SAT

Digital SAT Math Full Test 5B

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.
1/4 × (x − 7) = 3. What value satisfies the equation?
- A3
- B7
- C19
- D28

Question group 22

2.
If f(x) = 5x − 2, which expression is equivalent to f(x + 3)?
- A5x + 1
- B5x + 13
- C5x + 15
- D5x + 17

Question group 33

3.
If 4b − 3 > 7, what is the greatest possible integer value of −2b + 4?
- A−2
- B−1
- C0
- D1

Question group 44

4.
Which expression is equivalent to (x² + 6x + 9)/(x² + 7x + 12)?
- A(6x + 9)/(7x + 12)
- B(x + 4)/(x + 3)
- C(x + 3)/(x + 4)
- Dx + 3

Question group 55

5.If (x⁴y³)/(x²)² × y^m = 1, what is the value of m?

Question group 66

6.
A certain type of floor tile covers an area of 7.75 square feet for every three tiles. How many tiles of this type are needed to cover an area of 186 square feet?
- A24
- B72
- C186
- D558

Question group 77

7.
A square has a diagonal length of 12√2 inches. What is the area of the square in square inches?
- A12
- B24
- C72
- D144

Question group 88

8.(2y − (2y + 1))/(3y + 5) = (4y + (3 − 4y))/y. What is the value of y?

Question group 99

9.
2y + x = 9 27 − 3x = 6y The system of equations shown has how many solutions?
- A0
- B1
- C2
- DInfinitely many

Question group 1010

10.
An electrician charges a service call fee, plus an additional fee for every hour on the job. The graph shows the relationship between the hours worked and the total price of the job. Based on the graph, how much would the electrician charge for a job that takes 20 hours?
- A$600
- B$700
- C$1,200
- D$1,500

Question group 1111

11.
The graph represents the change in price per share (in dollars) of a certain stock during two business weeks. If the coordinates of the maximum are (a, b) and the coordinates of the minimum are (c, d), what is the value of (d − b)/(c − a)?
- A−17
- B−19/3
- C−17/3
- D3

Question group 1212

12.
Kush currently scores 400 on the SAT Math section. He sets a goal to improve this score by 1% each day. At this rate, approximately how many days will it take him to score an 800?
- A40
- B50
- C60
- D70

Question group 1313

13.The table gives values of f(x) and g(x), and h(x) = f(x)/g(x). For what value of x is h(x) undefined?

Question group 1414

14.
The scatterplot shows planting time and crop yield. What is the approximate difference between the yield predicted by the line of best fit and the greatest outlier?
- A10
- B15
- C20
- D25

Question group 1515

15.
Line a is parallel to line c. Which of the following statements is true?
- Ax° + y° = 80°
- Bx° + y° = 100°
- Cx° = y°
- Dx° + y° = 180°

Question group 1616

16.
For the system of inequalities shown, what is the greatest possible value of x?
- A2
- B1
- C0
- D−1

Question group 1717

17.
If 4 knives, 5 spoons, and 6 forks cost $7.90 and 2 knives, 2 spoons, and 5 forks cost $5.80, how much do 2 knives, 3 spoons, and 1 fork cost?
- A$2.10
- B$3.30
- C$4.70
- D$5.80

Question group 1818

18.
If x ≠ 3, which of the following is equivalent to 1 / (1/(x − 3) + 1/(y + 5))?
- A((x − 3)(y + 5))/(x + y + 2)
- B(x + y + 2)/((x − 3)(y + 5))
- C((x + 3)(y − 5))/(x + y + 2)
- D(5x − 3y)/(x + y + 2)

Question group 1919

19.
The range of the parabola shown in the graph above is y ≥ −4. If y = ax² + bx + c is used to represent the graph, what is the value of a?
- A1/3
- B2/3
- C3/2
- D3

Question group 2020

20.A thrift store prices a piece of used furniture at $100. The price is marked down an additional p percent every month until it is sold. If the piece of furniture is sold for $64 after two months, what is p?

Question group 2121

21.
The graph shows restaurant wait times on Friday and Saturday. On average, how many minutes longer are people willing to wait on Saturday than on Friday?
- A1.3
- B11.3
- C34
- D68

Question group 2222

22.The figure shows a rodeo arena divided into 12 equal sections, 4 of which contain bulls. If 64 + 16π/3 yards are needed to reinforce all the edges of the 4 bull sections, what is the radius, in yards, of the arena?

Module 2

Math · 35 min · 22 questions

Question group 123

23.The function f(x) is defined as f(x) = 2g(x), where f(x) = x + 5. What is the value of f(3)?

Question group 224

24.
Which of the following expressions is equivalent to (24x⁴ + 36x³ − 12x²)/(12x²)?
- A2x² + 3x
- B2x² + 3x − 12
- C2x² + 3x − 1
- D24x⁴ + 36x³ − 1

Question group 325

25.
A group of 150 first-year students was randomly selected for a survey that asked whether they were excited to continue their foreign language studies in the next school year. Of this group, 93 said yes, 37 said no, and 20 were not sure. If 1,195 first-year students are currently enrolled in foreign language studies, which of the following is most likely a valid conclusion?
- AAbout 740 first-year students are excited to continue foreign language studies next year.
- BAbout 440 first-year students are not excited to continue foreign language studies next year.
- CAbout 240 first-year students are not excited to continue foreign language studies next year.
- DAbout 130 first-year students do not know yet whether they are excited to continue foreign language studies next year.

Question group 426

26.
A trucking firm needs to hire at least 8 employees. Drivers are paid $1,120 per week and mechanics are paid $900 per week. The weekly budget is no more than $8,300. Which system of inequalities represents this situation, where x is the number of drivers and y is the number of mechanics?
- A2020(x + y) ≤ 8300
- Bx + y ≤ 8; 1120x + 900y ≤ 8300
- Cx + y ≥ 8; 900x + 1120y ≤ 8300
- Dx + y ≥ 8; 1120x + 900y ≤ 8300

Question group 527

27.y = 3x² + 7x − 4 y − x = −7 How many solutions does the system have?

Question group 628

28.
A land trust begins with 720 acres and adds land at a constant rate of 84 acres per year. If f(x) = ax + b models the acreage with x measured in months, when f(x) = 1126, what is x?
- A4.83
- B13.4
- C58
- D406

Question group 729

29.
g(x) = 3x² + 12x + 3. What is the minimum value of g(x) + 3?
- A−9
- B−6
- C−2
- D6

Question group 830

30.
2x² + 4x − 3 = 0. Which of the following represents the solutions?
- A(−2 ± √10)/2
- B(−4 ± √10)/2
- C(−2 ± √7)/2
- D(2 ± √10)/2

Question group 931

31.
An algae culture increases by 50% each day. After 3 days there are 6,750 cells. Approximately how many cells were present initially?
- A2,000
- B3,000
- C4,500
- D6,600

Question group 1032

32.
A student’s average score on 5 quizzes is 80. If the lowest score is removed, the average of the remaining 4 quizzes is 83. What was the lowest score?
- A28
- B35
- C68
- D77

Question group 1133

33.
In the figure, lines m and n are parallel. If AB = 5, AC = 13, and DE = 9, what is BD?
- A12
- B21.6
- C23.4
- D33.6

Question group 1234

34.
Maple syrup costs $33 per gallon and pancake syrup costs $14 per gallon. A mixture contains 8 gallons total. If x is the number of gallons of pancake syrup, which equation gives the total cost c?
- Ac = −19x + 264
- Bc = −14x + 33
- Cc = 14x
- Dc = 19x + 112

Question group 1335

35.
A landscaping company mows x properties per month. For each property, maintenance starts at c dollars and the company charges y dollars per square yard. The average lawn area is z square yards. Which expression represents monthly revenue?
- Axyz + c
- B(yz + c)x
- C(yz + c)mx
- D(xyz + c)m

Question group 1436

36.2x + 8y = 9 3x + 5y = 10 If (x, y) is a solution to the system, what is x/y?

Question group 1537

37.
|(4 + 2x)/(x + 2)| = x. What is the solution set?
- ANo solution
- B{−2}
- C{2}
- D{−2, 2}

Question group 1638

38.
Which of the following equations could be for the graph of the polynomial shown?
- Af(x) = −x²(x + a)(x − d)
- Bf(x) = −x²(x − a)(x − d)
- Cf(x) = −x(x − a)(x − d)
- Df(x) = x²(x − a)(x − d)

Question group 1739

39.
y = ax² − b²/4. Which of the following is equivalent to the equation shown?
- At = (√(ax) + b/2)(√(ax) − b/2)
- Bt = (√a·x + b/2)(√a·x − b/2)
- Ct = (√a·x − b/2)²
- Dt = (√a·x + b/2)²

Question group 1840

40.
The graphs of the two equations shown intersect at (a, 15.5) and (c, d). What is the value of d?
- A−1
- B1
- C3/2
- D3

Question group 1941

41.A machine shop has a box of metal disks as shown in the table. There are 3 small zinc disks for every 5 large zinc disks and 4 small copper disks for every 7 large copper disks. If a small disk is chosen at random, what is the probability that it will be copper?

Question group 2042

42.
x² + y² + 12x + 14y = −4. What is the radius of the circle given by the equation?
- A−4
- B−1
- C9
- D16

Question group 2143

43.
Cylinder A and cylinder B are right cylinders. Based on the volume and radius relationship given in the source, what is the ratio of cylinder B’s height to cylinder A’s height?
- A4:5
- B1:1
- C5:4
- D25:16

Question group 2244

44.In triangle ABC, angle A and angle C are equal, and AC is 48 inches long. If tan ∠A = 0.75, what is the area of the triangle, in square inches?