# 5 Sample SAT Mathematics Questions

Not everyone gets along with the numbers. And for these people, SAT math questions can be a complete nightmare! To help you with this we have brought here 5 examples of test questions and an explanation of what each one tests and what is the correct way to approach them! Come on?

## 5 SAT Mathematics questions commented

### Question 1

The recommended daily calcium intake for a 20-year-old is 1,000 milligrams (mg). One cup of milk contains 299 mg of calcium and one cup of juice contains 261 mg of calcium. Which of the following inequalities represents the possible number of cups of milk m and cups of juice j a 20-year-old could drink in a day to meet or exceed the recommended daily calcium intake from these drinks alone?

A. 299 m+ 261 j≥ 1,000
B. 299
m + 261 j > 1,000
C. (299 /
m ) + ( 261 / j ) ≥ 1,000
D. (299 / m ) + (261 / j )> 1,000

This is one of the SAT Mathematics questions in which the use of a calculator is released. For the resolution, however, this help from heaven will not be so necessary. In this case, alternative A is the correct option. That’s because multiplying the number of cups of milk by the amount of calcium that each cup contains and multiplying the number of cups of juice by the amount of calcium that each cup contains will provide the total amount of calcium from each source.

From there you must find the sum of these two numbers to define the total amount of calcium. As the question asks that the calcium from these two sources meet or exceed the recommended daily intake, the sum of these two products must be greater than or equal to 1,000 mg.

### Question 2

A research assistant randomly selected 75 undergraduate students from the list of all students enrolled in the psychology-degree program at a large university. She asked each of the 75 students, “How many minutes per day do you typically spend reading?” The mean reading time in the sample was 89 minutes, and the margin of error for this estimate was 4.28 minutes. Another research assistant intends to replicate the survey and will attempt to get a smaller margin of error. Which of the following samples will most likely result in a smaller margin of error for the estimated mean time students in the psychology-degree program read per day?

A. 40 randomly selected undergraduate psychology-degree program students
B. 40 randomly selected undergraduate students from all degree programs at the college
C. 300 randomly selected undergraduate psychology-degree program students
D. 300 randomly selected undergraduate students from all degree programs at the college

This is a “Problem Solving and Data Analysis” question, one of the SAT Mathematics question categories. In this regard, specifically, the use of calculators is also released. In this case, the correct answer is alternative C, since increasing the sample size (by randomly selecting participants from the population of original interest) is likely to result in a decrease in the margin of error.

### Question 3

The first metacarpal bone is located in the wrist. The scatterplot below shows the relationship between the length of the first metacarpal bone and height for 9 people. The line of best fit is also shown. How many of the nine people have an actual height that differs by more than 3 centimeters from the height predicted by the line of best fit?

A. 2
B. 4
C. 6
D. 9

Some SAT Mathematics questions, like this one, are accompanied by visual materials (graphs, tables, etc.). Your task in this type of question is to interpret the information to find the answer. In this question, for example, option B is the correct one. People who have the first metacarpal bones that are 4.0, 4.3, 4.8 and 4.9 centimeters long are 3 cm higher than the height provided by the best fit line.

### Question 4

The mean number of students per classroom, y , at Central High School can be estimated using the equation y = 0.8636x + 27.227, where x represents the number of years since 2004 and x ≤ 10. Which of the following statements is the best interpretation of the number 0.8636 in the context of this problem?

A. The estimated mean number of students per classroom in 2004
B. The estimated mean number of students per classroom in 2014
C. The estimated yearly decrease in the mean number of students per classroom
D. The estimated yearly increase in the mean number of students per classroom

This is a question from the “Heart of Algebra” category, one of the types of Mathematics questions at SAT. In this, in particular, the use of a calculator is not allowed. To arrive at the answer, then, you must keep in mind that when an equation is written in the form y = mx + b, the coefficient of the term x (in this case 0.8636) is the slope. The slope of a linear equation gives the amount that the average number of students per classroom (represented by y) changes per year (represented by x). Thus, alternative D is the correct answer!

### Question 5

If y = x³ + 2x + 5 and z = x² + 7x + 1, what is 2y + z in terms of x?

A. 3x³ + 11x + 11
B. 2x³ + x² + 9x + 6
C. 2x³ + x² + 11x + 11
D. 2x³ + 2x² + 18x + 12

This question, in turn, is part of the section “Passport to Advanced Mathematics”, which has non-linear expressions or expressions in which a variable is raised to an exponent that is not 0 or 1. In this specific question, the use of the calculator is not permitted.

In this case, the correct answer is alternative C. This is because, replacing the equivalent expressions ayez in 2y + z, you find the expression 2 (x³ + 2x + 5) + x² + 7x + 1. From there you must apply the distributive property to multiply x³ + 2x + 5 by 2 and then combine similar terms in the expression. 