Q. If the area of triangle JKL is 30 cm² and the base JK is 10 cm, what is the height from point L?
A.
3 cm
B.
6 cm
C.
5 cm
D.
4 cm
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Solution
Area = 1/2 * base * height. 30 = 1/2 * 10 * height. Therefore, height = 6 cm.
Correct Answer: C — 5 cm
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Q. If the center of a circle is at (0, 0) and it passes through the point (3, 4), what is the radius of the circle?
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Solution
The radius is the distance from the center to the point, which is √(3² + 4²) = √25 = 5.
Correct Answer: A — 5
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Q. If the center of a circle is at (0, 0) and it passes through the point (3, 4), what is the equation of the circle?
A.
x² + y² = 25
B.
x² + y² = 12
C.
x² + y² = 7
D.
x² + y² = 16
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Solution
The radius is 5 (distance from (0,0) to (3,4)), so the equation is x² + y² = 5² = 25.
Correct Answer: A — x² + y² = 25
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Q. If the circumradius of triangle ABC is 10 cm and the area is 48 cm², what is the length of the side opposite to angle A?
A.
12 cm
B.
14 cm
C.
16 cm
D.
18 cm
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Solution
Using the formula R = (abc)/(4 * Area), we can find the side opposite to angle A. Let a = side opposite to A. Then, a = (4 * Area * R) / (bc) = (4 * 48 * 10) / (b * c).
Correct Answer: B — 14 cm
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Q. If the circumradius R of triangle ABC is 5 cm, what is the maximum area of the triangle?
A.
12.5 cm²
B.
15 cm²
C.
20 cm²
D.
25 cm²
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Solution
The maximum area of a triangle with circumradius R is given by the formula Area = (abc)/(4R). For maximum area, the triangle should be equilateral, thus Area = (3√3/4) * (R^2) = (3√3/4) * (5^2) = 25√3/4 cm².
Correct Answer: C — 20 cm²
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Q. If the coordinates of the vertices of a triangle are (1, 1), (4, 5), and (7, 2), what is the perimeter of the triangle?
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Solution
Calculate distances AB, BC, CA and sum them: AB = 5, BC = 5, CA = 7. Perimeter = 5 + 5 + 7 = 17.
Correct Answer: B — 14
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Q. If the coordinates of the vertices of a triangle are (1, 2), (3, 4), and (5, 2), what is the perimeter of the triangle?
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Solution
Perimeter = AB + BC + CA = √[(3-1)² + (4-2)²] + √[(5-3)² + (2-4)²] + √[(1-5)² + (2-2)²] = 2.83 + 2.83 + 4 = 10.
Correct Answer: B — 10
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Q. If the coordinates of the vertices of a triangle are (1, 2), (4, 6), and (7, 2), what is the perimeter of the triangle?
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Solution
Perimeter = AB + BC + CA = √[(4-1)² + (6-2)²] + √[(7-4)² + (2-6)²] + √[(1-7)² + (2-2)²] = 3 + √(9 + 16) + 6 = 3 + 5 + 6 = 14.
Correct Answer: B — 14
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Q. If the coordinates of the vertices of a triangle are A(1, 1), B(4, 5), and C(7, 2), what is the area of the triangle?
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Solution
Area = 1/2 | x1(y2-y3) + x2(y3-y1) + x3(y1-y2) | = 1/2 | 1(5-2) + 4(2-1) + 7(1-5) | = 1/2 | 3 + 4 - 28 | = 1/2 * 21 = 10.5.
Correct Answer: B — 12
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Q. If the data set has a mean of 30 and a median of 25, what does this indicate?
A.
Data is symmetrical
B.
Data is positively skewed
C.
Data is negatively skewed
D.
Data is uniform
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Solution
Since the mean is greater than the median, the data is positively skewed.
Correct Answer: B — Data is positively skewed
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Q. If the data set has a mean of 30 and a standard deviation of 10, what is the z-score of the value 40?
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Solution
Z-score = (X - Mean) / Standard Deviation = (40 - 30) / 10 = 1
Correct Answer: C — 2
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Q. If the data set has a mean of 30 and a standard deviation of 10, what is the z-score of a value 40?
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Solution
Z-score = (X - Mean) / Standard Deviation = (40 - 30) / 10 = 1.
Correct Answer: C — 2
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Q. If the data set has a mean of 30 and a variance of 16, what is the standard deviation?
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Solution
Standard Deviation = √Variance = √16 = 4.
Correct Answer: A — 4
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Q. If the data set has a mean of 50 and a median of 45, what can be said about the data distribution?
A.
Symmetric
B.
Positively skewed
C.
Negatively skewed
D.
Uniform
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Solution
Since the mean is greater than the median, the distribution is positively skewed.
Correct Answer: B — Positively skewed
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Q. If the data set has a mean of 50 and a standard deviation of 10, what is the z-score of the value 70?
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Solution
Z-score = (X - Mean) / Standard Deviation = (70 - 50) / 10 = 2.
Correct Answer: B — 2
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Q. If the data set has a mean of 50 and a variance of 16, what is the standard deviation?
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Solution
Standard Deviation = √Variance = √16 = 4.
Correct Answer: B — 4
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Q. If the data set is 1, 2, 2, 3, 4, 4, 4, 5, what is the mode?
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Solution
Mode = 4 (most frequent value).
Correct Answer: C — 4
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Q. If the data set is 4, 4, 4, 5, 5, 6, what is the mode?
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Solution
Mode = 4 (most frequent value).
Correct Answer: A — 4
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Q. If the data set is {5, 7, 7, 8, 10}, what is the mode?
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Solution
Mode = 7 (most frequently occurring value).
Correct Answer: B — 7
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Q. If the data set is {5, 7, 8, 9, 10}, what is the interquartile range?
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Solution
Q1 = 7, Q3 = 9; Interquartile Range = Q3 - Q1 = 9 - 7 = 2.
Correct Answer: B — 3
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Q. If the data set is {5, 7, 8, 9, 10}, what is the standard deviation?
A.
1.58
B.
2.58
C.
3.58
D.
4.58
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Solution
Mean = 7.8. Variance = [(5-7.8)² + (7-7.8)² + (8-7.8)² + (9-7.8)² + (10-7.8)²]/5 = 2.5. Standard Deviation = √2.5 ≈ 1.58.
Correct Answer: A — 1.58
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Q. If the data set is: 3, 7, 7, 19, what is the median?
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Solution
Median = (7 + 7) / 2 = 7.
Correct Answer: A — 7
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Q. If the data set is: 5, 7, 8, 9, 10, what is the median?
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Solution
Median is the middle value. Here, the middle values are 7 and 8, so Median = (7+8)/2 = 7.5.
Correct Answer: B — 8
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Q. If the data set {1, 2, 3, 4, 5} is transformed to {2, 3, 4, 5, 6}, what happens to the standard deviation?
A.
Increases
B.
Decreases
C.
Remains the same
D.
Cannot be determined
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Solution
The standard deviation remains the same because the transformation is a shift.
Correct Answer: C — Remains the same
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Q. If the data set {10, 20, 30, 40, 50} is transformed to {x + 5}, what happens to the standard deviation?
A.
Increases
B.
Decreases
C.
Remains the same
D.
Cannot be determined
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Solution
Standard deviation remains the same as adding a constant does not affect dispersion.
Correct Answer: C — Remains the same
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Q. If the data set {3, 7, 8, 12, 14} has a median of 8, what is the first quartile?
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Solution
Q1 is the median of the first half of the data set {3, 7}, which is 7.
Correct Answer: B — 7
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Q. If the data set {3, 7, 8, 12, 14} is given, what is the median?
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Solution
Median is the middle value, which is 8.
Correct Answer: A — 8
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Q. If the data set {5, 7, 8, 9, 10} has a mean of 7.8, what is the sum of the deviations from the mean?
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Solution
The sum of deviations from the mean is always 0.
Correct Answer: A — 0
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Q. If the determinant | x 2 | | 3 4 | = 0, find x.
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Solution
Setting the determinant to zero gives x*4 - 2*3 = 0, thus x = 1.5.
Correct Answer: B — 2
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Q. If the directrix of a parabola is given by the equation y = -p, what is the equation of the parabola?
A.
y^2 = 4px
B.
x^2 = 4py
C.
y^2 = -4px
D.
x^2 = -4py
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Solution
The equation of a parabola with directrix y = -p is y^2 = -4px.
Correct Answer: C — y^2 = -4px
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