DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 32)

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Problem 1 :

An isosceles right triangle has a hypotenuse of length 58 inches. What is the perimeter, in inches, of this triangle?

A) 29√2

B) 58√2

C) 58 + 58√2

D) 58 + 116√2

Solution :

Problem 2 :

21x²+ 41x + 10 = 0

The above equation can be factored into (3x + a)(7x + b), where a and b are integer constants or factored into (3x + c)(7x + d), where c and d non-integer constants. What is the value of a + c?

Solution :

Problem 3 :

When an Alvia high-speed train that is stopped in Barcelona leaves the station, its speed increases (accelerates) at a constant rate of 3,888 kilometers per hour squared (km/hr²). If h is the time, in hours, it takes for the train to reach a speed of 250 km/hr, which of the following equations best describes this situation?

Choose 1 answer :

Solution :

Problem 4 :

7kx + 13my = 20.5

6kx + 5my = -48

In the given system of equations, k and m are constants. The system has a solution of (2, y). What is the value of k?

Solution :

Problem 5 :

The scatterplot above shows the numbers of grams of both total protein and total fat for eight sandwiches on a restaurant menu. The line of best fit for the data is also shown. According to the line of best fit, which of the following is closest to the predicted increase in total fat, in grams, for every increase of 1 gram in total protein?

Solution :

Problem 6 :

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 7 :

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 8 :

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 9 :

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 10 :

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

A) b = ak/(a - k)

B) b = ak/(a + k)

C) b = ak²/(a - k)

D) b = ak²/(a - k²)

Solution :

Problem 11 :

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 12 :

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

Solution :

Problem 13 :

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 14 :

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 15 :

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

sin x° = 4/5

What is cos(90° − x°) ?

Solution :

Problem 16 :

f(x) = a(x – b)² + k

In the function above, a, b and k are constants. If a and k are negative numbers, which of the following CANNOT be true?

A) f(5) = –1

B) f(1) = k

C) f(2) = b

D) f(3) = 1

Problem 17 :

(a – 2)x + (b + 2)y = 8

bx + ay = 4

In the system of equations above, a and b are constants. If the system has infinitely many solutions, what is the value of a?

A) -4/3

B) -2/3

C) 2/3

D) 4/3

Solution :

Problem 18 :

A cylinder was altered by increasing the radius of its circular base by 10 percent and decreasing its height by k percent. If the volume of the resulting cylinder is 8.9% greater than the volume of the original cylinder, what is the value of k?

A) 8.9

B) 10

C) 12

D) 15

Solution :

Problem 19 :

When Albert starts walking, Kimberly is 60 yards ahead of him. They are moving in the same direction on the same straight path. Albert walks 8 yards for every 4 yards that Kimberly walks. Albert walks 3 yards per second. At these relative rates, in how many seconds will Albert catch up with Kimberly?

A) 20

B) 25

C) 30

D) 40

Solution :

Problem 20 :

In the xy-plane above, the graph of y = a(x – 3)² – 2, where a is a constant, intersects line ℓ at points P(0, 16) and Q. What is the equation of line?

A) y = -8x + 16

B) y = -4x + 16

C) y = -3x + 16

D) y = -2x + 16

Solution :