SAT

Digital SAT Math Full Test 4A

70 min · 2 sections · 44 questions

Section

Module 1

Math · 35 min · 22 questions

The questions in this section address a number of important math skills. Use of a calculator is permitted for all questions. NOTES Unless otherwise indicated: - All variables and expressions represent real numbers. - Figures provided are drawn to scale unless stated otherwise. - All figures lie in a plane. - The domain of a given function f is the set of all real numbers x for which f(x) is a real number. For multiple-choice questions, solve each problem and choose the correct answer from the choices provided. Each multiple-choice question has a single correct answer. For student-produced response questions, solve each problem and enter your answer in the box. If a question has more than one correct answer, enter only one of them.

Question group 11

1.
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

Question group 22

2.What number is 5% greater than 200?

Question group 33

3.
Which of the following is closest to the price in U.S. dollars of an ounce of gold in the year 1970?
- A$245
- B$520
- C$610
- D$1,225

Question group 44

4.
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

Question group 55

5.
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

Question group 66

6.
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

Question group 77

7.
Which of the following models the function as presented in the graph above?
- Af of x equals x squared
- Bf of x equals x squared plus 1
- Cf of x equals 2 to the x-th power
- Df of x equals 3 to the x-th power plus 1

Question group 88

8.Parallelogram ADEC has a side of the line segment D E of length 10 units, and a side of the line segment D A of length 5 units. The length from A to B is 3 units. What is the area of the parallelogram in square units?

Question group 99

9.
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

Question group 1010

10.
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

Question group 1111

11.An airplane travels 3,000 miles in 10 hours. What is its speed in miles per hour?

Question group 1212

12.2x-3y=5 4x+y=17 If (x, y) is a solution to the above system of equations, what is the value of y?

Question group 1313

13.
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

Question group 1414

14.
In the function with values given above, in which C is a constant, if f (2) = 8, what is the value of f (3)?
- A16
- B27
- C64
- D80

Question group 1515

15.he height of a certain triangle is twice the width of its base. If the area of the triangle is 25 square units, what is the height of the triangle?

Question group 1616

16.
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

Question group 1717

17.
Based on the information in the table, what is the mass of a solid steel wall that has a volume of 300 cubic meters?
- A26 kilograms
- B8,150 kilograms
- C432,000 kilograms
- D2,355,000 kilograms

Question group 1818

18.The mean height of seven teenage boys is 67 inches. If one of the boys has a height of 74 inches, what is the mean height of the remaining boys to the nearest tenth of an inch?

Question group 1919

19.
∠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

Question group 2020

20.
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

Question group 2121

21.
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

Question group 2222

22.
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

Module 2

Math · 35 min · 22 questions

Question group 123

23.
In the line formed by the equation y + 5 = 7x, what is the value of the y intercept?
- A-5
- B-1
- C5
- D7

Question group 224

24.
Twenty students were asked the combined total number of servings of fruits and vegetables they have each day. The results are presented in the histogram above. What is the median number of servings of fruits and vegetables consumed each day?
- A4
- B5
- C6
- D7

Question group 325

25.
Which of the following is equivalent to the fraction with numerator x squared minus 81 and denominator x plus 9
- Ax+9
- Bx-9
- Cx squared minus 3
- Dx squared plus 3

Question group 426

26.
What is the best approximation of the slope of the line graphed above?
- Aone half
- Btwo thirds
- Cfour thirds
- D2

Question group 527

27.
Walter is going backpacking on a trail. The total distance of the trail is 300 miles. If he has already traveled 100 miles on the trail, how many miles per day, m, will he need to travel in order to complete his journey in D days?
- Am equals 200 over D
- Bm equals 300 D
- Cm equals D over 300
- Dm equals 200 plus D

Question group 628

28.
Which of the following expressions is equivalent to 2(x − 4) + 4?
- A2x − 4
- B2x + 4
- C4x − 4
- D4x + 4

Question group 729

29.
The number of dollars, C, it costs for Halle to run a restaurant is modeled by the function C(m) = 10m + 10,000 in which m is the number of meals served. What is the meaning of the 10 in this function?
- AThe total cost for all the meals sold.
- BThe fixed costs for the restaurant to operate.
- CThe profit the restaurant has for each meal sold.
- DThe additional cost to the restaurant for each additional meal

Question group 830

30.
Which of the following represents the graph of one half y plus 2 equals negative x
- Ahttps://s4-media1.study4.com/media/dsat_media/img/images_ed65c04856f60a8728852874b47c5688.png
- Bhttps://s4-media1.study4.com/media/dsat_media/img/images_7c3548aea2db108eeaed9c8948b71aca.png
- Chttps://s4-media1.study4.com/media/dsat_media/img/images_0a454f118b8303ae9819d1f817082df9.png
- Dhttps://s4-media1.study4.com/media/dsat_media/img/images_608d6bc56b47762043ba9416a6d48526.png

Question group 931

31.
In a survey of 1,000 likely voters, one half like Candidate A, one third like Candidate B, and the remainder like neither candidate. If a likely voter is selected at random, what is the probability that they will like neither candidate?
- A1 over 12
- Bone sixth
- Cone fourth
- Done third

Question group 1032

32.A silverware drawer has a total of 80 forks and spoons. If there are 5 forks for every 3 spoons, how many forks are there in the drawer?

Question group 1133

33.
Traffic density is measured in vehicles/mile/lane. The traffic density in a city is portrayed in the graph below Between what two hours does the traffic density increase the most?
- ABetween 7 a.m. and 9 a.m.
- BBetween 9 a.m. and 11 a.m.
- CBetween 1 p.m. and 3 p.m.
- DBetween 3 p.m. and 5 p.m.

Question group 1234

34.
In the system of inequalities y + 10 ≤ 3x and x ≤ −y − 2, what is the maximum value of y?
- A-6
- B-4
- C0
- D3

Question group 1335

35.
A meal costs x dollars. The sales tax on the meal is 7%. If the cashier accidentally subtracted the sales tax from the price of the meal instead of adding it, what would the price be in terms of x?
- A0.07x
- B0.7x
- C0.93x
- D1.07x

Question group 1436

36.Ken’s commute takes 25 more minutes in the evening than it does in the morning. If his total daily commute takes 95 minutes, how long does his morning commute take in minutes?

Question group 1537

37.
The function f is determined by f of x equals the fraction with numerator x cubed and denominator 4 plus 3 . What is the value of f(2)?
- A1
- B5
- C6
- D9

Question group 1638

38.If the volume of a right rectangular prism is 90 cubic inches, and the product of the length and width of the prism is 30 square inches, what is the height of the prism?

Question group 1739

39.x squared minus x minus 20 equals 0 What is the sum of the solutions to the equation above?

Question group 1840

40.
The above circle graph gives the percentages of 800 city residents who voted in favor of a tax levy (“YES”) and those who voted against it (“NO”). If the central angle formed by the portion of the circle allocated to “NO” is 45°, how many of the residents voted “NO”?
- A90
- B100
- C110
- D120

Question group 1941

41.
Density, mass, and volume are related by this formula: If the mass of an object is 2 kilograms and its volume is 8 liters, what is the object’s density in k g over L
- Aone eighth
- Bone fourth
- Cone half
- Dthree fourths

Question group 2042

42.
What percentage of 70 is 35?
- A40%
- B50%
- C75%
- D200%

Question group 2143

43.A line that is perpendicular to the line with the equation y = −3x + 5 has a y intercept of 4. What is the y value of a point in this perpendicular line when its x value is 3?

Question group 2244

44.
In triangle ABC above, the line segment A C is 24 units long and the line segment B C is 7 units long. What is th cosine of ∠ABC?
- A7 over 25
- B7 over 24
- C24 over 27
- D25 over 27