 60°, and 90° triangles significant in trigonometry?

They have unique side length ratios that are consistent. Signup and view all the answers

What is the relationship between the angles and side lengths of similar triangles characterized by the notation ΔABC ∼ ΔDEF?

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

In the context of similar triangles, what role does the order of vertices play?

It determines which angles correspond to which sides. Signup and view all the answers

When relating the sides of a right-angled triangle to angle θ, which side is correctly identified as the adjacent side?

The side that forms angle θ with the hypotenuse Signup and view all the answers

Which trigonometric ratio represents the relationship between the adjacent side and the hypotenuse?

Cosine Signup and view all the answers

If sin θ = 0.5, which of the following could represent angle θ in degrees?

30° Signup and view all the answers

What is the value of cosec θ if sin θ = 0.8?

1.25 Signup and view all the answers

Which relationship between sine and cosecant is always true?

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

What is the cosecant function defined as in relation to a right-angled triangle?

The ratio of hypotenuse to opposite Signup and view all the answers

When using a calculator to compute trigonometric ratios, what is a critical step to perform beforehand?

Configure the calculator to degrees mode Signup and view all the answers

In special angles, what is the sine value for an angle of 45°?

$rac{ ext{1}}{ ext{ extsf{√2}}}$ Signup and view all the answers

Which reciprocal ratio correctly relates to the tangent function?

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

For which angle is the cosine value equal to 0?

90° Signup and view all the answers

What is the cosine value of a 30° angle?

$rac{ ext{sqrt}(3)}{2}$ Signup and view all the answers

In which quadrant is the cosine function positive?

Quadrant I and IV Signup and view all the answers

Which function is undefined at an angle of 90°?

tan θ Signup and view all the answers

Which statement correctly describes the sine function y = sin θ?

The y-intercept is (0°, 0). Signup and view all the answers

If the sine function is represented as y = a sin θ + q, what is the effect of |a| < 1?

Vertical compression Signup and view all the answers

What is the sine value for an angle corresponding to the maximum turning point of the sine function?

1 Signup and view all the answers

What does the term angle of elevation refer to?

Angle formed by the line of sight above horizontal Signup and view all the answers

In two-dimensional trigonometry, how are the angle of elevation and angle of depression related?

They are always equal. Signup and view all the answers

What is the range of the cosine function over one complete cycle?

[-1, 1] Signup and view all the answers

Which of the following represents the tangent of an angle in a right triangle?

Opposite divided by Adjacent Signup and view all the answers

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

√3 Signup and view all the answers

Which trigonometric function corresponds to the ratio of the opposite side to the adjacent side in a right triangle?

Tangent Signup and view all the answers

What is the value of sin 45°?

√2/2 Signup and view all the answers

If the opposite side of a right triangle is 3 and the adjacent side is 4, what is the sine of the angle formed?

3/4 Signup and view all the answers

What is the angle corresponding to a tangent value of √3?

60° Signup and view all the answers

Which of the following statements is true regarding the cosine function?

cos 45° = √2/2 Signup and view all the answers

What angle corresponds to a sine value of 1/2?

30° Signup and view all the answers

In which quadrant does the sine function remain positive?

Quadrant II Signup and view all the answers

If tan(θ) = 1, what is the value of θ?

45° Signup and view all the answers

What is the relationship between the sine and cosine of a 30° angle?

sin 30° + cos 30° = 1 Signup and view all the answers

What is true about the diagonals in a rhombus?

They intersect at 90 degrees. Signup and view all the answers

Which statement about the interior angles of a quadrilateral is correct?

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

Which type of quadrilateral has only one pair of parallel sides?

Trapezium Signup and view all the answers

What can be concluded if $b^2 = a^2 + c^2$ for a triangle?

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

Which property distinguishes a square from other quadrilaterals?

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

Which of the following describes a kite?

A quadrilateral with two pairs of adjacent sides equal. Signup and view all the answers

Which property is true for all rectangles?

Diagonals are congruent and bisect each other. Signup and view all the answers

Which of the following is a characteristic of a trapezium?

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

What does the mid-point theorem state about a triangle?

The mid-point line is parallel and half the length of the third side. Signup and view all the answers

In a parallelogram, which statement is incorrect?

Only one pair of opposite sides need to be equal. Signup and view all the answers

What is the range of the function $y = a an heta + q$?

All real numbers Signup and view all the answers

What effect does an amplitude of $|a| > 1$ have on the graph of the function $y = a an heta + q$?

Vertical stretch of the graph branches Signup and view all the answers

Which statement about the domain of the tangent function is correct?

The domain includes all angles except 90° and 270° Signup and view all the answers

How does a negative value of $a$ in the function $y = a an heta + q$ affect the graph?

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

What type of triangle has all sides of different lengths?

Scalene triangle Signup and view all the answers

What do the angles of a triangle sum up to?

180° Signup and view all the answers

Which congruency rule is applied if two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle?

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

What can be said about two similar triangles?

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

What is the period of the function $y = a an heta + q$?

180° Signup and view all the answers

In a right triangle, how is an exterior angle related to interior angles?

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

What does the line segment joining the mid-points of two sides of a triangle represent in relation to the third side?

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

If the length of the third side of a triangle is 10 units, what is the length of the segment joining the mid-points of the other two sides?

5 units Signup and view all the answers

Which of the following applications of the Mid-Point Theorem utilizes it to prove segment proportions?

Geometric proofs related to similar triangles Signup and view all the answers

What essential property of a parallelogram can be derived from the mid-points of its opposite sides?

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

When constructing the coordinates of a quadrilateral, why is the order of the vertices important?

It defines the shape and connectivity of the figure. Signup and view all the answers

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

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

What does the gradient of a line represent?

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

In which of the following scenarios would the Mid-Point Theorem NOT apply?

Within non-triangular polygons Signup and view all the answers

Which statement about the angles formed by two pairs of opposite angles in a parallelogram is correct?

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

Which concept involves determining the angle relationships and lengths from bisected segments?

Similarity in triangles Signup and view all the answers

What does the gradient of a horizontal line equal?

0 Signup and view all the answers

How do the gradients of two perpendicular lines relate to each other?

Their product is equal to -1. Signup and view all the answers

Which formula can be used to find a straight line given two points?

$y - y_1 = rac{y_2 - y_1}{x_2 - x_1}(x - x_2)$ Signup and view all the answers

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

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

What is the significance of the mid-point formula?

It determines the coordinates between two points. Signup and view all the answers

What does it mean for two points to be collinear?

They lie on the same line. Signup and view all the answers

What happens to the gradient as the change in x approaches zero?

The gradient becomes undefined. Signup and view all the answers

Which statement about parallel lines is true?

They have equal gradients. Signup and view all the answers

What property distinguishes similar triangles from non-similar triangles?

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

If triangles ABC and DEF are similar, which of the following ratios is correct?

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

Which statement accurately describes the angles in similar triangles?

Corresponding angles are equal. Signup and view all the answers

Which is a true statement about the side ratios of similar triangles with angles of 30°, 60°, and 90°?

The ratios will always be 1:√3:2. Signup and view all the answers

What must be true regarding the order of vertices in similar triangles?

It defines the correspondence of angles and sides. Signup and view all the answers

How do the ratios of corresponding sides in two similar triangles relate?

They are not affected by the size of the triangles. Signup and view all the answers

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

Triangle ABC and triangle DEF are similar. Signup and view all the answers

What is the significance of the angles 30°, 60°, and 90° in relation to similar triangles?

They form a right triangle with unique side ratios. Signup and view all the answers

What effect does a negative value of $a$ have in the function $y = a an heta + q$?

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

Which statements correctly describe the range of the function $y = a an heta + q$?

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

For triangles to be similar, which property must they have in common?

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

What is the significance of the value of $q$ in the equation for the cosine function?

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

What is the correct classification of a triangle that has one angle greater than 90° and two equal sides?

Obtuse isosceles triangle Signup and view all the answers

Which congruency rule is applied when two sides and the included angle of one triangle are equal to those of another triangle?

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

What do you call the vertical lines that the tangent graph approaches but never touches?

Asymptotes Signup and view all the answers

In the cosine function $y = a ext{cos}( heta) + q$, if $|a| > 1$, what happens to the graph?

The graph undergoes vertical stretch. Signup and view all the answers

Which statement about the period of the tangent function $y = an heta$ is true?

It is 180°. Signup and view all the answers

Which of the following correctly describes the sine function in a right-angled triangle?

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

What is the relationship between sine and cosecant in trigonometry?

$\sin heta \times \csc heta = 1$ Signup and view all the answers

For angle $ heta$, if the opposite side has a length of 6 and the hypotenuse has a length of 10, what is $ an heta$?

$\frac{6}{4}$ Signup and view all the answers

What does the mnemonic 'Soh Cah Toa' specifically help to remember?

The ratios of the sides in a right-angled triangle Signup and view all the answers

If $ an heta = 3$, what is the ratio of the opposite side to the adjacent side?

$\frac{3}{1}$ Signup and view all the answers

Which statement is true regarding the reciprocal ratios of the trigonometric functions?

$\cot heta = \frac{1}{\tan heta}$ Signup and view all the answers

Which of the following values represents the cosine of a 30° angle?

$\frac{\sqrt{3}}{2}$ Signup and view all the answers

To determine the value of $ an 45°$, what is the correct calculation?

$1$ Signup and view all the answers

What is the sum of the sine squared and cosine squared of any angle?

$1$ Signup and view all the answers

If the adjacent side has a length of 5 and the hypotenuse has a length of 13, what is $rac{1}{\cos heta}$?

$\frac{13}{5}$ Signup and view all the answers

What is the value of $\sin 30^\circ$?

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

Which statement best describes the positive trigonometric ratios in Quadrant III?

Only $\tan \theta$ and $\cot \theta$ are positive. Signup and view all the answers

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

$q$ Signup and view all the answers

If $\tan \theta$ is undefined, which angle could represent $\theta$?

$90^\circ$ Signup and view all the answers

In the context of the Sine function, what does the variable $a$ affect when $|a| > 1$?

Amplitude change Signup and view all the answers

What is the cosine value at the maximum turning point of the cosine function in the interval $[0^\circ, 360^\circ]$?

$1$ Signup and view all the answers

When calculating $\cot \theta$, which of the following ratios is used?

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

What is the maximum turning point of the sine function over one complete cycle?

At $90^\circ$ Signup and view all the answers

What is the angle of elevation equal to when looking from an object below the horizontal plane?

The angle of depression from the object Signup and view all the answers

Which function indicates a vertical shift of the sine function upwards?

$y = \sin \theta + q$ where $q > 0$ Signup and view all the answers

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

360° Signup and view all the answers

Which of the following properties is unique to a rectangle?

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

Which statement is true about the diagonals of a rhombus?

Diagonals are perpendicular to each other. Signup and view all the answers

What defines a kite in terms of its sides?

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

Which of the following is not a property of a parallelogram?

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

To determine if a triangle is right-angled using the Pythagorean theorem, which condition must be met?

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

How can one identify a trapezium?

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

In the context of the mid-point theorem, what is true about the 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

What is the gradient of a horizontal line?

0 Signup and view all the answers

Which quadrilateral is defined by having all sides equal and all angles equal to 90°?

Square Signup and view all the answers

Which of the following describes the relationship between the gradients of two perpendicular lines?

Their product is -1. Signup and view all the answers

How is the mid-point M of a line segment defined in terms of its endpoints 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 condition is necessary for two points to be collinear?

They must have a constant gradient between them. 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

What is the gradient when the change in y is 0?

0 Signup and view all the answers

Which formula is used to calculate the gradient of a line segment?

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

What happens to the gradient of a line as the two points converge to become the same point?

It becomes undefined. Signup and view all the answers

What can be said about the line joining the mid-points of two sides of a triangle in relation to the third side?

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

In the mid-point theorem, what is the relationship of the line segment between the mid-points to the length of the third side?

The segment is half the length of the third side. Signup and view all the answers

Which concept is crucial in proving the properties of shapes like parallelograms using triangles?

Triangles can be congruent by the AAS criterion. Signup and view all the answers

What does the gradient of a line represent?

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

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

Using the formula $ ext{distance} = |x₂ - x₁| + |y₂ - y₁|$. Signup and view all the answers

What is the significance of the mid-point theorem in coordinate geometry?

It assists in calculating mid-points and segment lengths. Signup and view all the answers

In order to prove that a quadrilateral is a parallelogram using triangle properties, which condition must be established?

It is necessary for one pair of opposite sides to be equal and parallel. Signup and view all the answers

What is a fundamental characteristic of similar triangles?

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

Which property holds true regarding quadrilateral ABCD given the coordinates A(1, 1), B(3, 1), C(3, 3), and D(1, 3)?

It is a rectangle. Signup and view all the answers

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

√3 Signup and view all the answers

Which equation allows you to find the angle from the tangent ratio if you know the opposite and adjacent sides?

tan θ = opposite / adjacent Signup and view all the answers

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

1 Signup and view all the answers

What is the value of sin 30°?

1/2 Signup and view all the answers

If the sine of an angle θ equals 1/2, what could be a possible angle?

30° Signup and view all the answers

How can angle B be determined from point Q(-2, 3) in the Cartesian plane when using the tangent ratio?

B = 180° - tan^{-1}(3/2) Signup and view all the answers

In a right triangle with an adjacent side of length 4 and an opposite side of length 3, what is the tangent of the angle opposite the side of length 3?

3/4 Signup and view all the answers

What is the cosine of 60°?

1/2 Signup and view all the answers

When solving a trigonometric equation, if the rearranged equation exceeds the domain of sine function, which of the following statements is true?

The equation will have no solution. Signup and view all the answers

For point P(2, 3), what is the tangent of angle A formed between the line OP and the positive x-axis?

3/2 Signup and view all the answers

What property of similar triangles indicates that their corresponding sides are proportional?

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

Which of the following statements about the order of vertices in similar triangles is true?

It is crucial for maintaining the correct correspondence between angles. Signup and view all the answers

If triangles ΔABC and ΔDEF are similar, which ratio correctly represents their corresponding sides?

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

In a set of similar triangles with angles of 30°, 60°, and 90°, how do their corresponding side ratios compare?

They remain equal regardless of triangle sizes. Signup and view all the answers

What defines the relationship between corresponding angles in similar triangles?

They are always equal. Signup and view all the answers

Why is the concept of similar triangles significant in trigonometry?

It helps define trigonometric ratios through side length ratios. Signup and view all the answers

Given two similar triangles, what can you conclude about their perimeters relative to each other?

Their perimeters are in the same proportion as their corresponding sides. Signup and view all the answers

When working with similar triangles, which statement about the ratios of sides is incorrect?

The ratios must vary if the triangles are of different shapes. Signup and view all the answers

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

√3 Signup and view all the answers

If two sides of a right triangle are known, which trigonometric ratio would you use to find an angle?

Any of sine, cosine, or tangent depending on the sides Signup and view all the answers

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

1 Signup and view all the answers

How do you find the angle corresponding to a given tangent ratio?

Use the inverse tangent function Signup and view all the answers

What is the angle formed at point B when coordinates Q(-2, 3) are used?

123.7° Signup and view all the answers

Which of the following statements is correct regarding the domain of the sine and cosine functions?

Both sine and cosine are limited to values between -1 and 1 Signup and view all the answers

If the opposite side measures 3 and the adjacent side measures 4, what is the value of the tangent ratio?

3/4 Signup and view all the answers

In the Cartesian plane, if you draw a line from the origin to point P(2, 3), what is the tangent of the angle A formed with the x-axis?

3/2 Signup and view all the answers

What is the relationship between the sides and angles in a right-angled triangle when determining the sine ratio?

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

What is the cosine ratio of an angle in a right-angled triangle defined as?

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

Which of the following represents the definition of tangent for an angle theta?

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

What effect does a value of $|a| < 1$ have on the function $y = a an heta + q$?

It results in a vertical compression. Signup and view all the answers

Which of the following describes the domain of the function $y = an heta$?

$0° ext{ to } 360°, heta eq 90°, 270°$ Signup and view all the answers

What is the reciprocal of the tangent function called?

Cotangent Signup and view all the answers

If an angle theta has a sine value of $rac{3}{5}$, what is the value of cosec theta?

$rac{5}{3}$ Signup and view all the answers

What is the relationship between the interiors angles of any triangle?

The sum is always 180°. Signup and view all the answers

How is the range of the cosine function determined when $a > 0$?

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

Which relationship is true regarding the sine and cosecant of an angle theta?

$ ext{sin } heta imes ext{cosec } heta = 1$ Signup and view all the answers

For two triangles to be congruent, which condition must be met according to the congruency rules?

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

What is the valid way to express $ ext{sec } heta$ using sine?

$rac{1}{ ext{cos } heta}$ Signup and view all the answers

In the mnemonic 'Soh Cah Toa', what does 'Toa' represent?

Tangent ratio Signup and view all the answers

Which statement is true regarding the characteristics of similar triangles?

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

What is the vertical shift caused by the value $q$ in the function $y = a an heta + q$ when $q < 0$?

Shift down by $|q|$ units. Signup and view all the answers

What should you do before calculating trigonometric functions on a calculator?

Set to Degrees mode Signup and view all the answers

Which congruency rule applies when two sides and the angle between them of one triangle are equal to two sides and the included angle of another triangle?

SAS Signup and view all the answers

Which of the following is a property of the sides in a right-angled triangle according to the Pythagorean theorem?

Square of hypotenuse equals sum of squares of other two sides Signup and view all the answers

When comparing the sine and cosine functions, how can the cosine graph be transformed to match the sine graph?

By shifting it right by 90°. Signup and view all the answers

What is the sine of a 90° angle?

1 Signup and view all the answers

Which property defines an equilateral triangle?

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

In which quadrant is the cosine function positive?

Quadrant I Signup and view all the answers

What is the maximum turning point of the cosine function?

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

Which trigonometric function has the value $0$ at $90^ ext{o}$?

cos Signup and view all the answers

For the function $y = a an heta + q$, what does a < 0 signify?

Reflection about the x-axis Signup and view all the answers

Which of the following defines the angle of depression?

Angle formed by line of sight below the horizontal plane Signup and view all the answers

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

$rac{1}{2}$ Signup and view all the answers

Which statement accurately describes the range of the sine function?

From $-1$ to $1$ Signup and view all the answers

What is the relationship between the angles of elevation and depression from the same point?

They are equal Signup and view all the answers

What is the period of the sine function?

360° Signup and view all the answers

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

All sides are equal in length 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

In which quadrilateral do the diagonals bisect each other at 90°?

Kite Signup and view all the answers

Which statement is true regarding a rhombus?

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

Which of the following accurately describes a trapezium?

Has one pair of opposite sides parallel Signup and view all the answers

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

The line segment joining the mid-points of two sides is parallel to the third side 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

Which property is NOT true for all parallelograms?

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

Identify the characteristics of a rectangle that differentiate it from a standard parallelogram.

Diagonals are equal in length Signup and view all the answers

What property describes the line segment joining the mid-points of two sides of a triangle in relation to the third side?

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

What is the relationship between the length of the line segment joining the mid-points of two sides of a triangle and the length of the third side?

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

How can the mid-point theorem be applied in geometric proofs?

To prove parallelism and segment proportions. Signup and view all the answers

In coordinate geometry, what is necessary to apply the concept of mid-points?

Coordinates of the vertices. Signup and view all the answers

What characterizes the gradient of a line joining two points?

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

Which method can be used to find the distance between two points (x₁, y₁) and (x₂, y₂)?

Apply the Pythagorean theorem: $AB = \sqrt{(x₂ - x₁)^2 + (y₂ - y₁)^2}$. Signup and view all the answers

What must be shown to prove that MNOP is a parallelogram given parallelogram ABCD?

That both pairs of opposite angles are equal. Signup and view all the answers

Which property allows you to calculate the gradient of a line efficiently?

Knowing the coordinates of the points. Signup and view all the answers

What is the main purpose of finding mid-points in geometric problems?

To establish relationships in triangles and quadrilaterals. Signup and view all the answers

In the context of triangles, proving similarity often involves which concept?

Applying the mid-point theorem. 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

Which of the following statements about gradients is true?

The gradient of a vertical line is undefined. Signup and view all the answers

How do you find the gradient between two points A(x₁, y₁) and B(x₂, y₂)?

m = (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) = \left( \frac{x₁ + x₂}{2}, \frac{y₁ + y₂}{2} \right) Signup and view all the answers

If two lines are parallel, what can be said about their gradients?

They are equal. Signup and view all the answers

What condition must be true for two lines to be considered perpendicular?

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

Which method can be used to confirm that two points are collinear?

Using the gradient method. Signup and view all the answers

What is the gradient of a horizontal line?

0 Signup and view all the answers

Gr 10 Math June P2 Medium

Questions and Answers

What is the value of the sine function for an angle theta in a right-angled triangle?

Which of the following statements about trigonometric ratios is false?

What does the mnemonic 'Soh Cah Toa' help to remember?

What is the reciprocal of the sine function?

If angle theta is known, how can you find the value of cosine theta?

What must be true about triangles for them to be considered similar?

Which of the following statements about the ratios of similar triangles is correct?

Which relationship correctly describes the tangent of angle theta?

To calculate trigonometric ratios using a calculator, which mode should it be set to for angle measurements in degrees?

If two triangles are similar, which property regarding their angles holds true?

What is the primary use of the Pythagorean theorem in relation to trigonometric functions?

In similar triangles, how is the order of the vertices important?

Which of the following is a characteristic of the ratios in similar triangles with angles of 30°, 60°, and 90°?

Which trigonometric function relates the opposite side to the adjacent side in a right triangle?

For triangles ΔABC and ΔDEF where ΔABC ∼ ΔDEF, what can be deduced about the relationship between side lengths?

Which of the following reciprocal identities is correct?

When comparing the sides of similar triangles, which ratio is commonly used to express the relationship between the sides?

Which of the following constitutes a valid comparison between the angles in two similar triangles?

What are the positive trigonometric ratios in Quadrant II?

What is the sine of 90 degrees?

Which of the following is true regarding the tangent function?

In the case of the function y = a sin θ + q, what effect does a < 0 have?

Which angle corresponds to a sine value of 1/2?

What is the range of the cosine function over one complete cycle?

What is the equivalent of the angle of elevation concerning the angle of depression?

What is the x-intercept of the function y = cos θ?

Which of the following ratios is NOT a definition of a trigonometric ratio for a right triangle?

What is the maximum turning point of the sine function?

How does the value of $q$ in the function $y = a an heta + q$ affect the graph?

What is the range of the function $y = a an heta + q$?

Which classification applies to a triangle with one angle greater than 90° and two unequal sides?

What type of triangle is defined by having all three sides equal in length?

According to congruency rules, which condition is sufficient to prove two triangles are congruent?

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

Which statement is true regarding the cosine graph compared to the sine graph?

What is the period of the tangent function $y = an heta$?

What occurs when $|a| > 1$ in the function $y = a an heta + q$?

Which congruency rule is applicable if two angles and the included side of one triangle are equal to two angles and the included side of another triangle?

In a 30°-60°-90° triangle, what is the length of the hypotenuse if the length of the side opposite the 30° angle is 1?

What is the tangent value of a 45° angle?

If the sine of angle θ is 1/2, what is the possible value of θ?

For a right triangle with an opposite side of length 3 and an adjacent side of length 4, what is the angle corresponding to the tangent ratio?

What is the cosine value of a 60° angle?

If the angle B corresponds to the point Q(-2, 3) in the Cartesian plane, what is the value of B?

What is the relationship between the sine and cosine of a 45° angle?

What value does tan θ equal when the opposite side is 5 and the adjacent side is 0?

In general, what is the maximum value of sin θ?

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

Which of the following quadrilaterals has all sides of equal length?

Which statement about a rectangle is true?

What does the Mid-Point Theorem state?

Which of the following shapes is a trapezium?

Which quadrilateral is classified as both a rhombus and a rectangle?

In which of the following quadrilaterals do the diagonals bisect each other at right angles?

What are the properties of a parallelogram?

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

What is the converse of the Mid-Point Theorem?

What is the gradient of a horizontal line?

Which of the following describes the relationship of gradients between two perpendicular lines?

Which formula represents the equation of a straight line in standard form?

How do you calculate the mid-point M(x, y) between the points A(x₁, y₁) and B(x₂, y₂)?

When given two points, how can we determine if they are collinear?

What determines the steepness of a straight line in the gradient formula?

If line WX has a gradient of 3, what must be the gradient of line YZ for them to be perpendicular?

Which statement is true about the gradients of parallel lines?

What is the relationship between the line segment joining the mid-points of two sides of a triangle and the third side?

How does the length of the line segment joining the mid-points of a triangle's sides compare to the length of the third side?

In the proof of parallelogram MNOP from parallelogram ABCD, which property is utilized to prove congruency between triangles?

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

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

Which application of the Mid-Point Theorem is focused on calculating distances in the Cartesian plane?

In parallelogram ABCD, which property is NOT true?

When constructing a figure on the Cartesian plane, which order must the points be joined?

What can be concluded if both pairs of opposite angles in quadrilateral MNOP are equal?

What is one major use of the Mid-Point Theorem in geometric proofs?

What can be concluded about the side lengths of similar triangles?

Which of the following is a property of corresponding angles in similar triangles?

If triangles ΔABC and ΔDEF are similar, what does the notation ΔABC ∼ ΔDEF specifically indicate?