Digital SAT Math Practice Test with Answers (Part - 10)

Question 1 :

If 9 ≤ –5x – 6 ≤ 34, a is the greatest possible value of x, and b is the least possible value of x, what is the value of a – b ?

Solution :

Question 2 :

At a certain airline, the total cost of checking in a bag is the sum of a fixed fee of $25, and an additional charge of $3 each pound the bag’s weight exceeds the overweight limit of 50 pounds. The total cost C, in dollars, of checking in an overweight bag weighing x pounds can be found by using the formula C = ax – b, where a and b are constants. What is the value a + b?

Answer :

Question 3 :

The function f is defined above. Which of the following CANNOT be f(x) for any value of x?

A)  -6

B)  -4

C)  1

D)  3

Answer :

Question 4 :

A function f(x) has two properties :

f(a + b) = f(a) - b

f(2) = 10

What is the value of f(5)?

A)  5

B)  7

C)  9

D)  11

Answer :

Question 5 :

If (x + y)² – (x – y)² = 60 and x and y are positive integers, which of the following could be a value of x + y?

A)  6

B)  8

C)  10

D)  12

Answer :

Question 6 :

The function f is defined by a polynomial. If f(0) = 3, which of the following must be true about f(x)?

A)  The remainder when f(x) is divided by x + 3 is 0.

B)  The remainder when f(x) is divided by x - 3 is 0.

C)  The remainder when f(x) is divided by x is -3.

D)  The remainder when f(x) is divided by x is 3.

Answer :

Question 7 :

The table above summarizes the orders that need to be processed by a warehouse on a certain day. If T represents the total number of hours needed to process all the orders in the table, which of the following inequalities gives the possible values of T?

A)  8 ≤ T ≤ 16

B)  8 ≤ T ≤ 21

C)  9 ≤ T ≤ 16

D)  9 ≤ T ≤ 21

Answer :

Question 8 :

In the figure above, ACDE is a square and ABC is a right triangle. If AB = 3 and BC = 5, what is the length of BD (not shown)?

A)  √53

B)  √62

C)  8

D)  √65

Answer :

Question 9 :

In right triangle ABC above, what is the value of y?

Answer :

Question 10 :

A biologist uses the model above to estimate the length ℓ of a garden snake, in inches, based on the snake's age a, in months. According to the model, by how many inches in length does a garden snake grow over 5 months?

Answer :

Question 11 :

The total price of x pens is 4 dollars and the total price of y notebooks is 6 dollars. Which of the following expresses the total of 9 pens and 7 notebooks in dollars?

Answer :

Question 12 :

For every transaction made, an electronic payment system charges $0.30 plus 2% of the amount of the transaction. If the system charges $5.00 for a transaction, which of the following equations gives the amount a, in dollars, of the transaction?

Answer :

Question 13 :

A)  0

B)  2

C)  6

D)  12

Answer :

Question 14 :

A country consists of a mainland and 9 outlying islands. If the mainland’s population is 6 times the average population of the islands, then the mainland’s population is what fraction of the total population of the country?

Answer :

Question 15 :

A weather station summarizes the accuracy of its daily rain forecasts for the past year (365 days) in the table above. What fraction of the station’s daily forecasts last year were correct?

A)  15/73

B)  3/5

C)  15/19

D)  59/73

Answer :

Question 16 :

In the figure above, ∠BAC = 30°, ∠BCA = 45° and AB = 8, what is the length of BC?

A)  4

B)  4√2

C)  4√3

D)  8√2

Answer :

Question 17 :

The table above lists the resting breath rates (in breaths per minute) of 15 college-age students. If a student with a resting breath rate of 18 breaths per minute is added to the values listed, which of the following statistical measures of the data will change?

I. Mean

II. Median

III. Range

A)  I only

B)  I and II only

C)  II and III only

D)  I, II and III

Answer :

Question 18 :

In the figure above, AB is an arc of the circle with center O. if the area of sector OAB is 96π, what is the length of arc AB?

A)  6π

B)  8π

C)  10π

D)  12π

Answer :

Question 19 :

In the xy-plane, the points (a, 7) and (b, 12) lie on the graph of y = x² + 3. What is the minimum possible value of a + b?

A)  -5

B)  -1

C)  1

D)  5

Answer :

Question 20 :

x² - 4x + y² + 6y = 12

The graph of the equation above in the xy-plane is a circle. What is the circumference of the circle?

A)  5π

B)  10π

C)  25π

D)  50π

Answer :

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