DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 220)

Problem 1 :

In the xy-plane, a unit circle with center at the origin O contains point A with coordinates (1, 0) and point B with coordinates (-5/√61, 5/√61,) If the measure of angle AOB is w radians, what is the value of tan w?

Solution :

Problem 2 :

In the figure of a regular pentagon above, CD is parallel to AB. If x° is the measure of ∠DCE, what is the value of x?

Solution :

Problem 3 :

In the triangle above, the sine of ∠BAC, is 0.6 and the area of triangle ABC is 216. What is the length of BC?

Solution :

Problem 4 :

A surveyor drew the diagram above to find the distance across a pond. If AB = 150 meters and AD = 90 meters, what is the distance, in meters, from point B to point C?

Solution :

Problem 5 :

In the equation above, which of the following represents b in terms a and k?

Solution :

Problem 6 :

A line in the xy-plane passes through the origin and has a slope of 1/7. Which of the following points lies on the line?

A)  (0, 7)

B)  (1, 7)

C)  (7, 7)

D)  (14, 2)

Solution :

Problem 7 :

If x > 3, which of the following is equivalent to

Solution :

Problem 8 :

If (ax + 2)(bx + 7) = 15x² + cx + 14 for all values of x, and a + b = 8, what are the two possible values for c?

A)  3 and 5

B)  6 and 35

C)  10 and 21

D)  31 and 41

Solution :

Problem 9 :

A summer camp counselor wants to find a length, x, in feet, across a lake as represented in the sketch above. The lengths represented by AB, EB, BD, and CD on the sketch were determined to be 1800 feet, 1400 feet, 700 feet, and 800 feet, respectively. Segments AC and DE intersect at B, and ∠AEB and ∠CDB have the same measure. What is the value of x ?

Solution :

Problem 10 :

In a right triangle, one angle measures x°, where 

sin x° = 4/5

What is cos(90° − x°) ?

Solution :

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