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Marilyn K.

Tutor for 4 years

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SAT II Mathematics Level 2

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Question:

The radius and height of a cylinder are equal and the volume of the cylinder is 4. What is the height of the cylinder? A. 2.92 B. 3.14 C. 1.46 D. 0.73

Marilyn K.

Answer:

The correct answer is A. The volume of a cylinder is V = 1/2(pi•r^2)h. In this scenario h = r and V = 4 so 4 = 1/2 pi h^3 h = cube root(4 • 2 • pi) = 2.93

SAT

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Question:

Carla is paying $70.50 per day to visit Disney World. She is taxed 6.5% for her ticket each day and charged an additional one time untaxed fee of 5 dollars to use the trolley. Which of the following equations shows the cost of Carla visiting Disney World for x days. A. (70.50x + 5)1.065 B. (70.50 + 5)1.065x C. (70.50)1.065x + 5 D. x(1.065•70.50 + 5)

Marilyn K.

Answer:

Option C is correct. The total amount that Carla will spend at Disney is the ticket price, the 6.5% tax on the ticket price, and the 5 dollar trolley fee. If Carla visited for x days, then the total ticket price would be 70.50 times the number of days (x) and the tax (6.5%) times the ticket price (70.50) times the total number of days. This can be written as x • 1.065 • 70.50. Finally, we need to add the 5 dollars fee once with no tax, giving us option C

Calculus

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Question:

What is the integral of (x^3/sqrt((x^2)+9)) dx

Marilyn K.

Answer:

x = 3 tan (theta) dx = 3 sec^2 (theta) d(theta) sqrt(x^2 + 9) = sqrt(9tan^2(theta) + 9) = 3sqrt(tan^2(theta) + 1) = 3sqrt(sec^2(theta)) = 3sec (theta) so the integral of (x^3/sqrt((x^2)+9)) dx = integral of 27tan^3(theta) • 3sec^2(theta) / 3sec(theta) d(theta) = integral of 27tan^3(theta) • 3sec(theta) d(theta) = 27 integral of ((sec^2(theta) - 1) (sec(theta))(tan(theta)) d(theta)) u = sec(theta) du = sec(theta)tan(theta) 27 integral of ((sec^2(theta) - 1) (sec(theta))(tan(theta)) d(theta)) = 27 integral of (u^2 - 1) du =27 (u^3/3 - u) + C = 9u^3 - 27u + C =9sec^3(theta) - 27sec(theta) + C

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