Digital SAT Math Full Test 4B

Which of the following expressions is equivalent to one half x cubed times open paren x squared minus 4 close paren ?

• Aone half x to the sixth power minus 2 x squared
• Bone half x to the sixth power minus 2
• Cone half x to the fifth power minus 2 x cubed
• Done half x to the fifth power minus 4 x squared

2x-5y=3 x+2y=6 If (a, b) is the solution to the system of equations above, what is the value of a?

• A1
• B2
• C3
• D4

A museum gift shop provides a 10% discount for museum members. If a customer who is a museum member purchases a book from the store for $18, what was the original price of the book prior to the discount (ignore sales tax)?

• A$12
• B$20
• C$22
• D$26

The Statue of Liberty has a height of 93 meters. A model toy version (done to scale) of the Statue of Liberty is 1/500th the height of the actual statue. Given that there are 100 centimeters in a meter, what is the height of the model in centimeters, calculated to the nearest whole centimeter?

• A19 cm
• B86 cm
• C186 cm
• D320 cm

A equals the fraction with numerator v squared and denominator R The acceleration of an object moving in a circle is determined by the equation above, in which v is the velocity of the object, A is its acceleration, and R is the radius of the circle. What is the value of the radius in terms of the other variables?

• AR equals 2 v over A
• BR equals the fraction with numerator v squared and denominator A
• CR equals A v squared
• DR equals 1 over A v squared

If y equals b x squared plus 5 when x = 2 and y = 17, what is the value of the constant b?

• A-5
• B3
• C4
• D12

Francisco is packing two bags for his trip. The capacity of the small bag is one third that of the larger bag. If the total capacity of the two bags together is 80 liters, what is the capacity of the smaller bag?

• A5 liters
• B8 liters
• C12 liters
• D20 liters

In the year 1990, approximately 2 million U.S. residents were Internet users. In the year 2000, approximately 115 million U.S. residents were Internet users. Assuming the growth of Internet users was at a steady geometric rate, which function could be used to model the number of Internet users, I, in millions of people, T years after 1990?

• AI(T) = 2 × (1.5) T
• BI(T) = 2 × (0.5) T
• CI(T) = 2 × (1.5) −T
• DI(T) = 2 × (2.5) −T

∠X is measured in degrees. If the cosine of ∠X is the fraction with numerator the square root of 2 and denominator 2 , what is the sine of (90 − ∠X)?

• Aone half
• Bthe fraction with numerator the square root of 2 and denominator 2
• Cthe fraction with numerator the square root of 3 and denominator 2
• Dthe fraction with numerator 2 and denominator the square root of 3

x cubed plus x squared minus 20 x Which of the following is NOT a factor of the above expression?

• Ax-4
• Bx-7
• Cx+5
• Dx

There are 10 cards, each distinctly numbered from 1 to 10. After a card is selected from the randomly shuffled set, it is returned to the set. If someone first picks a 3 and then picks a 2, what is the probability that on the third selection the person will pick a 9?

• A1 over 20
• Bone tenth
• Cone ninth
• Done sixth

In the equation 3x − 6 = 3(x − a), the constant a is greater than 2. Which of the following statements must be true?

• AThe equation has exactly one solution
• BThe equation has exactly two solutions.
• CThe equation has infinitely many solutions.
• DThe equation has no solution

In normal atmospheric conditions, the speed of sound through dry air can be approximated with the following equation, in which V represents the velocity in meters per second and T represents the air temperature in degrees Celsius. V = 331.4 + 0.6T What is the speed of sound in air that is 15 degrees Celsius?

• A−537.3 meters per second
• B14.8 meters per second
• C340.4 meters per second
• D423.5 meters per second

For the line l, y = ax + n, where a and n are distinct nonzero constants. Which of these lines must be perpendicular to line l?

• Ay = nx + a
• By = ax − n
• Cy equals negative 1 over a x minus n
• Dy = −ax + n

If the fraction with numerator x raised to the two thirds power and denominator x raised to the one sixth power equals the fraction with numerator x to the a-th power and denominator the square root of x , what is the value of a?

• A1
• B2
• C3
• D6

Nyla is driving X miles per hour. Given that there are 5,280 feet in a mile, what is her speed in feet per second?

• Aopen paren the fraction with numerator 60 and denominator 5 comma 280 close paren times x
• Bopen paren the fraction with numerator 3 comma 600 and denominator 5 comma 280 close paren times x
• Copen paren the fraction with numerator 5 comma 280 and denominator 60 close paren times x
• Dopen paren the fraction with numerator 5 comma 280 and denominator 3 comma 600 close paren times x

the fraction with numerator 2 x minus 6 and denominator 2 equals x plus k If the equation above has an infinite number of solutions, what is the value of the constant k?

• Ak = −7
• Bk = −3
• Ck = 0
• Dk = 2

In the equation 3 = |x − 1|, how many solutions are there?

• AExactly 1
• BExactly 2
• CNone
• DInfinite

At exactly how many points will the function f of x equals x squared minus 3 x minus 4 intersect the x-axis?

• A0
• B1
• C2
• D3

A city’s population at the beginning of 2010 was 50,000 residents. At the beginning of 2011, its population was 45,000 residents, and at the beginning of 2012, its population was 40,500 residents. If the city’s population has continued to change at the same rate each year, which function models the city’s population T years after 2010?

• AP(T) = 50,000 × (0.9) T
• BP(T) = 40,500 × (0.09) T
• CP(T) = 50,000 × (1.1) T
• DP(T) = 45,000 × (1.09) T

Diana walks at a pace of 100 steps per minute. On Monday, she walks a total of 6,000 steps. If she maintains her pace and wants to increase the total number of steps on Tuesday to 10,000, how many additional hours will she need to walk on Tuesday compared to Monday?

• Aone sixth of an hour
• Bone fourth of an hour
• Ctwo thirds of an hour
• D1 hour

The linear function g can be written in the form g(x) = mx + b, in which m and b are constants. If g(1) = 7 and g(3) = 11, what is the value of m

• A-3
• B-1
• C2
• D6

Two hot air balloons were initially at the same height in the air at 200 feet. After 10 minutes go by, one balloon’s height has increased by 30% and the other balloon’s height has decreased by 15%. At that point, how many feet apart in height would the two balloons be?

• A60 feet
• B70 feet
• C80 feet
• D90 feet

If 2 x squared plus b x plus 4 equals 0 , for what values of b will there be no real solutions?

• Ab is greater than the square root of 2
• Bthe absolute value of b is less than or equal to the negative square root of 2
• Cb is greater than or equal to 4
• Dthe absolute value of b is less than 4 the square root of 2

A pizza parlor has a goal of making at least $10,000 a month in revenue from selling pizzas. The parlor sells small pizzas for $10 each and large pizzas for $20 each. If the total number of pizzas sold in a month must be less than 800, which system of inequalities would represent the number of small pizzas, S, and the number of large pizzas, L, that would meet the pizza parlor’s requirements?

• AS + L < 800 10S + 20L ≥ 10,000
• BS + L ≥ 800 10S + 20L < 10,000
• C10S + 20L < 800 S + L < 10,000
• D10S + 20L ≥ 800 S + L > 10,000

The reproduction number, called RO, is used to calculate the spread of disease. If a virus has an RO of 6, an infected person will likely directly infect six other people. Based on this, if 20 people are infected with a virus that has an RO of 4.2, how many people will these 20 people most likely directly infect?

• A46
• B54
• C84
• D98

{2, 3, 6, 6, 7} Which expression gives the complete set of potential values of a single number x that can be added to the above set of data without changing the median of the set?

• Ax ≥ 7
• Bx < 2
• Cx < 6
• Dx ≥ 6