SAT

Digital SAT Math Full Test 3

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.
What is an equivalent form of (0.8a + 0.7b) − (1.4a − 0.3b)?
- A2.2a + b
- B−0.6a + b
- C1.12a − .21b
- D−0.6a − 0.4b

Question group 22

2.
Based on the graph of the line above, what is its slope?
- A2 3
- B1
- C3 2
- D4 3

Question group 33

3.If 12x − 10 = 4, what is − 5 + 6x?

Question group 44

4.
The volume of a cylinder, v, is given by the equation v = πr 2 h, in which r is the radius of the cylinder and h is the height of the cylinder. What is the height in terms of the other variables
- Aℎ = 𝑣 𝜋 𝑟 2
- Bℎ = 𝜋 √ 𝑟 𝑣
- Cℎ = 2 𝜋 𝑣 𝑟
- Dℎ = 𝜋 𝑟 2 𝑣

Question group 55

5.
Voter turnout rates for different U.S. presidential elections are given in the following graph: During what year was voter turnout the highest?
- A1996
- B2004
- C2008
- D2016

Question group 66

6.
Which of these options is equivalent to the following expression? ( 2 𝑦 2 − 𝑦 ) = ( 2 𝑦 2 + 2 𝑦 )
- A4 𝑦 4 − 2 𝑦 2
- B4 𝑦 2 − 2 𝑦
- C−3y
- D6y + 2

Question group 77

7.
In the figure above, lines ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ 𝐴 𝐸 𝐵 , ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ 𝐶 𝐸 , and ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ 𝐷 𝐸 all intersect at point E and have measures as indicated. What is the measure of angle ∠CED?
- A20°
- B30°
- C45°
- D60°

Question group 88

8.( 𝑥 + 2 ) 3 = 2 7 What positive value of x would make the above equation true?

Question group 99

9.
A restaurant tabulated meals from 100 of its diners to record if the diner ordered an appetizer and/or a dessert with a meal. Based on the table above, what is the probability that if a diner ordered dessert, they would also order an appetizer?
- A1 5
- B3 1 0
- C3 8
- D3 7

Question group 1010

10.y=2x-3 What is the x-coordinate of the x-intercept of the line with the above equation?

Question group 1111

11.
The graph of 𝑦 = 1 2 𝑥 − 2 in the xy-plane is a line. What is the y-intercept of this line?
- A−2. 5
- B−2
- C1 2
- D2

Question group 1212

12.If 3 = 3 2 ( 4 𝑥 − 2 𝑦 ) and 𝑦 = 1 2 𝑥 , what is the value of y?

Question group 1313

13.
Which of the following would be points at which the function y = (x + 4) (x − 5) x intersects the x axis? I. (−4, 0) II. (5, 0) III. (0, 0)
- AI only
- BII only
- CI and III only
- DI, II, and III

Question group 1414

14.
𝐵 ( ℎ ) = 1 0 0 0 × 2 ℎ The growth of a population of bacteria is modeled by the above function, in which B(h) represents the number of bacteria after h hours have passed. After how many hours will the population of bacteria be 8 times its initial number?
- A1 hour
- B2 hours
- C3 hours
- D4 hours

Question group 1515

15.
Pete was playing a children’s game that had a spinner with values 1-6; with each turn, he spins the spinner twice and finds the total. He tabulated the combined values of two combined spins from a total of 40 different turns as shown above. What fraction of all his combined spins were 6 or less?
- A1 4 0
- B9 4 0
- C1 3 4 0
- D7 2 0

Question group 1616

16.
The population of the greater metropolitan area of Mexico City was estimated to have been 22,000,000 at the end of the year 2020. If the Mexico City area represented 17% of all of Mexico’s population at the end of 2020, what would be the closest estimate of Mexico’s total population?
- A4,000,000
- B26,000,000
- C104,000,000
- D129,000,000

Question group 1717

17.For the function f as defined below, what is the value of f (5)? 𝑓 ( 𝑥 ) = ( 𝑥 − 3 ) ( 𝑥 + 1 )

Question group 1818

18.
The solutions to this set of inequalities are found in which quadrant(s) of the xy-coordinate plane y>x+1 and y<-2x-3
- AOnly quadrant 1
- BOnly quadrant 3
- CQuadrants 1 and 4 only
- DQuadrants 2 and 3 only

Question group 1919

19.
If a computer costs $2,000 and depreciates (i.e., the value decreases) by the same amount each year, how much is the annual amount of depreciation if after 6 years the computer is worth $800?
- A$80
- B$100
- C$200
- D$400

Question group 2020

20.
If a circle graphed in the xy-coordinate plane has a center at (3, 4) and intersects the origin, what is the equation of the circle?
- A( 𝑥 − 3 ) 2 + ( 𝑦 − 4 ) 2 = 2 5
- B( 𝑥 + 3 ) 2 − ( 𝑦 + 4 ) 2 = 2 5
- C𝑥 2 + 𝑦 2 = 4 9
- D𝑥 2 + 𝑦 2 = 2 5

Question group 2121

21.
Susan blinks an average of 20 times per minute while awake. In the 16 hours she is awake in a day, how many times will she blink?
- A320
- B7,680
- C12,400
- D19,200

Question group 2222

22.
Hugo’s $3,000 monthly budget is broken down in this table: Hugo is trying to allocate more money into savings. If he cut his allocation towards miscellaneous expenses by half and allocated this amount to savings, by what percentage would his monthly savings increase?
- A20%
- B50%
- C65%
- D80%

Module 2

Math · 35 min · 22 questions

Question group 123

23.
The function g is defined by 𝑔 ( 𝑥 ) = 𝑥 3 2 What is the value of g(−2)?
- A-4
- B-2
- C-1
- D4

Question group 224

24.
For the linear function f, the table above shows some values of x and the corresponding values of f(x). Which of the following equations correctly defines the function?
- A𝑓 ( 𝑥 ) = 1 3 𝑥 − 2
- B𝑓 ( 𝑥 ) = 2 3 𝑥 − 1
- C𝑓 ( 𝑥 ) = 𝑥 − 6
- D𝑓 ( 𝑥 ) = 3 𝑥 + 2

Question group 325

25.
Which of these is equivalent to 3 √ 𝑎 × 𝑎 5 3 ?
- A𝑎 3 2
- B𝑎 4 3
- C𝑎 2
- D𝑎 5

Question group 426

26.
If y = ax in which a is a constant and y = 16 when x = 8, what is the value of x when y is −3?
- A-6
- B-1.5
- C1
- D8.5

Question group 527

27.
𝑎 𝑥 2 + 𝑏 𝑥 + 𝑐 = 2 𝑥 2 + 1 6 𝑥 + 3 2 In the equation above, a, b, and c are all constants. What is the sum of a, b, and c?
- A48
- B50
- C52
- D64

Question group 628

28.
S(w)=500+10w Ana receives an allowance of $10 per week. The function above shows how much money she will have in her savings account after w weeks, assuming she saves all her allowance in the account. What does the number 500 represent in the function?
- AThe money in her account at the beginning of the time period
- BThe money in the account at the end of the time period
- CThe weekly increase in money in the account
- DThe net profit she receives after expenses

Question group 729

29.On a map, 1 inch represents 3 miles in actual distance. If there is a rectangular plot of land on the map with a width of 2 inches and a length of 3 inches, what would be the actual area of the rectangular plot of land in square miles?

Question group 830

30.
Samara drove on a 400-mile trip. If the first half of the trip took her 4 hours of driving to complete and the second half took her 6 hours of driving to complete, what was her average driving speed for the whole 400-mile trip?
- A20 miles per hour
- B35 miles per hour
- C40 miles per hour
- D80 miles per hour

Question group 931

31.
The above triangles ABC and DEF are similar to one another, with angle B corresponding to angle E. What is the tangent of angle C?
- A5 1 3
- B5 1 2
- C1 0 1 3
- D1 2 1 3

Question group 1032

32.
If the airplane continues to decrease in value at a linear rate, at what year after purchase will the plane first closely approximate a value of zero dollars?
- A10 years after purchase
- B15 years after purchase
- C20 years after purchase
- D25 years after purchase

Question group 1133

33.
If x is increased by 400%, what is the result in terms of x?
- Az
- B2x
- C4x
- D5x

Question group 1234

34.
In the figure above, ABCD and AEFG are similar rectangles. If ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ 𝐴 𝐵 is 4 units long, , and ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ 𝐵 𝐶 is 6 units long ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ ̅ 𝐹 𝐺 is 10 units long, what is the perimeter of rectangle AEFG?
- A24 units
- B48 units
- C50 units
- D72 units

Question group 1335

35.
How many zeros will a line with the equation y = k have in which k is a constant greater than zero?
- AZero
- BOne
- CTwo
- DCannot be determined from the given information

Question group 1436

36.Based on the information in the table, what is the median quiz score of the combined set of both classes?

Question group 1537

37.
What would be the value(s) of x that would be a solution or solutions to this equation? 𝑥 2 − 4 𝑥 − 2 = 4
- A-2
- B2
- C4
- DThere are no solutions

Question group 1638

38.
What is the vertex of a parabola with the equation 𝑦 = ( 𝑥 − 6 ) 2 ?
- A(−6, 0)
- B(0, 0)
- C(6, 0)
- D(0, 6)

Question group 1739

39.
Out of all the 44 people to serve as president of the United States before the year 2020, 14 of them had previously been U.S. vice president. Which function expresses the relationship between the number of presidents, P, and vice presidents who became presidents, V?
- AV = 14P
- B𝑉 = 7 2 2 𝑃
- C𝑉 = 1 1 4 𝑃
- D𝑉 = 2 2 7 𝑃

Question group 1840

40.− 1 4 𝑥 + 1 6 𝑦 = 1 2 2 𝑦 = 3 𝑥 + 𝑎 If the above set of equations has infinitely many solutions, what is the value of the constant a?

Question group 1941

41.
Julian and Maria are budgeting for their upcoming wedding reception. They are inviting people from each side of their families—J people from Julian’s side of the family and M people from Maria’s side of the family. They are planning on spending $40 per person invited to the wedding reception. If they want to keep the cost of the wedding reception to less than $18,000, and have more than 200 people in attendance, which system of inequalities would represent these conditions?
- A𝑀 + 𝐽 ≤ 2 0 0 4 0 𝑀 + 𝐽 ≥ 1 8 , 0 0 0
- B𝑀 + 𝐽 > 4 0 1 8 , 0 0 0 + 𝑀 + 𝐽 > 2 0 0
- C𝑀 + 𝐽 > 1 8 , 0 0 0 𝑀 + 𝐽 4 0 < 2 0 0
- D𝑀 + 𝐽 > 2 0 0 4 0 ( 𝑀 + 𝐽 ) < 1 8 , 0 0 0

Question group 2042

42.
Given that there are 5,280 feet in a mile, which of the following would most closely approximate 30 miles per hour in feet per second?
- A28 feet/second
- B44 feet/second
- C176 feet/second
- D158,400 feet/second

Question group 2143

43.The circle graphed above has a center of C, a radius of 7 units, and a central angle ∠ACB with a measure of 100°. What is the area of the sector of the circle designated by ∠ACB to the nearest whole square unit?

Question group 2244

44.
At a café, each cup of coffee has 95 milligrams of caffeine, and each cup of tea has 26 milligrams of caffeine. Shantiel goes to the store and purchases only cups of coffee and tea. If the number of cups of coffee that Shantiel purchased was half the number of cups of tea that she purchased, and the total milligrams of caffeine in all the drinks she purchased was 735, how many cups of coffee did she purchase?
- A2
- B3
- C5
- D6