Q. If a line has the equation y = 3x + 2, what is the y-intercept?
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Solution
The y-intercept is the value of y when x = 0, which is 2.
Correct Answer:
A
— 2
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Q. If a line segment is divided into two equal parts, what is the measure of each part if the total length is 12 cm?
A.
4 cm
B.
5 cm
C.
6 cm
D.
7 cm
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Solution
If the total length is 12 cm and it is divided into two equal parts, each part measures 12/2 = 6 cm.
Correct Answer:
C
— 6 cm
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Q. If a line segment is drawn from the center of a circle to the midpoint of a chord, what can be said about this line segment?
A.
It is perpendicular to the chord.
B.
It bisects the chord.
C.
It is the radius.
D.
It is the diameter.
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Solution
A line segment drawn from the center of a circle to the midpoint of a chord is perpendicular to the chord.
Correct Answer:
A
— It is perpendicular to the chord.
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Q. If a number is multiplied by 3 and then increased by 4, the result is 19. What is the number?
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Solution
Let the number be x. The equation is 3x + 4 = 19. Subtracting 4 gives 3x = 15, so x = 5.
Correct Answer:
B
— 6
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Q. If a number is multiplied by 3 and then increased by 9, the result is 30. What is the number?
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Solution
Let the number be x. The equation is 3x + 9 = 30. Subtracting 9 from both sides gives 3x = 21. Dividing by 3 gives x = 7.
Correct Answer:
B
— 6
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Q. If a number is multiplied by 4 and then increased by 8, the result is 32. What is the number?
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Solution
Let the number be x. Then, 4x + 8 = 32. Subtracting 8 from both sides gives 4x = 24. Dividing by 4 gives x = 6.
Correct Answer:
A
— 4
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Q. If a number is multiplied by 6 and then decreased by 4, the result is 14. What is the number?
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Solution
Let the number be x. The equation is 6x - 4 = 14. Adding 4 gives 6x = 18, so x = 3.
Correct Answer:
C
— 5
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Q. If a number is multiplied by 6 and then increased by 5, the result is 41. What is the number?
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Solution
Let the number be x. The equation is 6x + 5 = 41. Subtracting 5 gives 6x = 36, so x = 6.
Correct Answer:
C
— 8
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Q. If a number is multiplied by 7 and then decreased by 14, the result is 0. What is the number?
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Solution
Let the number be x. The equation is 7x - 14 = 0. Adding 14 to both sides gives 7x = 14. Dividing by 7 gives x = 2.
Correct Answer:
B
— 2
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Q. If a parallelogram has a base of 6 cm and a height of 4 cm, what is its area?
A.
24 cm²
B.
20 cm²
C.
18 cm²
D.
12 cm²
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Solution
The area of a parallelogram is calculated as base × height. Thus, the area is 6 cm × 4 cm = 24 cm².
Correct Answer:
A
— 24 cm²
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Q. If a parallelogram has one angle measuring 60 degrees, what are the measures of the other three angles?
A.
60, 120, 60
B.
60, 120, 120
C.
60, 60, 120
D.
120, 120, 60
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Solution
In a parallelogram, opposite angles are equal and adjacent angles are supplementary. Thus, if one angle is 60 degrees, the opposite angle is also 60 degrees, and the adjacent angles are 120 degrees.
Correct Answer:
B
— 60, 120, 120
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Q. If a parallelogram has one angle measuring 60°, what are the measures of the other three angles?
A.
60°, 120°, 60°, 120°
B.
60°, 60°, 60°, 60°
C.
120°, 60°, 120°, 60°
D.
90°, 90°, 90°, 90°
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Solution
In a parallelogram, opposite angles are equal and adjacent angles are supplementary. Thus, if one angle is 60°, the opposite angle is also 60°, and the adjacent angles are 120°.
Correct Answer:
A
— 60°, 120°, 60°, 120°
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Q. If a parallelogram has one angle measuring 70 degrees, what are the measures of the other three angles?
A.
70, 110, 70
B.
70, 70, 110
C.
110, 70, 110
D.
110, 110, 70
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Solution
In a parallelogram, opposite angles are equal and consecutive angles are supplementary. Therefore, if one angle is 70 degrees, the opposite angle is also 70 degrees, and the other two angles are 110 degrees each.
Correct Answer:
B
— 70, 70, 110
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Q. If a parallelogram has one angle measuring 70 degrees, what is the measure of the opposite angle?
A.
70 degrees
B.
110 degrees
C.
90 degrees
D.
180 degrees
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Solution
In a parallelogram, opposite angles are equal. Therefore, if one angle is 70 degrees, the opposite angle is also 70 degrees.
Correct Answer:
A
— 70 degrees
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Q. If a parallelogram has vertices at (0, 0), (2, 3), (5, 3), and (3, 0), what is its area?
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Solution
The area of a parallelogram can be calculated using the formula: Area = base * height. The base is 5 - 0 = 5 and the height is 3. Therefore, area = 5 * 3 = 15.
Correct Answer:
B
— 8
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Q. If a parallelogram has vertices at (2, 3), (5, 3), (6, 1), and (3, 1), what is its area?
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Solution
Base = 5 - 2 = 3, Height = 3 - 1 = 2. Area = base * height = 3 * 2 = 6.
Correct Answer:
B
— 8
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Q. If a pizza is cut into 4 equal slices and you eat 1, what fraction of the pizza is left?
A.
1/2
B.
1/4
C.
3/4
D.
2/4
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Solution
4 - 1 = 3 slices left, so 3/4 of the pizza is left.
Correct Answer:
C
— 3/4
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Q. If a point P divides the line segment joining A(2, 3) and B(8, 7) in the ratio 1:3, what are the coordinates of point P?
A.
(5, 5)
B.
(4, 4)
C.
(6, 6)
D.
(3, 3)
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Solution
Using the section formula: P = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) where m=1, n=3, A(2,3), B(8,7). P = ((1*8 + 3*2)/(1+3), (1*7 + 3*3)/(1+3)) = (5, 5).
Correct Answer:
A
— (5, 5)
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Q. If a point P divides the line segment joining A(2, 3) and B(8, 7) in the ratio 3:1, what are the coordinates of P?
A.
(5, 4)
B.
(6, 5)
C.
(7, 6)
D.
(4, 5)
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Solution
Using the section formula: P = ((3*8 + 1*2)/(3+1), (3*7 + 1*3)/(3+1)) = (6, 5).
Correct Answer:
B
— (6, 5)
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Q. If a point P divides the segment joining A(1, 2) and B(5, 6) in the ratio 3:1, what are the coordinates of P?
A.
(3, 4)
B.
(4, 5)
C.
(2.5, 3.5)
D.
(3.5, 4.5)
Show solution
Solution
Using the section formula: P = ((mx2 + nx1)/(m+n), (my2 + ny1)/(m+n)) = ((3*5 + 1*1)/(3+1), (3*6 + 1*2)/(3+1)) = (3.5, 4.5).
Correct Answer:
D
— (3.5, 4.5)
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Q. If a point P divides the segment joining A(2, 1) and B(8, 5) in the ratio 3:1, what are the coordinates of P?
A.
(5, 3)
B.
(6, 4)
C.
(4, 2)
D.
(3, 2)
Show solution
Solution
Using the section formula: P = ((3*8 + 1*2)/(3+1), (3*5 + 1*1)/(3+1)) = (5, 3).
Correct Answer:
A
— (5, 3)
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Q. If a point P divides the segment joining A(2, 3) and B(8, 7) in the ratio 3:1, what are the coordinates of P?
A.
(5, 4)
B.
(6, 5)
C.
(7, 6)
D.
(4, 5)
Show solution
Solution
Using the section formula: P = ((3*8 + 1*2)/(3+1), (3*7 + 1*3)/(3+1)) = (6, 5).
Correct Answer:
B
— (6, 5)
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Q. If a polygon has 5 sides, what is it called?
A.
Triangle
B.
Quadrilateral
C.
Pentagon
D.
Hexagon
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Solution
A polygon with 5 sides is called a pentagon.
Correct Answer:
C
— Pentagon
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Q. If a polygon has 8 sides, what is it called?
A.
Hexagon
B.
Heptagon
C.
Octagon
D.
Nonagon
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Solution
A polygon with 8 sides is called an octagon.
Correct Answer:
C
— Octagon
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Q. If a polynomial is given by P(x) = x^2 - 4x + 4, what is its factored form?
A.
(x - 2)(x - 2)
B.
(x + 2)(x + 2)
C.
(x - 4)(x + 4)
D.
(x + 4)(x - 4)
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Solution
P(x) = x^2 - 4x + 4 = (x - 2)(x - 2) or (x - 2)^2.
Correct Answer:
A
— (x - 2)(x - 2)
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Q. If a quadrilateral has angles measuring 90 degrees, 85 degrees, 95 degrees, and x degrees, what is the value of x?
A.
90 degrees
B.
80 degrees
C.
85 degrees
D.
75 degrees
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Solution
The sum of the interior angles of a quadrilateral is 360 degrees. Therefore, x = 360 - (90 + 85 + 95) = 360 - 270 = 90 degrees.
Correct Answer:
D
— 75 degrees
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Q. If a quadrilateral has sides of lengths 5 cm, 12 cm, 13 cm, and 14 cm, is it a cyclic quadrilateral?
A.
Yes
B.
No
C.
Not enough information
D.
Only if it is a rectangle
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Solution
A quadrilateral is cyclic if the sum of opposite angles is 180 degrees. The given side lengths do not provide enough information to determine if it is cyclic.
Correct Answer:
B
— No
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Q. If a quadrilateral has two pairs of opposite sides that are equal, what can be concluded about the quadrilateral?
A.
It is a rectangle
B.
It is a rhombus
C.
It is a parallelogram
D.
It is a trapezoid
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Solution
A quadrilateral with two pairs of opposite sides that are equal is a parallelogram by definition.
Correct Answer:
C
— It is a parallelogram
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Q. If a quadrilateral has two pairs of opposite sides that are equal, what type of quadrilateral is it?
A.
Rectangle
B.
Rhombus
C.
Trapezoid
D.
Parallelogram
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Solution
A quadrilateral with two pairs of opposite sides that are equal is classified as a parallelogram.
Correct Answer:
D
— Parallelogram
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Q. If a quadrilateral is a kite, what can be said about its diagonals?
A.
They are equal
B.
They bisect each other
C.
One diagonal bisects the other
D.
They are perpendicular
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Solution
In a kite, one diagonal bisects the other diagonal.
Correct Answer:
C
— One diagonal bisects the other
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