Mathematics for IGCSE & O level - Pythagoras' Theorem And Trigonometry (Section 2)
1
What is the value of tan(180° - θ) in relation to tan(θ)?
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(B)
-tan θ
2
What are the basic components needed for solving trigonometry problems?
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A
B
C
D
3
What is the inverse function for cosine?
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(B)
arccos
4
The angle that a line is on an object vector above a horizontal plane is called the angle of:
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(B)
elevation
5
What is the cosine of a right angle?
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(A)
0
6
If you know the hypotenuse and one leg of a right triangle, how do you find the other leg?
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(C)
Use the Pythagorean Theorem.
7
When using the Law of Sines, what information is typically needed?
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B
C
8
Which theorem is helpful to calculate the lengths of the sides of a right-angled triangular prism?
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(B)
Pythagorean Theorem
9
What is the relationship between the angles in a right-angled triangle?
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(B)
The sum of the two non-right angles is 90 degrees.
10
What is the value of sin(30°) ?
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(B)
0.5
11
Which of the following is the correct formula for calculating the length of a diagonal in a cuboid?
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(B)
d = √(a² + b² + c²)
12
Which trigonometric ratio is defined as Adjacent/Hypotenuse?
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(B)
Cosine
13
Which of the following is/are essential to solving a right triangle problem?
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A
C
14
What is the inverse function to find the angle when you know the ratio for the sides 'Opposite' and 'Hypotenuse'?
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(A)
sin⁻¹
15
Which of the following statements is correct in relation to the trigonometric ratios and angles in a triangle?
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(A)
The sine of an angle is equivalent to the cosine of its complement.
16
Which of the following methods can be used to find the unknown sides?
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(D)
All of the above
17
What is the measure of a right angle?
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(C)
90 degrees
18
In a right-angled triangle, which of the following must be known in order to calculate the length of a missing side?
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A
C
19
If sin θ = 0.5, then which of the following is not a possible value for θ?
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(C)
210°
20
What are the two possible angles to solve a triangle with, when applying the ambiguous case?
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(A)
Acute and obtuse
21
What specific measurements do you need to apply the formula: Area = 1/2 * ab * sin C?
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(A)
Lengths of sides 'a' and 'b', and the measure of angle C
22
Given sides a = 6cm, b = 8cm and the angle between them, C, is 30°. What is the area of this triangle?
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(A)
12 cm²
23
Which of the following is a correct application of the formula for area of a triangle: Area = 1/2 * ab * sin C?
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(A)
Knowing sides a = 5, b = 8, and angle C = 30 degrees
24
What is the key to calculating the area of a non-right-angled triangle when you know two sides and their included angle?
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(C)
Area = 1/2 * a * b * sin C
25
What is the value of tan 45°?
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(B)
1
26
In a right-angled triangle, what is the side *opposite* a given angle (other than the right angle)?
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(D)
The side directly across from the angle
27
If you know all three sides of a triangle, which rule is appropriate for calculating the angles?
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(B)
Law of Cosines
28
What type of triangle can be solved with the Pythagorean theorem?
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(C)
Right-angled triangle
29
Which of the following is correct regarding the sides of a right-angled triangle?
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(B)
The hypotenuse is always opposite the right angle.
30
A ladder leans against a wall. If the ladder is the hypotenuse, which sides of the right triangle formed by the ladder, wall, and ground represent the adjacent and opposite sides to the angle formed by the ladder and the ground?
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(B)
Adjacent: Ground, Opposite: Wall
31
What is the area of a parallelogram with base 5 cm, height 10 cm and an included angle of 30 degrees?
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(B)
25 cm²
32
If the bearing from point X to point Y is 270 degrees, in what direction is point Y from point X?
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(D)
West
33
If tan(x) = 1, what is x (in degrees)?
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(C)
45°
34
Which of the following correctly describes a three-figure bearing?
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(B)
A direction measured from the North in degrees, given with three digits.
35
Which rule is primarily used to find missing side lengths and angles in a non-right-angled triangle when the lengths of all three sides are known?
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(B)
Cosine Rule
36
Which of the following statements is/are true about the bearing of a point?
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A
B
37
In the context of solving problems using ratios, what should be the first step?
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(B)
Draw a clearly labeled diagram.
38
Which is the following is a correct expression for the angle of elevation?
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(B)
The angle between a horizontal line and a line of sight above the horizontal.
39
If the angle of elevation from a boat to the top of a cliff is 60°, and the cliff is 20 meters tall, what is the approximate distance from the boat to the base of the cliff?
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(B)
17.32 meters
40
Which of the following statements is true about the angles in a right-angled triangle?
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(D)
Both B and C
41
When using the Law of Cosines, what information is typically needed?
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A
C
42
What must be considered when using the sine rule to solve a triangle when given two sides and an angle that is *not* included?
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(C)
Whether there are two possible solutions
43
What is the value of the angle whose sine is 0?
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(A)
0
44
Which sides are needed to find an angle when using tangent ratio?
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(C)
Opposite and adjacent
45
What is the value of cos(0°)?
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(B)
1
46
Which of the following can be determined using the cosine rule?
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A
B
47
When the area of a triangle is calculated using 1/2 * ab * sin C, what does 'C' represent?
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(B)
The angle at vertex C
48
A parallelogram has adjacent sides of 8 cm and 10 cm. The angle between them is 30 degrees. What is the area of the parallelogram?
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(B)
80 cm²
49
What does it mean for two angles to be complementary?
