SAT, ACT, New SAT, PSAT and SAT Subject Test Practice Problems are provided for students of OptimalSATPrep.com and others.
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?
#TJprep #SHSAT #SSAT #AOS #SATnew
The figure below shows an isosceles right triangle with an inscribed circle P and an equilateral triangleACD with an inscribed circle O. What is the ratio of the area of circle O to the area of circle P?
2 liters of H2 and 2 liters of N2 gases are mixed at a high enough temperature for the reaction to go to completion at constant temperature in a closed system with final volume of 4 liters.
1. What is the final pressure?
2. How many liters of NH3 will be produced?
3. How many liters of H2 and N2 will be left over?
#SATIIChemistry
The figure below shows two semicircles with diameter OP and AB. Right triangles OQP and ACB are inscribed in the larger and the smaller semicircles respectively. Line segment ratios are as specified. What is ratio of the shaded region outside OQP to the shaded area outside ACB?
#SATII Math #ACT
80 g of CaCO3(s) is mixed with 300 ml of 0.5M HCl at STP. How many ml of CO2 gas will be produced?
#SATIIchemistry
The figure below shows two adjacent right triangles, ABP and AXP with degree measures as shown and AP =8. What is the length of AC?
#ACT #SAT II #TJprep
At how many points graphs of X^2 + Y^2 = 9 and X*2 - Y^2 = 9 intersect?
#SAT #PSAT #SATII #ACT
The figure below shows a right triangle ABC with a square PQRC and smaller right triangles APQ and QRB drawn within ABC. What is the ratio of area of the green region to area of the yellow region?
#ACT #SATII
The figure below shows a right triangle (legs 8 and 15) with an inscribed circle. What is the area of the circle?
#ACT # SATII
If 4 P - 6 Q = 10
then
(3^ 2P) / (27 ^ Q) = ?
#newSAT #newPSAT
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)?
#NewSAT #NewPSAT
ABC and PQT are two equilateral angles. The sides of ABC are 6 units long and the altitudes of PQT are SQRT (3). What is the ratio of area of PQT to area of ABC?
#SATprep #SATMathII
f(x) = X^2 - 4 and g(x) x^3 - 8. What value of x [-8,8] will satisfy both equations?
#SATprep #PSATPREP #ACTprep
For non zero integers, A, B, C, and D, if A is B% of C then BAD is what % of DAD?
#SATprep #ACTprep
Aman, Brad and Chris raised money for their startup business. If the ratio of money raised by Aman to that by Brad is 3:5 and the ratio of money raised by Brad to that by Chris is 2:3. If the three friends together raised $6.2 million, what is difference between the money raised by Chris and the money raised by Abel?
#SATprep #ACTprep
A mobile phone has a sticker (bar code) price of $D. If a discount of $m was offered to a buyer, disregarding any sales tax, by what %, the price of the mobile phone was reduced?
#SATprep #PSATprep #ACTprep
On a map 1" represents 6 kilometers (km). What is the area of a national park in square km, if it's area on the map is 25 square inches?
#SATprep #PSATprep #ACTprep
One mole of Oxygen gas reacts with two moles of Hydrogen gas to produce about 237 kilojoules of energy. How many moles of hydrogen gas will react with sufficient moles of oxygen to produce 1000 kilojoules of energy?
#SAT #ACT #SATchemistry
Simplify the expression to a single term:
Cos X - Cos (X + 90) for (0 < X < 90)
#SAT $PSAT #ACT
On the New SAT, every multiple choice question will have 4 possible answer choices. What is the probability that a student can get 4 out of 5 questions correct by randomly guessing on such a test?
#SATprep #ACTprep
