# SAT Math Practice Test Questions and FAQs

Are you looking for convenient SAT math prep options to help your student learner maximize the efficiency of their time spent on SAT math practice? Does your student learner work best when they have someone to talk through questions with, rather than just a textbook or study guide? Schoolhouse.world has created a leading platform to connect students preparing for the SAT math section with other learners and tutors around the world to get the best results on their SAT exams. Schoolhouse combines group tutoring with real SAT math practice tests and specific practice SAT math problems to provide any learner with the tools they need to solve the various SAT math problems they will encounter during the SAT.

## What’s in the math section of the SAT, and how can I prepare for it?

As the leading college admissions test in the world, the math section of SAT is not an easy challenge. The problems presented will test any student’s understanding of broad mathematical concepts, how to apply and execute those concepts accurately, and will explore their knowledge and ability to identify and apply these known solutions to “real-world” problems as presented on the test. Many students choose to receive tutoring to help them achieve their best possible score, whether it be help with the pacing of the test through timed SAT math practice tests, or individual review of common SAT math practice questions and how to solve them.

The Math portion of the SAT consists of two sections. It includes a calculator section lasting fifty-five (55) minutes, with thirty (30) multiple choice questions and eight (8) student-response questions known as “grid-ins,” and a no-calculator section lasting twenty-five (25) minutes, with fifteen (15) multiple choice questions and five (5) grid-ins.

In the two sections making up the Math portion of the SAT, the questions are selected from four different focuses: (1) “Heart of Algebra”, where questions highlight linear equations and systems, (2) “Problem Solving and Data Analysis”, which tests a student’s ability to identify and resolve real-world mathematical solutions, and (3) “Passport to Advanced Math”, which requires a student to understand and manipulate advanced equations to provide correct responses. The exam also includes a catch-all forth category, (4) “Additional Topics in Math”, where common problems include geometry and trigonometry-based questions.

In any of the above focuses, test takers must be able to identify important data points, correctly apply relevant SAT-level mathematical concepts, and produce an accurate answer in order to generate high scores on the SAT math exam. By exploring these key test-taking attributes in group settings, such as those provided by Schoolhouse.world, student learners have the opportunity to experience these concepts and rigorously practice them with others while being able to resolve the group’s questions with the session tutor in a supportive and informative environment. The more practice SAT math problems a student learner is exposed to before the actual exam, the more likely they will score well on the exam.

## Example SAT Math Problems

Here is an example of a real practice SAT math problem a student may encounter on the exam:

A company’s manager estimated that the cost C, in dollars, of producing n items is C = 7n + 350. The company sells each item for $12. The company makes a profit when the total income from selling a quantity of items is greater than the total cost of producing that quantity of items. Which of the following inequalities gives all possible values of n for which the manager estimates that the company will make a profit?

A) n < 70

B) n < 84

C) n > 70

D) n > 84

**Solution**: First, we must designate a formula for revenue. Revenue would equate to $12 times the quantity of products sold. In order for the company to be profitable, Revenue must be greater than profit.

**Revenue = 12n**

**Cost = 7n + 350**

**Revenue > Cost**

**12n > 7n + 350**

**5n > 350**

**n > 70**

Therefore, the answer is choice **C**.

Here's one for "Problem Solving and Data Analysis":

A graphic designer creates an image for a t-shirt that measures 8 inches tall and 10 inches wide. She can use this image for small and medium t-shirts, but she must increase the size for a large t-shirt. She wants her final image for the large t-shirts to measure 9 inches tall and 11.25 inches wide. At what percent must she print out the image to obtain these measurements?

A) 88.90%

B) 107.5%

C) 112.5%

D) 125%**

**Solution**: The large shirts need a large image, so the correct answer must be greater than 100%. Eliminate (A). Now, check the remaining answers, starting with (B). If the original height of the 8 inches is printed out at 107.5%, the result will be 8x1.075 = 8.6 This is not the required height of 9 inches, so eliminate (B) and try (C). Since 8 x 1.125 = 9, (C) has the correct height. There is no need to try the width, since it must work; (D) would make both dimensions too large.

Here's one for "Passport to Advanced Math":

For which value of c does the equation 2x

^{2}+ c = 8x have exactly 1 value for x?A) -8

B) 0

C) 2

D) 8

**Solution**: The first step of this problem is to determine what type of equation this is. Once identified as a quadratic equation, you must set the equation equal to 0, so:

**2x ^{2} + c = 8x**

**2x ^{2} - 8x + c = 0**

The question is asking for the value of *c,* so start by testing the given values. Beginning with answer (C) and making c=2:

**2x ^{2} - 8x + 2 = 0**

Now, solve the equation and determine whether there's only one value of x. If you try to factor, you'll find that the quadratic doesn't break into clean binomials, so this is likely not the answer. Try another, such as (D), where c=8.

**2x ^{2} - 8x + 8 = 0.**

Factor out the 2 first, then factor:

**2(x ^{2} - 4x + 4) = 0**

**2(x-2)(x-2) = 0**

**x-2 = 0, so x = 2.**

There's only one value for x, so (D) is the answer.

Here's one for "Additional Topics in Math":

Which of the following is the correct form of -3

i− 3^{8 }i− 3^{6 }i− 1, where the imaginary numberiis such thati= -1? (solve without calculator)^{2}A) -1

B) -1 - 3i

C) -7 - 3i

D) -1 − 3i

**Solution:** We know that the imaginary number *i* is such that *i ^{2 }*= -1.

Therefore, i^{8 }= (i^{2})^{4 }= (−1)^{4} = 1.

Similarly, i^{6 }= (i^{2})^{3 }= (−1)^{3 }= −1.

Therefore, we can write the given expression (−3i^{8} − 3i^{6} − 3i – 1) as:

**= -3 x 1 − 3 x (-1) − 3 i − 1**

**= -3 + 3 − 3 i − 1**

**= -1 − 3 i**

**Therefore, the answer is (D).**

A test-taking student must be able to identify the call of the question, determine the relevant mathematical equation to resolve the question, and perform the calculations accurately and efficiently, with consideration for the time limits for the SAT math section, to produce the correct answer. If a student fails to quickly identify what the question is asking and the equation or mathematical concept needed to resolve it, they may spend valuable time generating an incorrect answer, and, perhaps more importantly, less time to resolve other questions they are able to answer correctly.

For many student learners, repetition and practice via review of SAT math practice problems and answers are the keys to performing well on the actual exam. For others, consistent reinforcement by tutors and peers of the core mathematical concepts behind a problem, and how they operate to resolve the question, provide the best means of achieving high test scores. No matter how best your student learns, the free group tutoring sessions at Schoolhouse.world can provide the reinforcement and confidence your student needs to conquer the SAT math exam.

## How does Schoolhouse.world help my student learner practice the problems and answers found in the SAT math section?

As any good tutor will tell you, there is no secret recipe they can provide to a student that guarantees their success on any particular test. Rather, it is the repetition of the key concepts of the subject provided by tutoring sessions, and constantly reinforced with individual study, that produces successful results on test day. In the case of the SAT math section, this means fluency in numerous equations and solution approaches, combined with accurate and effective methods of determining the important information presented in the test question and applying the correct solution to the data at hand.

At Schoolhouse.world, our online small-group tutoring sessions allow students to practice required math skills with other learners in a guided setting with the help of a Schoolhouse tutor. The tutor leads the tutoring groups through actual SAT math practice worksheets and questions, including fully timed SAT math practice tests, and helps teach the best methods for quickly and efficiently solving the various types of problems commonly found on the SAT. The volunteer tutors are comprised of other successful test takers who have gone through the same preparation and practice a current test taker must complete to be successful, and they understand the knowledge needed to excel on the exam, along with helpful tips and tricks to reduce pressure and stress during your study sessions and on test day. By encountering and resolving difficult sample test questions in advance of test day with the help of the tutor and study group, a test taker can build fluency with different equations and the ability to quickly identify which solution should be utilized for a particular question, ensuring they have the confidence to approach and resolve any question on test day.

In addition, the small group settings also allow for group question and answer sessions, so a student may benefit from the questions another student asks, and vice versa, without the stress, worry, or embarrassment that sometimes comes with asking for help with a tough question. This team learning atmosphere allows a student to connect with other learners who are experiencing the same ups and downs that come with intensive test preparation, and creates a collaborative, positive atmosphere for success.

## Preparation breeds Confidence. Confidence breeds Success.

For some students, the knowledge that they have put in the time and effort to thoroughly prepare for test day makes all the difference in the world. While the stress and worry of another standardized test can sometimes slow down even the most accomplished student, repeated practice and reinforcement of likely solutions and means of solving common problems can provide a clear head and confidence to succeed on test day.

This is particularly important because of the time limit requirements of the test. Efficiency and accurate speed are important test-taking skills, and preparation for the SAT Math exam via timed tests allows a student to practice not just their ability to recall how to identify and resolve an equation, but to do so accurately and efficiently with a “real-world” timing aspect, just like on the exam. With both portions of the entire SAT math exam lasting only a combined eighty (80) minutes, spending too long on one question, even if it produces a correct answer, can prove the difference between a good score and an average one, particularly if easier questions remain unanswered later in the exam. Indeed, even on the calculator portion of the exam, many students choose to not use a calculator at all, finding answers take longer to resolve via the calculator than by hand. Whatever method works best for your learner, it is far better to practice and understand in advance the best method for your student, rather than wasting precious minutes during the exam on finding a particular function button on your calculator.

## Prepare and Succeed with Schoolhouse.world!

Here’s a simple reality: there are no inherently “good” or “bad” test takers, despite what you might have heard from the local private test tutor. There are, however, test takers who have put in the time and effort to practice the skills required to succeed on a given test, and those who have not. Help provide your student learner the skills and confidence needed to achieve their best score on the SAT math section by encouraging them to sign up and attend schoolhouse.world's group tutoring sessions. When you see your learner combine preparation with acquired knowledge and self-confidence, no test is too hard, no question too difficult.

Set your learner on the path to SAT math exam success today by signing them up for the free group tutoring sessions on Schoolhouse!

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