This is our free SAT Math practice test for section 4 of the new SAT. This is the portion of the math test that allows the usage of a calculator. The calculator is meant to save you time, which will allow you to focus on complex modeling and reasoning. Be aware that not all of the problems will require the use of a calculator. The SAT math test is designed to measure fluency, conceptual understanding, and applications. This section will include 30 multiple choice questions and 8 gridin questions.
Directions for Questions 130: Solve each problem and then select the best answer from the choices provided. Directions for Questions 3138: Solve each problem and then type in the correct answer. Use the forward slash symbol ( / ) for fractions.
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Question 1 of 38
1. Question
A teacher gave his students 5 vocabulary words to memorize. Each day thereafter, he gave his students an additional 3 vocabulary words to memorize. After 25 days, how many vocabulary words had his students memorized?
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Question 2 of 38
2. Question
The table above shows the mass, radius, axis period, radius of orbit, and period of revolution of the Sun and the planets in our solar system. Based on the table, if Earth, Mars, or Jupiter was chosen at random, what is the probability that the chosen planet’s mass would be greater than 10 x 10^{24} ?CorrectIncorrect 
Question 3 of 38
3. Question
The sum of two positive integers is 13. The difference between these numbers is 7. What is their product?
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Question 4 of 38
4. Question
In the given figure, the measure of angle OAC is 60 degrees, and the center of the circle is 0. If the circle has a radius of 6, what is the length of segment DB?CorrectIncorrect 
Question 5 of 38
5. Question
Which of the following lists every positive nonprime factor of 20?
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Question 6 of 38
6. Question
What is the difference between the median and the mode in the following set of data?
72, 44, 58, 32, 34, 68, 94, 22, 67, 45, 58
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Question 7 of 38
7. Question
What is the total number of degrees in the interior angles of a regular hexagon?
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Question 8 of 38
8. Question
A pool that holds 35,000 cubic feet of water is being filled by a pump at a rate of 200 cubic feet per minute. At the same time, water is draining out through an open valve accidentally left open. If the pool is full in 200 minutes, at what rate is the water draining out?
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Question 9 of 38
9. Question
What is the sum of the areas of the three rectangles that are drawn below the graph of the line y = 2^{x} ?CorrectIncorrect 
Question 10 of 38
10. Question
A perfect sphere with a diameter of 5 meters is inscribed in a cube. Which of the following best approximates the volume of the space between the sphere and the cube?
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Question 11 of 38
11. Question
What is the value of a + b?CorrectIncorrect 
Question 12 of 38
12. Question
A passenger ship left Southampton, England for the Moroccan coast. The ship travelled the first 230 miles at an average speed of 20 knots, then increased its speed for the next 345 miles to 30 knots. It travelled the remaining 598 miles at an average speed of 40 knots. What was the ship’s approximate average speed in miles per hour? (1 knot = 1.15 miles per hour)
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Question 13 of 38
13. Question
What is the value of y, if lines a, b, and c are parallel?CorrectIncorrect 
Question 14 of 38
14. Question
If AB is parallel to DC, and AD is parallel to BC, what is the value of b − a?CorrectIncorrect 
Question 15 of 38
15. Question
The circumference of a right circular cylinder is half its height. The radius of the cylinder is x. What is the volume of the cylinder in terms of x?
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Question 16 of 38
16. Question
The speed of a subway train is represented by the equation z = s^{2} + 2s for all situations where 0 ≤ s ≤ 7, where z is the rate of speed in kilometers per hour and s is the time in seconds from the moment the train starts moving. In kilometers per hour, how much faster is the subway train moving after 7 seconds than it was moving after 3 seconds?
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Question 17 of 38
17. Question
At a certain lab, the ratio of scientists to engineers is 5:1. If 75 new team members are hired in the ratio of two engineers per scientist, the new ratio of scientists to engineers would be approximately 2:3. Approximately how many scientists currently work at the lab?
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Question 18 of 38
18. Question
In the xycoordinate plane, a circle with center (−4, 0) is tangent to the line y = −x. What is the circumference of the circle?
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Question 19 of 38
19. Question
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Question 20 of 38
20. Question
Line x can be described by the function ƒ(x) = 5x. Line y is parallel to Line x such that the shortest distance between Line y and Line x is 5, and the yintercept of Line y is negative. What is a possible equation for line y?
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Question 21 of 38
21. Question
In a recent survey of two popular bestselling books, twofifths of the 2,200 polled said they did not enjoy the second book, but did enjoy the first book. Of those, 40% were adults over 18. If threeeighths of those surveyed were adults over 18, how many adults over 18 did not report that they enjoyed the first book but not the second book?
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Question 22 of 38
22. Question
At the Monterey Bay Aquarium, the ratio of the number of stingrays to starfish is 7 to 56. If 6 more starfish were added to the exhibits, the new ratio would be 7 to 58. How many total stingrays and starfish will be in the Monterey Bay Aquarium’s exhibits after the starfish are added?
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Question 23 of 38
23. Question
If (m,ƒ(m)) represents a point on the graph ƒ(m) = 2m + 1, which of the following could be a portion of the graph of the set of points (m,(ƒ(m))^{2})?
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Question 24 of 38
24. Question
Parallelogram QRST has an area of 120 and its longest side (QT) is 24. The angle opposite the vertical is 30°, and the vertical is from R to point U, which lies along QT. What is the length of the hypotenuse of the triangle formed from segments RU, QU, and QR, rounded to the nearest whole number?
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Question 25 of 38
25. Question
The initial number of elements in Set A is x, where x > 0. If the number of elements in Set A doubles every hour, which of the following represents the increase in the number of elements in Set A after exactly one day?
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Question 26 of 38
26. Question
A birthday cake with a height of 4 inches is cut into two pieces such that each piece is of a different size. If the ratio of the volume of the larger slice to the volume of the smaller slice is 5 to 3, what is the degree measure of the cut made into the cake?
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Question 27 of 38
27. Question
An individual invested $25,000 for 1 year at the rate of 15% annually, compounded quarterly. What percent of the individual’s return after nine months was profit?
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Question 28 of 38
28. Question
VitaDrink contains 30 percent concentrated nutrients by volume. EnergyPlus contains 40 percent concentrated nutrients by volume. Which of the following represents the percent of concentrated nutrients by volume in a mixture of v gallons of VitaDrink, e gallons of EnergyPlus, and w gallons of water?
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Question 29 of 38
29. Question
On a coordinate plane, (a, b) and (a + 5, b + c), and (13, 10) are three points on line l. If the xintercept of line l is −7, what is the value of c?
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Question 30 of 38
30. Question
A bag contains 80% yellow marbles and 20% turquoise marbles. What is the probability, approximately, of obtaining exactly two turquoise marbles out of three randomly selected marbles?
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Question 31 of 38
31. Question
The sum of the two digits for positive twodigit integer x is 5. If x is prime and x < 25, what is the value of x?
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Question 32 of 38
32. Question
If the remainder is 3 when a positive twodigit integer, z, is divided into 15, what is the remainder when z is divided by 11?
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Question 33 of 38
33. Question
A circle is drawn on the coordinate plane such that two points lie on the circumference of the circle. What is the maximum possible distance between these two points if the area of the circle is 64π?
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Question 34 of 38
34. Question
A certain circle has a circumference of 12π. If line segment AC is tangent to the circle at point B, AB = BC, and AC = 16, what is the distance between the center of Circle X and point C?
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Question 35 of 38
35. Question
Among a group of pet owners, 80 people own dogs, 41 people own cats, and 54 people own fish. Ten people in the group own dogs and cats. Nineteen own dogs and fish, and a dozen own cats and fish. If seven people own all three types of pets, how many of them own dogs only?
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Question 36 of 38
36. Question
What is the area of triangle ABC that lies on the coordinate plane with vertices at (2,4), (5,8), and (8,2)?
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Question 37 of 38
37. Question
If Angle BAC = 70 and Angle ABC = 50, how much greater than a is the value of b?CorrectIncorrect 
Question 38 of 38
38. Question
A gym teacher is dividing a group of students into different teams of at least four or more students for various sports events at a track meet. There is no limit to the number of teams that can enter the competition, and students can be members of multiple teams. If the number of possible teams is less than 180, what is the greatest number of students that can make up a team?
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