DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 26)

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Problem 1 :

The scatterplot shows the relationship between two variables, x and y. A line of best fit is also shown.

Which of the following equations best represents the line of best fit shown?

A) y = 2.8 + 1.7x

B) y = 2.8 - 1.7x

C) y = -2.8 + 1.7x

D) y = -2.8 - 1.7x

Solution :

Problem 2 :

The graph opf y = f(x) is shown in the xy-plane above. What is the value of f(0)?

A) -3

B) 0

C) ⅗

D) 3

Solution :

Problem 3 :

Which expression is equivalent to

(m⁴q⁴z^-1)(mq⁵z³),

where m, q and z are positive?

A) m⁴q²⁰z^-3

B) m⁵q⁹z²

C) m⁶q⁸z^-1

D) m²⁰q¹²z^-2

Solution :

Problem 4 :

g(m) = -0.05m + 12.1

The given function g models the number of gallons of gasoline that remains from a full gas tank in a car after driving m miles. According to the model, about how many gallons of gasoline are used to drive each mile?

A) 0.05

B) 12.1

C) 20

D) 242.0

Solution :

Problem 5 :

The given equation relates the positive numbers b, x, and y. Which equation correctly expresses x in terms of b and y?

Solution :

Problem 6 :

If f(x – 1) = –5x + 2, what is f(x + 2) equal to?

A) –5x – 2

B) –5x – 13

C) –5x – 14

D) –5x² – 10x + 2

Solution :

Problem 7 :

If (2√a - √b)/2√b = 1/4, what is the value of a/b?

A) 2/3

B) 3/4

C) 4/9

D) 9/16

Solution :

Problem 8 :

In the figure above, three identical circles with radius of 5 are tangent to one another. If lines ℓ and m are parallel and tangent to the circles, what is the value of h, the distance between the two lines?

A) 5√2 + 10

B) 10√3 + 5

C) 5√3 + 10

D) 10√3 + 10

Solution :

Problem 9 :

The population of a nation decreases by 2.5% every 10 years. If the population was 10,000,000 people in 2000, which of the following expressions estimates the population of the nation in the year 2040?

A) 10,000,000(0.025)⁴⁰

B) 10,000,000(0.025)⁴

C) 10,000,000(0.975)⁴⁰

D) 10,000,000(0.975)⁴

Solution :

Problem 10 :

x² – 5x – 11 = a(x² – 1) + b(x + 1) + c

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

Solution :

Problem 11 :

The selected values of a function shown in the table above represent a linear function. Which of the following equal to f(x)?

A) 36

B) 40

C) 42

D) 44

Solution :

Problem 12 :

If 3(a + 2b - c) = 12, what is the value of a + 2b in terms of c ?

A) 3c - 4

B) c - 12

C) c + 4

D) c - 4

Solution :

Problem 13 :

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

A) 100°

B) 120°

C) 135°

D) 145°

Solution :

Problem 14 :

If 8ⁿ x 4² = 2¹⁰, what is the value of n ?

A) 2

B) 3

C) 4

D) 5

Solution :

Problem 15 :

For what value of n is |n + 4| + 1 less than 0?

A) -5

B) -4

C) 3

D) There is no such value of n

Solution :

Problem 16 :

In the figure above, the circles are tangent each other and the radii are in a ratio 1 : 2. If the sum of their areas is 80π, what is the length of AB?

A) 12

B) 16

C) 18

D) 24

Solution :

Problem 17 :

In right triangle ABC above, AD = 10 and BC = 25. If the value of sin∠BCD is 0.6, what is the area of triangle BCD?

A) 50

B) 75

C) 100

D) 150

Solution :

Problem 18 :

In p = a² – 4a + 8, what is the least possible value of p + 6?

A) 2

B) 4

C) 8

D) 10

Solution :

Problem 19 :

Which of the following functions could represent the graph of y = f(x) shown in the xy-plane above?

A) f(x) = ⅓(x - 3)(x² - 4x + 3)

B) f(x) = -⅓(x - 3)(x² - 2x - 3)

C) f(x) = -⅓(x + 3)(x² + 4x + 3)

D) f(x) = -⅓(x + 3)(x² - 4x + 3)

Solution :

Problem 20 :

In the xy-plane above, a circle is tangent to the x-axis at R and the y-axis at P, and line ℓ passes through the points of tangency. If the area of the circle is 100π, what is the equation of line ℓ?

A) y = -x + 5

B) y = -x + 10

C) y = -x + 50

D) y = -x + 100

Solution :