1 (Answer is B) The total amount of liquid is V+J. The amount of alcohol is .4*V. Hence the answer is .4V/(V+J) * 100. (The 100 just converts the fraction to a percentage.)

2. (Answer is D) Where V is her   income,  the  tax is .06(V-V*).  Her  tax will therefore be 5% of her  income if .06(V-V*)=.05V. Solve this equation for V and we find that it must be that V=6V*.

3. (Answer is C.)

4. (Answer is D.) First calculate dp(q)/dq=-20/(q+1)^3. Then substitute q=0 into this expression to find that dp(0)/dq= - 20.

 5. (Answer is E.) The slope of the line at any X is 4-14X. Where X=7, the slope is equal to 4-98=-94.

 6. (Answer is C) At a local maximum, it must be that the derivative of f() with respect to x is zero. This happens when 3 x^2-3=0. There are two solutions to this equation, x=1 and x=-1. But at a local maximum it also must be that the second derivative is negative or zero. The second derivative of f at x is equal to 6x. The only point at which the first derivative is zero and the second derivative is not positive is the point x=-1.

7. (Answer is C) This problem applies the chain rule. Remember that according to the chain rule, if h(x)=f(g(x)), then h'(x)=f'(g(x))g'(x). For this example, let g(x)=2x^2+3.    (Where the notation ^ means "raised to the power")

8.  (Answer is A) The indefinite integral is  I(x)=10x-{1\over 2}x^2.   Then the definite integral that we seek is I(4)-I(0)=32-0=32.