Math Quiz

Question 1:

What is the value of the expression (sin^2θ + cos^2θ) when θ = 30°?

a) 1/2
b) 3/4
c) 2/3
d) 1

Question 2:

If f(x) = 2x^2 + 5x - 3, what is the value of f(-1)?

a) -2
b) -3
c) 0
d) 2

Question 3:

The sum of two numbers is 15, and their product is 56. What are the two numbers?

a) 8 and 7
b) 9 and 6
c) 10 and 5
c) 12 and 3

Question 4:

If log(base2)(x) + log(base2)(x + 16) = 4, what is the value of x?

a) 4
b) 8
c) 16
d) 32

Question 5:

If a car travels at a speed of 60 km/h for the first hour and 80 km/h for the second hour, what is the average speed of the car for the entire journey?

a) 60km/h
b) 65km/h
c) 70km/h
d) 75km/h

Question 6:

What is the value of (1 + tan^2(45°))/(sec^2(30°) + cos^2(60°))?

a) 1/2
b) 2
c) 3/2
d) 1

Question 7:

If the complex number z = 3 + 4i, what is the absolute value of z?

a) 3
b) 4
c) 5
d) 7

Question 8:

If the determinant of a 2x2 matrix is 5 and the trace is 2, what are the eigenvalues of the matrix?

a) 1 and 3
b) -1 and 5
c) 2 and 3
d) 4 and 1

Question 9:

A right circular cone with height 12 cm and base radius 5 cm is cut by a plane parallel to its base. The smaller cone that is removed has a height of 4 cm. What is the volume of the remaining frustum?

a) 75π cm³
b) 100π cm³
c) 125π cm³
d) 150π cm³

Question 10:

If the vectors A = 2i + 3j and B = 4i - j, what is the angle between A and B in degrees?

a) 30°
b) 45°
c) 60°
d) 90°