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 medium
A circle has been divided into three nonoverlapping regions: I, II, and III. The area of region I is \(4\pi \) square centimeters (\(cm^{2}\)), the area of region II is \(12\pi \) \(cm^{2}\), and the area of region III is \(16\pi \) \(cm^{2}\). If a point in the circle is selected at random, what is the probability of selecting a point that does not lie in region II? (Express your answer as a decimal or fraction, not as a percent.)
▶️Answer/Explanation
Ans: 5/8, .625
To find the probability of selecting a point that does not lie in region II, we need to find the total area of the circle and subtract the area of region II, then divide by the total area of the circle.
Given:
Area of region I = \(4\pi \text{ cm}^2\)
Area of region II = \(12\pi \text{ cm}^2\)
Area of region III = \(16\pi \text{ cm}^2\)
The total area of the circle is the sum of the areas of all three regions:
\[4\pi + 12\pi + 16\pi = 32\pi \text{ cm}^2\]
So, the probability of selecting a point that does not lie in region II is:
\[\frac{4\pi + 16\pi}{32\pi} = \frac{20\pi}{32\pi} = \frac{5}{8}\]
Therefore, the probability is \(\frac{5}{8}\).
Question Medium
As a literature major in college, Sean has read books written by a variety of European authors. The table above shows the numbers of books written by British, French, and German authors that Sean has read, categorized by the century in which the books were written.
If a book referred to by the table that was written in the twentieth century is to be selected at random, the probability that the book was written by a British author is 15/n Which of the following best describes n in this context?
A. The total number of books referred to by the table
B. The number of books referred to by the table that were written in the twentieth century
C. The number of books referred to by the table that were written by British authors
D. The number of books referred to by the table that were written by either French authors or German authors
▶️Answer/Explanation
Ans: B
In this context, \( n \) represents the number of books referred to by the table that were written in the twentieth century.
The probability of selecting a book written by a British author from those written in the twentieth century is given as \( \frac{15}{n} \).
So, the correct answer is:
\(\boxed{\text{B) The number of books referred to by the table that were written in the twentieth century}}\).
Question medium
A forest contains different species of trees. Let t represent the total number of trees in the forest, let h represent the number of hickory trees, and let k represent the number of oak trees. If a tree is selected at random from the forest,which expression represents the probability of selecting a tree that is neither hickory nor oak?
A) \(\frac{h+k}{t}\)
B) \(\frac{t-h-k}{t}\)
C) \(\frac{h+k-t}{t}\)
D) \(\frac{t+h+k}{t}\)
▶️Answer/Explanation
B) \(\frac{t-h-k}{t}\)
We’re looking for the probability of selecting a tree that is neither hickory nor oak. This means we want the total number of trees that are neither hickory nor oak divided by the total number of trees.
The total number of trees that are neither hickory nor oak is \(t – (h + k)\), as \(h\) represents the number of hickory trees and \(k\) represents the number of oak trees. The total number of trees is \(t\).
So, the probability expression is:
\[
\frac{t – (h + k)}{t}
\]
Simplifying:
\[
\frac{t – h – k}{t}
\]
Thus, the correct answer is B) \(\frac{t – h – k}{t}\).
Questions Medium
In a survey of 240 television viewers, 3/5 indicated that they like comedies, some indicated that they do not like comedies, and the rest did not respond. If one of the 240 viewers is selected at random, the probability is 1/15 that the viewer selected did not respond. How many of the 240 viewers indicated that they do not like comedies?
▶️Answer/Explanation
Ans: 80
In the survey, \(\frac{3}{5}\) of the 240 television viewers indicated that they like comedies. So, the number of viewers who like comedies is \(\frac{3}{5} \times 240 = 144\).
The probability that the viewer selected did not respond is \(\frac{1}{15}\) of the total viewers, which is 240.
The number of viewers who indicated that they do not like comedies can be calculated by subtracting the number of viewers who like comedies and the number of viewers who did not respond from the total number of viewers:
\[240 – 144 – \frac{1}{15} \times 240 = 240 – 144 – 16 = 80\]
Therefore, \(80\) of the \(240\) viewers indicated that they do not like comedies.
Question Medium
The figure shown is divided into 100 squares of equal area, where 60 squares are shaded.
If one of these squares is selected at random how much greater is the probability of selecting a shaded square than the probability of selecting a square that is not shaded ?
A) 0.20
8) 0.40
C) 0,60
D) 0.80
▶️Answer/Explanation
A) 0.20
Probability of selecting a shaded square = $\frac{\text{Number of shaded squares }}{ \text{Total number of squares Probability of selecting a shaded square}}= \frac{60}{ 100 }= 0.6$
Probability of selecting an unshaded square =$\frac{\text{ Number of unshaded squares} }{\text{ Total number of squares Probability of selecting an unshaded square}}= \frac{40}{ 100 }= 0.4$
Difference between the probabilities $\text{= Probability of selecting a shaded square – Probability of selecting an unshaded square Difference between the probabilities }= 0.6 – 0.4 = 0.2$
Therefore, the probability of selecting a shaded square is 0.2 greater than the probability of selecting an unshaded square.
The correct answer is A) 0.20.
Question Medium
The table shows the results of a poll that was used to determine support for a county proposal. The results are categorized by county and opinion. If one person who responded to the poll is selected at random, which of the following statements results in the greatest value?
A) The probability that the person is undecided, given that the person is from County 1
B) The probability that the person is undecided, given that the person is from County 2
C) The probability that the person is from County 1, given that the person is undecided
D) The probability that the person is from County 2, given that the person is undecided
▶️Answer/Explanation
D