The fraction (a^3 + a^-3) / a^-3) is equivalent to:
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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 Word Problem for TJ/Blair/HSPT/SSAT/SAT Prep. (Hard). Tsrget Time. 25-35 seconds.
A genetics lab has wrinkled and smooth pea plans in the ratio of 5:7. If 10n wrinkled and 9n smooth pea plants are added, the new ratio of wrinkled:smooth plants becomes 5:6. What is the value of n?
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A Word Problem for TJ/Blair/HSPT/SHSAT Prep. (Easy). Target Time. 15-35 seconds.
How many perfect cubes between 1 and 1000 are not perfect squares?
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A Proportion Problem for TJ/Blair/HSPT/SSAT/SAT Test Prep. (Medium). Target Time. 15-30 seconds.
A photo editor reduced the length and the width each of a photo by 60% making the photo too small. Then he increased each dimension by 25%. What was the net % change in the area of the photograph?
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A Function Problem for TJ/Blair/SHSAT/HSPT Test Prep. (Hard). Target Time. 30-60 seconds.
The figure below defines two functions (relationships) of t and u. Examine the function and answer the question.
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A Word Problem for TJ/Blair/HSPT/SSAT/SHSAT Prep. (Hard). Tartget Time. 20-35 seconds.
X and Y are two integers. If the difference of X and Y is the same as twice the sum of X and Y, what is the ratio of X:Y?
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An Algebra Problem for TJ/Blair/HSPT/SSAT Test Prep (Easy). Target Time. 15-30 seconds.
Find the positive number such that the cube of the number is equal to the square of of twice the number?
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A Counting Problem for TJ/Blair/HSPT/SHSAT Test Prep. (Medium). Target Time. 20-35 seconds.
There are three ways to go from your home room to the tennis court. From the tennis court, there are three ways to go home, namely catch the late bus, walk on the road or take a shortcut through the woods. How many ways are there to go from the school home room to your home via the tennis court?
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A Rate-Distance Problem for TJ/HSPT/Blair/SSAT Prep (Easy). Target Time. 15-20 seconds.
Jill biked at 10 mph for 3Hrs and then walked at 4 mph for 2 Hrs, what was Jill's average speed for the entire trip?
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A Basic Algebra Problem for TJ/SHSAT/HSPT/SSAT/Blair Prep (Medium). Target Time. 29-30 seconds.
Evaluate the algebraic expression given below:
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A Geometry Question for TJ/Blair/SHSAT/HSPT Prep (Medium). Target Time. 20-25 seconds.
The figure below shows two paths PTRQ (which contains a semicircle) and ACDFB.. What is the difference in the lengths of the two paths (assume the semicircle is part of the path)?
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A Ratio Problem for TJ/Blair/HSPT/SHSAT Prep (Medium). Target 15-30 seconds.
At a wedding reception the ratio of males:females is 9:7. If a total of 1120 person were presents, what is the difference between the number of males and females?
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An Arithmetic Problem for TJ/HSPT/Blair/SHSAT Prep (Easy). Target Time. 15-30 seconds.
The sum of three smallest prime numbers greater than 0 is smaller than the sum of next three consecutive odd integers by how much?
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A Word Problem for TJ/Blair/SHSAT/HSPT Prep (Easy). 15-20 seconds.
What is the Sum of the prime factors of 1715?
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A Counting Problem for TJ/Blair/HSPT/SHSAT Prep (Hard). Target Time 20-45 seconds.
If a fair coin is tossed 6 times, what is the probability of getting 2 or more heads?
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An Algebra-Geometry Problem for TJ/Blair/SHSAT Prep. (Hard). Target Time. 20-40 seconds.
What is the area of a a square MNOP with M (-2,8) and O (2,2) ?
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A Work Problem for TJ/Blair/HSPT/SSSAT/SHSAT Prep (Medium). Target Time. 15-30 seconds.
If, eating together, six monkeys can eat a total of 6 bananas in six hours, then working at the same rate, four monkeys will take how many hours to eat four bananas?
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A Simple Linear Equation Problem for TJ/SSAT/SHSAT/Blair/ISEE Prep (Easy). Target Time. 19015 seconds.
What is X in the following Equation?
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A Simple Algebra Problem for #TJ/SSAT/HSPT/Blair Prep (Easy). Target Time. 15-20 seconds.
Solve for X if 3 X + 5 = - 5 X + 3
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A Word Problem for TJ/SSAT/HSPT/Blair/AOS Prep (Hard). Target Time. 20-35 seconds.
A cricket chirps 60 times per minute whereas a frog croaks every 1.5 minutes.. If the cricket chirps and the frog croaks at 2 PM and they continue to chirp and croak respectively, at their constant rates, how many times they will chirp/croak at the same time between 2 PM and 3 PM?
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