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Tiffany I.

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SAT II Mathematics Level 2

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Question:

Each edge in a cube is 4 cm. What is the total surface area of the cube in square cm?

Tiffany I.

Answer:

Since the surface area is the total area of the entire face of the object, we find the total area of all 6 faces of the cube. A cube is made up of 6 squares so all we need is the area of 1 square and we can multiple that by 6 to get the total answer. A cube has the same edges throughout the entire object so the total area of one face would be 4 x 4, which equals 16. Multiple 16 by 6 to get the total surface are would be 96. So the surface area of the cube would be 96 square cm.

Trigonometry

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Question:

In right triangle ABC, c = 17, a = 15, b = 8 and angle C is a right angle. Express tan B.

Tiffany I.

Answer:

According to the rules of a right triangle, in order to find the tangent of angle B, it is best to draw out the triangle. After drawing out the triangle, we see that side a and side c are adjacent to angle B and side b is across from angle B. And according to the rules of SOHCAHTOA, in order to find the tangent of an angle, we divide the opposite side by the adjacent side. So in order to find tangent of angle B, we divide 8 by 15. We don't use 17 because that is considered the hypotenuse since it is directly across from the 90 degree angle. Thus, tan B would be 8/15.

Calculus

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Question:

What is the derivative of 5x^2?

Tiffany I.

Answer:

Whenever you take the derivative, you move the exponent of the variable into the front and multiply it to the coefficient. When we do that, we get a new coefficient of 10. Then, you must also decrease the variable's exponent by 1. So our new exponent is 1. The complete answer would then be 10x.

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