SAT MAth Practice questions – all topics
- Problem-solving and Data Analysis Weightage: 15% Questions: 5-7
- Ratios, rates, proportional relationships, and units
- Percentages
- One-variable data: distributions and measures of centre and spread
- Two-variable data: models and scatterplots
- Probability and conditional probability
- Inference from sample statistics and margin of error
- Evaluating statistical claims: observational studies and Experiments
SAT MAth and English – full syllabus practice tests
Question Easy
Each face of a fair number cube is labeled with a number from 1 through 6 , with a different number appearing on each face. If the number cube is rolled one time, what is the probability that the number 2 will be shown on the top face?
A) \(\frac{1}{6}\)
B) \(\frac{2}{6}\)
C) \(\frac{4}{6}\)
D) \(\frac{5}{6}\)
▶️Answer/Explanation
Ans:A
Each face of a fair number cube is labeled with a number from 1 through 6, with each number appearing exactly once. The question asks for the probability that the number 2 will be shown on the top face when the cube is rolled once.
Since the number cube has 6 faces, each face has an equal probability of landing on the top face. The probability \(P\) of any specific face (in this case, the face with the number 2) landing on top is given by:
\[
P(\text{number 2 on top}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{1}{6}
\]
Therefore, the correct answer is:
\[
\boxed{\frac{1}{6}}
\]
Question Easy
A certain rock band released 20 music albums from 1963 to 1970, as shown in the bar graph. If one of these albums is selected at random, what is the probability of selecting an album that was released in 1964? (Express your answer as a decimal or fraction, not as a percent.)
▶️Answer/Explanation
Ans:7 / 20, .35
Total number of albums released:
According to the bar graph, the number of albums released each year from 1963 to 1970 is as follows:
1963: 2 albums
1964: 7 albums
1965: 3 albums
1966: 3 albums
1967: 2 albums
1968: 1 album
1969: 1 album
1970: 1 album
\[
2+7+3+3+2+1+1+1=20 \text { albums }
\]
Number of albums released in 1964 :- 7 albums
\[
P=\frac{\text { Number of albums released in } 1964}{\text { Total number of albums }}=\frac{7}{20}
\]
Thus, the probability of selecting an album that was released in 1964 is:
\[
\frac{7}{20}
\]
Question Easy
In a group of 8 children, 2 have freckles and 6 do not have freckles. If one of the 8 children is selected at random, what is the probability of selecting a child who has freckles?
A. 0.25
B. 0.33
C. 0.50
D. 0.75
▶️Answer/Explanation
Ans: A
Total number of children: 8
Number of children with freckles: 2
\[
\text{Probability} = \frac{\text{Number of children with freckles}}{\text{Total number of children}} = \frac{2}{8} = \frac{1}{4} = 0.25
\]
So, the diameter of Saturn, to the nearest ten thousand kilometers, is:
\[
\boxed{120,000}
\]
Question Easy
The table summarizes the number of public schools in two California counties in 2017.
A public middle school will be selected at random from the two counties. What is the probability, to the nearest hundredth, of selecting a school in San Diego County?
A)0.05
B)0.19
C)0.28
D)0.69
▶️Answer/Explanation
C)0.28
The table summarizes the number of public schools in two California counties in 2017. We need to find the probability of selecting a public middle school in San Diego County.
From the table, the number of middle schools in San Diego County is 165, and the total number of middle schools in both counties is 587.
The probability \(P\) of selecting a middle school in San Diego County is given by:
\[ P = \frac{\text{Number of middle schools in San Diego}}{\text{Total number of middle schools}} \]
\[ P = \frac{165}{587} \]
Calculating this value to the nearest hundredth:
\[ P \approx \frac{165}{587} \approx 0.281 \]
Rounding to the nearest hundredth:
\[ P \approx 0.28 \]
The correct answer is C) 0.28.
Questions Easy
The probability of an unfair coin landing heads side up is 0.6. A student tossed this coin into the air9 times. It landed tails side up 5 times and heads side up 4 times. What is the probability that the coin will
land heads side up on the 10th toss?
A) 0.4
B) 0.5
C) 0.6
D) 1
▶️Answer/Explanation
Ans: C
The probability of the unfair coin landing heads side up is given as 0.6. This probability is intrinsic to the coin and does not change with previous outcomes. Thus, regardless of the results of the previous 9 tosses, the probability that the coin will land heads side up on the 10th toss remains: \[ \boxed{0.6} \]
Questions Easy
The table shows the number of different colors of marbles in a bag. If a marble is chosen at random from the bag, what is the probability that the marble will be blue?
A.\(\frac{30}{40}\)
B.\(\frac{22}{40}\)
C.\(\frac{18}{40}\)
D.\(\frac{10}{40}\)
▶️Answer/Explanation
Ans: D
Rationale
Choice D is correct. If a marble is chosen at random from the bag, the probability of choosing a marble of a certain color is the number of marbles of that color divided by the total number of marbles in the bag. Since there are 10 blue marbles in the bag, and there are 40 total marbles in the bag, the probability that the marble chosen will be blue is \(\frac{10}{40}\).
Choices A, B, and C are incorrect. These represent the probability that the marble chosen won’t be blue (choice A), will be green (choice B), and won’t be green (choice C).
Questions Easy
On Tuesday, a local gas station had 135 customers. The table above summarizes whether or not the customers on Tuesday purchased gasoline, a beverage, both, or neither. Based on the data in the table, what is the probability that a gas station customer selected at random on that day did not purchase gasoline?
A.\(\frac{15}{50}\)
B.\(\frac{15}{40}\)
C.\(\frac{35}{50}\)
D.\(\frac{50}{135}\)
▶️Answer/Explanation
Ans:
Rationale
Choice D is correct. The total number of gas station customers on Tuesday was 135. The table shows that the number of customers who did not purchase gasoline was 50. Finding the ratio of the number of customers who did not purchase gasoline to the total number of customers gives the probability that a customer selected at random on that day did not purchase gasoline, which is \(\frac{50}{135}\).
Choice A is incorrect and may result from finding the probability that a customer did not purchase a beverage, given that the customer did not purchase gasoline. Choice B is incorrect and may result from finding the probability that a customer did not purchase gasoline, given that the customer did not purchase a beverage. Choice C is incorrect and may result from finding the probability that a customer did purchase a beverage, given that the customer did not purchase gasoline.
Questions Easy
The table above shows the number of students from two different high schools who completed summer internships in each of five years. No student attended both schools. Of the students who completed a summer internship in 2010, which of the following represents the fraction of students who were from Valley High School?
A.\(\frac{10}{140}\)
B.\(\frac{65}{140}\)
C.\(\frac{75}{140}\)
D.\(\frac{65}{75}\)
▶️Answer/Explanation
Ans: B
Rationale
Choice B is correct. According to the table, 140 students from the two high schools completed summer internships in 2010. Of these, 65 were from Valley High School. Therefore, of the students who completed 65 summer internships in 2010, \(\frac{65}{140}\) represents the fraction who were from Valley High School.
Choice A is incorrect. This is the difference between the numbers of students from the two high schools who completed internships in 2010 divided by the total number of students from the two schools who completed internships that year. Choice C is incorrect. This is the fraction of students from Foothill High School who completed internships out of all the students who completed internships in 2010. Choice D is incorrect. This is the number of students from Valley High School who completed internships in 2010 divided by the number of students from Foothill High School who completed internships in 2010.
Questions Easy
A total of 25 men registered for singing lessons. The frequency table shows how many of these singers have certain voice types. If one of these singers is selected at random, what is the probability he is a baritone?
A.0.10
B. 0.40
C.0.60
D. 0.67
▶️Answer/Explanation
Ans: B
Rationale
Choice B is correct. This probability is calculated by dividing the number of baritone singers by the total number of men registered for singing lessons. It’s given that a total of 25 men registered for singing lessons and that there are 10 baritones. Therefore, the probability of selecting a baritone from this group at random is \(\frac{10}{25}\) , which is equivalent to 0.40.
Choice A is incorrect. This would be the probability of selecting a baritone at random if there were 100 total men who registered for singing lessons. Choice C is incorrect. This is the probability of selecting a singer at random who isn’t a baritone. Choice D is incorrect. This would be the probability of selecting a baritone at random if there were 15 total men registered for singing lessons.
Questions Easy
A survey taken by 1,000 students at a school asked whether they played school sports. The table below summarizes all 1,000 responses from the students surveyed.
How many of the males surveyed responded that they do not play a school sport?
A. 109
B. 252
C. 468
D. 688
▶️Answer/Explanation
Ans: B
Rationale
Choice B is correct. The table summarizes all 1,000 responses from the students surveyed. If 312 are males who play a sport, 220 are females who play a sport, and 216 are females who do not play a sport, then 1,000 — 312 — 220 – 216 = 252 males who do not play a sport.
Choices A, C, and D are incorrect. If 109 males who do not play a sport responded, then the table summary would be 109 + 312 + 220 + 216 = 857 total student responses rather than 1,000. If 468 males who do not play a sport responded, then the table summary would be 468 + 312 + 220 + 216 = 1,216 total student responses rather than 1,000. If 688 males who do not play a sport responded, then the table summary would be 688 + 312 + 220 + 216 = 1,436 total student responses rather than 1,000.
Questions Easy
Each rock in a collection of 70 rocks was classified as either igneous, metamorphic, or sedimentary, as shown in the frequency table.
If one of these rocks is selected at random, what is the probability of selecting a rock that is igneous?
A.\(\frac{10}{27}\)
B.\(\frac{10}{33}\)
C.\(\frac{10}{60}\)
D.\(\frac{10}{70}\)
▶️Answer/Explanation
Ans: D
Rationale
Choice D is correct. If one of the rocks in the collection is selected at random, the probability of selecting a rock that is igneous is equal to the number of igneous rocks in the collection divided by the total number of rocks in the collection. According to the table, there are 10 igneous rocks in the collection, and it’s given that there’s a total of 70 rocks in the collection. Therefore, if one of the rocks in the collection is selected at random, the probability of selecting a rock that is igneous is \(\frac{10}{70}\).
Choice A is incorrect. This is the number of igneous rocks in the collection divided by the number of sedimentary rocks in the collection, not divided by the total number of rocks in the collection. Choice B is incorrect. This is the number of igneous rocks in the collection divided by the number of metamorphic rocks in the collection, not divided by the total number of rocks in the collection. Choice C is incorrect. This is the number of igneous rocks in the collection divided by the number of rocks in the collection that aren’t igneous, not divided by the total number of rocks in the collection.
Questions Easy
Of the 8 planets in our solar system, 4 are considered rocky. If a student randomly selects 1 of those 8 planets as a topic for a report, what is the probability that the selected planet will be rocky?
A.\(\frac{1}{8}\)
B.\(\frac{1}{4}\)
C.\(\frac{1}{2}\)
D.2
▶️Answer/Explanation
Ans: C
Rationale
Choice C is correct. If one of these planets is selected at random, the probability that the selected planet will be rocky is calculated by dividing the number of planets that are considered rocky by the total number of planets. It’s given that 4 of the 8 total planets are considered rocky. Therefore, the probability that the selected planet will be rocky is \(\frac{4}{8}\) which is equivalent to \(\frac{1}{2}\).
Choices A and B are incorrect. These represent the probability if 1 of the 8 planets was considered rocky (choice A) and if 2 of the 8 planets were considered rocky (choice B). Choice D is incorrect and may result from dividing the total number of planets by the number of planets that are considered rocky.
Questions Easy
In a study of cell phone use, 799 randomly selected US teens were asked how often they talked on a cell phone and about their texting behavior. The data are summarized in the table above. If one of the 799 teens surveyed is selected at random, what is the probability that the teen talks on a cell phone daily?
A.\(\frac{1}{799}\)
B.\(\frac{415}{799}\)
C.\(\frac{384}{415}\)
D.\(\frac{384}{799}\)
▶️Answer/Explanation
Ans: B
Rationale
Choice B is correct. If one of the teens surveyed is selected at random, the probability that the teen talks on a cell phone daily is equal to the quotient of the total number of teens who reported that they talk on a cell phone daily, 415, and the total number of teens surveyed, 799. Therefore, this probability is equal to \(\frac{415}{799}\). Choice A is incorrect. This fraction represents the probability of selecting at random any one of the 799 teens surveyed. Choice C is incorrect and may result from conceptual errors. Choice D is incorrect. This fraction represents the probability of selecting at random one of the 799 teens surveyed who doesn’t talk on a cell phone daily.
Questions Easy
A store received a shipment of 1,000 MP3 players, 4 of which were defective. If an MP3 player is randomly selected from this shipment, what is the probability that it is defective?
A. 0.004
B. 0.04
C.04
D.
▶️Answer/Explanation
Ans: A
Rationale
Choice A is correct. The probability of randomly selecting a defective MP3 player from the shipment is equal to the number of defective MP3 players divided by the total number of MP3 players in the shipment. Therefore, 4 the probability is \(\frac{4}{1,000}\) , which is equivalent to 0.004.
Choice B is incorrect because 0.04 represents 4 defective MP3 players out of 100 rather than out of 1,000.
Choice C is incorrect because 0.4 represents 4 defective MP3 players out of 10 rather than out of 1,000. Choice D is incorrect. This is the number of defective MP3 players in the shipment.
Questions Easy
There are n nonfiction books and 12 fiction books on a bookshelf. If one of these books is selected at random, what is the probability of selecting a nonfiction book, in terms of n ?
A.\(\frac{n}{12}\)
B.\(\frac{n}{n+12}\)
C.\(\frac{12}{n}\)
D.\(\frac{12}{n+12}\)
▶️Answer/Explanation
Ans: B
Rationale
Choice B is correct. Since there are n nonfiction and 12 fiction books on the bookshelf, 5 + 12 represents the total number of books. If one of these books is selected at random, the probability of selecting a nonfiction book is equivalent to the number of nonfiction books divided by the total number of books. Therefore, the probability of selecting a nonfiction book, in terms of n, is \(\frac{n}{n+12}\).
Choice A is incorrect. This expression represents the number of nonfiction books divided by the number of fiction books. Choice C is incorrect. This expression represents the number of fiction books divided by the number of nonfiction books. Choice D is incorrect. This expression represents the probability of selecting a fiction book.
Questions Easy
A bag contains a total of 60 marbles. A marble is to be chosen at random from the bag. If the probability that a blue marble will be chosen is 0.35, how many marbles in the bag are blue?
A 21
B. 25
C. 35
D. 39
▶️Answer/Explanation
Ans: Rationale
Choice A is correct. Multiplying the number of marbles in the bag by the probability of selecting a blue marble gives the number of blue marbles in the bag. Since the bag contains a total of 60 marbles and the probability that a blue marble will be selected from the bag is 0.35, there are a total of (0.35)(60) = 21 blue marbles in the bag.
Choice B is incorrect and may result from subtracting 35 from 60. Choice C is incorrect. This would be the number of blue marbles in the bag if there were a total of 100 marbles, not 60 marbles. Choice D is incorrect. This is the number of marbles in the bag that aren’t blue.
Questions Easy
There are 20 buttons in a bag: 8 white buttons, 2 orange buttons, and 10 brown buttons. If one of these buttons is selected at random, what is the probability of selecting a white button?
A.\(\frac{2}{20}\)
B.\(\frac{8}{20}\)
C.\(\frac{10}{20}\)
D.\(\frac{12}{20}\)
▶️Answer/Explanation
Ans: B
Rationale
Choice B is correct. It’s given that there are 20 buttons in a bag and § of the buttons are white. If one button from the bag is selected at random, the probability of selecting a white button is the number of white buttons in the bag divided by the total number of buttons in the bag. Therefore, if one button from the bag is selected at random, the probability of selecting a white button is \(\frac{8}{20}\).
Choice A is incorrect. This is the probability of selecting an orange button from the bag.
Choice C is incorrect. This is the probability of selecting a brown button from the bag.
Choice D is incorrect. This is the probability of selecting a button that isn’t white from the bag.
Questions Easy
—13,4,23
A data set of three numbers is shown. If a number from this data set is selected at random, what is the probability of selecting a negative number?
A.0
B.\(\frac{1}{3}\)
C. \(\frac{2}{3}\)
D.1
▶️Answer/Explanation
Ans: B
Rationale
Choice B is correct. If a number from the data set is selected at random, the probability of selecting a negative number is the count of negative numbers in the data set divided by the total count of numbers in the data set. It’s given that a data set of three numbers is shown. It follows that the total count of numbers in the data set is 3. In the data set shown, -13 is the only negative number. It follows that the count of negative numbers in the data set is 1. Therefore, if a number from the data set is selected at random, the probability of selecting a negative number is \(\frac{1}{3}\).
Choice A is incorrect. This is the probability of selecting a negative number from a data set that doesn’t contain any negative numbers.
Choice C is incorrect. This is the probability of selecting a positive number, not a negative number, from the data set.
Choice D is incorrect. This is the probability of selecting a negative number from a data set that contains only negative numbers.