Q. If the coordinates of point A are (2, 3) and point B are (5, 7), what is the distance between points A and B?
A.
5 units
B.
4 units
C.
3 units
D.
6 units
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Solution
Using the distance formula, d = √[(x2 - x1)² + (y2 - y1)²] = √[(5 - 2)² + (7 - 3)²] = √[3² + 4²] = √25 = 5 units.
Correct Answer:
A
— 5 units
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Q. If the diameter of a circle is 14 cm, what is the circumference? (Use π = 22/7)
A.
44 cm
B.
28 cm
C.
22 cm
D.
14 cm
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Solution
Circumference = πd = (22/7) * 14 = 44 cm.
Correct Answer:
A
— 44 cm
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Q. If triangle DEF is similar to triangle XYZ and the sides of DEF are 3 cm, 4 cm, and 5 cm, what are the lengths of the corresponding sides of triangle XYZ if the ratio of similarity is 2:1?
A.
6 cm, 8 cm, 10 cm
B.
3 cm, 4 cm, 5 cm
C.
1.5 cm, 2 cm, 2.5 cm
D.
4 cm, 5 cm, 6 cm
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Solution
If the ratio of similarity is 2:1, then the sides of triangle XYZ will be 2 times the sides of triangle DEF, giving 6 cm, 8 cm, and 10 cm.
Correct Answer:
A
— 6 cm, 8 cm, 10 cm
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Q. If two angles are complementary, what is the sum of their measures?
A.
90 degrees
B.
180 degrees
C.
360 degrees
D.
270 degrees
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Solution
Complementary angles are two angles whose measures add up to 90 degrees.
Correct Answer:
A
— 90 degrees
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Q. If two angles of a triangle are 30 degrees and 70 degrees, what type of triangle is it?
A.
Acute
B.
Obtuse
C.
Right
D.
Equilateral
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Solution
Since all angles are less than 90 degrees, the triangle is acute.
Correct Answer:
A
— Acute
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Q. If two circles intersect at two points, what can be said about the line joining these points?
A.
It is a diameter
B.
It is a chord
C.
It is a tangent
D.
It is a secant
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Solution
The line joining the two points of intersection of two circles is called a chord.
Correct Answer:
B
— It is a chord
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Q. What is the length of the radius of a circle if its circumference is 31.4 cm?
A.
5 cm
B.
10 cm
C.
15 cm
D.
20 cm
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Solution
The circumference C of a circle is given by C = 2πr. Thus, r = C / (2π) = 31.4 / (2π) ≈ 5 cm.
Correct Answer:
A
— 5 cm
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Q. What is the radius of a circle if its area is 100π cm²?
A.
10 cm
B.
5 cm
C.
20 cm
D.
15 cm
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Solution
The area of a circle is A = πr². Setting 100π = πr² gives r² = 100, thus r = 10 cm.
Correct Answer:
A
— 10 cm
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Q. What is the radius of a circle if the area is 154 square cm? (Use π = 22/7)
A.
6 cm
B.
7 cm
C.
8 cm
D.
9 cm
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Solution
Area of a circle = πr². Thus, 154 = (22/7)r². Solving gives r² = 154 * 7 / 22 = 49, so r = 7 cm.
Correct Answer:
B
— 7 cm
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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. Which of the following statements is true about similar triangles?
A.
They have the same area
B.
Their corresponding angles are equal
C.
Their corresponding sides are equal
D.
They have the same perimeter
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Solution
Similar triangles have equal corresponding angles, which is the defining property of similarity.
Correct Answer:
B
— Their corresponding angles are equal
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