DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 240)

Problem 1 :

In the xy-plane above, line ℓ is defined by the equation 3x + 4y = 12 and OP is perpendicular to line ℓ. What is the length of OP?

A)  1.6

B)  2.4

C)  3.2

D)  3.6

Solution :

Problem 2 :

If f(x) = 2^x and f(x – 1) = f(x) – 8, what is the value of x?

A)  2

B)  4

C)  6

D)  8

Solution :

Problem 3 :

If f[(x - 2)/2] = 5x - 10, which of the following represents f(x)?

A)  f(x) = 10x - 5

B)  f(x) = 10x + 5

C)  f(x) = 10x

D)  f(x) = 10x + 10

Solution :

Problem 4 :

In the figure above, PA and PB are tangent to circle O with radius AO = 6. If the measure of ∠APB is 60°, which of the following is closest to the area of the shaded region?

A)  20

B)  25

C)  28

D)  30

Solution :

Problem 5 :

f(x) = x² + mx + 4

In the function above, f(x) > 0 for all values of x. Which of the following could be the value of m?

A)  8

B)  6

C)  4

D)  2

Solution :

Problem 6 :

A small shop can manufacture 4 windows every 5 hours. At that rate, how long will it take to manufacture 7 windows?

A)  8 hr

B)  8 hr 15 min

C)  8 hr 30 min

D)  8 hr 45 min

Solution :

Problem 7 :

If X is 20% of Y and Y is 30% of Z, then what percent of Z is X?

A)   5%

B)  6%

C)  8%

D)  12%

Solution :

Problem 8 :

The graph of the function g in the xy-plane is shown above. If f is another function defined in the same xy-plane and f(1) = 1, then g could be which of the following?

A)  f - 1

B)  f - 2

C)  f + 1

D)  f + 2

Solution :

Problem 9 :

This year, Roger beat Rafael in 25% of their tennis matches. If Rafael won 18 matches, how many matches did Roger win?

A)  2

B)  3

C)  4

D)  6

Solution :

Problem 10 :

One calorie is equivalent to 4.184 joules of energy. One calorie also represents the amount of energy required to raise the temperature of 1 gram of water by 1° Celsius. Based on this information, raising the temperature of 1 gram of water by 120° Fahrenheit would require how many joules of energy, to the nearest hundredth? (1° Celsius = 33.8° Fahrenheit) ​

A)  12.76

B)  13.88

C)  14.32

D)  14.85

Solution :

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