## 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

**[Calc]**** ****Question** ** **medium

A study conducted by a mobile phone company found that the average battery life of a random sample of its phones is 4.6 hours, with an associated margin of error of 0.5 hours. The study was then repeated with a much larger sample size, with the mean and margin of error of the new sample being calculated in the same way as the original study.

Which of the following is most likely true?

A) The margin of error from the new study is larger than the margin of error from the original study

B) The margin of error from the new study is smaller than the margin of error from the original study.

C) The mean from the new study is larger than the mean from the original study.

D) The mean from the new study is smaller than the mean from the original study

**▶️Answer/Explanation**

**B) The margin of error from the new study is smaller than the margin of error from the original study.**

The margin of error in a statistical study is influenced by the sample size. Generally, larger sample sizes result in smaller margins of error.

Given that the second study was conducted with a much larger sample size, it’s reasonable to assume that the margin of error from the new study is smaller than the margin of error from the original study.

**[Calc]**** ****Question** ** ****Medium**

Based on the data from a random sample of a population, the mean value of the population was estimated to be 5.1, with an associated margin of error of 0.2. Which of the following is a plausible value for the mean of the population ?

A) 4.7

B) 4.8

C) 5.2

D) 5.5

**▶️Answer/Explanation**

C) 5.2

The mean value of the population is estimated to be 5.1, with a margin of error of 0.2. We need to find which of the following values is a plausible mean for the population.

1. Calculate the range of plausible values:

\[

\text{Lower bound} = 5.1 – 0.2 = 4.9

\]

\[

\text{Upper bound} = 5.1 + 0.2 = 5.3

\]

2. Determine which of the given values fall within this range:

A) 4.7 (not within 4.9 to 5.3)

B) 4.8 (not within 4.9 to 5.3)

C) 5.2 (within 4.9 to 5.3)

D) 5.5 (not within 4.9 to 5.3)

Thus, the plausible value for the mean of the population is:

\(\boxed{5.2} \)

The answer is:\(\boxed{C} \)

*Question*

In 480 BC, the population of the Persian Empire was approximately 49.4 million. The population of the Persian Empire was 44% of the world population at that time. Which of the following is the best estimate of the world population in 480 BC?

- 21.7 million
- 89.1 million
- 93.4 million
- 112.3 million

**▶️Answer/Explanation**

D

*Questions *

Two independent surveys asked random samples of 500 people about the distances they commute to work each day. The results of the surveys are detailed in the table below.

Which statement is true based on the results of these surveys?

- There is a greater variation in the distribution of the distances people commute to work in Survey A.
- There is a greater variation in the distribution of the distances people commute to work in Survey B.
- The variation in the distribution of the distances people commute is the same in both surveys.
- It is impossible to determine the variation in the distribution of the distances people commute because the means are different.

**▶️Answer/Explanation**Ans: C

*Question*

The function $f$ is linear, $f(2)=17$, and $f(8)=19$. If $f(x)=m x+b$, where $m$ and $b$ are constants, what is the value of $b$ ?

A. 11

B. 13

C. $\frac{49}{3}$

D. $\frac{55}{3}$

**▶️Answer/Explanation**

Ans: C

*Questions *

A psychologist designed and conducted a study to determine whether playing a certain educational game increases middle school students’ accuracy in adding fractions. For the study, the psychologist chose a random sample of 35 students from all of the students at one of the middle schools in a large city. The psychologist found that students who played the game showed significant improvement in accuracy when adding fractions. What is the largest group to which the results of the study can be generalized?

A. The 35 students in the sample

B. All students at the school

C. All middle school students in the city

D. All students in the city

**▶️Answer/Explanation**

Ans: B