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Overview Math Test - No Calculator is the third section of the SAT, and the first of the two math sections. You will have 25 minutes to answer 20 questions. This allows you 40 seconds per question, but some questions will take more time than others. The non-calculator section is used to assess your understanding and application of mathematical techniques and concepts, rather than spending time on basic computations that can be done in the real world with a calculator. SAT Math Test - No Calculator 25 minutes 20 questions 40 seconds per question The Math - No Calculator section consists of a combination of multiple choice and fill-in-the-blank questions - 15 multiple choice and 5 “student-produced responses,” or grid-in questions. You will be provided with instructions about how to bubble in the grid-in questions, as seen below. Notice that the grid in questions cannot be negative, as there is no way to mark a negative sign. Also note that while you can either bubble an answer as a fraction or a decimal, you cannot bubble in a mixed number (must instead be written as an improper fraction). While the SAT categorizes their math questions into one of four subsections, only the following three subsections will appear on the non calculator section. 1. Heart of Algebra These types of questions will focus on the skills learned in Algebra I, specifically dealing with linear equations and inequalities. Students may be asked to solve or interpret linear equations or inequalities with one or two variables, and may be asked to create, solve, and interpret systems of equations or inequalities. The SAT focuses on skills that may be useful in your future career, so many of the questions will be application questions where you must apply your knowledge of linear equations/inequalities to the real world. Example: “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?” 2. Passport to Advanced Math These types of questions will cover topics that are essential for students to master before continuing into advanced math. Students will be asked to create and solve quadratic equations. You may also be asked to add, subtract, multiply, and divide polynomial expressions, and understand the different characteristics of polynomial functions. You will be asked to solve equations that include rational exponents and radicals, and you will be expected to understand and use function notation. Example: "The graph of y = (2x − 4)(x − 4) is a parabola in the xy-plane. In which of the following equivalent equations do the x- and y-coordinates of the vertex of the parabola appear as constants or coefficients?" 3. Additional Topics in Math This subsection focuses on geometric and trigonometric concepts, such as special right triangles and trigonometric ratios. You may be asked to solve for the area and volume of shapes. All necessary volume formulas will be provided on the formula sheet at the beginning of the test. You will also be tested on concepts such as degree-radian conversion, arc length, and trigonometric functions and identities. You may also be asked about similarity and congruence, and will have to apply various theorems to determine side or angle measurements. Example: "Which of the following is equal to sin(π/5)?" We break these subsections down even further to focus on the specific skills necessary to be successful on SAT Math - No Calculator. Systematic Approach to the SAT Math Test - No Calculator When approaching a question, consider asking yourself the following questions: 1) What concept is being tested? Some questions will only involve one math concept, while others may require you to utilize a variety of mathematical knowledge. For example, the following question tests students on a single concept (slope application). 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 question is testing you on your knowledge of the application of linear equations and the meaning of slope. In the equation y = 0.8636x + 27.227, the number 0.8636 represents the slope. Another term for slope is the rate of change, or how much y changes with respect to x. In the context of the problem, the slope would represent how the mean number of students per classroom at Central High School changed each year. Since the slope is positive, the number of students per classroom increased each year. Therefore, the best answer choice here is D. However, many of the questions on the SAT Math section will expect you to apply multiple concepts at once. The question below tests you on two concepts: Properties of Exponents and Rearranging Equations. If where a > 0 and x > 0, which of the following equations gives a in terms of x? a) b) c) d) We are being asked to solve for a in terms of x. To get a by itself, we can take both sides of the equation to the reciprocal power. This will turn the left side of the equation into a1, or a. The properties of exponents state that a negative exponent means to take the reciprocal. x-2 then becomes . Therefore, the answer is B.x1/2 2) Can you recall formulas associated with the tested concept? Write down any formulas you know related to the tested concept. Even if you’re not sure how to solve the problem, seeing the formulas in front of you may cause you to recognize where to plug in the given values to solve the problem. 3) What is given in the problem? Convert any information provided in the problem into a mathematical expression or equation. This can be especially helpful with word problems. When students aren’t sure how to approach a problem, they tend to waste time by sitting there and staring at the problem. However, the answer to a question doesn’t usually magically appear before your eyes. By writing down the information provided in the problem, you can help your brain see the problem in a new way. 4) Can you draw a picture to help you solve the problem? Similarly, if a shape or image is described but not provided for you, try to draw a picture of what the question is telling you. 5) If all else fails, make an educated guess. If you don’t understand the question after following these steps, or you feel that the question will take too long to answer, circle it and come back later, after completing all of the questions that you do know how to do. If you have time left, try to answer the question, and if not, make an educated guess given the information provided. Tips and Strategies Underline important parts of the question. Many silly mistakes that students make on the SAT occur due to not reading the question correctly. By underlining key words and phrases, you can make sure that you are solving for the right thing. Skimming over words like “not” and “except” can cause students to miss a question they otherwise would have gotten correct. Don’t rush through the easier questions. Since every question on the SAT is worth the same number of points, it is important to make sure that you don’t make any silly mistakes on the easier questions. By taking your time on the easier questions, you can make sure you are getting the maximum number of questions right that you can. Answer every question, but don’t spend too much time with the ones you don’t know. There may be questions on the SAT Math Test - No Calculator that you don’t know how to do. However, be sure to answer every question, even if you don’t know it, since there are no penalties for wrong answers. However, once you know that you don’t know how to do a question, mark it and move on from it so you can ensure that you can maximize your points with the ones that you do know. Be sure to leave a bit of time at the end so that you can go back to these questions. Remember that every question is worth the same amount - the easy questions are worth just as much as the hard ones. Therefore, make sure to spend enough time on the easier questions to ensure you don’t make silly mistakes and lose easy points. On the multiple choice section, eliminate any answer choices you know are wrong. Maybe you are having trouble getting the right answer, but you have a decent understanding of the concept being tested. See if any of the answer choices make no sense in the context of the problem. If you can eliminate one or more choices, you will increase your chances of getting the question correct. Example: y = x2 2y + 6 = 2(x + 3) If (x, y) is a solution to the system of equations above and x > 0, what is the value of xy? a) 1 b) 2 c) 3 d) 9 Even if you don’t know the exact method to solve this problem, you may be able to eliminate one or more answer choices. You are being asked to find the value of x times y. Since y = x2, xy must be the product of a number and its square. The factors of 1 are 1 and 1, and 1 squared is 1, so choice A is an option. Since 2 and 3 are both prime, their only factors are 1 and 2, and 2 and 3 respectively. Since 1 squared is not 2 or 3, we can eliminate B and C. The factors of 9 and 1, 3, and 9. 3 squared is 9, but 9 times 3 is 27, which is not an answer choice. We can therefore eliminate D as well, just by comparing the answer choices to the question.
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