Digital SAT Math Practice Test – Hardest Questions You May See

Digital SAT Math covers two modules each containing 22 questions. In total, SAT test takers have to answer 44 Math questions. Solving as many Digital SAT Math practice tests as possible is key to SAT success. We’ve created a Digital SAT Math Practice Test of the 19 hardest questions in this test. You can practice this Digital SAT Math Practice test and assess how sharp your SAT Math skills are.

💡You might be interested in reading the Digital SAT Math Ultimate Guide post!

First, we explain the structure of Digital SAT Math, how we picked the hardest questions for the Digital SAT Math Practice Test and then you will see the questions.

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📌 Hint: Do not skip this article, you will find FREE Digital SAT Math Prep resources throughout the article.

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Before You Start The Digital SAT Math Practice Test

Before you start the Digital SAT Math Practice Test, we would like to explain how we created the test and how you should interpret your results. College Board assesses the students’ attainment of critical college and career readiness knowledge and skills in math in math sections of the Digital SAT.

Digital SAT Math covers four content domains.

1. Algebra. In this domain, SAT measures the ability to analyze, fluently solve, and create linear equations and inequalities and analyze and fluently solve equations and systems of equations using multiple techniques. You might be interested in seeing our SAT Algebra post. It covers the hack points you should know and 31 SAT Algebra Practice Questions!
2. Advanced Math. This domain measures skills and knowledge central for progression to more advanced math courses, including demonstrating an understanding of absolute value, quadratic, exponential, polynomial, rational, radical, and other nonlinear equations. You might be interested in seeing our SAT Advanced Math post. It covers the hack points you should know and 27 SAT Advanced Math Practice Questions!
3. Problem-solving and Data Analysis. In this domain, SAT measures the ability to apply quantitative reasoning about ratios, rates, and proportional relationships; understand and apply unit rates; and analyze and interpret one- and two-variable data. You might be interested in seeing our SAT Problem-Solving and Data Analysis post. It covers the hack points you should know and 15 SAT Problem-Solving and Data Analysis Practice Questions!
4. Geometry and Trigonometry. This fourth domain measures the ability to solve problems focusing on area and volume; angles, triangles, trigonometry; and circles. You might be interested in seeing our SAT Geometry and Trigonometry post. It covers the hack points you should know and SAT Geometry Practice Questions!

💡You might be interested in reading the 7-Step Digital SAT Math Study Guide post!

Anna B. Scored 800 on SAT Math!

Anna B. is one of our thousands of successful SAT students. She scored 800 on SAT Math. You can watch her SAT story.

SAT Math Content Domains, Skills, and Knowledge Testing Points

Under each content domain, there are several skills and knowledge testing domains with a total of 19 skill and knowledge testing points. The following table summarizes the Digital SAT Math contain domains, each skill and knowledge testing point under each content domain and approximately how many questions appear from each content domain.

Content Domains	Algebra	Advanced Math	Problem-solving and Data Analysis	Geometry and Trigonometry
Skill and Knowledge Testing Points	Linear equations in one variable	Equivalent expressions	Ratios, rates, proportional relationships, and units	Area and volume
	Linear equations in two variables	Nonlinear equations in one variable and systems of equations in two variables	Percentages	Lines, angles, and triangles
	Linear functions	Nonlinear functions	One-variable data: distributions and measures of center and spread	Right triangles and trigonometry
	Systems of two linear equations in two variables		Two-variable data: models and scatterplots	Circles
	Linear inequalities in one or two variables		Probability and conditional probability
			Inference from sample statistics and margin of error
			Evaluating statistical claims: observational studies and experiments
Number of Questions	13 to 15 questions.	13-15 Questions	5-7 Questions	5-7 Questions

Once you grasp the details of how to approach each skill and knowledge testing point question, you will double your chances of reaching an 800 score on the SAT Math test.

💡You can see our Free SAT Math Exercises which has 50 exercises on all SAT Math domains. 

SFBS Digital SAT Math Prep Through Questions Program

San Francisco Business School offers a comprehensive Digital SAT Math Prep program taught by 99th-percentile SAT Instructors and exam experts. The program cracks down each content domain and 19 skills and knowledge testing points through 322 realistic Digital SAT Math questions. You will see all the different types of questions that may appear in Digital SAT.

How Hard Are the Actual Digital SAT Math Questions?

In your actual Digital SAT test, there will be two Math sections and in each, there will be 22 questions. You will be allowed to use a calculator in each module. The Digital SAT is an adaptive exam. It starts with easy questions, and as you answer each question correctly, the difficulty of the questions will get harder. Since it is a computer-adaptive test, it is crucial to respond to the first questions in the exam correctly.

College Board categorizes the Digital SAT Math questions into three difficulty levels: easy, medium, and hard.  Typically, the Digital SAT exam starts with medium-difficulty questions, and depending on the correct or wrong answers of the test-taker, the rest of the questions appear.

💡You might be interested in reading the Digital SAT Math Prep: 7 Steps to Get 800 on SAT Math post!

Watch SAT Math Prep Online Course – Sample Lecture on YouTube

We have a sample 8-minute video lecture from our SAT Math Prep Online Course on YouTube. You can watch below.

Important Points About This Test

In this Digital SAT Math Practice Test, we picked 19 hard questions for each skill and knowledge testing point. So, this test does not resemble the typical skill and knowledge testing point distribution on a Digital SAT Math practice test. Instead, we wanted to show you the hardest questions you may see in each skill and knowledge testing point. Therefore, there are fewer questions from the SAT Algebra and Advanced Math content domains and more questions from problem-solving and data analysis and SAT Geometry and Trigonometry content domains.

📚 San Francisco Business School offers a vast amount of FREE Digital SAT Prep Online materials. See it on the Free Digital SAT Prep Online Library.

Besides, since these are the hardest questions for each skill and knowledge testing point, it is very normal that you will spend longer than usual time to solve each question. It is also super normal that you may score lower than your previous Digital SAT Math Practice tests in this one. Because a typical Digital SAT Math Practice Test covers easy, medium, and hard questions. However, this one contains only the hardest questions.

Are you ready to take a challenging Digital SAT Math Practice Test Now?

SFBS offers a Free Digital SAT Math Prep course. The course goes through a particular skill and knowledge testing point and improves your problem-solving skills and test-taking strategies.

Digital SAT Math Practice Test – Hardest Questions

Question 1

The equation 9x + 5 =a(x+b), where a and b are constants, has no solutions. Which of the following must be true?

I. a = 9
II. b = 5
III. b ≠

A. None

B. I only

C. I and II only

D. I and III only

Content Domain: Algebra

Skill and Knowledge Testing Point: Linear equations in one variable

Question 2

To earn money for college, Avery works two part-time jobs: A and B. She earns $10 per hour working at job A and $20 per hour working at job B. In one week, Avery earned a total of s dollars for working at job B. In one week, Avery earned a total of s dollars for working at the two part-time jobs. The graph above represents all possible combinations of the number of hours Avery could have worked at the two jobs to earn s dollars. What is the value of s ?

A. 128

B. 160

C. 200

D. 320

Content Domain: Algebra

Skill and Knowledge Testing Point: Linear equations in two variables

Question 3

An object hangs from a spring. The formula relates the length , in centimeters, of the spring to the weight , in newtons, of the object. Which of the following describes the meaning of the 2 in this context?

A. The length, in centimeters, of the spring with no weight attached

B. The weight, in newtons, of an object that will stretch the spring 30 centimeters

C. The increase in the weight, in newtons, of the object for each one-centimeter increase in the length of the spring

D. The increase in the length, in centimeters, of the spring for each one-newton increase in the weight of the object

Content Domain: Algebra

Skill and Knowledge Testing Point: Linear functions

Digital SAT Math Practice Test – Question 4

Store A sells raspberries for $5.50 per pint and blackberries for $3.00 per pint. Store B sells raspberries for $6.50 per pint and blackberries for $8.00 per pint. A certain purchase of raspberries and blackberries would cost $37.00 at Store A or $66.00 at Store B. How many pints of blackberries are in this purchase?

A. 4

B. 5

C. 8

D. 12

Content Domain: Algebra

Skill and Knowledge Testing Point: Systems of two linear equations in two variables

Question 5

Ken is working this summer as part of a crew on a farm. He earned $8 per hour for the first 10 hours he worked this week. Because of his performance, his crew leader raised his salary to $10 per hour for the rest of the week. Ken saves 90% of his earnings from each week. What is the least number of hours he must work the rest of the week to save at least $270 for the week?

A. 38

B. 33

C. 22

D. 16

Content Domain: Algebra

Skill and Knowledge Testing Point: Linear inequalities in one or two variables

Question 6

In the expression above, b and c are positive integers. If the expression is equivalent to x+b and x ≠ b, which of the following could be the value of c ?

A. 4

B. 6

C. 8

D. 10

Content Domain: Advanced Math

Skill and Knowledge Testing Point: Equivalent expressions

Question 7

If and are the two solutions to the system of equations above, what is the value of ?

A. -3

B. -2

C. -1

D. 1

Content Domain: Advanced Math

Skill and Knowledge Testing Point: Nonlinear equations in one variable and systems of equations in two variables

Question 8

x
1
2
3

For the exponential function , the table above shows several values of and their corresponding values of , where is a constant greater than 1. If is a constant and , what is the value of ?

Content Domain: Advanced Math

Skill and Knowledge Testing Point: Nonlinear functions

Question 9

Anita created a batch of green paint by mixing 2 ounces of blue paint with 3 ounces of yellow paint. She must mix a second batch using the same ratio of blue and yellow paint as the first batch. If she uses 5 ounces of blue paint for the second batch, how much yellow paint should Anita use?

A. Exactly 5 ounces

B. 3 ounces more than the amount of yellow paint used in the first batch

C. 1.5 times the amount of yellow paint used in the first batch

D. 1.5 times the amount of blue paint used in the second batch

Content Domain: Problem-Solving and Data Analysis

Skill and Knowledge Testing Point: Ratios, rates, proportional relationships, and units

Digital SAT Math Practice Test – Question 10

37% of the items in a box are green. Of those, 37% are also rectangular. Of the green rectangular items, 42% are also metal. Which of the following is closest to the percentage of the items in the box that are not rectangular green metal items?

A. 1.16%

B. 57.50%

C. 94.25%

D. 98.84%

Content Domain: Problem-Solving and Data Analysis

Skill and Knowledge Testing Point: Percentages

Question 11

The mean amount of time that the 20 employees of a construction company have worked for the company is 6.7 years. After one of the employees leaves the company, the mean amount of time that the remaining employees have worked for the company is reduced to 6.25 years. How many years did the employee who left the company work for the company?

A. 0.45

B. 2.30

C. 9.00

D. 15.25

Content Domain: Problem-Solving and Data Analysis

Skill and Knowledge Testing Point: One-variable data: distributions and measures of center and spread

Question 12

The scatterplot above shows the size x and the sale price y of 25 houses for sale in Town H. Which of the following could be an equation for a line of best fit for the data?

A. y = 200x + 100

B. y = 100x + 100

C. y = 50x + 100

D. y = 100x

Content Domain: Problem-Solving and Data Analysis

Skill and Knowledge Testing Point: Two-variable data: models and scatterplots

Digital SAT Math Practice Test – Question 13

The table summarizes the distribution of age and assigned group for 90 participants in a study.

One of these participants will be selected at random. What is the probability of selecting a participant from group A, given that the participant is at least 10 years of age? (Express your answer as a decimal or fraction, not as a percent.)

Content Domain: Problem-Solving and Data Analysis

Skill and Knowledge Testing Point: Probability and conditional probability

Question 14

The results of two random samples of votes for a proposition are shown above. The samples were selected from the same population, and the margins of error were calculated using the same method. Which of the following is the most appropriate reason that the margin of error for sample A is greater than the margin of error for sample B?

A. Sample A had a smaller number of votes that could not be recorded.

B. Sample A had a higher percentage of favorable responses.

C. Sample A had a larger sample size.

D. Sample A had a smaller sample size.

Content Domain: Problem-Solving and Data Analysis

Skill and Knowledge Testing Point: Inference from sample statistics and margin of error

Question 15

To determine the mean number of children per household in a community, Tabitha surveyed 20 families at a playground. For the 20 families surveyed, the mean number of children per household was 2.4. Which of the following statements must be true?

A. The mean number of children per household in the community is 2.4.

B. A determination about the mean number of children per household in the community should not be made because the sample size is too small.

C. The sampling method is flawed and may produce a biased estimate of the mean number of children per household in the community.

D. The sampling method is not flawed and is likely to produce an unbiased estimate of the mean number of children per household in the community.

Content Domain: Problem-Solving and Data Analysis

Skill and Knowledge Testing Point: Evaluating statistical claims: observational studies and experiments

Question 16

What is the area, in square units, of the triangle formed by connecting the three points shown?

Content Domain: Geometry and Trigonometry

Skill and Knowledge Testing Point: Area and volume

Digital SAT Math Practice Test – Question 17

In triangle RST, angle T is a right angle, point L lies on , point K lies on , and is parallel to . If the length of is 72 units, the length of is 24 units, and the area of triangle RST is 792 square units, what is the length of , in units?

Content Domain: Geometry and Trigonometry

Skill and Knowledge Testing Point: Lines, angles, and triangles

Question 18

Triangle ABC is similar to triangle DEF, where A corresponds to D and C corresponds to F. Angles C and F are right angles. If and DF = 125, what is the length of ?

A.

B.

C.

D.

Content Domain: Geometry and Trigonometry

Skill and Knowledge Testing Point: Right triangles and trigonometry

Question 19

A circle in the xy-plane, the graph of is a circle. What is the radius of the circle?

A. 5

B. 6.5

C.

D.

Content Domain: Geometry and Trigonometry

Skill and Knowledge Testing Point: Circles

Digital SAT Math Practice – 19 Hardest Questions YouTube Video

View our 19 Hardest Digital SAT Math Practice Questions YouTube Video.

Answers and Rationales for the Digital SAT Math Practice Test

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💡Do not forget to visit SAT Math Exercises which has 50 exercises on all SAT Math domains. It’s for free!