The figure below shows a circle with a secant and a tangent. What is the measure of arc x?
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Practice Problems
SAT, ACT, New SAT, PSAT and SAT Subject Test Practice Problems are provided for students of OptimalSATPrep.com and others.
A Ratio Problem for SAT/ACT/PSAT Prep. (Medium). Tsarget Time. 20-35 seconds.
The figure below shows a number line segment with points P, Q, R and S in that order.
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A Geometry Problem for SAT/ACT/PSAT/SAT Math Level II Problem. (Hard). Target Time 25-45 seconds.
Three congruent circles of greatest possible area are cut out card board shaped like an equilateral triangle. What is the ratio of the total area of the three circles to the rest of the triangle?
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An Algebra Question for SAT/PSAT/ACT Prep. (Medium). Target Time. 15-30 seconds.
If (6 X^2 + 9) / (k + 5) = (2 Y + 27) / (15 + 3 k), what X in terms of Y ?
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A Rate-Work Problem for SAT/ACT/PSAT Prep (Medium). Target Time. 20-35 seconds.
Viraj can paint his car in 12 Hrs. His younger brother Rajit and Viraj together can paint the same car in 10 Hrs. Working alone, Rajit will take how many hours to paint the car?
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A Geometry Problem for SAT Prep/ ACT Prep (Medium. Target Time. 20-35 serconds.
The figure below shows a square ABCD and two semicircular arcs. What is the area of the shaded region?
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A Geometry Problem for SAT/ACT Prep. (Easy). Target /time. 20-35 seconds for each part.
The figure below shows three semicircles with diameters as shown.
1. What is the total length o the curved path from P to S?
2. What is the total area of the three semicircles?
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A Geometric Ratio Problem for SAT/ACT Prep. (Medium). Target Time. 25-40 seconds.
The figure below shows a rectangle ABCD withe a quarter circle at each corner. The four quarter circles are congruent. Tha radius of the quarter circle is 1/3 the with of the rectangle and a 1/4th the length of the rectangle. What the ratio of the shaded area to the unshaded area within the rectangle?
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A Logarithm Problem for the SATII Subject Test Math II. (Medium). Target Time.. 15-35 seconds.
What is X, if log base6 ( log base5 X ) = 0 ?
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A Geometry Problem for SAT/PSAT/ACT Prep. (Medium). Target Time. 20-30 seconds.
The figure below shows a triangle with angles as marked. What is the sum i=of P and Q in terms of T ?
An Algebra Problem for SAT/PSAT/ACT Prep. (Hard). Target Time. 20-40 seconds.
A 45 liter tank contains a solution comprising 20% coolant and 80% water. A900 liter container contains a mixture of 95% coolant and 5% water. How many liters of the tank's solution should be replaced by the equal amount of content from the container so that the tank solution will become 45% coolant and 55% water?
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A Word Problem for SAT/ACT/PSAT Prep. (Medium). Target Time. 25-45 secoinds.
Sarah caught three times as many fish as Hanna and 4 times as many fish as Sophia. If Hanna caught 60 fish, how many fish did Sarah catch?
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A Work_Rate Problem for SAT/PSAT/ACT Prep (Medium). Target Time. 20-40 seconds.
If 8 Thomases can eat 60 bagel pizzas in 15 minutes, then at the same rate 15 Thomases will take how many minutes to eat 3000 bagel pizzas?
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An Algebra Problem for SAT/ACT/PSAT Prep. (Easy). Target Time. 10-35 seconds.
X and Y are positive Integers. If X = (3Y)^2, what is the value of 81 Y^4 in terms of X ?
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A Geometry Problem for SAT/ACT Prep. (Easy). Target Time. 20-30 seconds.
The figure below shows a rectangle ABCD. PQ = UT = 1/2 AD and RS = VW = 1/4 AB. AW = VB = DR = SC and AP = QD = BU = TC. What is the ratio of the area of the octagon to the area of the rectangle?
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A Ratio Problem for SAT/ACT/PSAT Prep. (Hard). Target Time. 15-45 seconds.
A, B, C and D are positive integers with 8 T = 3 U and 9 U = 5 B. What is the ration of T/B to B/T ?
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Typo corrected on February 22, 2015. Thank you for point out that the original problem made bo sense as it made U = 0.
A Word Problem for SAT/PSAT/ACT Prep. (Medium), Target Time. 20-35 seconds.
Ram and Zuhayr are standing in line to buy movie tickets. If Ram is 27th from the front of the line, Zuhayr is 59th from the back of the line and there are 23 persons standing between Ram and Zuhayr, how many persons are standing in the line?
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A Geometry Problem for SAT/ACT/SAT Subject Test Math II. (Hard). Target Time. 35-50 seconds.
The figure below shows the top of a cylinder of radius 4 and height 12. From this cylinder, a right triangular pyramid is cut out. What is lateral surface area of the triangular pyramid city out ?
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A Geomtry-Algebra Problem for TJ Exam Prep/SAT/ACT. (Hard). Target Time. 20-50 seconds.
The figure shown below contains all corners of 90 degrees. The dimensions are as shown. What is the value of PQ (P times Q) ?
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A Trigonometry Problem for SAT Subject Test Math level II (Medium). Target Time. 20-40 seconds.
How many real values of X satisfy the equation Sin (X/2) = Sin X, and what are they ?
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