# Digital SAT Math Questions

For some of you reading this blog, the digital SAT has arrived. For others, it will be here by March 2024. Whichever group you’re in, I’m sure you’re eager to practice some digital SAT math questions. This article will give you the opportunity to do just that.

However, before we practice any SAT math questions, we will review the topics you can expect to see in the math section, ranging from easy to advanced, so you know exactly what you’re up against.

## Here are the topics we’ll cover:

To start, let’s discuss how many math questions you’ll face on the new digital SAT.

## How Many Math Questions Are on the SAT Now?

The digital testing format includes some new adjustments to the math sections. So, it’s no wonder that we are constantly asked, how many questions are on the SAT now?

The new format consists of 2 math sections, each containing 22 questions (for a total of 44). You’ll have 70 minutes to complete both sections.

Also, it’s worth noting that the digital SAT does not include calculator and no-calculator sections. Rather, you can use a calculator for all SAT math questions. You may use your own calculator or the online calculator provided to you in the test.

KEY FACT:

There are 44 questions in total in the math sections of the SAT.

Now, let’s discuss the digital SAT math topics you’ll encounter on the test.

## What Are the SAT Math Topics?

There are 4 major categories that the College Board uses to classify the content of the digital SAT math sections:

1. Algebra: (13-15 questions) Includes linear equations, systems of linear equations, linear functions, and linear inequalities.
2. Advanced Math: (13-15 questions) Includes quadratic and polynomial functions, exponents and roots, and rational expressions and equations.
3. Problem-Solving and Data Analysis: (5-7 questions) Includes ratios, rates, and proportions; percentages; and probability, scatterplots, and statistical inference.
4. Geometry and Trigonometry: (5-7 questions) Includes area and volume; lines, angles, and triangles; right triangles and trigonometry; and circles.

KEY FACT:

The 4 major categories of digital SAT math topics are Algebra, Advanced Math, Problem-Solving and Data Analysis, and Geometry and Trigonometry.

## The Ideal Way to Prepare for Your SAT

In past articles, we have discussed tips for creating the best possible SAT study plan, but we will review some of those tips here as well. When thinking about your SAT math study plan, just remember that the SAT is unpredictable. In other words, you don’t know what questions you’ll get from which math topics on test day. Thus, when considering your test prep or SAT math strategies, remember that you will have the most success by following a linear and structured SAT math study plan. In other words, follow a study plan that allows you to learn each topic one at a time, and then practice each topic until you have achieved mastery.

TTP PRO TIP:

Linear and topical learning is the best way to learn SAT math.

Let’s review how topical studying works in the Target Test Prep digital SAT math course.

### An Example of Topical Studying and Practice

In the Target Test Prep course, each chapter features a series of lessons containing sample SAT math questions related to each topic taught. For example, in our quadratic equations chapter, we have a lesson about the quadratic formula. That lesson teaches students all they need to know about the quadratic formula and presents practice questions on that topic. This structure is repeated throughout the quadratics chapter for various lessons.

Upon completion of the chapter, students take numerous chapter tests, which range from easy questions, to medium questions, to hard SAT math questions, to the hardest SAT math questions. Completing these chapter tests and doing a score analysis helps students see how well they understand the material they just learned and helps them work on time-management strategies. This process of completing practice tests and sample questions is repeated for each chapter in the TTP course.

TTP PRO TIP:

Topical learning should always be followed up with topical practice.

Now, before we dive into new SAT practice questions, let’s discuss the question types in the SAT math section.

## The Question Types in SAT Math

There are two major types of questions in SAT math.

• multiple-choice questions
• student-produced responses (formerly called grid-in)

Let’s quickly review each of these problem types, and then dive into doing some digital SAT practice questions.

### Multiple-Choice Questions

There are 33 multiple-choice math questions on the SAT. Multiple-choice questions should be quite familiar to you, as you’ve seen them throughout your academic career. However, one major difference between SAT math multiple-choice questions and “traditional” multiple-choice questions is that SAT questions present 4 answer choices, while the traditional ones present 5. Of course, there is still just 1 correct answer.

### Student-Produced Response Questions

Student-produced response questions, formerly known as grid-in questions, make up 11 out of the 44 questions in the math section. Also, on the digital SAT, you won’t have to enter answers into a grid, as was the case with the paper version of the test. Rather, after an answer is calculated, you type your answer into a box on the computer screen. Additionally, note that your answer can now be a negative number, a change from the previous version of the SAT.

Here are some important rules for entering a student-produced response:

• If you find more than 1 answer, enter only 1 answer.
• A positive answer can be as many as 5 digits. A negative answer can be as many as 6 digits, including the negative sign.
• If you obtain a fractional answer that exceeds the available spaces, such as 175/3216, you may either reduce the fraction or express it as its decimal equivalent.
• If a decimal answer doesn’t fit, truncate or round it at the fourth digit.
• Enter a mixed number as an improper fraction or its decimal equivalent.
• Do not enter symbols, including commas, percent signs, or dollar signs.

Now that we have done an overview of the digital SAT question types, let’s jump into some practice!

## Digital SAT Math Practice Questions

### Practice Question 1: Linear Equations – Easy

Which equation has the same solution as 3x + 10 = -2x – 5?

• 6x + 5 = 5x + 8
• 11 – 2x = 17
• 4x + 1 = x – 3
• 3x + 5 = x + 2

#### Solution:

First, let’s solve the equation given in the question stem.

3x + 10 = -2x – 5

5x = -15

x = -3

We see that the equation is satisfied for x = -3. Now we will solve each equation in the answer choices until we obtain a solution that has a solution of x = -3.

Choice (A)

6x + 5 = 5x + 8

x = 3

Eliminate (A).

Choice (B)

11 – 2x = 17

-2x = 6

x = -3

This is the desired solution.

### Practice Question 2: Systems of Linear Equations – Medium

3x – y = 7

2x + 2y = 10

Which ordered pair (x, y) is a solution to the given system of equations?

• (-3, -2)
• (-3, 2)
• (3, -2)
• (3, 2)

#### Solution:

Let’s use the elimination method to solve this system of linear equations.

3x – y = 7  (equation 1)

2x + 2y = 10  (equation 2)

Step 1: Multiply equation 1 by 2.

2(3x – y = 7)

6x – 2y = 14  (new equation 1)

Step 2: Add new equation 1 to equation 2 and solve for x.

6x – 2y = 14
+ 2x + 2y = 10
8x = 24

x = 3

We now substitute 3 for x into either equation to solve for y. Let’s choose equation 2.

2(3) + 2y = 10

2y = 4

y = 2

We see that x = 3 and y = 2.

### Practice Question 3: Exponents – Hard

If 3^10 + 3^12 = (10)(9^x), then x is equal to which of the following?

• 0
• 3
• 5
• 6

#### Solution:

First, we must factor out 3^10 on the left-hand side of the equation, giving us:

3^10(1 + 3^2) = (10)(9^x)

3^10(1 + 9) = (10)(9^x)

(3^10)(10) = (10)(9^x)

3^10 = 9^x

We must get the bases to be the same on each side of the equation. Noting that 9 = 3^2, we have:

3^10 = (3^2)^x

3^10 = 3^(2x)

Now that the bases are equal, we can equate the exponents.

10 = 2x

5 = x

### Practice Question 4: Inequalities – Easy

If 5x – 8 < 8x – 23, which of the following cannot be a value of x?

• 0
• 6
• 12
• 18

#### Solution:

Let’s solve the inequality for x.

5x – 8 < 8x – 23

-3x < -15

We divide the equation by -3. Doing so requires us to reverse the inequality sign.

x > 5

### Practice Question 5: Linear Functions – Medium

If f(x) = 2x – 3 and f(n) = 7, what is the value of n?

#### Solution:

Using the given function, we know that f(n) = 2n – 3. Thus, we see that:

f(n) = 2n – 3

7 = 2n – 3

10 = 2n

5 = n

### Practice Question 6: Factoring a Quadratic – Medium

What is one possible x-intercept of the graph of y = -x^2 – 3x + 4?

• 1
• 2
• 3
• 4

#### Solution:

Recall that an x-intercept occurs when y = 0. So, our first step is to set the equation equal to 0, and then solve for x. Thus, we have:

0 = -x^2 – 3x + 4

First, let’s factor out -1 from the right side, making the resulting quadratic expression easier to factor.

0 = (-1)(x^2 + 3x – 4)

Now we divide both sides of the equation by -1, thus eliminating the -1. Doing so makes the quadratic even easier to factor.

0 = x^2 + 3x – 4

0 = (x + 4)(x – 1)

x + 4 = 0   or   x – 1 = 0

x = -4        or   x = 1

### Practice Question 7: Solving Rational Equations – Hard

What is the solution set for the rational equation given below?

-12 / (x^2 – 7x + 12) + 7 / (x – 4) = 1

• x = -3 or x = -4
• x = -3 or x = 6
• x = 5 or x = 9
• x = 7 or x = 6

#### Solution:

We first factor the quadratic expression in the denominator of the first fraction.

-12 / (x – 4)(x – 3) + 7 / (x – 4) = 1

We multiply the entire equation by the lowest common denominator of the fractions, which is (x – 4)(x – 3), and then we cancel.

(x – 4)(x – 3) [-12 / (x – 4)(x – 3) + 7 / (x – 4) = 1]

All fractions have been eliminated, so we now can easily solve for x.

-12 + 7(x – 3) = (x – 4)(x – 3)

-12 + 7x – 21 = x^2 – 7x + 12

7x – 33 = x^2 – 7x + 12

0 = x^2 – 14x + 45

0 = (x – 9)(x – 5)

x – 9 = 0   or   x – 5 = 0

x = 9        or   x = 5

### Practice Question 8: Percents – Easy

What is 14% of 13,000?

• 18,200
• 1,820
• 182
• 18.2

#### Solution:

First, convert 14% to its decimal equivalent 0.14, and then we perform the multiplication.

0.14 x 13,000 = 1,820

### Practice Question 9: Geometry – Medium

From the figure above, which of the following is equal to a?

• b + d
• b + c
• c + d
• b + c + d

#### Solution:

The geometry rule to use here is that the measure of an exterior angle is equal to the sum of the measures of the two opposite (remote) interior angles.

In our sketch, the angle measuring a degrees is the exterior angle, and the opposite interior angles are those measuring d degrees and c degrees. Thus, we know that a = c + d.

### Practice Question 10: Trigonometry – Medium

If angle q is in the first quadrant and sin q = 3/5, what is the value of (1 – cos q)?

• 1/5
• 2/5
• 3/5
• 4/5

#### Solution:

Let’s use the trigonometric identity (sin x)^2 + (cos x)^2 = 1 to determine the value of cos q.

(3/5)^2 + (cos q)^2 = 1

9/25 + (cos q)^2 = 1

(cos q)^2 = 1 – 9/25

(cos q)^2 = 16/25

cos q = +/- 4/5

Because angle q is in the first quadrant, only 4/5 is a possible value for cos q.

Thus, (1 – cos q) = 1 – 4/5 = 1/5.

## Digital SAT Math Questions: In Summary

The digital SAT presents 2 math sections containing a total of 44 questions.

There are 20+ major topics covered in these questions, and there is no way to predict exactly which topics will be tested.

So, the best way to study the material tested on the digital SAT is topically, learning one topic at a time until you have mastered it.

### There are 2 question types on the SAT:

• multiple-choice
• student-produced responses

Multiple-choice questions have only 4 possible answer choices.

Student-produced response questions are similar to grid-in questions in that you have no answer choices. On the digital SAT, you must type your calculated answer into an answer box.

In this article, we presented 10 digital SAT practice questions representing a variety of topics and question types. It is important to be familiar and comfortable with all of the topics and question types you may encounter when you take the digital SAT.

## What’s Next?

I hope this article has been helpful in providing you with a variety of digital SAT math questions to practice with. To stay on track during your studies, consider checking out our article providing tips for getting and staying motivated

Remember, if you have great prep and the wherewithal to keep focused on your studying, you’ll be well-prepared for test day.

Good luck!