SAT/ACT Prep Practice Problems

SAT, ACT, New SAT, PSAT  and SAT Subject Test Practice Problems are provided for students of OptimalSATPrep.com and others.

A Word Problem for TJ/AOS/SHSAT/SSAT Prep. (Medium). Target Time. 15-30 seconds.

A person's estate was divided into four shares. The third largest share was one fourth of the largest share; the 2nd largest share was four times as large as the smallest share, and the smallest share was 1/8th of the largest share. If the difference between the smallest and the 2nd smallest share is $49 million, What was the value of the entire estate?

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A Function Problem for the NewSAT/PSAT Prep. (Medium), Target Time. 15-40 seconds per part.

Two mathematically inclined ants are racing to a piece of candy. Ant 1 starts at point M and reaches for a candy at point Q. Ant 2 starts at point A and reaches for a candy at point M. The diagram is not drawn to scale. Ant 1 follows a semicircular path with diameter  MN = NO = OP = PQ. Ant 2 follows a square path where AB = BC = CD = AD. MN = AD = X.

1. Express the distance traveled by ant 1 as f(X)

2. Express the distance traveled by ant 2 as g(X)

3. Express the difference between f(X) - g(X) as a function of X

4. Which ant chose the more efficient scenic route?

5. What would have been the most efficient path? 

6. If ant 1 and ant 2 reduced the length of their respective path steps (diameter of the semicircle or side of the square to smallest possible step each could take) A) what would be the shape of the path each would take and B) What would be the difference between f(X) and g(X)?

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Mathematical Ants Racing to Candy