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
The table shows the average time \(t\), in minutes, it takes Oliver to walk a certain distance \(d\), in miles. Which equation could represent this linear relationship?
A) \(t=40 d\)
B) \(t=25 d\)
C) \(t=\frac{1}{25} d\)
D) \(t=\frac{1}{40} d\)
▶️Answer/Explanation
Ans:B
To determine which equation represents the linear relationship between the distance \(d\) (in miles) and the average time \(t\) (in minutes), we can start by finding the slope of the relationship from the data points provided in the table.
Given data points are:
\[
(0.16, 4), (0.48, 12), (0.72, 18)
\]
To find the slope, use the formula for the slope of a line:
\[
\text{slope} = \frac{\Delta t}{\Delta d}
\]
Calculate the slope between two points, for example, (0.16, 4) and (0.48, 12):
\[
\text{slope} = \frac{12 – 4}{0.48 – 0.16} = \frac{8}{0.32} = \frac{8 \div 0.32}{1 \div 0.32} = \frac{25}{1} = 25
\]
So, the slope is 25. This indicates that for every mile, the time taken increases by 25 minutes.
The linear equation in the form \( t = m d \), where \(m\) is the slope, is:
\[
t = 25d
\]
Question Medium
\[
r=\frac{10}{3} s
\]
The given equation shows a proportional relationship between the variables \(r\) and \(s\). Which expression is equivalent to \(6 r\) ?
A) \(20 \mathrm{~s}\)
B) \(60 \mathrm{~s}\)
C) \(\frac{5}{9} s\)
D) \(\frac{16}{3} \mathrm{~s}\)
▶️Answer/Explanation
Ans:A
The given equation shows a proportional relationship between the variables \( r \) and \( s \):
\[
r = \frac{10}{3} s
\]
We need to find the expression equivalent to \( 6r \).
First, substitute \( r \) with \(\frac{10}{3}s \):
\[
6r = 6 \left(\frac{10}{3}s\right)
\]
Multiply the constants:
\[
6r = \frac{60}{3}s = 20s
\]
Question Medium
In Pacific Northwest Native American cultures, people make totem poles to depict family legends and historical events. Jolon made a totem pole in \(x\) hours. He spent \(\frac{1}{6}\) of the total time designing the pole, \(\frac{1}{3}\) of the total time sketching the design on the pole, \(\frac{1}{4}\) of the total time chiseling the design on the pole, and the remaining 24 hours of the total time sanding and painting the pole. Which of the following equations can be used to determine the total number of hours, \(x\), he spent making the totem pole?
A) \(x=\frac{1}{13} x+24\)
B) \(x=\frac{3}{13} x+24\)
C) \(x=\frac{2}{3} x+24\)
D) \(x=\frac{3}{4} x+24\)
▶️Answer/Explanation
Ans: D
To determine the total number of hours \(x\) that Jolon spent making the totem pole, we need to account for the different portions of time he spent on various activities:
- \(\frac{1}{6}x\) hours designing the pole
- \(\frac{1}{3}x\) hours sketching the design on the pole
- \(\frac{1}{4}x\) hours chiseling the design on the pole
- 24 hours sanding and painting the pole
The total time spent on these activities must add up to \(x\) hours. Therefore, the equation can be written as:
\[
x = \frac{1}{6}x + \frac{1}{3}x + \frac{1}{4}x + 24
\]
First, find a common denominator for the fractions \(\frac{1}{6}\), \(\frac{1}{3}\), and \(\frac{1}{4}\). The least common denominator is 12. Rewrite the fractions with the common denominator:
\[
\frac{1}{6}x = \frac{2}{12}x
\]
\[
\frac{1}{3}x = \frac{4}{12}x
\]
\[
\frac{1}{4}x = \frac{3}{12}x
\]
Add these fractions together:
\[
\frac{2}{12}x + \frac{4}{12}x + \frac{3}{12}x = \frac{9}{12}x = \frac{3}{4}x
\]
Now, substitute back into the original equation:
\[
x = \frac{3}{4}x + 24
\]
Thus, the correct equation is:
\[
\boxed{D}
\]
Question medium
$
R(t)=1,830-790(2.71)^{-.18 t}
$
The function \(R\) gives the predicted average rating, expressed as a number of points, in the German chess federation database for a player based on the number of years, \(t\), the player has participated in professional chess tournaments. Which of the following represents the predicted average rating of a player who has just entered their first professional chess tournament?
A. \(R(-0.18)\)
B. \(R(0)\)
C. \(R(790)\)
D. \(R(1,830)\)
▶️Answer/Explanation
Ans:B
To find the predicted average rating for a player who has just entered their first professional chess tournament, we need to substitute \(t = 0\) into the function \(R(t)\).
\[R(t) = 1,830 – 790(2.71)^{-0.18t}\]
Substituting \(t = 0\):
\[R(0) = 1,830 – 790(2.71)^{-0.18(0)}\]
\[R(0) = 1,830 – 790(2.71)^0\]
\[R(0) = 1,830 – 790(1)\]
\[R(0) = 1,830 – 790\]
\[R(0) = 1,040\]
So, the predicted average rating of a player who has just entered their first professional chess tournament is \(1,040\), which corresponds to option B.
Question Medium
In 2015, a certain country had an adult population of 250 million people, of which 160 million were internet users and 90 million were not internet users. Of the adult population that used the internet, 52.8 million people had accessed two or more social media websites.
In 2015, what fraction of the adult internet users in this country had accessed two or more social media websites?
A) \(\frac{21}{100}\)
B) \(\frac{33}{100}\)
C) \(\frac{53}{100}\)
D) \(\frac{59}{100}\)
▶️Answer/Explanation
B
The fraction of adult internet users in this country who accessed two or more social media websites can be calculated as follows:
\[ \text{Fraction} = \frac{\text{Number of adult internet users accessing two or more social media websites}}{\text{Total number of adult internet users}} \]
\[ \text{Fraction} = \frac{52.8}{160} \]
Calculating:
\[ \text{Fraction} \approx \frac{52.8}{160} \approx 0.33 \]
Converting to a fraction:
\[ \text{Fraction} = \frac{33}{100} \]
Therefore, the answer is:
\[ \boxed{B) \, \frac{33}{100}} \]