Mathematics for IGCSE & O level - Pythagoras' Theorem And Trigonometry (Section 7)
1
When using a three-figure bearing, which direction is the reference point for measuring the angle?
Trả lời
(C)
North
2
What does the term 'adjacent' refer to in the context of a right triangle and a given angle?
Trả lời
(C)
The side next to the angle that is not the hypotenuse.
3
What does 'tan' represent in trigonometry?
Trả lời
(B)
Opposite/Adjacent
4
What should be the mode of the calculator be set on to calculate the angles?
Trả lời
(B)
Deg
5
What is the appropriate formula to use, to calculate the area of a triangle when the length of two sides and an included angle are given?
Trả lời
(C)
Area = 1/2 * a * b * sin C
6
To use the formula Area = 1/2 * ab * sin C, which elements must be known?
Trả lời
A
B
7
What key elements are needed to accurately calculate the area of a triangle using the 1/2 * ab * sin C formula?
Trả lời
A
B
C
8
Which rule allows you to find the area of a triangle if you know two sides and the included angle?
Trả lời
(C)
Area = 1/2 * ab * sin C
9
To solve for angles in a right-angled triangle, you can use:
Trả lời
A
B
C
10
What does the abbreviation SSS represent, as it relates to using the Cosine Rule?
Trả lời
(A)
Side Side Side
11
A ship travels from point A on a bearing of 000 degrees for 6 km, and then 090 degrees for 8 km. How can we determine the distance the ship is from the starting point?
Trả lời
(C)
Pythagorean Theorem
12
If you have a triangle with sides 8 cm, 10 cm, and an included angle of 45 degrees, what is the area?
Trả lời
(A)
28.3 cm²
13
What must the sum of the two acute angles in a right-angled triangle always equal?
Trả lời
(C)
90 degrees
14
If the bearing of point B from point A is 090 degrees, which direction is point B in relation to A?
Trả lời
(B)
East
15
Which trigonometric ratio is defined as Opposite/Adjacent?
Trả lời
(C)
Tangent
16
If the height of a tower and the angle of elevation from a point on the ground to the top of the tower are known, what can be determined?
Trả lời
(C)
Both A and B
17
What is the relationship between the sine and cosine of complementary angles?
Trả lời
(A)
They are equal.
18
If a right triangle has a hypotenuse of 10 and one leg of 8, what is the length of the other leg?
Trả lời
(B)
4
19
Which sides of a right triangle are used when calculating the tangent of an angle?
Trả lời
(B)
Opposite and adjacent
20
If cos θ = -0.5, and θ is between 0 and 180 degrees, what is the value of θ?
Trả lời
(C)
120°
21
If the bearing of point B from point A is 120°, what is the bearing of point A from point B (approximately)?
Trả lời
(C)
300°
22
If you know two angles of a triangle, can you determine the third angle?
Trả lời
(C)
Yes, the sum of angles is 180 degrees.
23
Which statements are correct about angle calculations using trigonometric ratios?
Trả lời
A
B
C
24
What is the inverse function of the tangent function?
Trả lời
(C)
Arctangent
25
What is the result when you find the sine of an angle and then take the arcsine of that value?
Trả lời
(B)
The original angle
26
If sin(θ) = 0.5, what is the value of θ?
Trả lời
(A)
30 degrees
27
Which of the following is the Sine Rule?
Trả lời
(C)
a/sin A = b/sin B = c/sin C
28
What can be determined by knowing the measurements of the angles in a triangle, and the lengths of the sides of a right-angled triangle?
Trả lời
A
B
D
29
In a right-angled triangle, what is the side directly across from a reference angle called?
Trả lời
(C)
Opposite
30
What is the relationship between a and A in the sine rule?
Trả lời
(A)
a is opposite angle A
31
If sin(θ) = 0.7, what is the approximate value of θ (in degrees)?
Trả lời
(B)
44.4°
32
If you are given the lengths of the two legs of a right triangle, how do you find the hypotenuse?
Trả lời
(C)
Use the Pythagorean Theorem.
33
In a right-angled triangle, the side opposite the right angle is called:
Trả lời
(C)
Hypotenuse
34
Which of the following statements is true about the area of a square?
Trả lời
(C)
Area = side * side
35
Which of the following is/are required to be known in order to solve a right-angled triangle problem?
Trả lời
A
B
36
Which of the following are used to solve for non-right-angled triangles?
Trả lời
A
B
37
What ratio does the tangent function represent?
Trả lời
(C)
Opposite / Adjacent
38
In the cosine rule, how do you know which angle to calculate the cos of?
Trả lời
(A)
The angle opposite the longest side.
39
Which of the following are necessary to calculate the area of a non-right triangle using the formula Area = 1/2 * ab * sin C?
Trả lời
A
B
40
What is needed in order to use inverse trig functions on a calculator?
Trả lời
A
C
41
If a boat sails 6km on a bearing of 000 degrees (North) and then 8km on a bearing of 090 degrees (East), which theorem would you use to calculate the distance from the starting point?
Trả lời
(B)
Pythagorean Theorem
42
In the context of 3D geometry, which theorem is most relevant for calculating lengths or angles?
Trả lời
(D)
Both b and c
43
The angle of depression from a point A to a point B is 40°. What is the angle of elevation from B to A?
Trả lời
(A)
40°
44
Which trigonometric functions are needed to solve non-right-angled triangles?
Trả lời
A
B
45
Which trigonometric ratio is used when you know two sides and want to find an angle in a right-angled triangle?
Trả lời
(D)
All of the above
46
What is the value of cos(30°)?
Trả lời
(B)
√3/2
47
In a triangle, if all three sides are known, which rule can be applied to find the angles?
Trả lời
(C)
Cosine Rule
48
What is the inverse function for tangent?
Trả lời
(C)
Arctangent
49
What is the bearing of a point that is directly west of your location?
Trả lời
(D)
270°
50
Which of the following describes the relationship between the sides of a right-angled triangle?
Trả lời
(B)
The square of the hypotenuse is equal to the sum of the squares of the other two sides.
