#1
What is the formula to calculate simple interest?
(P × r × t) / 100
ExplanationP is principal, r is interest rate, t is time.
#2
What is the result of 5! (factorial)?
120
ExplanationFactorial of a number is the product of all positive integers up to that number.
#3
What is the Pythagorean theorem?
a^2 + b^2 = c^2
ExplanationIn a right-angled triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
#4
What is the value of pi (π) correct to two decimal places?
3.14
ExplanationPi is the mathematical constant representing the ratio of a circle's circumference to its diameter.
#5
What is the area of a circle with radius 5 units?
25π square units
ExplanationThe area of a circle is given by the formula A = πr^2.
#6
Which of the following is the correct formula for the compound interest?
P × (1 + r)^t
ExplanationP is principal, r is interest rate, t is time.
#7
What is the square root of 169?
13
ExplanationThe square root of a number is a value that, when multiplied by itself, gives the original number.
#8
In a right triangle, if one acute angle is 30 degrees, what is the measure of the other acute angle?
60 degrees
ExplanationIn a right triangle, the sum of the two acute angles is 90 degrees.
#9
What is the value of sin(π/6)?
1/2
ExplanationThe sine function relates the angle of a right triangle to the ratio of the length of the opposite side to the hypotenuse.
#10
What is the value of cos(π/3)?
1/2
ExplanationThe cosine function relates the angle of a right triangle to the ratio of the length of the adjacent side to the hypotenuse.
#11
What is the derivative of x^2 with respect to x?
2x
ExplanationThe derivative represents the rate of change of a function.
#12
What is the integral of e^x with respect to x?
e^x + C
ExplanationThe integral represents the antiderivative or the reverse process of differentiation.
#13
What is the value of ∫(2x + 3) dx?
x^2 + 3x + C
ExplanationThe integral represents the antiderivative or the reverse process of differentiation.
#14
What is the integral of 1/(x ln(x)) dx?
ln|ln(x)| + C
ExplanationIntegrate using the natural logarithm function.
#15
What is the integral of (2x + 3)^2 dx?
(2x + 3)^3/3 + C
ExplanationIntegrate using the power rule for integration.