Mathematics for IGCSE & O level - Pythagoras' Theorem And Trigonometry (Section 3)
1
If the bearing from point X to point Y is 135 degrees, what is the bearing from point Y to point X?
答え
(C)
225 degrees
2
Which information is required to use the formula for the area of a triangle: 1/2 * base * height?
答え
(C)
The base and the perpendicular height to that base.
3
What is a key characteristic of all right-angled triangles?
答え
(B)
One angle measures 90 degrees
4
If a boat sails 4 km on a bearing of 000 degrees and then 3 km on a bearing of 090 degrees, what is the distance of the boat from the starting point?
答え
(A)
5 km
5
If a ladder leans against a wall and makes an angle of 60° with the ground, and the ladder is 10 meters long, how high up the wall does the ladder reach?
答え
(B)
8.66 meters
6
Which tools/concepts are necessary for applying the trigonometry ratios?
答え
A
C
D
7
What are the essential requirements for using the cosine rule to find an angle?
答え
(B)
All three sides
8
Which rule is typically used when you need to find missing sides and angles in a non-right-angled triangle given two sides and an included angle?
答え
(C)
Cosine Rule
9
What is the Pythagorean theorem primarily used for?
答え
(C)
Finding the sides of a right-angled triangle
10
Which of the following statements is/are true when using Pythagoras' Theorem?
答え
A
B
C
11
What is the value of cos(180°)?
答え
(C)
-1
12
What is a three-figure bearing and how is it typically expressed?
答え
(B)
An angle measured clockwise from North, expressed with three digits.
13
If a triangle has sides of 5 cm, 7 cm, and 9 cm, which rule is the most appropriate to determine the angles?
答え
(B)
The Cosine Rule
14
What is the main purpose of using three-figure bearings?
答え
(B)
To indicate a specific direction
15
What is a three-figure bearing?
答え
(A)
An angle measure clockwise from the north direction
16
In a non-right angled triangle, with sides a,b and c and the angles opposite them A, B and C, which formula represents the cosine rule correctly?
答え
(A)
a²=b²+c²-2bc cos A
17
What is the approximate value of the angle θ (in degrees) if tan(θ) = 1.732?
答え
(C)
60°
18
What does 'TOA' stand for in SOH CAH TOA?
答え
(B)
Tangent = Opposite / Adjacent
19
If two sides of a triangle are 5 cm and 12 cm, and the angle between them is 30 degrees, what is the area of the triangle?
答え
(C)
15 cm²
20
In a right-angled triangle, if you know one acute angle and the length of one side, what can you find?
答え
A
B
C
21
Which statement correctly describes a bearing?
答え
(A)
It is an angle measured clockwise from North.
22
If a boat travels 5km on a bearing of 060 degrees and then 7km on a bearing of 150 degrees, what geometrical shape describes the boat's path?
答え
(C)
An obtuse angle
23
If you are given an angle and the adjacent side of a right triangle, which trigonometric function is best to find the opposite side?
答え
(C)
Tangent
24
What is the formula for Pythagoras' theorem?
答え
(B)
a^2 + b^2 = c^2
25
To find the area of any triangle given two sides and an included angle, which of the following formulas can be used?
答え
(B)
Area = 1/2 * ab * sin C
26
Which of the following are true about the Cosine Rule?
答え
A
B
D
27
Which rule is best when you know two sides and the included angle of a non-right triangle and want to find the length of the third side?
答え
(C)
Cosine Rule
28
In the context of a three-dimensional rectangular prism, what formula is used to calculate the length of the diagonal?
答え
(B)
d = √(a² + b² + c²)
29
What is the formula for finding the area of a triangle if two sides, *a* and *b*, and the *included* angle *C* are known?
答え
(C)
Area = 1/2 * a * b * sin C
30
Which trigonometric function is defined as the ratio of the opposite side to the hypotenuse in a right-angled triangle?
答え
(A)
Sine
31
If the distance from a point on the ground to the base of a building is 50 meters and the angle of elevation to the top of the building is 45 degrees, what is the height of the building?
答え
(B)
50 meters
32
What is the primary goal of trigonometry?
答え
(B)
To study the relationships between the sides and angles of triangles.
33
If you know the angle and the hypotenuse of a right triangle, which trigonometric ratio can you use to find the length of the opposite side?
答え
(A)
Sine
34
Which of the following rules can be utilized to determine the area of any given triangle?
答え
(D)
All of the above
35
If you know two sides of a right triangle, which theorem can you use to find the third side?
答え
(C)
Pythagorean Theorem
36
What is the value of tan(0°)?
答え
(A)
0
37
If the bearing from A to B is 180 degrees, what is the direction of B from A?
答え
(B)
South
38
In the context of the cosine rule, what is the formula for finding the angle A in a triangle with sides a, b, and c?
答え
(A)
cos A = (b² + c² - a²) / (2bc)
39
Which of the following statements is/are correct about the relationships in a right-angled triangle?
答え
A
B
C
40
If the hypotenuse of a right triangle is 10 and one leg is 6, what is the length of the other leg?
答え
(B)
8
41
Which of the following is a valid application of the cosine rule: a² = b² + c² - 2bc cos A?
答え
A
B
C
42
If you are given the lengths of all three sides (a, b, and c) of a triangle, what can you directly calculate using the Cosine Rule?
答え
(A)
The angles of the triangle.
43
What does the abbreviation 'CAH' represent in the mnemonic SOH CAH TOA?
答え
(A)
Cosine Adjacent Hypotenuse
44
If cos(θ) = 0.8, what is θ (approximately)?
答え
(A)
36.9°
45
If the sides of a right-angled triangle are 6cm and 8cm, what is the hypotenuse?
答え
(A)
10cm
46
Which of the following statements are true about the angles of elevation and depression?
答え
A
C
47
What is the value of cos(0)?
答え
(B)
1
48
In a triangle, which of the following scenarios allows you to directly apply the cosine rule?
答え
A
B
49
If sin(A) = sin(B) and A and B are angles in a triangle, what can be concluded about the relationship between A and B?
答え
(D)
A and B are supplementary, or A=B
50
What does the term 'bearing' refer to in navigation?
答え
(B)
The direction of travel, measured as an angle from North.
