Q. What is the relationship between the lengths of two tangents drawn from an external point to a circle?
-
A.
They are equal
-
B.
One is longer than the other
-
C.
They are perpendicular to the radius
-
D.
They are parallel
Solution
The lengths of two tangents drawn from an external point to a circle are equal.
Correct Answer:
A
— They are equal
Learn More →
Q. What is the relationship between the radius and diameter of a circle?
-
A.
The radius is twice the diameter.
-
B.
The diameter is twice the radius.
-
C.
The radius and diameter are equal.
-
D.
The radius is half the diameter.
Solution
The diameter of a circle is twice the length of the radius.
Correct Answer:
B
— The diameter is twice the radius.
Learn More →
Q. What is the relationship between the radius and the tangent at the point of contact on a circle?
-
A.
They are equal
-
B.
They are perpendicular
-
C.
They are parallel
-
D.
They are collinear
Solution
The radius drawn to the point of contact is always perpendicular to the tangent at that point.
Correct Answer:
B
— They are perpendicular
Learn More →
Q. What is the relationship between the sides of a right triangle?
-
A.
The sum of the two shorter sides equals the longest side
-
B.
The longest side is equal to the sum of the other two sides
-
C.
The square of the longest side equals the sum of the squares of the other two sides
-
D.
All sides are equal
Solution
In a right triangle, the square of the longest side (hypotenuse) equals the sum of the squares of the other two sides (Pythagorean theorem).
Correct Answer:
C
— The square of the longest side equals the sum of the squares of the other two sides
Learn More →
Q. What is the result of (2x + 3)(x - 1)?
-
A.
2x^2 + x - 3
-
B.
2x^2 + 5x - 3
-
C.
2x^2 - x + 3
-
D.
2x^2 - 5x - 3
Solution
Step 1: Use the distributive property: 2x^2 - 2x + 3x - 3. Step 2: Combine like terms: 2x^2 + x - 3.
Correct Answer:
B
— 2x^2 + 5x - 3
Learn More →
Q. What is the result of (3x^2 + 2x) + (4x^2 - 5x)?
-
A.
7x^2 - 3x
-
B.
7x^2 + 3x
-
C.
x^2 - 3x
-
D.
x^2 + 3x
Solution
Step 1: Combine like terms: (3x^2 + 4x^2) + (2x - 5x) = 7x^2 - 3x.
Correct Answer:
A
— 7x^2 - 3x
Learn More →
Q. What is the result of (x + 2)(x - 2)?
-
A.
x^2 - 4
-
B.
x^2 + 4
-
C.
2x
-
D.
x^2 + 2
Solution
Step 1: Recognize this as a difference of squares: (a + b)(a - b) = a^2 - b^2. Step 2: Here, a = x and b = 2. Result is x^2 - 4.
Correct Answer:
A
— x^2 - 4
Learn More →
Q. What is the result of (x + 2)(x - 3)?
-
A.
x^2 - x - 6
-
B.
x^2 + x - 6
-
C.
x^2 - 6
-
D.
x^2 + 6
Solution
Use the distributive property: x^2 - 3x + 2x - 6 = x^2 - x - 6.
Correct Answer:
A
— x^2 - x - 6
Learn More →
Q. What is the result of factoring the expression x^2 + 7x + 10?
-
A.
(x + 5)(x + 2)
-
B.
(x - 5)(x - 2)
-
C.
(x + 10)(x - 1)
-
D.
(x - 10)(x + 1)
Solution
Step 1: Find two numbers that multiply to 10 and add to 7: 5 and 2. Step 2: Factor: (x + 5)(x + 2).
Correct Answer:
A
— (x + 5)(x + 2)
Learn More →
Q. What is the result of factoring the polynomial x^2 + 7x + 10?
-
A.
(x + 5)(x + 2)
-
B.
(x + 10)(x - 1)
-
C.
(x - 5)(x - 2)
-
D.
(x + 1)(x + 10)
Solution
Step 1: Find two numbers that multiply to 10 and add to 7: 5 and 2. Step 2: Factor: (x + 5)(x + 2).
Correct Answer:
A
— (x + 5)(x + 2)
Learn More →
Q. What is the result of factoring the polynomial x^2 - 9?
-
A.
(x - 3)(x + 3)
-
B.
(x - 9)(x + 1)
-
C.
(x + 3)(x + 3)
-
D.
x(x - 9)
Solution
x^2 - 9 is a difference of squares, which factors to (x - 3)(x + 3).
Correct Answer:
A
— (x - 3)(x + 3)
Learn More →
Q. What is the section formula for dividing a line segment in the ratio 2:3?
-
A.
(2x2 + 3x1)/(2 + 3), (2y2 + 3y1)/(2 + 3)
-
B.
(3x2 + 2x1)/(3 + 2), (3y2 + 2y1)/(3 + 2)
-
C.
(x1 + x2)/2, (y1 + y2)/2
-
D.
(x2 - x1)/(y2 - y1)
Solution
The section formula for dividing a line segment in the ratio m:n is ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)).
Correct Answer:
A
— (2x2 + 3x1)/(2 + 3), (2y2 + 3y1)/(2 + 3)
Learn More →
Q. What is the section formula for dividing the line segment joining points (1, 2) and (4, 6) in the ratio 2:1?
-
A.
(2, 3)
-
B.
(3, 4)
-
C.
(2.5, 4)
-
D.
(3, 5)
Solution
Using the section formula: P = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) where m=2, n=1, P = ((2*4 + 1*1)/(2+1), (2*6 + 1*2)/(2+1)) = (3, 4).
Correct Answer:
B
— (3, 4)
Learn More →
Q. What is the section formula for dividing the line segment joining points (2, 3) and (8, 7) in the ratio 1:3?
-
A.
(5, 4)
-
B.
(6, 5)
-
C.
(4, 5)
-
D.
(3, 4)
Solution
Using the section formula: P(x, y) = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) where m=1, n=3. P = ((1*8 + 3*2)/(1+3), (1*7 + 3*3)/(1+3)) = (6, 5).
Correct Answer:
B
— (6, 5)
Learn More →
Q. What is the section ratio of the point (4, 5) that divides the line segment joining (2, 3) and (6, 7) internally?
-
A.
1:1
-
B.
2:1
-
C.
3:1
-
D.
1:2
Solution
Using the section formula, the ratio is 1:1 since the coordinates are equidistant from the midpoint (4, 5).
Correct Answer:
B
— 2:1
Learn More →
Q. What is the semi-perimeter of a triangle with sides 10 cm, 14 cm, and 16 cm?
-
A.
20 cm
-
B.
25 cm
-
C.
30 cm
-
D.
22 cm
Solution
Semi-perimeter = (10 + 14 + 16) / 2 = 40 / 2 = 20 cm.
Correct Answer:
B
— 25 cm
Learn More →
Q. What is the semi-perimeter of a triangle with sides 7 cm, 8 cm, and 9 cm?
-
A.
12 cm
-
B.
14 cm
-
C.
16 cm
-
D.
18 cm
Solution
Semi-perimeter = (7 + 8 + 9) / 2 = 24 / 2 = 12 cm.
Correct Answer:
B
— 14 cm
Learn More →
Q. What is the semi-perimeter of a triangle with sides measuring 7 cm, 8 cm, and 9 cm?
-
A.
12 cm
-
B.
14 cm
-
C.
16 cm
-
D.
18 cm
Solution
Semi-perimeter = (7 + 8 + 9) / 2 = 24 / 2 = 12 cm.
Correct Answer:
B
— 14 cm
Learn More →
Q. What is the simplified form of the expression (x^2 - 1)/(x - 1)?
-
A.
x + 1
-
B.
x - 1
-
C.
x^2 + 1
-
D.
x^2 - 1
Solution
Step 1: Factor the numerator: (x - 1)(x + 1)/(x - 1). Step 2: Cancel (x - 1): x + 1.
Correct Answer:
A
— x + 1
Learn More →
Q. What is the simplified form of the expression 2(x + 3) - 4?
-
A.
2x + 2
-
B.
2x + 6
-
C.
2x + 10
-
D.
2x - 4
Solution
Step 1: Distribute: 2x + 6 - 4. Step 2: Combine like terms: 2x + 2.
Correct Answer:
B
— 2x + 6
Learn More →
Q. What is the simplified form of the expression 2√(8) + 3√(2)?
-
A.
4√(2)
-
B.
6√(2)
-
C.
8√(2)
-
D.
5√(2)
Solution
Step 1: Simplify 2√(8) = 2 * 2√(2) = 4√(2). Step 2: Combine: 4√(2) + 3√(2) = 7√(2).
Correct Answer:
A
— 4√(2)
Learn More →
Q. What is the simplified form of the expression 2√18 + 3√8?
-
A.
6√2
-
B.
12√2
-
C.
8√2
-
D.
10√2
Solution
Step 1: Simplify √18 = 3√2 and √8 = 2√2. Step 2: Substitute: 2(3√2) + 3(2√2) = 6√2 + 6√2 = 12√2.
Correct Answer:
A
— 6√2
Learn More →
Q. What is the simplified form of the expression 3(x + 2) - 2(x - 1)?
-
A.
x + 8
-
B.
x + 7
-
C.
x + 6
-
D.
x + 5
Solution
Step 1: Distribute: 3x + 6 - 2x + 2. Step 2: Combine like terms: (3x - 2x) + (6 + 2) = x + 8.
Correct Answer:
B
— x + 7
Learn More →
Q. What is the simplified form of the expression 3x^2 - 2x + 4x^2 - 5?
-
A.
7x^2 - 5
-
B.
x^2 - 5
-
C.
x^2 + 5
-
D.
7x^2 + 5
Solution
Step 1: Combine like terms: (3x^2 + 4x^2) + (-2x) - 5 = 7x^2 - 5.
Correct Answer:
A
— 7x^2 - 5
Learn More →
Q. What is the sine of a 30-degree angle?
-
A.
0
-
B.
0.5
-
C.
0.707
-
D.
1
Solution
The sine of 30 degrees is 0.5.
Correct Answer:
B
— 0.5
Learn More →
Q. What is the slope of a line that is perpendicular to a line with a slope of -3?
-
A.
1/3
-
B.
-1/3
-
C.
3
-
D.
-3
Solution
The slope of a line perpendicular to another is the negative reciprocal. The negative reciprocal of -3 is 1/3.
Correct Answer:
A
— 1/3
Learn More →
Q. What is the slope of the line passing through the points (1, 2) and (3, 8)?
Solution
Slope (m) = (y2 - y1) / (x2 - x1) = (8 - 2) / (3 - 1) = 6 / 2 = 3.
Correct Answer:
B
— 4
Learn More →
Q. What is the slope of the line passing through the points (1, 2) and (4, 6)?
Solution
Slope formula: m = (y2 - y1) / (x2 - x1) = (6 - 2) / (4 - 1) = 4 / 3.
Correct Answer:
B
— 2
Learn More →
Q. What is the slope of the line passing through the points (2, 3) and (5, 11)?
Solution
The slope m of a line through two points (x1, y1) and (x2, y2) is given by m = (y2 - y1) / (x2 - x1). Here, m = (11 - 3) / (5 - 2) = 8 / 3.
Correct Answer:
B
— 3
Learn More →
Q. What is the slope of the line represented by the equation 2y - 4x = 8?
Solution
First, rewrite the equation in slope-intercept form (y = mx + b).\n1. 2y = 4x + 8\n2. y = 2x + 4.\nThe slope (m) is 2.
Correct Answer:
A
— 2
Learn More →
Showing 2161 to 2190 of 2594 (87 Pages)
