DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 11)

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Problem 1 :

x² + 14x + y² = 6y + 109

In the xy-plane, the graph of the given equation is a circle. What is the length of the circle’s radius?

A) √109

B) √149

C) √167

D) √341

Solution :

Problem 2 :

Store A sells raspberries for $5.50 per pint and blackberries for $3.00 per pint. Store B sells raspberries for $6.50 per pint and blackberries for $8.00 per pint. A certain purchase of raspberries and blackberries would cost $37.00 at store A or $66.00 at store B. How many pints of blackberries are in this purchase?

A) 12

B) 8

C) 5

D) 4

Solution :

Problem 3 :

g(x) = x² + 55

What is the minimum value of the given function?

A) 3,025

B) 110

C) 55

D) 0

Solution :

Problem 4 :

The function ℎ is defined by h(x) = a^x + b, where a and b are positive constants. The graph of y = h(x) in the xy-plane passes through the points (0, 10) and (-2, ³²⁵⁄3₆). What is the value of ab?

A) ¼

B) ½

C) 54

D) 60

Solution :

Problem 5 :

(x − 1)² = -4

How many distinct real solutions does the given equation have?

A) Exactly one

B) Exactly two

C) Infinitely many

D) Zero

Solution :

Problem 6 :

Solution :

Problem 7 :

y = -2.5

y = x² + 8x + k

In the given system of equations, k is a positive integer constant. The system has no real solutions. What is the least possible value of k ?

Solution :

Problem 8 :

If x^a = y, y^b = z and z^c = x, then what is the value of abc?

Solution :

Problem 9 :

If a : b = 4 : 1, then what is the value of √(a/b) + √(b/a)?

A) 1½

B) 5/2

C) 4

D) 5

Solution :

Problem 10 :

What is the value of x, in the figure above?

A) 20

B) 4√6

C) 2√3

D) 48

Solution :

Problem 11 :

In the xy-plane above, the corss-section view of a tunnel under a bridge with an opening in the shape of a parabolic arch is shown. A large rectangular house trailer can be moved along a highway that passes through the tunnel. If the trailer is 8 meters wide and 6 meters tall, what is the height, h in meters, of the tunnel in the center?

Solution :

Problem 12 :

In the xy-plane, a parabola with equation y = (x – 5)² – 10 intersects a line with equation y = 6 at two points, A and B. What is the length of AB?

Solution :

Problem 13 :

In the xy-plane above, the area of ΔPOB is three times the area of ΔPOA, and points A, B and P lie on the lie ℓ. What is the value of a?

Solution :

Problem 14 :

C(n) = 3,400 – n

A manufacturing company sells a certain product for $6 per unit. The cost, C, of producing n units is estimated by the formula above. How many units must the company produce and sell to earn a profit of $2,200?

Solution :

Problem 15 :

In the figure above, line ℓ is tangent to both circles A and B at points P and Q respectively. The radius of circle A is 4 and the radius of circle B is 9. What is the length of PS?

Solution :

Problem 16 :

|n - 2| < 5

How many integers n satisfy the inequality above?

A) Six

B) Seven

C) Eight

D) Nine

Solution :

Problem 17 :

The road above shows Alicia's speed during a road trip. She stopped at a rest stop during her trip to take a nap. Based on the graph, Alicia stopped for her nap after how many hours of driving?

A) 1

B) 2

C) 3

D) 4

Solution :

Problem 18 :

In the figure above, DE is parallel to AB. If AD = 6, DC = 3 and AB = 18, what is the length of DE?

A) 3

B) 6

C) 9

D) 12

Solution :

Problem 19 :

A school district wants to make at least 600 but no more than 700 computers available to students. To meet this goal, the superintendent puts aside a budget to install 8 new computers every month. If there is a total of 200 computers available at the schools in the districts currently, which of the following inequalities gives the possible number of months t for which the school district can contribute to add new computers? Assume t is an integer.

A) 50 ≤ t ≤ 62

B) 50 ≤ t ≤ 63

C) 75 ≤ t ≤ 87

D) 75 ≤ t ≤ 88

Solution :

Problem 20 :

The net effective charge between two particles as a proportion of total charge is represented by E in the formula above, where P is the magnitude of the positive charge and N is the magnitude of the negative charge. Which of the following expresses N in terms of P and E?