Q. If the vector A = 5i + 12j is scaled by a factor of 2, what is the new vector?
A.
10i + 24j
B.
5i + 12j
C.
2i + 3j
D.
7i + 14j
Show solution
Solution
Scaling A by 2 gives 2A = 2(5i + 12j) = 10i + 24j.
Correct Answer:
A
— 10i + 24j
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Q. If the vectors A = 1i + 2j and B = 2i + 1j, find A · B. (2023)
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Solution
A · B = (1)(2) + (2)(1) = 2 + 2 = 4
Correct Answer:
B
— 5
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Q. If the vectors A = 2i + 2j and B = 2i - 2j, find A · B.
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Solution
A · B = (2)(2) + (2)(-2) = 4 - 4 = 0.
Correct Answer:
B
— 4
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Q. If the vectors A = 2i + 3j and B = 3i + 4j are perpendicular, what is the value of A · B?
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Solution
Since A and B are perpendicular, A · B = 0.
Correct Answer:
A
— 0
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Q. If the vectors A = 3i + 4j and B = 4i + 3j, what is the scalar product A · B?
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Solution
A · B = (3)(4) + (4)(3) = 12 + 12 = 24.
Correct Answer:
A
— 25
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Q. If the vectors A = 5i + 5j and B = 5i - 5j, what is the scalar product A · B?
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Solution
A · B = (5)(5) + (5)(-5) = 25 - 25 = 0.
Correct Answer:
B
— 0
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Q. If the vectors A = 6i + 8j and B = 2i + 3j, what is A · B? (2020)
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Solution
A · B = (6)(2) + (8)(3) = 12 + 24 = 36.
Correct Answer:
A
— 42
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Q. If the vectors A = 6i + 8j and B = 3i + 4j are perpendicular, what is the value of A · B? (2021)
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Solution
A · B = (6)(3) + (8)(4) = 18 + 32 = 50, but since they are perpendicular, A · B = 0.
Correct Answer:
A
— 0
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Q. If the vectors A and B are such that A · B = |A| |B|, what is the angle between them?
A.
0°
B.
90°
C.
180°
D.
None of the above
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Solution
If A · B = |A| |B|, then cos(θ) = 1, which means θ = 0°.
Correct Answer:
A
— 0°
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Q. If two angles are complementary and one angle measures 30 degrees, what is the measure of the other angle? (2023)
A.
60 degrees
B.
90 degrees
C.
30 degrees
D.
45 degrees
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Solution
Complementary angles add up to 90 degrees. If one angle is 30 degrees, the other angle must be 90 - 30 = 60 degrees.
Correct Answer:
A
— 60 degrees
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Q. If two angles are complementary and one angle measures 35 degrees, what is the measure of the other angle? (2023)
A.
45 degrees
B.
55 degrees
C.
65 degrees
D.
75 degrees
Show solution
Solution
Complementary angles sum up to 90 degrees. If one angle is 35 degrees, the other angle is 90 - 35 = 55 degrees.
Correct Answer:
B
— 55 degrees
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Q. If two angles are equal and their sum is 180 degrees, what is the measure of each angle? (2022)
A.
90 degrees
B.
60 degrees
C.
45 degrees
D.
30 degrees
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Solution
If two angles are equal and their sum is 180 degrees, each angle must be 180 / 2 = 90 degrees.
Correct Answer:
A
— 90 degrees
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Q. If two angles are supplementary and one angle is three times the other, what are the measures of the angles?
A.
30 degrees and 150 degrees
B.
45 degrees and 135 degrees
C.
60 degrees and 120 degrees
D.
75 degrees and 105 degrees
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Solution
Let the angles be x and 3x. Then, x + 3x = 180. Solving gives x = 45 degrees and 3x = 135 degrees.
Correct Answer:
C
— 60 degrees and 120 degrees
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Q. If two angles are supplementary and one angle is twice the other, what are the measures of the angles? (2022)
A.
30 degrees and 60 degrees
B.
45 degrees and 135 degrees
C.
90 degrees and 90 degrees
D.
40 degrees and 140 degrees
Show solution
Solution
Let the smaller angle be x. Then the larger angle is 2x. Since they are supplementary, x + 2x = 180 degrees, which gives 3x = 180 degrees, so x = 60 degrees. The angles are 60 degrees and 120 degrees, which is not in the options. The correct answer is 40 degrees and 140 degrees.
Correct Answer:
D
— 40 degrees and 140 degrees
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Q. If two angles are supplementary and one angle measures 110 degrees, what is the measure of the other angle? (2019)
A.
70 degrees
B.
80 degrees
C.
90 degrees
D.
100 degrees
Show solution
Solution
Two angles are supplementary if their sum is 180 degrees. Therefore, if one angle is 110 degrees, the other angle = 180 - 110 = 70 degrees.
Correct Answer:
A
— 70 degrees
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Q. If two angles are supplementary and one angle measures 120 degrees, what is the measure of the other angle? (2022)
A.
60 degrees
B.
90 degrees
C.
120 degrees
D.
180 degrees
Show solution
Solution
Supplementary angles sum up to 180 degrees. Therefore, the other angle = 180 - 120 = 60 degrees.
Correct Answer:
A
— 60 degrees
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Q. If two angles are supplementary and one angle measures 75 degrees, what is the measure of the other angle?
A.
85 degrees
B.
90 degrees
C.
95 degrees
D.
105 degrees
Show solution
Solution
Supplementary angles sum up to 180 degrees. Therefore, the other angle = 180 - 75 = 105 degrees.
Correct Answer:
D
— 105 degrees
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Q. If two circles intersect at points A and B, and the distance between their centers is 10 cm, what is the maximum possible radius of each circle? (2021)
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
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Solution
The maximum radius of each circle can be half the distance between the centers, which is 10 cm.
Correct Answer:
B
— 10 cm
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Q. If two intersecting lines form an angle of 40 degrees, what is the measure of the vertically opposite angle? (2023)
A.
40 degrees
B.
60 degrees
C.
80 degrees
D.
100 degrees
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Solution
Vertically opposite angles are equal. Therefore, the vertically opposite angle is also 40 degrees.
Correct Answer:
A
— 40 degrees
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Q. If two lines are cut by a transversal and the corresponding angles are equal, what can be said about the two lines? (2020)
A.
They are parallel
B.
They are perpendicular
C.
They intersect
D.
They are skew lines
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Solution
If the corresponding angles are equal, it indicates that the two lines are parallel.
Correct Answer:
A
— They are parallel
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Q. If two lines are intersected by a transversal and the sum of the interior angles on the same side of the transversal is 200 degrees, what can be concluded about the two lines? (2022)
A.
They are parallel
B.
They are perpendicular
C.
They intersect
D.
They are skew lines
Show solution
Solution
If the sum of the interior angles on the same side of the transversal is greater than 180 degrees, the two lines must intersect.
Correct Answer:
C
— They intersect
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Q. If two lines are perpendicular, what is the measure of the angle formed between them? (2019)
A.
45 degrees
B.
90 degrees
C.
180 degrees
D.
60 degrees
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Solution
Perpendicular lines intersect at right angles, which measure 90 degrees.
Correct Answer:
B
— 90 degrees
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Q. If two lines are perpendicular, what is the measure of the angles formed?
A.
45 degrees
B.
90 degrees
C.
180 degrees
D.
60 degrees
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Solution
Perpendicular lines intersect at right angles, which measure 90 degrees.
Correct Answer:
B
— 90 degrees
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Q. If two lines intersect and form angles of 120 degrees and x degrees, what is the value of x? (2022)
A.
60 degrees
B.
120 degrees
C.
90 degrees
D.
180 degrees
Show solution
Solution
The angles formed by intersecting lines are supplementary. Therefore, 120 + x = 180, which gives x = 60 degrees.
Correct Answer:
A
— 60 degrees
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Q. If two lines intersect and form angles of 40 degrees and x degrees, what is the value of x?
A.
40 degrees
B.
140 degrees
C.
180 degrees
D.
60 degrees
Show solution
Solution
The angles formed by intersecting lines are supplementary. Therefore, x = 180 - 40 = 140 degrees.
Correct Answer:
B
— 140 degrees
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Q. If two lines intersect and one of the angles formed is 120 degrees, what is the measure of the vertically opposite angle? (2022)
A.
60 degrees
B.
120 degrees
C.
90 degrees
D.
180 degrees
Show solution
Solution
Vertically opposite angles are equal. Therefore, the vertically opposite angle is also 120 degrees.
Correct Answer:
B
— 120 degrees
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Q. If two lines intersect and one of the angles formed is 40 degrees, what is the measure of the adjacent angle? (2020)
A.
40 degrees
B.
140 degrees
C.
180 degrees
D.
90 degrees
Show solution
Solution
Adjacent angles formed by intersecting lines are supplementary, meaning they add up to 180 degrees. Therefore, if one angle is 40 degrees, the adjacent angle is 180 - 40 = 140 degrees.
Correct Answer:
B
— 140 degrees
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Q. If two lines intersect and one of the angles is 40 degrees, what is the measure of the vertically opposite angle? (2023)
A.
40 degrees
B.
80 degrees
C.
60 degrees
D.
20 degrees
Show solution
Solution
Vertically opposite angles are equal when two lines intersect. Therefore, if one angle is 40 degrees, the vertically opposite angle is also 40 degrees.
Correct Answer:
A
— 40 degrees
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Q. If two lines intersect and the measures of the angles formed are in the ratio 2:3, what is the measure of the larger angle?
A.
72 degrees
B.
108 degrees
C.
60 degrees
D.
90 degrees
Show solution
Solution
Let the angles be 2x and 3x. Since they are supplementary, 2x + 3x = 180 degrees. Thus, 5x = 180 degrees, x = 36 degrees. The larger angle is 3x = 108 degrees.
Correct Answer:
B
— 108 degrees
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Q. If two lines intersect and the measures of the two adjacent angles are 30 degrees and x degrees, what is the value of x?
A.
30 degrees
B.
150 degrees
C.
120 degrees
D.
90 degrees
Show solution
Solution
Adjacent angles formed by intersecting lines are supplementary. Therefore, 30 + x = 180, which gives x = 150 degrees.
Correct Answer:
B
— 150 degrees
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