Digital SAT Math Practice Test with Answers (Part - 15)

Question 1 :

f(x) = a|x - b| - 6|x - b| + 3

For the function f, a and b are constants, and the graph of y = f(x) in the xy-plane passes through the point (5, 3). If f(8) > 3, which of the following could be a value of a + b?

A)  5

B)  8

C)  11

D)  14

Answer :

Question 2 :

Exponential function h is defined by h(x) = b^x, where b is a non-zero constant. If h(11)/2 = 864 ⋅ h(8), what is the value of b?

Answer :

Question 3 :

f(x) = 2x + 3

g(x) = 7x - 2

h(x) = 5x + 6

The functions f, g and h are defined as shown. If f(x) ⋅ g(x) - h(x) = ax² + bx + c, where a, b and c are constants, what is the value of b?

A)  -5

B)  12

C)  20

D)  22

Answer :

Question 4 :

The frequency table summarizes a data set of the weights, rounded to the nearest pound, of 71 tortoises. A weight of 39 pounds is added to the original data set, creating a new data set of the weights, rounded to the nearest pound, of 72 tortoises. Which statement best compares the mean and median of the new data set to the mean and median of the original data set?

A)  The mean of the new data set is greater than the mean of the original data set, and the median of the new data set is greater than the median of the original data set.

B)  The mean of the new data set is greater than the mean of the original data set, and the medians of the two data sets are equal.

C)  The mean of the new data set is less than the mean of the original data set, and the median of the new data set is less than the median of the original data set.

D)  The mean of the new data set is less than the mean of the original data set, and the medians of the two data sets are equal.

Answer :

Question 5 :

In a convex pentagon ABCDE, segment AB is parallel to segment DE. The measure of angle B is 139 degrees, and the measure of angle D is 174 degrees. What is the measure in degrees, of angle C?

Answer :

Question 6 :

In triangles LMN and RST, angles L and R each have measure 60°, LN = 10, and RT = 30. Which additional piece of information is sufficient to prove that triangle LMN is similar to triangle RST?

A)  MN = 7 and ST = 7

B)  MN = 7 and ST = 21

C)  The measures of angles M and S are 70° and 60°, respectively.

D)  The measures of angles M and T are 70° and 50°, respectively.

Answer :

Question 7 :

Points X, Y and Z are on a circle with center O. The measure of ∠OXY is 30°. If OZ = 9, what is the length of minor arc XY?

A)  2π

B)  5π

C)  6π

D)  8π

Answer :

Question 8 :

The expression 6x⁴ + 31x² + 35 can be written as (3x² + a)(2x² + b), where a and b are positive integers, or as (3x² + c)(2x² + d), where c and d are positive nonintegers. What is the value of a + c?

Answer :

Question 9 :

What is the area, in square units, of the triangle formed by connecting the three points?

Answer :

Question 10 :

For triangles ABC and FGH, angles B and G each measures 51°, the length of AB is 6, and the length of FG is 18. Which additional piece(s) of information is(are) sufficient to prove that triangle ABC is similar to FGH?

I. The measure of angle A is equal to the measure of angle F.

II. The measure of angle C is equal to the measure of angle H.

III. The length of FH is 3 times the length of AC.

A)  I is sufficient, III is sufficient, and III is sufficient.

B)  I is sufficient and II is sufficient, but III is not.

C)  II is sufficient and III is sufficient, but I is not.

D)  III is sufficient, but I is not and III is not.

Answer :

Question 11 :

Rectangle ABCD is similar to rectangle EFGH. The area of rectangle ABCD is 648 square inches, and the area of rectangle EFGH is 72 square inches. The length of the longest side of rectangle ABCD is 36 inches. What is the length, in inches, of the longest side of rectangle EFGH?

A)  4

B)  9

C)  12

D)  36

Answer :

Question 12 :

For a baobab tree habitat in South Africa, a scientist randomly selected 50 baobab trees that were 17 years old and randomly assigned them to two groups. Each group was subjected to a different watering pattern for 2 consecutive years to observe whether the watering pattern affects the trees’ growth rate. Based on the design of the study, what is the largest group to which these results can be applied?

A)  All the 50 baobab trees that were selected in this habitat

B)  All the baobab trees that were 19 years old in this habitat

C)  All the baobab trees that were 17 years old in South Africa

D)  All the baobab trees that were 17 years old in this habitat

Answer :

Question 13 :

The positive number a is 230% of the number b, and a is 60% of the number c. If c is p% of b, which of the following is closest to the value of p?

A)  138

B)  217

C)  283

D)  383

Answer :

Question 14 :

The equation x² +  y² – 8x + 12y – 16q = 0 represents circle A in the xy-plane, where q is a constant. Circle B has the same center as circle A. The point (16, –6) lies on circle B and the area enclosed by circle B is 4 times the area enclosed by circle A. What is the value of q?

A)  –2

B)  –1

C)  3

D)  6

Answer :

Question 15 :

The function g is defined for all real numbers x ≠ 5 by

where k is a constant. For x > 5, the function g has a minimum value of 18. What is the value of k?

A)  81

B)  52

C)  349

D)  106

Answer :

Question 16 :

The number of zebras in a population 2018 in was 1.27 times the number of zebras in this population in 2014. If the number of zebras in this population in 2014 is p% of the number of zebras in this population in 2018, what is the value of p, to the nearest whole number?

Answer :

Question 17 :

To study the moisture content in a group of trees, samples from the trunk of each tree were taken from 25 trees and cut in the shape of a cube. The length of the edge of one of these cubes is 2.00 centimeters. If this cube has a mass of 2.56 grams, what is the density of this cube, in grams per cubic centimeter?

Answer :

Question 18 :

140 is p% greater than 10. What is the value of p?

A)  1,400

B)  1,300

C)  140

D)  130

Answer :

Question 19 :

In a scale model of an office building, a length of 1 inch is equivalent to a length of 17/3 feet in the actual office building. If a length in the actual office building measures x feet, which expression represents the corresponding length, in inches, in the model in terms of x?

A)  3x/(17)(12)

B)  17x/(12)(3)

C)  3x/17

D)  17x/3

Answer :

Question 20 :

A landscaper uses a hose that puts 88x ounces of water in a bucket in 5y minutes. Which expression represents the number of ounces of water the hose puts in the bucket in 9y minutes at this rate?

A)  9x/440

B)  440x/9

C)  5x/792

D)  792x/5

Answer :

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