Gr 10 Math June P2 Easy

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

The ratio of the hypotenuse to the opposite side

The ratio of the opposite side to the hypotenuse (correct)

The ratio of the adjacent side to the hypotenuse

The ratio of the adjacent side to the opposite side

Which mnemonic helps remember the trigonometric ratios?

Angle Side Formula

Cos Tan Sin

Ratios To Use

Soh Cah Toa (correct)

What is the reciprocal of cosine?

Sine

Cosecant

Secant (correct)

Cotangent

What relationship holds true for sine and cosecant?

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

Which of the following sides in a triangle is NOT used in the definition of tangent?

Base Signup and view all the answers

What is the correct way to express cotangent?

The reciprocal of tangent Signup and view all the answers

What should you check before using a calculator for trigonometric calculations?

The calculator is in degrees mode Signup and view all the answers

Which trigonometric ratio can be calculated directly without a calculator for certain special angles?

Sine Signup and view all the answers

Which expression represents the theorem of Pythagoras in a triangle?

hypotenuse² = opposite² + adjacent² Signup and view all the answers

Which of the following is the cosine ratio?

Adjacent to hypotenuse Signup and view all the answers

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

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

If triangles have angles of 30°, 60°, and 90°, what can be said about their side ratios?

The ratios are always equal, regardless of triangle size. Signup and view all the answers

For similar triangles ΔABC and ΔDEF, which statement about their corresponding angles is correct?

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

Which of the following ratios holds true for similar triangles?

AB/DE = AC/DF Signup and view all the answers

What must be true about the order of vertices when labeling similar triangles?

Corresponding vertices must match. Signup and view all the answers

When examining similar triangles, which of the following conclusions is incorrect?

The triangles must have identical side lengths. Signup and view all the answers

Which statement regarding the key ratios of similar triangles is true?

The ratios are equal when the triangles are similar. Signup and view all the answers

What is a key characteristic of similar triangles concerning angle measures?

Corresponding angles are equal. Signup and view all the answers

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

2 Signup and view all the answers

Which ratio is correct for sin 60°?

√3/2 Signup and view all the answers

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

1 Signup and view all the answers

What is the tangent of 45°?

1 Signup and view all the answers

To find an angle in a right triangle when given two side lengths, what must be used?

Trigonometric ratios Signup and view all the answers

What is the value of cos 30°?

√3/2 Signup and view all the answers

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

1 Signup and view all the answers

How do you find the angle given a ratio like an A = 3/2?

Use inverse tangent function Signup and view all the answers

What is the range of values for the sine function?

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

What is the opposite side for point P(2, 3) in relation to angle A?

3 Signup and view all the answers

What is the correct definition of sine for a right-angled triangle?

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

Which trigonometric function is undefined at $90^ heta$?

Tangent Signup and view all the answers

In which quadrant are both sine and cosecant positive?

Quadrant II Signup and view all the answers

What is the sine value of $30^ heta$?

1/2 Signup and view all the answers

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

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

What is the range of the sine function?

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

Which of the following ratios is defined as $rac{y}{x}$?

Tangent Signup and view all the answers

What happens to the graph of $y = a ext{sin} heta$ if $a < 0$?

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

What is the cosine of $0^ heta$?

1 Signup and view all the answers

Which angle is equivalent to the angle of elevation from a point below the horizontal plane?

The angle of depression from the same point. Signup and view all the answers

What is the definition of a quadrilateral?

A closed shape consisting of four straight line segments. Signup and view all the answers

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

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

What distinguishes a square from a rhombus?

A square has all four angles equal to 90°. Signup and view all the answers

What is true about the diagonals of a rhombus?

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

Which statement about a trapezium is correct?

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

What characteristic is common to both rectangles and rhombuses?

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

In which type of quadrilateral are both pairs of opposite angles equal?

Square Signup and view all the answers

If two triangles have their corresponding angles equal, what can be concluded about them?

They are similar. Signup and view all the answers

According to the properties of a kite, which statement is correct?

The longer diagonal bisects the other diagonal. Signup and view all the answers

Which triangles can be proven congruent using the AAS criterion?

Triangles with two angles and one non-included side equal. Signup and view all the answers

What does the Mid-Point Theorem state about the line segment joining the mid-points of two sides of a triangle?

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

Which statement correctly describes the converse of the Mid-Point Theorem?

If a line is drawn through the mid-point of one side parallel to the second side, it will bisect the third side. Signup and view all the answers

What is one application of the Mid-Point Theorem?

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

What geometric properties can be used to prove that MNOP is a parallelogram?

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

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

Using the Pythagorean theorem to find the length. Signup and view all the answers

What is a characteristic feature of a quadrilateral named ABCD based on its coordinates?

It can only be referred to in alphabetical order. Signup and view all the answers

What condition is necessary for line segment DE in the Mid-Point Theorem?

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

What is the significance of proving that triangles CDZ and ABX are congruent?

It establishes that angles in corresponding positions are equal. Signup and view all the answers

Which of the following best describes a property of a parallelogram?

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

What would be the outcome if a line is drawn through the midpoint of one side of a triangle parallel to the other side?

It will bisect the remaining side of the triangle. Signup and view all the answers

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

{ f(\theta) : f(\theta) \in \mathbb{R} } Signup and view all the answers

What happens to the graph of the cosine function when $q < 0$?

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

Which of the following is NOT a characteristic of the cosine function?

y-intercept at (0°, 0) Signup and view all the answers

What is the period of the sine and cosine functions?

360° Signup and view all the answers

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

180° Signup and view all the answers

Which classification describes a triangle with all three sides of different lengths?

Scalene Signup and view all the answers

Which rule states that two triangles are congruent if two sides and the included angle of one triangle are equal to those of another triangle?

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

Which aspect is affected by the value of $a$ in the functions of the form $y = a an \theta + q$?

Steepness of the branches Signup and view all the answers

What is the y-intercept of the cosine function expressed in the form $y = a an \theta + q$?

a + q Signup and view all the answers

Which statement describes an obtuse triangle?

One angle is greater than 90°. Signup and view all the answers

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

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

How is the gradient (m) of a line defined?

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

Which of the following describes a horizontal line?

Has a gradient equal to zero Signup and view all the answers

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

y = mx + c Signup and view all the answers

How would you conclude that two points are collinear?

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

What is the gradient of two lines that are perpendicular to each other?

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

Which formula calculates the mid-point M(x, y) between two points A(x₁, y₁) and B(x₂, y₂)?

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

Which property is true for vertical lines?

They have an undefined gradient Signup and view all the answers

What determines the gradient of a line joining two points?

Ratio of the vertical change to horizontal change Signup and view all the answers

What must be true for two triangles to be considered similar?

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

Which of the following ratios is always true for similar triangles?

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

In the context of similar triangles, what is a crucial factor when labeling their vertices?

Corresponding vertices must be labeled consistently. Signup and view all the answers

When comparing angles of similar triangles, what can be concluded about the angles?

They are equal. Signup and view all the answers

What is the relationship between the side lengths of any three similar triangles with angles of 30°, 60°, and 90°?

The ratios of the corresponding side lengths will be the same. Signup and view all the answers

If triangles ΔABC and ΔDEF are shown to be similar, which statement regarding their areas is true?

Their area ratio is the square of the ratio of their corresponding sides. Signup and view all the answers

Which of the following correctly describes the corresponding angles in similar triangles?

They are congruent. Signup and view all the answers

What is the primary relevance of similar triangles in trigonometry?

They provide a basis for defining trigonometric ratios. Signup and view all the answers

What is the value of cosecant in terms of sine for an angle θ?

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

Which ratio correctly defines tangent for angle θ?

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

What relationship holds between sine and cosecant?

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

How should a calculator be set before performing trigonometric calculations?

In degrees mode Signup and view all the answers

Which of the following is the definition of secant for angle θ?

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

What is true about the sine function's output?

It ranges from -1 to 1 Signup and view all the answers

What values can the tangent of an angle take?

Any real number Signup and view all the answers

For a right triangle with angle θ, which side is referred to as the adjacent side?

The side next to θ Signup and view all the answers

Which of the following angles has a sine value of 1?

90° Signup and view all the answers

What is the correct value of cosine for angle 0°?

1 Signup and view all the answers

In which quadrant are both tangent and cotangent positive?

Quadrant III Signup and view all the answers

What is the sine value of $60^ heta$?

$\frac{\sqrt{3}}{2}$ 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 statements about the sine function is true?

Its range is from -1 to 1. Signup and view all the answers

Which criterion states that two triangles are congruent if two angles and the included side are equal?

AAS Signup and view all the answers

What happens to the graph of $y = a \sin \theta$ if $a > 1$?

It stretches vertically. Signup and view all the answers

Which statement accurately describes a trapezium?

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

What is the effect of a negative value of $q$ in the function $y = a \sin \theta + q$?

Shifts the graph downward. Signup and view all the answers

What is a defining property of a rectangle that differentiates it from a parallelogram?

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

For which special angle is the tangent value undefined?

$90^ heta$ Signup and view all the answers

What is the definition of cosine for an angle $ heta$ in a right-angled triangle?

Adjacent over Hypotenuse Signup and view all the answers

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

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

What does the angle of depression signify?

Angle below the horizontal line to an object above. Signup and view all the answers

What must be true for two triangles to be similar?

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

Which quadrilateral has both pairs of opposite sides equal and diagonals that bisect each other?

Rectangle Signup and view all the answers

What value does cosine take at angle $90^ heta$?

$0$ Signup and view all the answers

In the CAST diagram, which quadrant has all trigonometric ratios positive?

Quadrant I Signup and view all the answers

In a kite, what is a characteristic of the diagonals?

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

Which of the following is true about a square?

It is a type of rectangle and rhombus. Signup and view all the answers

What property distinguishes similar triangles from congruent triangles?

Similar triangles have angles in proportion. Signup and view all the answers

What is the length of the hypotenuse in a 45°-45°-90° triangle?

√2 Signup and view all the answers

What is the sine value of 60°?

√3/2 Signup and view all the answers

Which ratio represents tan 30°?

√3/3 Signup and view all the answers

For a triangle with angles of 30°, 60°, and 90°, what is the length opposite the 30° angle?

1 Signup and view all the answers

What is the angle B when considering point Q(-2, 3) using the tangent ratio?

123.7° Signup and view all the answers

What is the cosine value of 30°?

√3/2 Signup and view all the answers

Which trigonometric function helps to find the angle corresponding to a given ratio?

Inverse trigonometric function Signup and view all the answers

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

√3 Signup and view all the answers

What must be true for the sine of an angle θ when determining valid solutions?

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

What is the tangent value of 45°?

1 Signup and view all the answers

What is the range of the cosine function in the form of ( y = a \cos \theta + q ) when ( a > 0 )?

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

Which of the following correctly states the x-intercepts for the cosine function?

(90°, 0) and (270°, 0) Signup and view all the answers

How is the amplitude of the tangent function affected by the variable ( a )?

It affects the steepness of the graph branches. Signup and view all the answers

What is the period of the tangent function?

180° Signup and view all the answers

What is true about the y-intercept of the sine function in the form of ( y = a \sin \theta + q )?

It equals ( q ). Signup and view all the answers

Which combination of properties could define an obtuse triangle?

One interior angle greater than 90°. Signup and view all the answers

For triangles, which statement about congruency is correct?

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

What can be said about the exterior angle of a triangle?

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

What condition would create an isosceles triangle?

At least two sides are equal, with angles opposite those sides equal. Signup and view all the answers

What is the y-intercept of the tangent function in the form of ( y = a \tan \theta + q )?

It equals ( a \tan 0° + q ). Signup and view all the answers

What does the Mid-Point Theorem imply about the line segment connecting the mid-points 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 necessary condition for a line to bisect the third side of a triangle according to the converse of the Mid-Point Theorem?

It must pass through the mid-point of one side and be parallel to another side. Signup and view all the answers

In which type of triangle should the Mid-Point Theorem be applied?

In any type of triangle, including scalene, isosceles, and equilateral. Signup and view all the answers

What outcome is observed when applying the Mid-Point Theorem to a triangle?

The segment joining the mid-points is both parallel to and half the length of the third side. Signup and view all the answers

What method is commonly used to investigate the Mid-Point Theorem visually?

Creating a large scalene triangle and connecting its mid-points. Signup and view all the answers

Which of the following applications does the Mid-Point Theorem NOT support?

Finding the area of trapezoids. Signup and view all the answers

When constructing a parallelogram using angles bisectors, which condition must be satisfied?

Opposite sides must be equal in length. Signup and view all the answers

What criterion is used to demonstrate that triangles are congruent in the proof of MNOP being a parallelogram?

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

How is the distance between two points calculated on a Cartesian plane?

By applying the Pythagorean theorem. Signup and view all the answers

What property is essential for the vertices of a figure when drawn on a Cartesian plane?

The order of letters for naming must indicate the joining sequence of points. Signup and view all the answers

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

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

How is the mid-point M(x, y) of the line segment between points A(x₁, y₁) and B(x₂, y₂) calculated?

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

What characteristic defines a straight line in terms of its gradient?

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

What is the product of the gradients of two lines that intersect perpendicularly?

-1 Signup and view all the answers

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

Horizontal lines have a gradient of zero Signup and view all the answers

Which formula is used to determine the distance between points (x₁, y₁) and (x₂, y₂)?

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

Which condition must be satisfied for two points to be collinear?

The gradient between them must be constant Signup and view all the answers

What defines the standard form of a straight line equation?

y = mx + c Signup and view all the answers

Which of the following is true about the lengths of the sides of the triangle used to define gradient?

The vertical side equals y₂ - y₁ and the horizontal side equals x₂ - x₁ Signup and view all the answers

Which trigonometric ratio is positive in Quadrant II?

sine Signup and view all the answers

What is the sine value of $60^ heta$?

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

What is the angle of depression equal to when viewing an object below the horizontal plane?

Angle of elevation from the corresponding point Signup and view all the answers

Which trigonometric ratio is undefined at $90^ heta$?

tan Signup and view all the answers

For the function $y = a \sin \theta + q$, what happens if $q < 0$?

Vertical shift down by $|q|$ units Signup and view all the answers

What is the range of the sine function?

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

In Quadrant IV, which trigonometric ratios are positive?

cos and sec Signup and view all the answers

What is the cosine value at $90^ heta$?

0 Signup and view all the answers

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

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

What is the cosine of 60°?

1/2 Signup and view all the answers

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

√3 Signup and view all the answers

Which of the following represents the tangent of 30°?

√3/3 Signup and view all the answers

What is the relationship between angle B and angle α in group Q(-2, 3)?

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

What is the hypotenuse length in a 45°-45°-90° triangle?

√2 Signup and view all the answers

If the tangent ratio of an angle is 3/2, what is this angle approximately equal to?

56.3° Signup and view all the answers

What is the sine value of 45°?

√2/2 Signup and view all the answers

For the point P(2, 3), what is the tangent ratio used to find the angle A?

3/2 Signup and view all the answers

What is the correct inverse trigonometric function to find the angle given sin θ = 1/2?

sin^-1 Signup and view all the answers

What is the sine of 30°?

1/2 Signup and view all the answers

What is the range of the function defined by the equation $y = a \cos \theta + q$ for $a > 0$?

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

Which statement about the cosine function is incorrect?

There are no x-intercepts in the cosine function. Signup and view all the answers

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

q Signup and view all the answers

What type of triangle has all equal side lengths?

Equilateral Signup and view all the answers

How are two triangles defined to be congruent?

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

What is the period of the sine and cosine functions?

360° Signup and view all the answers

What defines the vertical shift of the cosine function when using the equation $y = a \cos \theta + q$?

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

Which statement accurately describes the asymptotes of the tangent function?

Asymptotes occur at $\theta = 90°$ and $\theta = 270°$. 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 regarding the range of the tangent function is true?

The range is limited to {f(θ) : f(θ) ∈ ℝ}. Signup and view all the answers

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

They are equal regardless of the triangles' sizes. Signup and view all the answers

In similar triangles, corresponding angles:

Are equal in measure. Signup and view all the answers

What must be preserved when labeling similar triangles?

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

Which ratio represents the relationship between corresponding sides in similar triangles ΔABC and ΔDEF?

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

If two triangles have angles measuring 30°, 60°, and 90°, what can be concluded?

They are similar but not congruent. Signup and view all the answers

What happens when the angles in similar triangles remain constant?

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

How can similar triangles be identified?

By equal corresponding angles. Signup and view all the answers

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

Ratios are only equal in right-angled triangles. Signup and view all the answers

What is the relationship between sine and cosecant?

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

Which of the following is NOT a trigonometric ratio defined for the angle θ?

Geometric Mean Signup and view all the answers

Which of the following correctly defines the tangent of angle θ?

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

What type of triangle is necessary to define the trigonometric ratios sine, cosine, and tangent?

Right-angled triangle Signup and view all the answers

What angle must a scientific calculator be set to before performing trigonometric calculations?

Degree mode Signup and view all the answers

What is the reciprocal of tangent for angle θ defined as?

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

What does the Mid-Point Theorem state about the relationship between the mid-points of two sides of a triangle and the third side?

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

Which relationship is true for the cosine and secant?

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

In the converse of the Mid-Point Theorem, what happens when a line is drawn through the mid-point of one side of a triangle parallel to another side?

It bisects the third side. Signup and view all the answers

Which trigonometric function correlates with the ratio of the hypotenuse to the opposite side?

Cosecant Signup and view all the answers

What property relates to the lengths of the segments created by mid-points in a triangle?

The segment connecting the mid-points is half the length of the third side. Signup and view all the answers

For which angles are simple trigonometric ratios often derived without using a calculator?

Special angles like 30°, 45°, and 60° Signup and view all the answers

Which of the following applications utilizes the Mid-Point Theorem in geometric proofs?

Proving parallelism and segment proportions. Signup and view all the answers

Which equation correctly expresses the relationship between sine and the square of sine?

$ ext{sin }^2 heta = 1 - ext{cos }^2 heta$ Signup and view all the answers

How can the vertices of a figure be named for clarity when plotting on the Cartesian plane?

In alphabetical order for conventional reference. Signup and view all the answers

What is a critical step when using the Pythagorean theorem to find the distance between two points?

Finding the difference in both the x and y coordinates. Signup and view all the answers

In parallelogram ABCD, which relationship can be established about angles when proving that MNOP is a parallelogram?

Opposite angles are equal. Signup and view all the answers

When drawing figures on the Cartesian plane, what does the order of the letters indicate?

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

What geometric concept is essential for proving that triangles are similar using the properties stated?

Congruent angles are needed. Signup and view all the answers

What is the significance of using coordinates when drawing figures on the Cartesian plane?

Coordinates help derive the lengths of sides based on distances. Signup and view all the answers

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

$d = ext{sqrt}((x₁ - x₂)^2 + (y₁ - y₂)^2)$ 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

What is the gradient of a horizontal line?

Zero Signup and view all the answers

What can be said about parallel lines' gradients?

Their gradients are the same Signup and view all the answers

Which formula can be used to find the equation of a straight line?

$rac{y - y₁}{x - x₁} = rac{y₂ - y₁}{x₂ - x₁}$ Signup and view all the answers

What is the formula to calculate the mid-point of a line segment?

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

What characterizes two points being collinear?

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

How is the gradient of two intersecting lines related if they are perpendicular?

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

What is the gradient of a vertical line?

Undefined Signup and view all the answers

Which of the following statements is true regarding the distance formula?

It results in the same value regardless of point order Signup and view all the answers

What defines two triangles as similar?

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

Which of the following properties is unique to a rectangle?

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

Which of the following statements about a rhombus is true?

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

According to the properties of a square, which statement is incorrect?

The diagonals are unequal in length. Signup and view all the answers

Which quadrilateral has only one pair of opposite sides that are parallel?

Trapezium Signup and view all the answers

What is a necessary condition for two triangles to be congruent using the AAS criterion?

One side and two angles must be equal. Signup and view all the answers

If the sides of a quadrilateral are equal in length but not all angles are equal, it is classified as what?

Rhombus Signup and view all the answers

What is the total measure of interior angles in a quadrilateral?

360° Signup and view all the answers

Which type of trapezium has equal non-parallel sides?

Isosceles trapezium Signup and view all the answers

What remains constant among corresponding sides of similar triangles?

The ratio of their corresponding sides Signup and view all the answers

Which property must hold true for triangles Delta ABC and Delta DEF to be similar?

All corresponding angles are equal Signup and view all the answers

If triangles have angles of 30°, 60°, and 90°, what can be asserted about their corresponding sides?

Their corresponding sides will be proportional Signup and view all the answers

What is crucial when labeling vertices of similar triangles?

The order of vertices must correspond appropriately Signup and view all the answers

What is an implication of similar triangles regarding their dimensions?

Their corresponding sides are proportional Signup and view all the answers

In similar triangles, which of the following statements is false?

Angles can vary during comparison Signup and view all the answers

Which statement best describes the key ratios of the sides of similar triangles?

The ratios remain constant regardless of triangle size Signup and view all the answers

Which of the following must be true for two triangles to be classified as similar?

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

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

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

Which of the following expressions correctly represents cosecant?

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

What relationship holds true when multiplying sine and cosecant for an angle θ?

They equal 1. Signup and view all the answers

Which of these trigonometric ratios is defined as the ratio of adjacent to hypotenuse?

cos θ Signup and view all the answers

What must be done to calculate a reciprocal trigonometric ratio using a calculator?

Convert it to a standard trigonometric ratio. Signup and view all the answers

Which statement about the sine function is correct?

It ranges from -1 to 1. Signup and view all the answers

For which special angle is the sine value equal to $rac{1}{2}$?

30° Signup and view all the answers

Which of the following defines secant?

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

Which expression correctly represents the definition of cotangent?

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

What should be noted about scientific calculators when performing trigonometric calculations?

They must be in degrees mode. Signup and view all the answers

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

√2 Signup and view all the answers

Which of the following represents the sine value of 60°?

√3/2 Signup and view all the answers

Which ratio is correct for the tangent of angle θ when two sides of a triangle are known?

Opposite/Adjacent Signup and view all the answers

In a 30°-60°-90° triangle, what is the ratio of the length opposite the 60° angle compared to the hypotenuse?

√3/2 Signup and view all the answers

Which angle corresponds to a tangent ratio of 3/2 when using the inverse tangent function?

56.3° Signup and view all the answers

What caution should be taken when finding solutions to trigonometric equations?

Values may exceed limits of sine and cosine. Signup and view all the answers

What is the tangent value for a 45° angle?

1 Signup and view all the answers

For an angle with coordinates P(2, 3), which function can be used to determine the angle formed with the x-axis?

tangent Signup and view all the answers

What is the sine value of 30°?

1/2 Signup and view all the answers

What should you do first when solving a trigonometric equation?

Identify the trigonometric ratio involved. Signup and view all the answers

In which quadrant are both sine and cosine positive?

Quadrant I Signup and view all the answers

What is the sine value of $60^{ heta}$?

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

What is the tangent value of $30^{ heta}$?

$rac{1}{ ext{sqrt}(3)}$ Signup and view all the answers

What condition applies if $a < 0$ in the function $y = a ext{sin} heta$?

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

Which trigonometric function is undefined at $90^{ heta}$?

Tangent Signup and view all the answers

What is the maximum turning point of the sine function $y = ext{sin} heta$?

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

Which of the following statements is true regarding the angle of elevation and depression?

They are equal. Signup and view all the answers

What is the effect of a positive value of $q$ in the function $y = a ext{sin} heta + q$?

Shift up by $q$ units Signup and view all the answers

In which quadrant only the tangent ratio is positive?

Quadrant III Signup and view all the answers

What is the range of the sine function?

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

What is the range of the function in the form $y = a \sin \theta + q$ for $a > 0$?

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

Which of the following describes the y-intercept of the cosine function $y = a \cos \theta + q$?

a + q Signup and view all the answers

What is the domain of the tangent function $y = \tan \theta$?

[0°, 360°, θ ≠ 90°, 270°] Signup and view all the answers

How many maximum turning points does the cosine function have within the interval [0°, 360°]?

2 Signup and view all the answers

What does the notation ≡ indicate regarding two triangles?

They are congruent. Signup and view all the answers

In a right triangle, if the hypotenuse and one side are equal to those of another right triangle, which congruency rule applies?

RHS Signup and view all the answers

What is the period of the sine function?

360° Signup and view all the answers

Which of the following types of triangles has all three sides and angles the same?

Equilateral Signup and view all the answers

What happens to the graph of $y = a \sin \theta$ when $a < 0$?

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

What does the exterior angle of a triangle equal to?

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

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

It adds up to 360°. Signup and view all the answers

Which property differentiates a rectangle from other parallelograms?

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

Which quadrilateral has two pairs of adjacent sides that are equal?

Kite Signup and view all the answers

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

Rhombus Signup and view all the answers

Which condition must be satisfied for two triangles to be similar?

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

Which of the following quadrilaterals does not have parallel sides?

Trapezium Signup and view all the answers

What can be concluded if two triangles have their corresponding sides in proportion?

They are similar. Signup and view all the answers

Which of the following properties is unique to a square?

All four sides are equal. Signup and view all the answers

What does the Mid-Point Theorem state about the line segment joining the mid-points of two sides of a triangle?

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

If a triangle follows the AAS postulate, what can be said about it?

It is congruent to another triangle. Signup and view all the answers

What is the outcome when a line is drawn through the mid-point of a triangle's side parallel to the second side?

It bisects the third side. Signup and view all the answers

Which statement is true about a rhombus?

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

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

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

When exploring the Mid-Point Theorem, which observation can be made regarding triangle sides?

The length of the segment joining the mid-points equals half the length of the third side. Signup and view all the answers

In parallelogram ABCD, which property must hold true for it to be classified as a parallelogram?

One pair of opposite sides is both equal and parallel. Signup and view all the answers

What can be concluded from the congruence of triangles in the proof of parallelogram MNOP?

Their opposite sides are equal and the triangles are similar. Signup and view all the answers

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

Using the Pythagorean theorem. Signup and view all the answers

What is a key characteristic of the line segment connecting the mid-points regarding its relationship to the third side?

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

Which of the following best describes how points should be named when drawing figures on the Cartesian plane?

They must follow a specific alphabetical order. Signup and view all the answers

What defines a point in the context of coordinate geometry?

An ordered pair of numbers written as (x, y). Signup and view all the answers

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

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

How is the gradient of a line defined mathematically?

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

What is the relationship between two lines that are perpendicular to each other?

Their gradients are the negative reciprocals of each other. Signup and view all the answers

What is the y-intercept (c) in the straight line equation standard form $y = mx + c$?

It is the point where the line crosses the y-axis. Signup and view all the answers

What is the mid-point M(x, y) of a line segment connecting 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 describes a horizontal line?

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

In the formula for gradient, which change does the numerator represent?

The vertical change. Signup and view all the answers

Which condition would indicate that three points A, B, and C are collinear?

The gradients between pairs of points are equal. Signup and view all the answers

What happens to the gradient of a vertical line?

It is undefined. Signup and view all the answers

In a right-angled triangle formed by points A(x₁, y₁) and B(x₂, y₂), what does the hypotenuse represent?

The direct distance between the two points. Signup and view all the answers

Gr 10 Math June P2 Easy

Questions and Answers

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

Which mnemonic helps remember the trigonometric ratios?

What is the reciprocal of cosine?

What relationship holds true for sine and cosecant?

Which of the following sides in a triangle is NOT used in the definition of tangent?

What is the correct way to express cotangent?

What should you check before using a calculator for trigonometric calculations?

Which trigonometric ratio can be calculated directly without a calculator for certain special angles?

Which expression represents the theorem of Pythagoras in a triangle?

Which of the following is the cosine ratio?

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

If triangles have angles of 30°, 60°, and 90°, what can be said about their side ratios?

For similar triangles ΔABC and ΔDEF, which statement about their corresponding angles is correct?

Which of the following ratios holds true for similar triangles?

What must be true about the order of vertices when labeling similar triangles?

When examining similar triangles, which of the following conclusions is incorrect?

Which statement regarding the key ratios of similar triangles is true?

What is a key characteristic of similar triangles concerning angle measures?

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

Which ratio is correct for sin 60°?

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

What is the tangent of 45°?

To find an angle in a right triangle when given two side lengths, what must be used?

What is the value of cos 30°?

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

How do you find the angle given a ratio like an A = 3/2?

What is the range of values for the sine function?

What is the opposite side for point P(2, 3) in relation to angle A?

What is the correct definition of sine for a right-angled triangle?

Which trigonometric function is undefined at $90^ heta$?

In which quadrant are both sine and cosecant positive?

What is the sine value of $30^ heta$?

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

What is the range of the sine function?

Which of the following ratios is defined as $ rac{y}{x}$?

What happens to the graph of $y = a ext{sin} heta$ if $a < 0$?

What is the cosine of $0^ heta$?

Which angle is equivalent to the angle of elevation from a point below the horizontal plane?

What is the definition of a quadrilateral?

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

What distinguishes a square from a rhombus?

What is true about the diagonals of a rhombus?

Which statement about a trapezium is correct?

What characteristic is common to both rectangles and rhombuses?

In which type of quadrilateral are both pairs of opposite angles equal?

If two triangles have their corresponding angles equal, what can be concluded about them?

According to the properties of a kite, which statement is correct?

Which triangles can be proven congruent using the AAS criterion?

What does the Mid-Point Theorem state about the line segment joining the mid-points of two sides of a triangle?

Which statement correctly describes the converse of the Mid-Point Theorem?

What is one application of the Mid-Point Theorem?

What geometric properties can be used to prove that MNOP is a parallelogram?

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

What is a characteristic feature of a quadrilateral named ABCD based on its coordinates?

What condition is necessary for line segment DE in the Mid-Point Theorem?

What is the significance of proving that triangles CDZ and ABX are congruent?

Which of the following best describes a property of a parallelogram?

What would be the outcome if a line is drawn through the midpoint of one side of a triangle parallel to the other side?

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

What happens to the graph of the cosine function when $q < 0$?

Which of the following is NOT a characteristic of the cosine function?

What is the period of the sine and cosine functions?

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

Which classification describes a triangle with all three sides of different lengths?

Which rule states that two triangles are congruent if two sides and the included angle of one triangle are equal to those of another triangle?

Which aspect is affected by the value of $a$ in the functions of the form $y = a an \theta + q$?

What is the y-intercept of the cosine function expressed in the form $y = a an \theta + q$?

Which statement describes an obtuse triangle?

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

How is the gradient (m) of a line defined?

Which of the following describes a horizontal line?

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

How would you conclude that two points are collinear?

What is the gradient of two lines that are perpendicular to each other?

Which formula calculates the mid-point M(x, y) between two points A(x₁, y₁) and B(x₂, y₂)?

Which property is true for vertical lines?

What determines the gradient of a line joining two points?

What must be true for two triangles to be considered similar?

Which of the following ratios is defined as $rac{y}{x}$?