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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)?

14 (correct)

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

6x + 4 Signup and view all the answers

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

a^2 + b^2 = c^2 Signup and view all the answers

What is the value of sin(π/2)?

1 Signup and view all the answers

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(π/2) is 1.

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Description

Test your understanding of calculus and geometry with these important 12th-grade math questions. Challenge yourself with derivative calculations, integration, limits, and the Pythagorean theorem.