TJ Prep Problems

TJ Prep practice problems  for our students and readers. The problems provide a very small sampling of what Optimal TJ Prep students work with.

A Geometry Problem for TJ Exam Prep. (Hard). Target Time.15-45 seconds.

The figure below shows three equilateral triangles ABC, APQ and QCR and a parallelogram such that the ratio of AQ to QC is 2:3. What are

1. The ratio of the area of AQP to the area of QCR?

2. What is the ratio of the area of QCR to the area of ABC?

3. What is the ratio of the area of PQBR to the area of ABC?

#TJTEST #SHSAT

A Function Problem for New SAT/PSAT/TJ Test Prep. (Medium). Target Time. 20-35 seconds for each 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. A science question- Why do you think ants often don't travel on a straight path?

#NewSAT #NewPSAT

two ants' mathematical run