DIGITAL SAT MATH PROBLEMS AND SOLUTIONS
(Part - 41)

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Problem 1 :

The point (a, a) satisfies the linear inequality y ≤ mx + 1, and a is greater than 0. The value of m must greater than or equal to what value?

Solution :

Problem 2 :

From 2015 to 2016 the population of a town grew by 25%. From 2016 to 2017 the population grew by 16%. If population in 2017 was x, and the population in 2015 was kx, what is the value of k to the nearest hundredth?

Solution :

Problem 3 :

f(x) = -x³ + bx² + cx + d

The function passes through the points

(12, 0), (-12, 0), (0, 2088) and (p, 0),

where p < -12. What is the value of b + c + d?

Solution :

Problem 4 :

-19(6x - 4)² + 6(6x - 3)²

The given expression can be written as

where a, b and c are constants. What is the value of

a + b + c?

Solution :

Problem 5 :

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 6 :

In the figure above, O is the center of the circle, measure of arc ACB is 3π/2 radians and length of the chord AB is 4√2. What is the area of ΔOAB?

Solution :

Problem 7 :

9x + 5 = a(x + b)

In the equation above, a and b are constants. If the equation has no solution, which of the following must be true?

I. a = 9

II. b = 5

III. b ≠ 5/9

A) I only

B) II and II only

C) I and III only

D) I, II and III

Solution :

Problem 8 :

To earn money for college, Avery works two part-time jobs: A and B. She earns $10 per hour working at job A and $20 per hour working at job B. In one week, Avery earned a total of s dollars for working at the two part-time jobs. The graph above represents all possible combinations of the number of hours Avery could have worked at the two jobs to earn s dollars. What is the value of s?

A) 128

B) 160

C) 200

D) 320

Solution :

Problem 9 :

f(x) = ax² + bx + c

In the function f above, a, b and c are constants. The graph of f is a parabola which opens down and intersects x-axis at two points. If the parabola passes through the point (0, -24), the axis of symmetry is x = 4 and a + 2b = 30, then, which of the following must be true about the function f ?

A) f(x) = 2x² - 16x + 24

B) f(x) = -2x² - 16x + 24

C) f(x) = 2x² + 16x - 24

D) f(x) = -2x² + 16x - 24

Solution :

Problem 10 :

A) 8π/3 - 8√3

B) 8√3/3 - 8π

C) 8√3 - 8π/3

D) 8π - 8√3/3

Solution :

Problem 11 :

Let f(x² + 5x + 6) = 2x² + 10x and g(x) = 2f(x) + k. If g(9) = 7, what is the value of k?

Solution :

Problem 12 :

In a bag, there are two colors of marbles, red and blue. If the probability of selecting a blue marble is 0.6 and there are 36 red marbles, find the total number of marbles in the bag.

Solution :

Problem 13 :

In the xy-plane above, what is the area of ΔABC?

Solution :

Problem 14 :

The graph of y = -(x – 2)(x + 5) is shown in the xy-plane above. What is the area of triangle STR?

Solution :

Problem 15 :

f(x) = x⁵ + ax⁴ + bx³

g(x) = x⁵ + sx⁴ + tx³

If the polynomial h(x) = f(x) + g(x) is divisible by x⁴, which of the following must be true?

A) a = s = 0

B) a + s = 0

C) b = t = 0

D) b + t = 0

Solution :

Problem 16 :

In the xy-plane above, the slope of PQ is -1 and the slope of QR is ½. What is the slope of PR?

Solution :

Problem 17 :

In the figure above, O is the center of the circle. If the area of the circle is 100π and measure of angle POR is π/6 radians. What is the area of the parallelogram OPQR?

Solution :

Problem 18 :

In an xy-plane, the graph of the function

passes through the point (0, √35). If both a aad b are positive integers greater than 1 and a > b, then, what is the least possible value of x?

Solution :

Problem 19 :

In the figure above, O is the center of the circle. If the radius of the circle is 5 units, measure of arc BC is 60°, then what is the area of ΔABC?

A) 25

B) 25/2

C) 25√3

D) 25√3/2

Solution :

Problem 20 :

A function f is defined as f(x) = ax³ + bx² - 81ax – 81b and the factored form of f is f(x) = (2x + 3)(x + d)(x – d). If c² = d and c < 0, then what is the value of a + b + c?