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Ann S.

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SAT II Mathematics Level 2

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Question:

If $$(x+1)$$ is a factor of $$x^3+kx^2+11x+6$$ what is $$k$$ equal to?

Ann S.

Answer:

To answer this question you must consider what $$(x+1)$$ is a factor means conceptually. What is means is that when $$x=-1$$ the above function is equal to zero. Therefore $$(-1)^3+k(-1)^2+11(-1)+6$$ $$-1+k-11+6=0$$ $$k=6$$

Pre-Calculus

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Question:

Determine the equation a circle in standard form that has a radius of 7 and is centered at (-4,7).

Ann S.

Answer:

The equation of a circle in standard form, centered at (a,b) with a radius r, is $$(x-a)^{2}+(y-b)^{2}=(r)^{2}$$. If we are to substitute the values suggested: If we substitute a and b for the center suggested (-4,7) $$(x+4)^{2}+(y-7)^{2}=(r)^{2}$$ Then if we substitute 7 for the radius we finish the problem with a solution of $$(x+4)^{2}+(y-7)^{2}=(7)^{2}$$

ACT

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Question:

A grocer buys a rectangular prism-shaped melon container. The height of the melon container is one-third of the length, and the width is twice the length. If the container can hold 144 melons that take up one square foot each, how tall can the container be?

Ann S.

Answer:

When looking at a problem like this, the most important thing to recognize is that the ratio based relationships between the dimensions of the box are key to getting an answer. After recognizing this, the next step is to set up each of these values in terms of each other. (i.e) Step 1: H=(1/3)L W=2L Step 2: 6H=2L W=2L Step 3: 6H=2L=W Step 4: Determining the maximum volume (There's a Formula!!!! LxWxH) V=LxWxH V=3HxWxH (from step 2 6H = 2L, so 3H = L) V=3Hx6HxH (from step 3 W=6H) 144 = 18H^3 8 = H^3 2 = H

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