Q. Find the value of x in the equation x^2 - 9 = 0.
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Solution
Factoring gives (x - 3)(x + 3) = 0. Thus, the solutions are x = 3 and x = -3.
Correct Answer:
A
— 3
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Q. Find the value of x in the inequality 3x - 5 < 4.
A.
x < 3
B.
x > 3
C.
x < 1
D.
x > 1
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Solution
Add 5 to both sides: 3x < 9. Divide by 3: x < 3.
Correct Answer:
A
— x < 3
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Q. Find the x-intercepts of the equation 3x^2 + 12x + 12 = 0.
A.
x = -2
B.
x = -4
C.
x = 0
D.
x = -6
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Solution
Using the quadratic formula: a = 3, b = 12, c = 12. Discriminant = 12² - 4(3)(12) = 144 - 144 = 0. x = -b / 2a = -12 / 6 = -2.
Correct Answer:
B
— x = -4
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Q. Find the x-intercepts of the equation y = x^2 - 4.
A.
x = 2, -2
B.
x = 4, -4
C.
x = 0, 4
D.
x = -4, 0
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Solution
Set y = 0: 0 = x^2 - 4. This factors to (x - 2)(x + 2) = 0, giving x = 2 and x = -2.
Correct Answer:
A
— x = 2, -2
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Q. Find x if 2(x + 3) = 14.
A.
x = 4
B.
x = 5
C.
x = 6
D.
x = 7
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Solution
Step 1: Divide both sides by 2: x + 3 = 7. Step 2: Subtract 3 from both sides: x = 4.
Correct Answer:
A
— x = 4
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Q. Find x if 2(x + 3) = 16.
A.
x = 4
B.
x = 5
C.
x = 6
D.
x = 7
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Solution
Step 1: Divide both sides by 2: x + 3 = 8. Step 2: Subtract 3 from both sides: x = 5.
Correct Answer:
A
— x = 4
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Q. Find x if 2(x - 3) = 10.
A.
x = 5
B.
x = 8
C.
x = 10
D.
x = 13
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Solution
Step 1: Divide both sides by 2: x - 3 = 5. Step 2: Add 3 to both sides: x = 8.
Correct Answer:
B
— x = 8
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Q. Find x if 7x + 2 = 23.
A.
x = 2
B.
x = 3
C.
x = 4
D.
x = 5
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Solution
Step 1: Subtract 2 from both sides: 7x = 21. Step 2: Divide both sides by 7: x = 3.
Correct Answer:
C
— x = 4
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Q. Find x in the equation 2(x + 3) = 16.
A.
x = 4
B.
x = 5
C.
x = 6
D.
x = 7
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Solution
Step 1: Divide both sides by 2: x + 3 = 8. Step 2: Subtract 3 from both sides: x = 5.
Correct Answer:
C
— x = 6
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Q. Find x in the equation 3(x - 2) = 12.
A.
x = 4
B.
x = 6
C.
x = 8
D.
x = 10
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Solution
Step 1: Divide both sides by 3: x - 2 = 4. Step 2: Add 2 to both sides: x = 6.
Correct Answer:
B
— x = 6
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Q. Find x in the equation 4(x - 2) = 12.
A.
x = 2
B.
x = 4
C.
x = 6
D.
x = 8
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Solution
Step 1: Divide both sides by 4: x - 2 = 3. Step 2: Add 2 to both sides: x = 5.
Correct Answer:
C
— x = 6
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Q. For the data set 1, 2, 3, 4, 5, what is the median?
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Solution
Median is the middle value. The sorted data is 1, 2, 3, 4, 5. Median = 3.
Correct Answer:
B
— 3
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Q. For the data set 10, 20, 30, 40, 50, what is the median?
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Solution
Median = (30 + 40) / 2 = 35, since there are 5 numbers.
Correct Answer:
B
— 30
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Q. For the data set 12, 15, 12, 18, 20, what is the median?
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Solution
Median = 15, as the sorted data is 12, 12, 15, 18, 20.
Correct Answer:
A
— 15
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Q. For the data set 3, 7, 8, 12, what is the median?
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Solution
Median is the average of 7 and 8, which is 7.5.
Correct Answer:
B
— 8
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Q. For the dataset: 12, 15, 20, 22, 25, what is the median?
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Solution
To find the median, arrange the numbers: 12, 15, 20, 22, 25. The median is the middle value, which is 20.
Correct Answer:
B
— 20
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Q. For the dataset: 4, 8, 6, 5, 3, what is the median?
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Solution
First, arrange the numbers in ascending order: 3, 4, 5, 6, 8. The median is the middle value, which is 5.
Correct Answer:
B
— 5
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Q. For the following set of numbers: 5, 7, 9, 11, 13, what is the median?
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Solution
The median is the middle value, which is 9.
Correct Answer:
B
— 9
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Q. For the function y = sin(3x), what is the period?
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Solution
The period is calculated as 2π divided by the coefficient of x, which is 3, giving a period of 2π/3.
Correct Answer:
A
— π
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Q. For the numbers: 3, 3, 4, 5, 5, 5, 6, what is the mean?
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Solution
Mean = (3 + 3 + 4 + 5 + 5 + 5 + 6) / 7 = 31 / 7 ≈ 4.43.
Correct Answer:
B
— 5
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Q. From a point 25 meters away from the base of a building, the angle of elevation to the top of the building is 30 degrees. What is the height of the building?
A.
25/√3 meters
B.
15 meters
C.
20 meters
D.
10 meters
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Solution
Using tan(30) = height / 25, height = 25 * tan(30) = 25 * (1/√3) = 25/√3 meters.
Correct Answer:
A
— 25/√3 meters
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Q. From a point 30 meters away from the base of a tower, the angle of elevation to the top of the tower is 45 degrees. What is the height of the tower?
A.
30 meters
B.
45 meters
C.
60 meters
D.
15 meters
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Solution
Using tan(45) = height / 30, we have height = 30 * tan(45) = 30 * 1 = 30 meters.
Correct Answer:
A
— 30 meters
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Q. From a point on the ground, the angle of elevation to the top of a 15-meter tall building is 45 degrees. How far is the point from the base of the building?
A.
15 meters
B.
30 meters
C.
10 meters
D.
20 meters
Show solution
Solution
Using tan(45°) = height/distance, distance = height/tan(45°) = 15/1 = 15 meters.
Correct Answer:
A
— 15 meters
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Q. From a point on the ground, the angle of elevation to the top of a hill is 45 degrees. If the point is 50 meters away from the base of the hill, what is the height of the hill?
A.
50 meters
B.
25 meters
C.
70 meters
D.
45 meters
Show solution
Solution
Using tan(45°) = height/50, height = 50 * tan(45°) = 50 meters.
Correct Answer:
A
— 50 meters
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Q. Given the following set of numbers: 3, 7, 7, 2, 5, what is the mode?
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Solution
The mode is the number that appears most frequently. Here, 7 appears twice, which is more than any other number.
Correct Answer:
D
— 7
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Q. Given the numbers: 5, 7, 7, 8, 10, what is the mode?
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Solution
The mode is the number that appears most frequently. Here, 7 appears twice.
Correct Answer:
B
— 7
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Q. Given two parallel lines and a transversal, if one of the alternate exterior angles is 120 degrees, what is the measure of the other alternate exterior angle?
A.
60 degrees
B.
120 degrees
C.
180 degrees
D.
90 degrees
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Solution
Alternate exterior angles are equal when two parallel lines are cut by a transversal. Therefore, the other alternate exterior angle also measures 120 degrees.
Correct Answer:
B
— 120 degrees
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Q. Given two parallel lines and a transversal, if one of the interior angles measures 40 degrees, what is the measure of the corresponding angle?
A.
40 degrees
B.
140 degrees
C.
180 degrees
D.
90 degrees
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Solution
Corresponding angles are equal when two parallel lines are cut by a transversal. Therefore, the corresponding angle also measures 40 degrees.
Correct Answer:
A
— 40 degrees
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Q. Given two parallel lines and a transversal, if one of the same-side interior angles is 40 degrees, what is the measure of the other same-side interior angle?
A.
40 degrees
B.
140 degrees
C.
180 degrees
D.
90 degrees
Show solution
Solution
Same-side interior angles are supplementary. Therefore, if one angle is 40 degrees, the other must be 180 - 40 = 140 degrees.
Correct Answer:
B
— 140 degrees
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Q. Given two parallel lines cut by a transversal, if one of the alternate exterior angles is 120 degrees, what is the measure of the other alternate exterior angle?
A.
60 degrees
B.
120 degrees
C.
90 degrees
D.
180 degrees
Show solution
Solution
Alternate exterior angles are equal when two parallel lines are cut by a transversal. Thus, the other alternate exterior angle also measures 120 degrees.
Correct Answer:
B
— 120 degrees
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