DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 16)

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Problem 1 :

The function f is defined by f[(x - 1)/2] = x² + 1, what is the value of f(-3)?

A) 32

B) 26

C) 10

D) -10

Solution :

Problem 2 :

A neighborhood consists of a 2-hectare park and a 35-hectare residential area. The total number of trees in the neighborhood is 3,934. The equation 2x + 35y = 3,934 represents this situation. Which of the following is the best interpretation of x in this context?

A) The average number of trees per hectare in the park

B) The average number of trees per hectare in the residential area

C) The total number of trees in the park

D) The total number of trees in the residential area

Solution :

Problem 3 :

The graph shows the relationship between the number of shares of stock from Company A, x, and the number of shares of stock from Company B, y, that Simone can purchase. Which equation could represent this relationship?

A) y = 8x + 12

B) 8x + 12y = 480

C) y = 12x + 8

D) 12x + 8y = 480

Solution :

Problem 4 :

Circle A has a radius of 3n and circle B has a radius of 129n, where n is a positive constant. The area of circle B is how many times the area of circle A?

A) 43

B) 86

C) 129

D) 1,849

Solution :

Problem 5 :

A circle in the xy -plane has a diameter with endpoints (2, 4) and (2, 14). An equation of this circle is

(x − 2)² + (y - 9)² = r²,

where r is a positive constant. What is the value of r?

Solution :

Problem 6 :

The measure of angle R is 2π/3 radians. The measure of angle T is 5π/12 radians greater than the measure of angle upper R. What is the measure of angle upper T, in degrees?

A) 75

B) 120

C) 195

D) 390

Solution :

Problem 7 :

In the xy-plane, the line with equation ax – by = 5, where a and b are constants, is perpendicular to the line with equation 11x – 4y = 5. Which of the following equations represents a line that is perpendicular to the line with equation 11x + 12y = 5?

A) ax – 3by = 5

B) ax + 3by = 5

C) 3ax – by = 5

D) 3ax + by = 5

Solution :

Problem 8 :

In the xy-plane, the graph of the linear function f has a negative slope and a y-intercept at (0, k), where k is a positive constant. Which of the following must be true?

I. If a > b, then f(a) < f(b).

II. If a < 0, then f(a) > k.

III. If a > 0, then f(a) > 0.

A) I and II only

B) I and III only

C) II and III only

D) I, II and III

Solution :

Problem 9 :

If 2^x^{+ 3} – 2^x = k(2^x), what is the value of k?

A) 3

B) 5

C) 7

D) 8

Solution :

Problem 10 :

If √(x√x) = x^a, what is the value of a?

A) 1/2

B) 3/4

C) 1

D) 4/3

Solution :

Problem 11 :

The manufacturer wants to create a new alloy by mixing two metals. One metal is 35% copper and the other is 75% copper. How many kilograms of eah metal must be used to produce 80 kilograms of an alloy that is 50% copper?

Solution :

Problem 12 :

ax + 4y = 14

5x + 7y = 8

In the system of equations above, a is a constant and x and y are variables. If the system has no solution, what is the value of a?

A) 20/7

B) 35/4

C) -35/4

D) -20/7

Solution :

Problem 13 :

The graph of line l is shown in the xy-plane above. The equation of line n (not shown) is y = mx + b, where m and b are constants. If line l is perpendicular to line n, which of the following must be true?

A) m < 0

B) m > 0

C) b > 0

D) b < 0

Solution :

Problem 14 :

On Friday, Janice read x pages every 30 minutes for 4 hours and Kim read y pages for every 15 minutes for 5 hours. Which of the following represents the total number of pages read by Janice and Kim on Friday?

A) 4x + 5y

B) 8x + 20y

C) 20x + 8y

D) 120x + 75y

Solution :

Problem 15 :

Victor wants to sell 3 watches, each at the same price. After negotiating with customers, however, he ends up selling one at a 30% discount, one at a 20% discount and one at a 10% discount. If Victor sold the watches for a total of $240, how much money did he lose by giving the discounts?

(A) $45

(B) $60

(D) $90

Solution :