DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 31)

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Problem 1 :

f(x) = ax² + 8x + c

In the function above, a and c are constants. If f(-30) = f(6), what is the value of a?

Solution :

Problem 2 :

A circle has center G, and points M and N lie on the circle. Line segments MH and NH are tangent to the circle at points M and N, respectively. If the radius of the circle is 168 millimeters and the perimeter of quadrilateral GMHN is 3,856 millimeters, what is the distance, in millimeters, between G and H?

A) 168

B) 1,752

C) 1,760

D) 1,768

Solution :

Problem 3 :

The box plots above summarize the masses, in kilograms, of two groups of gazelles. Based on the box plots, which of the following statements must be true?

A) The mean mass of group 1 is greater than the mean mass of group 2.

B) The mean mass of group 1 is less than the mean mass of group 2.

C) The median mass of group 1 is greater than the median mass of group 2.

D) The median mass of group 1 is less than the median mass of group 2.

Solution :

Problem 4 :

The scatterplot above shows a company’s ice cream sales d, in dollars, and the high-temperature t, in degrees Celsius (°C), on 12 different days. A line of best fit for the data is also shown. Which of the following could be an equation of the line of best fit?

A) d = 0.03t + 402

B) d = 10t + 402

C) d = 33t + 300

D) d = 33t + 84

Solution :

Problem 5 :

Each dot in the scatterplot above represents the temperature and the number of people who visited a beach in Lagos, Nigeria, an one of eleven different days. The line of best fit for the data is also shown. The line of best fit for the data has a slope of approximately 57. According to this estimate, how many additional people per day are predicted to visit the beach for each 5°C increase in average temperature?

Solution :

Problem 6 :

C(x) = 200x + 150

R(x) = -0.5x² + 600x + 100

In the equations above, a company produces x units of a product per month, where C(x) represents the total cost and R(x) represents the total revenue for the month. The profit is the difference ween revenue and the cost where P(x) = R(x) – C(x). For what value of x will the company create the maximum profit for the month?

A) 200

B) 400

C) 600

D) 1200

Solution :

Problem 7 :

x³ – 3x + k = (x – 1)(ax² + bx + c)

In the equation above, a, b, c and k are constants. If the equation is true for all values of x, what is the value of c?

A) 4

B) 2

C) –2

D) –4

Solution :

Problem 8 :

A car traveled at an average speed of p miles per hour for h hours and consumed fuel at a rate of m miles per gallon. How many gallons of fuel did the car use for the trip?

A) p/hm

B) phm

C) ph/m

D) m/ph

Solution :

Problem 9 :

f(x) = (x + a)² – 36

In the function f above, a is a constant. If sum of the zeros of the function is -10, which of the following is the product of the zeros of the function?

A) –36

B) –26

C) –11

D) 26

Solution :

Problem 10 :

In the cylinder above, r is the radius of the base and h is the height of the cylinder. If the volume of the cylinder is equal to the surface area of the cylinder, which of the following is true about the cylinder?

A) r = h/2

B) r = 2h/(h - 2)

C) r = (h + 2)/h

D) r = (h - 2)/h

Solution :

Problem 11 :

If y = kx, where k is a constant, and y = 24 when x = 6, what is the value of y when x = 5 ?

A) 6

B) 15

C) 20

D) 23

Solution :

Problem 12 :

In the figure above, lines ℓ and m are parallel and lines s and t are parallel. If the measure of ∠1 is 35°, what is the measure of ∠2 ?

A) 35°

B) 55°

C) 70°

D) 145°

Solution :

Problem 13 :

For what value of n is |n - 1| + 1 equal to 0?

A) 0

B) 1

C) 2

D) There is no such value of n.

Solution :

Problem 14 :

The number of rooftops with solar panel installations in 5 cities is shown in the graph above. If the total number of installations is 27,500, what is an appropriate label for the vertical axis of the graph?

A) Number of installations (in tens)

B) Number of installations (in hundreds)

C) Number of installations (in thousands)

D) Number of installations (in tens of thousands)

Solution :

Problem 15 :

Based on the histogram above, of the following, which is closest to the average (arithmetic mean) number of seeds per apple?

A) 4

B) 5

C) 6

D) 7

Solution :

Problem 16 :

In the equation above, a and b are constants, where a < 0 and b > 0. For what value of a does the equation have infinitely many solutions?

Solution :

Problem 17 :

For what value of x is the function h above undefined?

Solution :

Problem 18 :

The state income tax where Alison lives is levied at the rate of k% of the first $30,000 of annual income plus (k + 4)% of any amount above $30,000. This year Alison’s income was $65,000 and he paid $9,850 for the income tax. What is the value of k?

Solution :

Problem 19 :

In the figure above, AB = 12, AC = 15 and CD = 6. Both AB and CD are perpendicular to AC. If the area of ΔABE is p and the area of ΔCDE is q, then what is the value of p – q?

Solution :

Problem 20 :

In the figure above, each of two circles has the same center O. If OP : OQ = 3 : 5 and the area of the shaded region is 40, what is the area of the larger circle?

Solution :