The figure below show quarter cutout from a cylindrical wooden block with dimensions as given. What is the total surface area and the volume of the block as shown?
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/AOS/PSAT/SAT Prep (Difficult). Target Time. 25-90 seconds.The figure below shows
The figure below shows a circle O with radius and a circle O with radius 3. Line PQ is tangent to both circles at points P and Q. What is the length of the line segment PQ?
An Algebra Question for TJ/Blair/AOS Test Prep (Easy). Target Time. 15-30 seconds.
If SQRT (C) -6 = Z+ 3, what is C in terms of Z ?
A Geometry Problem for TJ/Blair/AOS Prep (Difficult). Target Time. 45-90 seconds.
The figure below shows a square ABCD, an inscribed circle and 4 quarter circles. What is the area of the shaded region to the unshaped region?
An Arithmetic Problem for TJ/AOS/Blair/SHSAT Prep (Easy). Target Time. 25-30 seconds.-
After Jill gave 2/9th of her pencils to Joe, she had 49 pencils. How many pencils did Jill have in the beginning?
A Geommetry Problem for TJ/AOS/Blair/SHSAT Test Prep (Medium). Target Time. 20-45 seconds.
Two concentric (with the same center) spheres such that the radius of the smaller sphere is 1/3rd the radius of the larger sphere. What is the ratio of the volume of the space between the two spheres to the volume of the smaller sphere? Note. Volume of a sphere = 4/3rd Pi r^3 where Pi is approximately 22/7. Hint. The best way to solve the problem is not to use the formula for volume of a sphere.
A Speed-Distance Problem for TJ/Blair/AOS Test Prep (Medium). Target Time. 25-50 seconds.
A boy biked M miles at 16 MPH and then walked 8 miles at a speed of 6 MPH. What is was the boy's average speed for the entire trip?
A Math Word Problem for TJ/SHSAT/AOS/Blair Test Prep (Medium). Target Time 25-55 seconds.
A small piggy bank has nickels dimes and quarters. The number of nickels is twice the number of dimes, and the number of quarters is two fewer than the number of nickels. If the value of all the coins is $5.10, how many coins of each type are there?
A Geometry Problem for TJ/SAT/AOS/Blair Test Prep (Difficult). Target Time. 30-90 seconds.
The figure below shows an equilateral triangle ABC and a inscribed square PQRS. What is the ratio of the area of the triangle to the area of the square?
An Algebra Geometry Problem for TJ/AOS/Blair Test Prep (Medium). Target Time. 25-35 seconds.
The figure below shows a collection of tiles u units long and t unit wide. How many tiles (uxt) will be required to cover a a floor 60 t by 90 t units long?
An Medium Question for TJ/AOS/Blair Prep (Medium). Target Time. 15-35 seconds.
A cell phone must last between 12.5 Hrs and 16 Hrs. Write an absolute value inequality to describe this requirement.
An Arithmetic Problem for TJ/AOS/Blair/SHSAT Prep (Easy). Target Time. 15-25 seconds.
A plant biologist applied growth hormones to achieve a mean growth increase of 15 inches. The plants responded more actively than expected resulting in a mean growth increase of 18 inches. What was the additional percent increase over the original expectation?
A Math/Logic Problem for TJ/AOS/Blair/SHSAT Prep (Medium). Target Timer. 30-45 seconds.
What is the difference in degrees between the hour and minute hands of a clock at 140 and 945?
A Rate of Work Problem for TJ/AOS/Blair Test Prep (Easy). Target Time. 25-40 seconds.
If Six boys can eat 90 enchiladas in 45 Hrs. At the same rate, 15 boys will take how many Hrs to eat 300 enchiladas?
A Geometry Problem for TJ/AOS/Blair/SSAT Prep (Easy).
The figure below shows triangle ABC, exterior angles ABE and ACD with angle bisectors BQ and CP. What is the measure (value) of angles a + b ?
An Arithmetic Problem for TJ/AOS/Blair Test Prep (Medium). Target Time. 20-35 seconds.
T is 20% of 60% of B. U is 200% of 0.4% of B. What is the ratio of U to T?
A Mathematics Problem for TJ/AOS/Blair Test Prep (Medium). Target Time. 20-35 seconds.
The figure below shows several squares in a certain arrangement. The area of the shape is A and it's perimeter is P. if P = n A, what is the value of n ?
A Rational Fraction Problem for TJ/AOS/Blair Test Prep (medium). Target Time. 15-60 seconds.
The figure below shows a rational function. Which of the following values are possible values of the function?
A geometry Problem for TJ/AOS/AOS Test Prep (medium). Target Time. 20-45 seconds.
The figure below shows two circles connected by a trapezoid. The distance between PS and RQ is 6. What is the area of the trapezoid?
A Math Problem for TJ/SHSAT/AOS/Blair Test Prep (Medium). Target Time. 30-50 seconds.
Mr. Smith drives to his office in the morning and drives back to his home in the evening. If his morning driving speed was 50 MPH and his evening driving speed was 40 MPH (due to traffic) and if he took a total of two hours, what was the distance from his home to office. Assume that the distance is the same both way.