Q. If x ≡ 4 (mod 7) and y ≡ 3 (mod 7), what is the value of (x + y) mod 7?
Solution
x + y ≡ 4 + 3 ≡ 7 (mod 7), which is equivalent to 0.
Correct Answer:
A
— 0
Learn More →
Q. If x ≡ 4 (mod 7), which of the following could be a possible value of x?
Solution
11 mod 7 = 4, so x could be 11.
Correct Answer:
A
— 11
Learn More →
Q. If x ≤ 4, which of the following must be true?
-
A.
x + 1 ≤ 5
-
B.
x - 2 ≥ 2
-
C.
2x ≤ 8
-
D.
x + 3 > 8
Solution
If x ≤ 4, then 2x ≤ 8 is always true.
Correct Answer:
C
— 2x ≤ 8
Learn More →
Q. If x^2 + 2x + 1 = 0, what is the value of x?
Solution
This is a perfect square: (x + 1)^2 = 0 => x = -1.
Correct Answer:
A
— -1
Learn More →
Q. If x^2 - 5x + 6 = 0, what are the values of x? (2019)
-
A.
2, 3
-
B.
1, 6
-
C.
3, 2
-
D.
0, 6
Solution
Factoring gives (x - 2)(x - 3) = 0, so x = 2 or x = 3.
Correct Answer:
A
— 2, 3
Learn More →
Q. If x^2 - 6x + 9 = 0, what is the value of x?
Solution
This is a perfect square: (x - 3)^2 = 0, so x = 3.
Correct Answer:
A
— 3
Learn More →
Q. If x^3 - 8 = 0, what is the value of x?
Solution
x^3 = 8 => x = 2
Correct Answer:
A
— 2
Learn More →
Q. If x^3 = 8, then the value of x is?
Solution
Taking the cube root of both sides, x = 8^(1/3) = 2.
Correct Answer:
A
— 2
Learn More →
Q. If x^4 = 81, what is the value of x?
Solution
Taking the fourth root, x = 81^(1/4) = 3.
Correct Answer:
A
— 3
Learn More →
Q. If y < 2 and y + 3 > 0, which of the following is true?
-
A.
y < -3
-
B.
y > -3
-
C.
y < 0
-
D.
y > 0
Solution
From y + 3 > 0, we get y > -3. Since y < 2, the only true statement is y > -3.
Correct Answer:
B
— y > -3
Learn More →
Q. If y = cos^(-1)(1/2), what is the value of y?
-
A.
π/3
-
B.
π/4
-
C.
π/6
-
D.
π/2
Solution
cos^(-1)(1/2) = π/3, since cos(π/3) = 1/2.
Correct Answer:
A
— π/3
Learn More →
Q. If y = cos^(-1)(x), then dy/dx is:
-
A.
-1/√(1-x^2)
-
B.
1/√(1-x^2)
-
C.
0
-
D.
1
Solution
The derivative of cos^(-1)(x) is dy/dx = -1/√(1-x^2).
Correct Answer:
A
— -1/√(1-x^2)
Learn More →
Q. If y = cos^(-1)(x), then what is dy/dx?
-
A.
-1/√(1-x^2)
-
B.
1/√(1-x^2)
-
C.
1/x
-
D.
-1/x
Solution
The derivative of y = cos^(-1)(x) is dy/dx = -1/√(1-x^2).
Correct Answer:
A
— -1/√(1-x^2)
Learn More →
Q. If y = cos^(-1)(x), what is dy/dx?
-
A.
-1/√(1-x^2)
-
B.
1/√(1-x^2)
-
C.
0
-
D.
1
Solution
The derivative of cos^(-1)(x) is dy/dx = -1/√(1-x^2).
Correct Answer:
A
— -1/√(1-x^2)
Learn More →
Q. If y = sin^(-1)(x), then what is the derivative dy/dx?
-
A.
1/√(1-x^2)
-
B.
1/(1-x^2)
-
C.
√(1-x^2)
-
D.
1/x
Solution
The derivative of y = sin^(-1)(x) is dy/dx = 1/√(1-x^2).
Correct Answer:
A
— 1/√(1-x^2)
Learn More →
Q. If y = sin^(-1)(x), then x = sin(y) implies:
-
A.
y = x
-
B.
y = -x
-
C.
y = 1-x
-
D.
y = 1+x
Solution
By definition, if y = sin^(-1)(x), then x = sin(y).
Correct Answer:
A
— y = x
Learn More →
Q. If y = sin^(-1)(x), what is dy/dx?
-
A.
1/sqrt(1-x^2)
-
B.
1/(1-x^2)
-
C.
sqrt(1-x^2)
-
D.
1/x
Solution
The derivative of y = sin^(-1)(x) is dy/dx = 1/sqrt(1-x^2).
Correct Answer:
A
— 1/sqrt(1-x^2)
Learn More →
Q. If y = sin^(-1)(x), what is the second derivative d^2y/dx^2?
-
A.
0
-
B.
1/√(1-x^2)^3
-
C.
-1/√(1-x^2)^3
-
D.
undefined
Solution
The second derivative d^2y/dx^2 = -1/√(1-x^2)^3.
Correct Answer:
C
— -1/√(1-x^2)^3
Learn More →
Q. If y = tan^(-1)(x), then the range of y is:
-
A.
(-π/2, π/2)
-
B.
(0, π)
-
C.
(-π, π)
-
D.
[0, 1]
Solution
The range of y = tan^(-1)(x) is (-π/2, π/2).
Correct Answer:
A
— (-π/2, π/2)
Learn More →
Q. If y = tan^(-1)(x), then what is the second derivative d^2y/dx^2?
-
A.
0
-
B.
-2/(1+x^2)^2
-
C.
2/(1+x^2)^2
-
D.
1/(1+x^2)
Solution
The first derivative dy/dx = 1/(1+x^2). The second derivative d^2y/dx^2 = -2/(1+x^2)^2.
Correct Answer:
B
— -2/(1+x^2)^2
Learn More →
Q. If Y is the sister of Z and A is the mother of Z, how is Y related to A? (2023)
-
A.
Daughter
-
B.
Sister
-
C.
Niece
-
D.
Cousin
Solution
Y is the sister of Z, making her A's daughter as well.
Correct Answer:
B
— Sister
Learn More →
Q. If you add 12.11 and 0.3, how many decimal places should the answer have?
Solution
The answer should have 1 decimal place, as 0.3 has the least decimal places.
Correct Answer:
A
— 1
Learn More →
Q. If you are at point A and move 2 km north, then 2 km west, where are you relative to point A?
-
A.
2 km North-West
-
B.
2 km South-East
-
C.
2 km South-West
-
D.
2 km North-East
Solution
You are 2 km in the north-west direction from point A.
Correct Answer:
A
— 2 km North-West
Learn More →
Q. If you are at point A and move 2 miles south, then 2 miles west, which direction is point A from your current location?
-
A.
North-East
-
B.
South-West
-
C.
North-West
-
D.
South-East
Solution
Point A is to the north-west of your current location.
Correct Answer:
C
— North-West
Learn More →
Q. If you are at point A and move 2 miles south, then 2 miles west, which direction is point A from your current position?
-
A.
Northeast
-
B.
Southwest
-
C.
Southeast
-
D.
Northwest
Solution
Point A is southwest from your current position.
Correct Answer:
B
— Southwest
Learn More →
Q. If you are at point A and move 3 km east, then 4 km north, where are you relative to point A?
-
A.
3 km North-East
-
B.
4 km North-West
-
C.
5 km North-East
-
D.
7 km South-East
Solution
The distance from point A is 5 km in the north-east direction, calculated using the Pythagorean theorem.
Correct Answer:
C
— 5 km North-East
Learn More →
Q. If you are at point A and move 3 km north, then 4 km west, what is your final position relative to point A?
-
A.
3 km North
-
B.
4 km West
-
C.
5 km North-West
-
D.
7 km South-East
Solution
The final position is 5 km in the north-west direction from point A.
Correct Answer:
C
— 5 km North-West
Learn More →
Q. If you are at point A and move 3 km south, then 4 km west, where are you relative to point A?
-
A.
3 km North-East
-
B.
4 km South-West
-
C.
5 km South-West
-
D.
7 km East
Solution
You are 5 km away in the south-west direction from point A.
Correct Answer:
C
— 5 km South-West
Learn More →
Q. If you are at point A and move 3 miles east, then 4 miles north, what is your final position relative to point A?
-
A.
3 miles east
-
B.
4 miles north
-
C.
5 miles northeast
-
D.
7 miles northwest
Solution
Using the Pythagorean theorem, the distance from A is 5 miles northeast.
Correct Answer:
C
— 5 miles northeast
Learn More →
Q. If you are at point A and move 3 miles north, then 4 miles east, what is your final position relative to point A?
-
A.
3 miles north
-
B.
4 miles east
-
C.
5 miles north-east
-
D.
7 miles from A
Solution
Using the Pythagorean theorem, the distance from A is 5 miles in the north-east direction.
Correct Answer:
C
— 5 miles north-east
Learn More →
Showing 11941 to 11970 of 30480 (1016 Pages)