Challenging Math Concepts

Solve for x: 3x^2 - 12x + 9 = 0.

• x = 1, x = 3

• x = 0

• x = 2

• x = 4

Tags

CCSS.HSA-REI.B.4B

Analyze the function f(x) = x^3 - 6x^2 + 9x. What are its critical points?

• x = 1, x = 3

• x = 1, x = 2

• x = -1, x = 4

• x = 0, x = 2

Find the derivative of f(x) = sin(x) * e^x.

• f'(x) = e^x (sin(x) - cos(x))

• f'(x) = e^x (cos(x) + sin(x))

• f'(x) = e^x (sin(x) * cos(x))

• f'(x) = e^x (sin(x) + cos(x))

Use the identity sin^2(x) + cos^2(x) = 1 to simplify the expression: 1 - cos^2(x).

• 1 - sin^2(x)

• sin(x)

• sin^2(x)

• cos^2(x) + 1

Evaluate the limit: lim (x -> 0) (sin(x)/x).

• 1/2

• 0

• -1

• 1

Determine the continuity of the function f(x) = 1/(x-2) at x = 2.

• The function f(x) = 1/(x-2) has a removable discontinuity at x = 2.

• The function f(x) = 1/(x-2) is continuous at x = 2.

• The function f(x) = 1/(x-2) is defined at x = 2.

• The function f(x) = 1/(x-2) is not continuous at x = 2.

Calculate the integral of f(x) = 2x from x = 1 to x = 3.

• 4

• 10

• 6

• 8

If f(x) = x^2 + 3x, find f'(x) and f''(x).

• f'(x) = x + 3, f''(x) = 1

• f'(x) = 2x + 3, f''(x) = 2

• f'(x) = 2x + 6, f''(x) = 4

• f'(x) = 3x + 2, f''(x) = 0

Tags

CCSS.HSF.IF.A.2

Use the Law of Sines to find the missing angle in a triangle with angles A = 30°, B = 45°, and side a = 10.

• 105°

• 90°

• 60°

• 75°

Tags

CCSS.HSG.SRT.D.10

CCSS.HSG.SRT.D.11

Find the area under the curve of f(x) = x^2 from x = 0 to x = 4.

• 16

• 10

• 25

• 21.33