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Madison S.

ACT Prep & Math Tutor

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Geometry

TutorMe

Question:

Square ABCD has a perimeter of 60 inches. What is the area of ABCD, in square inches?

Madison S.

Answer:

1. What does perimeter equal ? (all of the sides of the shape added together) 2. What do we know about the perimeter of a square ? (all 4 sides are the same length) 3. How would we find the length of just one side ? (divide the perimeter by 4) ... 60 inches / 4 inches = ? = 15 inches ... each side of the square is 15 inches long 4. What is the formula for the area of a square ? (length x width) 5. Since both the length & width = 15 inches, what would the area of the square be ? ... 15 inches x 15 inches = 225 square inches ... ( * INCHES x INCHES = SQUARE INCHES * )

Calculus

TutorMe

Question:

Differentiate the given function: f (x) = 3 cos(x) - 7 sec(x) + 4

Madison S.

Answer:

1. You must MEMORIZE the derivatives of the Trig functions! 2. What is the derivative of [ cos(x) ] = ? [ -sin(x) ] 3. What is the derivative of [ sec(x) ] = ? [ sec(x) tan(x) ] 4. So when we plug those values back into the original equation, what do we get ? 5. WAIT! What happens to the +4 ? It doesn't have a Trig function ... (it goes away) 6. WHY?! (it does not have a variable attached to it - which is the same thing as having an (x) raised to the 0 power ... deriving means to take the exponent of the variable, drop it down to be multiplied to the constant, and subtracting 1 from the original exponent ... & we know that if we bring the 0 power down & multiply it times ANYTHING we will get ............ 0 !!! So the +4 disappears) 7. Plugging in to get the correct answer of ... f ' (x) = -3 sin(x) - 7 sec(x) tan(x)

ACT

TutorMe

Question:

The sum of two integers is 24. The product of the same two integers is 135. What is the smaller of the two integers? A. 11 B. 10 C. 9 D. 8 E. 7

Madison S.

Answer:

1. What are we looking for/What do the answers represent? (the SMALLER of the two integers) 2. So would you start with A. 11 or E. 7 ? (E. 7 because it's the smallest choice) 3. What do we know about the two integers ? (they add to equal 24 & multiply to equal 135) 4. So lets start "Plugging-In" to find the larger integer with E. 7 ... 24 = [small integer] + [large integer] 24 - 7 = [large integer] = 17 ...BUT... 7 x 17 = 119 ... NOT 135 ... CROSS IT OUT! 5. Try D. 8 ... 24 - 8 = 16 16 x 8 = 128 ... NOT 135 ... CROSS IT OUT! 6. Try C. 9 ... 24 - 9 = 15 15 x 9 = 135 .... WINNER! * [smaller integer] = 9 * [larger integer] = 15 9 + 15 = 24 9 x 15 = 135

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