Q. What is the measure of each angle in a regular quadrilateral? (2019)
A.
90 degrees
B.
60 degrees
C.
120 degrees
D.
180 degrees
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Solution
A regular quadrilateral is a square, and each angle in a square measures 90 degrees.
Correct Answer:
A
— 90 degrees
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Q. What is the measure of each angle in a square? (2023)
A.
90 degrees
B.
60 degrees
C.
120 degrees
D.
45 degrees
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Solution
Each angle in a square measures 90 degrees.
Correct Answer:
A
— 90 degrees
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Q. What is the measure of each angle in a triangle if one angle is 40 degrees and the other is 60 degrees? (2019)
A.
80 degrees
B.
100 degrees
C.
120 degrees
D.
140 degrees
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Solution
The sum of angles in a triangle is always 180 degrees. If one angle is 40 degrees and another is 60 degrees, the third angle is 180 - (40 + 60) = 80 degrees.
Correct Answer:
A
— 80 degrees
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Q. What is the measure of each angle in a triangle if one angle is 50 degrees and the other is 60 degrees? (2019)
A.
70 degrees
B.
80 degrees
C.
90 degrees
D.
100 degrees
Show solution
Solution
The sum of angles in a triangle is 180 degrees. Therefore, the third angle = 180 - (50 + 60) = 70 degrees.
Correct Answer:
A
— 70 degrees
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Q. What is the measure of the exterior angle of a triangle if the interior angles are 50 degrees and 60 degrees? (2021)
A.
70 degrees
B.
80 degrees
C.
90 degrees
D.
100 degrees
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Solution
The exterior angle of a triangle is equal to the sum of the two opposite interior angles. Therefore, the exterior angle = 50 + 60 = 110 degrees.
Correct Answer:
B
— 80 degrees
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Q. What is the measure of the exterior angle of a triangle if the two interior opposite angles are 50 degrees and 60 degrees? (2023)
A.
110 degrees
B.
100 degrees
C.
120 degrees
D.
130 degrees
Show solution
Solution
The exterior angle of a triangle is equal to the sum of the two opposite interior angles. Therefore, the exterior angle = 50 + 60 = 110 degrees.
Correct Answer:
A
— 110 degrees
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Q. What is the median of the following data set: 12, 15, 14, 10, 18? (2023)
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Solution
First, arrange the data in ascending order: 10, 12, 14, 15, 18. The median is the middle value, which is 14.
Correct Answer:
B
— 14
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Q. What is the median of the following data set: 3, 7, 9, 5, 11?
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Solution
First, arrange the data in ascending order: 3, 5, 7, 9, 11. The median is the middle value, which is 7.
Correct Answer:
B
— 7
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Q. What is the median of the following data set: 5, 3, 8, 6, 2, 4?
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Solution
Arrange the numbers: 2, 3, 4, 5, 6, 8. The median is the average of the 3rd and 4th values: (4 + 5) / 2 = 4.5.
Correct Answer:
C
— 5.5
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Q. What is the median of the following data: 1, 2, 3, 4, 5, 6, 7, 8?
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Solution
Arrange the numbers: 1, 2, 3, 4, 5, 6, 7, 8. The median is the average of the 4th and 5th values: (4 + 5) / 2 = 4.5.
Correct Answer:
B
— 4.5
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Q. What is the median of the following numbers: 10, 20, 30, 40, 50, 60, 70? (2022)
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Solution
The numbers are in order. The median is the 4th number, which is 40.
Correct Answer:
B
— 40
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Q. What is the median of the following numbers: 22, 18, 25, 30, 20? (2021)
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Solution
Arranging the numbers: 18, 20, 22, 25, 30. The median is the middle number, which is 22.
Correct Answer:
A
— 20
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Q. What is the median of the following numbers: 8, 3, 5, 12, 7, 10? (2023)
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Solution
Arrange the numbers: 3, 5, 7, 8, 10, 12. The median is the average of the 3rd and 4th numbers: (7 + 8) / 2 = 7.5.
Correct Answer:
C
— 8
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Q. What is the median of the following set of numbers: 3, 7, 5, 9, 1? (2021)
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Solution
To find the median, first arrange the numbers in ascending order: 1, 3, 5, 7, 9. The median is the middle number, which is 5.
Correct Answer:
B
— 5
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Q. What is the median of the following set: 4, 1, 7, 3, 9, 2? (2022)
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Solution
Arranging the numbers: 1, 2, 3, 4, 7, 9. The median is the average of the 3rd and 4th numbers: (3 + 4) / 2 = 3.5.
Correct Answer:
A
— 3
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Q. What is the middle term in the expansion of (x + 2)^6?
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Solution
The middle term in the expansion of (x + 2)^6 is the 4th term, which is C(6, 3)(x)^3(2)^3 = 20 * x^3 * 8 = 160x^3. The coefficient is 160.
Correct Answer:
C
— 80
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Q. What is the minimum value of f(x) = 2x^2 - 8x + 10? (2021)
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Solution
The minimum occurs at x = -b/(2a) = 8/(2*2) = 2. f(2) = 2(2^2) - 8(2) + 10 = 2.
Correct Answer:
A
— 1
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Q. What is the minimum value of f(x) = 4x^2 - 16x + 15? (2022)
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Solution
The minimum occurs at x = -b/(2a) = 16/(2*4) = 2. f(2) = 4(2^2) - 16(2) + 15 = 1.
Correct Answer:
B
— 2
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Q. What is the minimum value of the function f(x) = 2x^2 + 4x + 1? (2023)
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Solution
The vertex is at x = -4/(2*2) = -1. The minimum value is f(-1) = 2(-1)^2 + 4(-1) + 1 = -1.
Correct Answer:
B
— 1
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Q. What is the minimum value of the function f(x) = 3x^2 - 12x + 7? (2019)
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Solution
The minimum occurs at x = -b/(2a) = 12/(2*3) = 2. f(2) = 3(2^2) - 12(2) + 7 = 1.
Correct Answer:
B
— -1
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Q. What is the mode of the following data set: 2, 3, 4, 2, 5, 2, 3? (2023)
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Solution
Mode is the number that appears most frequently. Here, 2 appears 3 times.
Correct Answer:
A
— 2
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Q. What is the mode of the following data set: 2, 3, 4, 4, 5, 5, 5, 6? (2023)
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Solution
Mode is the number that appears most frequently. Here, 5 appears 3 times.
Correct Answer:
B
— 5
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Q. What is the mode of the following data set: 3, 7, 3, 2, 5, 3, 8? (2023)
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Solution
The mode is the number that appears most frequently. Here, 3 appears 3 times, which is more than any other number.
Correct Answer:
B
— 3
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Q. What is the mode of the following data set: 4, 1, 2, 4, 3, 4, 2? (2023)
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Solution
The number 4 appears most frequently (3 times). Hence, mode = 4.
Correct Answer:
D
— 4
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Q. What is the mode of the following data set: 4, 1, 2, 4, 3, 4, 5? (2019)
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Solution
The mode is the number that appears most frequently. Here, 4 appears 3 times, so the mode is 4.
Correct Answer:
C
— 4
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Q. What is the mode of the following data set: 5, 6, 7, 5, 8, 5, 9?
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Solution
Mode is the number that appears most frequently. Here, 5 appears four times.
Correct Answer:
A
— 5
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Q. What is the mode of the following numbers: 1, 1, 2, 3, 3, 3, 4, 4?
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Solution
The mode is 3, as it appears 3 times, more than any other number.
Correct Answer:
C
— 3
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Q. What is the mode of the following numbers: 1, 2, 2, 3, 4, 4, 4, 5?
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Solution
The mode is 4, as it appears 3 times, which is more than any other number.
Correct Answer:
D
— 4
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Q. What is the mode of the following numbers: 2, 3, 3, 4, 4, 5, 5, 5?
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Solution
The mode is 5, as it appears 3 times, which is more than any other number.
Correct Answer:
D
— 5
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Q. What is the mode of the following numbers: 4, 4, 5, 6, 6, 7, 8?
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Solution
The mode is 4, as it appears 2 times, which is more than any other number.
Correct Answer:
A
— 4
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