Q. What is the range of the data set: 15, 22, 8, 19, 30?
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Solution
Range = max - min = 30 - 8 = 22.
Correct Answer:
A
— 22
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Q. What is the range of the data set: 7, 3, 9, 5, 12?
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Solution
Range = max - min = 12 - 3 = 9.
Correct Answer:
B
— 6
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Q. What is the range of the following data set: 15, 22, 8, 19, 30?
Show solution
Solution
Range = max - min = 30 - 8 = 22.
Correct Answer:
A
— 22
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Q. What is the range of the function y = -x^2 + 4?
A.
y ≤ 4
B.
y ≥ 4
C.
y < 4
D.
y > 4
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Solution
The vertex is at (0, 4) and opens downwards, so the range is y ≤ 4.
Correct Answer:
A
— y ≤ 4
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Q. What is the range of the function y = 2sin(x)?
A.
[-2, 2]
B.
[-1, 1]
C.
[0, 2]
D.
(-∞, ∞)
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Solution
The range of y = 2sin(x) is [-2, 2] because the sine function oscillates between -1 and 1.
Correct Answer:
A
— [-2, 2]
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Q. What is the range of the function y = 4sin(x)?
A.
[-4, 4]
B.
[-1, 1]
C.
[0, 4]
D.
[-2, 2]
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Solution
The range of y = Asin(Bx) is [-|A|, |A|]. Here, A = 4, so the range is [-4, 4].
Correct Answer:
A
— [-4, 4]
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Q. What is the ratio in which the point (3, 4) divides the line segment joining (1, 2) and (5, 6)?
A.
1:2
B.
2:1
C.
3:1
D.
1:3
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Solution
Using the section formula, we can find the ratio by solving for m:n in the equations derived from the coordinates.
Correct Answer:
B
— 2:1
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Q. What is the ratio in which the point (3, 5) divides the line segment joining (1, 2) and (5, 8)?
A.
1:2
B.
2:1
C.
3:1
D.
1:3
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Solution
Using the section formula, we find the ratio is 2:1.
Correct Answer:
B
— 2:1
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Q. What is the ratio of the areas of two similar triangles if the ratio of their corresponding sides is 3:5?
A.
3:5
B.
9:25
C.
15:25
D.
5:3
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Solution
The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. (3/5)^2 = 9/25.
Correct Answer:
B
— 9:25
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Q. What is the ratio of the areas of two similar triangles if the ratio of their corresponding sides is 3:4?
A.
3:4
B.
9:16
C.
12:16
D.
1:1
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Solution
The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. Therefore, (3/4)^2 = 9/16.
Correct Answer:
B
— 9:16
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Q. What is the relationship between the angles formed by two intersecting lines?
A.
They are equal.
B.
They are complementary.
C.
They are supplementary.
D.
They are not related.
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Solution
The angles formed by two intersecting lines are supplementary, meaning they add up to 180 degrees.
Correct Answer:
C
— They are supplementary.
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Q. What is the relationship between the angles formed by two parallel lines cut by a transversal?
A.
All angles are equal.
B.
Corresponding angles are equal.
C.
Alternate exterior angles are equal.
D.
Both B and C.
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Solution
Corresponding angles and alternate exterior angles are equal when two parallel lines are cut by a transversal.
Correct Answer:
D
— Both B and C.
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Q. What is the relationship between the angles formed by two tangents drawn from a point outside the circle?
A.
They are equal
B.
They are supplementary
C.
They are complementary
D.
They are congruent
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Solution
The angles formed by two tangents drawn from a point outside the circle are equal.
Correct Answer:
A
— They are equal
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Q. What is the relationship between the angles formed by two tangents drawn from a point outside a circle?
A.
They are equal
B.
They are supplementary
C.
They are complementary
D.
They are congruent
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Solution
The angles formed by two tangents drawn from a point outside a circle to the points of tangency are equal.
Correct Answer:
A
— They are equal
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Q. What is the relationship between the angles in similar triangles?
A.
They are equal
B.
They are supplementary
C.
They are complementary
D.
They are congruent
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Solution
In similar triangles, corresponding angles are equal.
Correct Answer:
A
— They are equal
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Q. What is the relationship between the angles of a triangle and its sides?
A.
Larger angles are opposite longer sides
B.
Smaller angles are opposite longer sides
C.
All angles are equal
D.
None of the above
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Solution
In a triangle, larger angles are always opposite longer sides, which is a fundamental property of triangles.
Correct Answer:
A
— Larger angles are opposite longer sides
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Q. What is the relationship between the angles of two congruent triangles?
A.
They are always equal
B.
They can be different
C.
They are supplementary
D.
They are complementary
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Solution
In congruent triangles, all corresponding angles are equal.
Correct Answer:
A
— They are always equal
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Q. What is the relationship between the angles of two parallel lines cut by a transversal?
A.
They are all equal
B.
They are supplementary
C.
They are complementary
D.
They are congruent
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Solution
When two parallel lines are cut by a transversal, the interior angles on the same side are supplementary.
Correct Answer:
B
— They are supplementary
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Q. What is the relationship between the angles subtended by an arc at the center and at any point on the remaining part of the circle?
A.
The angle at the center is half
B.
The angle at the center is double
C.
They are equal
D.
The angle at the center is zero
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Solution
The angle subtended by an arc at the center is always double the angle subtended at any point on the remaining part of the circle.
Correct Answer:
B
— The angle at the center is double
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Q. What is the relationship between the angles subtended by the same arc at the center and at the circumference of the circle?
A.
The angle at the center is half of the angle at the circumference
B.
The angle at the center is equal to the angle at the circumference
C.
The angle at the center is double the angle at the circumference
D.
There is no relationship
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Solution
The angle subtended at the center of the circle is always double the angle subtended at the circumference by the same arc.
Correct Answer:
C
— The angle at the center is double the angle at the circumference
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Q. What is the relationship between the angles subtended by the same arc at the center and at any point on the circumference?
A.
The angle at the center is double
B.
The angle at the center is half
C.
They are equal
D.
They are supplementary
Show solution
Solution
The angle subtended at the center is always double the angle subtended at any point on the circumference.
Correct Answer:
A
— The angle at the center is double
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Q. What is the relationship between the angles subtended by the same arc at the center and at the circumference?
A.
They are equal
B.
The angle at the center is twice the angle at the circumference
C.
The angle at the circumference is twice the angle at the center
D.
They are complementary
Show solution
Solution
The angle subtended at the center is always twice the angle subtended at the circumference by the same arc.
Correct Answer:
B
— The angle at the center is twice the angle at the circumference
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Q. What is the relationship between the angles subtended by the same arc at the center and on the circumference of a circle?
A.
They are equal
B.
The angle at the center is twice the angle at the circumference
C.
The angle at the circumference is twice the angle at the center
D.
They are complementary
Show solution
Solution
The angle subtended at the center of a circle is always twice the angle subtended at the circumference by the same arc.
Correct Answer:
B
— The angle at the center is twice the angle at the circumference
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Q. What is the relationship between the angles subtended by the same arc at the center and at any point on the remaining part of the circle?
A.
They are equal
B.
The angle at the center is double
C.
The angle at the center is half
D.
They are supplementary
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Solution
The angle subtended at the center is always double the angle subtended at any point on the remaining part of the circle.
Correct Answer:
B
— The angle at the center is double
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Q. What is the relationship between the consecutive interior angles formed by a transversal intersecting two parallel lines?
A.
They are equal.
B.
They are complementary.
C.
They are supplementary.
D.
They are adjacent.
Show solution
Solution
Consecutive interior angles are supplementary when two parallel lines are cut by a transversal.
Correct Answer:
C
— They are supplementary.
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Q. What is the relationship between the exterior angle and the interior angle on the same side of a transversal intersecting two parallel lines?
A.
They are equal.
B.
They are complementary.
C.
They are supplementary.
D.
They are not related.
Show solution
Solution
The Exterior Angle Theorem states that the exterior angle is supplementary to the interior angle on the same side of the transversal.
Correct Answer:
C
— They are supplementary.
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Q. What is the relationship between the exterior angle and the interior angle on the same side when two parallel lines are cut by a transversal?
A.
They are equal.
B.
They are complementary.
C.
They are supplementary.
D.
They are not related.
Show solution
Solution
The exterior angle and the interior angle on the same side are supplementary when two parallel lines are cut by a transversal.
Correct Answer:
C
— They are supplementary.
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Q. What is the relationship between the exterior angle and the two interior opposite angles in a triangle formed by a transversal intersecting two parallel lines?
A.
The exterior angle is equal to the sum of the two interior opposite angles.
B.
The exterior angle is less than the sum of the two interior opposite angles.
C.
The exterior angle is greater than the sum of the two interior opposite angles.
D.
There is no relationship.
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Solution
The exterior angle is equal to the sum of the two interior opposite angles in a triangle.
Correct Answer:
A
— The exterior angle is equal to the sum of the two interior opposite angles.
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Q. What is the relationship between the exterior angle of a triangle and the two opposite interior angles?
A.
The exterior angle is equal to the sum of the opposite interior angles.
B.
The exterior angle is less than the sum of the opposite interior angles.
C.
The exterior angle is greater than the sum of the opposite interior angles.
D.
There is no relationship.
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Solution
The exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Correct Answer:
A
— The exterior angle is equal to the sum of the opposite interior angles.
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Q. What is the relationship between the lengths of the tangents drawn from an external point to a circle?
A.
They are equal
B.
They are unequal
C.
They depend on the radius
D.
They are always zero
Show solution
Solution
The lengths of the tangents drawn from an external point to a circle are always equal.
Correct Answer:
A
— They are equal
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