SAT

Digital SAT Math Full Test

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.
6 7 × 1 4 3 = ?
- A1 3
- B4
- C2 7 4
- D9

Question group 22

2.If 2 3 𝑥 − 1 = 1 6 𝑥 + 4 , what is the value of x?

Question group 33

3.
The graph of a line in the x-y plane is totally vertical and has a negative x intercept. Which of the following could represent a line with these conditions?
- Ax = −5
- By = −4
- Cy = −x − 2
- Dx = −4y

Question group 44

4.
If 𝑥 4 = 6 , what is 𝑥 8 ?
- A3
- B4
- C8
- D12

Question group 55

5.
What equation represents the relationship between mass, m, and volume, v, in the above graph?
- Av = 3m
- Bm = 3v
- Cm = 6v
- Dv = m + 2

Question group 66

6.
What is the median of this set of numbers? {2, 5, 7, 9, 12, 16}
- A7
- B8
- C8.5
- D9

Question group 77

7.
There are 3 teaspoons in a tablespoon and 16 tablespoons in a cup. How much of a cup or cups would there be in 12 teaspoons?
- A1 1 2 cup
- B1 4 cup
- C2 cups
- D6 cups

Question group 88

8.The total calories for a particular salad are 1,100. The salad consists of only cheese, vegetables, and dressing. If the total caloric value of the cheese and vegetables is 650, and each packet of dressing used on the salad has 75 calories, how many packets of dressing were used on the salad?

Question group 99

9.If 𝑥 2 6 = 𝑥 2 , what is the value of x?

Question group 1010

10.
Suppose the price of a product is typically p dollars. If a 30% discount is applied to the price, what is the discounted price in terms of p?
- A0.03p
- B0.3p
- C0.7p
- D1.3p

Question group 1111

11.
The equation for gravitational force, F g , is the following: F g = 𝐺 𝑚 1 𝑚 2 𝑟 2 G is the gravitational constant, m1 and m2 are the masses of objects, and r is the distance between the objects. How would the gravitational force between two objects change if the distance between the objects doubles while all other quantities remain the same?
- AIt would be twice the original force.
- BIt would be four times the original force
- CIt would be 1 2 of the original force.
- DIt would be 1 4 of the original force.

Question group 1212

12.
If there were a randomly selected pet owner from the table above, what is the probability that they would be a male cat owner?
- A4 0 1 8 8
- B4 0 1 0 0
- C6 0 1 8 8
- D4 0 7 8

Question group 1313

13.A restaurant charges $5 for a cheeseburger and $4 for a hamburger. If Connor wants to buy at least 2 of each sandwich and spend a total of between $20-$30 (inclusive) on sandwiches, what is a possible value for the number of cheeseburgers Connor purchased?

Question group 1414

14.
What is y in terms of x in the following inequality? 1 2 < − 4 𝑥 + 6 𝑦
- A3 + 2 𝑥 > 𝑦
- B6 𝑥 − 2 < 𝑦
- C1 2 𝑥 + 3 > 𝑦
- D2 + 2 3 𝑥 < 𝑦

Question group 1515

15.
A particular line is graphed in the xy-plane and uses only real numbers. The line has a positive slope and a positive y-intercept. Which of these points could be on the line?
- A(−4, 5)
- B(2, 0)
- C(3, −6)
- D(0, −1)

Question group 1616

16.Triangle ABC has a right angle B. If side AB has a length of 7 units and side BC has a length of 24 units, what is the length in units of side AC?

Question group 1717

17.
The function f is expressed as f(x) = k for all values of x, and k is a constant real number. Which of the following must be true? I. f(x) forms a line. II. f(x) has a slope of zero. III. f(x) has a range from − ∞ to + ∞.
- AI only
- BII only
- COnly I and II
- DOnly II and III

Question group 1818

18.
In a right rectangular prism, the smallest edge is 2 cm long. The next greatest edge is twice the length of the smallest edge, and the greatest edge is 3 times the length of the smallest edge. What is the surface area of the prism?
- A6 sq cm
- B24 sq cm
- C64 sq cm
- D88 sq cm.

Question group 1919

19.
Kamini wants to make money from recycling aluminum cans and glass bottles. Her local government pays her $0.10 per can and $0.16 for each bottle. If she wants to earn a total of at least $100 and has collected a total of 600 cans, what is the minimum number of bottles she would need to collect to reach her goal?
- A250
- B270
- C300
- D420

Question group 2020

20.What is the measure in degrees of ∠X given that AB, AC, CD, and DB are straight lines and C is the center of the circle?

Question group 2121

21.
Jane is watering her garden and spends 5 minutes watering each tree and 2 minutes watering each shrub. If she can spend no more than 30 minutes watering her garden, which inequality represents the number of T trees and S shrubs she can water given these constraints?
- A5T + 2S ≥ 30
- B5T + 2S ≤ 30
- C5 × T × S ≤ 30
- D5 > 30 × T × S

Question group 2222

22.
The price of a video streaming service increases by 15% each year. If the price, P, of the service begins at v dollars, what is the value of the constant c in the following function that models the price of the service t years after it begins? 𝑃 = 𝑣 𝑐 𝑡
- A0.15
- B0.85
- C1.15
- D1.55

Module 2

Math · 35 min · 22 questions

Question group 123

23.
Density equals mass divided by volume. If density is graphed as a line with mass corresponding to the y value and the volume corresponding to the x value, what aspect of the function corresponds to the density of the substance?
- Aslope
- By-intercept
- Cx-intercept
- Ddomain

Question group 224

24.
What is the sum of the following polynomials? 5 x cubed minus x plus 4 and 6 x cubed plus x squared minus 3
- A30 x to the sixth power plus x cubed minus x plus 1
- B30 x cubed plus 2 x squared plus x minus 1
- C11 x cubed plus x squared minus x plus 1
- D11 x cubed minus x squared plus x minus 1

Question group 325

25.
Which of the following is equivalent to 8 raised to the one third power ?
- A0
- B1
- C2
- D6

Question group 426

26.
2x − 3y = 7 6x + ky = 21 For what value of the constant k will the above system of equations have infinitely many solutions?
- A-9
- B-7
- C2
- D13

Question group 527

27.
What is the y-intercept of the graph of the function y equals 2 to the x-th power minus 3 ?
- A-3
- B-2
- C0
- D1

Question group 628

28.
Which of the following is an equivalent form of z = x − y?
- Az equals open paren the square root of x minus the square root of y close paren times open paren the square root of x minus the square root of y close paren
- Bz equals open paren the square root of x minus the square root of y close paren times open paren the square root of x plus the square root of y close paren
- Cz equals open paren the square root of x plus the square root of y close paren times open paren the square root of x plus the square root of y close paren
- Dz equals the fraction with numerator the square root of x plus the square root of y and denominator the square root of x minus the square root of y

Question group 729

29.
If x + 3 = y and xy = 40, what is the sum of x and y, given that both x and y are positive?
- A5
- B8
- C13
- D15

Question group 830

30.
The graph of the above line is portrayed by which of the following equations?
- Ay = 3
- By equals one third x
- Cy = 3x
- Dy = x + 3

Question group 931

31.2a − 3b = 5 3a − 2b = 10 The solution to the above system of equations is (a, b). What is the value of a − b?

Question group 1032

32.
Due to radiation, the mass of a substance decreases by 0.5% every day. Which type of function would properly model the mass of the substance as the days go by?
- Aincreasing linear
- Bdecreasing linear
- Cincreasing exponential
- Ddecreasing exponential

Question group 1133

33.
If Sarah took the subway from Times Square to Harlem, what was her speed in miles per hour, to the nearest tenth?
- A0.7 mph
- B3.4 mph
- C17.6 mph
- D204.0 mph

Question group 1234

34.If x + y = 7 and x − y = 3, what is the value of 3 x squared minus 3 y squared ?

Question group 1335

35.Water from the ocean has 3.5% salt, and water from the Dead Sea has 33.7% salt. If someone has 10 gallons of ocean water, how many gallons of water from the Dead Sea (measured to the nearest hundredth of a gallon) need to be added so that the solution has 10% salt?

Question group 1436

36.
Which of the following is a solution for x in the equation 4 x equals 2 minus 3 x squared ?
- Athe fraction with numerator negative 3 plus the square root of 10 and denominator 4
- Bthe fraction with numerator 2 minus the square root of 5 and denominator 3
- Cthe fraction with numerator the square root of 3 and denominator 4
- Dthe fraction with numerator negative 2 minus the square root of 10 and denominator 3

Question group 1537

37.
A function g(x) has values given in the table below: Which of the following would be a factor of g(x)?
- A(x − 1)(x + 2)
- B(x − 2)(x + 3)
- C(x + 1)(x − 2)
- D(x + 2)(x − 2)

Question group 1638

38.
Students at a university were surveyed as to whether they wanted a new library for the university. Out of the 100 students surveyed, 40% said they wanted a new library. What is justifiable based on this information?
- AOf the 100 students surveyed, 40 wanted a new library.
- B40% of all people in the university community want a new library
- CExactly 40 students at the university want a new library.
- DNo more than 40 university students want a new library.

Question group 1739

39.
A circle has the equation open paren x minus a close paren squared plus open paren y minus b close paren squared equals 9 , in which a and b are positive constants. What must the values of a and b be in order for all the x and y coordinates of the circle to be greater than zero?
- Aa < 9 and b > 9
- Ba is greater than the square root of 3 and b is greater than the square root of 3
- Ca > 6 and b < 6
- Da > 3 and b > 3

Question group 1840

40.
V e equals the square root of 2 G of M over r The escape velocity for a given spherical body, like a planet or a star, is given by the above formula, in which G is the gravitational constant, r is the distance from the center of the body’s mass to the object, and m is the mass of the spherical body. What is M in terms of the other variables?
- AM equals V e times G over 2 r
- BM equals 2 G over open paren V e close paren squared times r
- CM equals open paren V e close paren squared times r over 2 G
- DM equals 2 r of open paren the square root of V e close paren over G

Question group 1941

41.A sphere has a volume of 8 cubic feet. What is the volume in cubic feet of a sphere with twice the radius of the original one?

Question group 2042

42.
Which equation would portray the function graphed above?
- Ay = (x − 2)(x + 4)(x − 1)
- By = (x − 4)(x + 2)(x − 1)
- Cy = (x − 4)(x − 2)
- Dy = (x + 1)(x + 2)

Question group 2143

43.
If square ABCD has an area of 36 square units, what is the perimeter of square WXYZ given that each vertex of square WXYZ bisects the side of square ABCD that it intersects?
- A6
- B6 the square root of 3
- C12
- D12 the square root of 2

Question group 2244

44.h of t equals negative 16 t squared plus 16 t plus 10 The function above portrays the height, h, of a projectile t seconds after being thrown. Which of the following would be the time in seconds at which the height of the projectile is at its maximum value?