12th-Grade Math Challenge

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Questions and Answers

What is the derivative of sin(x) with respect to x?

  • cot(x)
  • cos(x) (correct)
  • sec(x)
  • tan(x)

What is the value of ∫(2x + 3) dx?

  • 2x^2 + 3x
  • 2x^2 + 3x + C
  • x^2 + 3x + C (correct)
  • x^2 + 3x

What is the value of lim(x->2) (3x^2 - 4x + 2)?

  • 10
  • 16
  • 14 (correct)
  • 12

What is the derivative of f(x) = 3x^2 + 4x - 7?

<p>6x + 4 (C)</p> Signup and view all the answers

In a right-angled triangle, what is the relationship between the lengths of the sides?

<p>a^2 + b^2 = c^2 (A)</p> Signup and view all the answers

What is the value of sin(Ï€/2)?

<p>1 (D)</p> Signup and view all the answers

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Study Notes

Calculus

  • The derivative of sin(x) with respect to x is cos(x).
  • The value of ∫(2x + 3) dx is x^2 + 3x + C, where C is the constant of integration.
  • The value of lim(x→2) (3x^2 - 4x + 2) is 2.

Derivatives

  • The derivative of f(x) = 3x^2 + 4x - 7 is f'(x) = 6x + 4.

Trigonometry

  • In a right-angled triangle, the lengths of the sides are related by the Pythagorean theorem: a^2 + b^2 = c^2, where a and b are the lengths of the legs, and c is the length of the hypotenuse.
  • The value of sin(Ï€/2) is 1.

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