SAT+math

The **SAT Reasoning Test** (formerly **Scholastic Aptitude Test** and **Scholastic Assessment Test**) is a [|standardized test] for [|college admissions] in the [|United States].
 * __SAT__**

For further information, please contact Mrs Hopkinson, University Counselor, at dhopkinson@isparis.edu You can also check the testing schedule on the ISP website, http://www.isparis.edu/page.cfm?p=493#sat, and to register for the SAT go to http://www.collegeboard.com


 * Critical reading, writing & Mathematics**

The [|Mathematics] section of the SAT is widely known as the Quantitative Section or Calculation Section. The mathematics section consists of three scored sections. There are two 25-minute sections and one 20-minute section, as follows: Notably, the SAT has done away with quantitative comparison questions on the math section, leaving only questions with [|symbolic] or [|numerical] answers.
 * Mathematics**
 * One of the 25-minute sections is entirely multiple choice, with 20 questions.
 * The other 25-minute section contains 8 multiple choice questions and 10 grid-in questions. The 10 grid-in questions have no penalty for incorrect answers because the student guessing isn't limited.
 * The 20-minute section is all multiple choice, with 16 questions.
 * New topics include Algebra II and scatter plots. These recent changes have resulted in a shorter, more quantitative exam requiring higher level mathematics courses relative to the previous exam.

With the recent changes to the content of the SAT math section, the need to save time while maintaining accuracy of calculations has led some to use [|calculator programs] during the test. These programs allow students to complete problems faster than would normally be possible when making calculations manually. The use of a graphing calculator is sometimes preferred, especially for geometry problems and questions involving multiple calculations. According to [|research] conducted by the CollegeBoard, performance on the math sections of the exam is associated with the extent of calculator use, with those using calculators on about a third to a half of the items averaging higher scores than those using calculators less frequently [|[8]]. The use of a graphing calculator in mathematics courses, and also becoming familiar with the calculator outside of the classroom, is known to have a positive effect on the performance of students using a graphing calculator during the exam. An **SAT calculator program** is a [|software application] that resides on a [|calculator] which is used in helping to answer [|SAT] questions. The programs themselves are different from SAT preparation books and classes in that they are actually used during the SAT test, and contain programs to answer questions with common SAT math formulas or simply answer common SAT questions.
 * Calculator Use**

Understanding the PSAT/NMSQT test sections
The primary aim of the math section is to **assess how well students understand math**. Can they, for example, apply what they already know to new situations and use what they know to solve non-routine problems? The math section of the PSAT/NMSQT requires a basic knowledge of:
 * Numbers and operation
 * Algebra and functions (though not content covered in third-year math classes—content that will appear on the SAT)
 * Geometry and measurement
 * Data analysis, statistics, and probability

Multiple choice
For multiple-choice questions, students must solve each problem and decide which of the five choices given is the best. Basic geometric formulas are included in the test booklet for reference, since the PSAT/NMSQT emphasizes application, rather than memorization, of this material. Learn more about the [|math multiple-choice] questions in the student section of this website.

Student-produced responses (Grid-ins)
Student-produced response questions: When students enter their responses to these questions on the answer sheet: Learn more about the [|student-produced response] questions in the student section of this website.
 * Do not include answer choices
 * May have more than one correct answer
 * Have no deduction for incorrect answers (because guessing is almost impossible)
 * It doesn't matter in which column students begin entering their answers; as long as the correct answer is gridded, students will receive credit.
 * Only answers entered in the ovals in each grid area will be correct. Students will not receive credit for anything written in the boxes above the ovals.

Math concepts
The following math concepts are covered in the PSAT/NMSQT.

Numbers and operation

 * Arithmetic word problems
 * Percent
 * Prime numbers
 * Ratio and proportion
 * Logical reasoning
 * Sets (union, intersection, and elements)
 * Properties of integers (even, odd, etc.)
 * Divisibility
 * Counting techniques
 * Sequences and series (including exponential growth)
 * Elementary number theory

Algebra and functions

 * Properties of exponents (including rational exponents)
 * Algebraic word problems
 * Substitution
 * Absolute value
 * Rational and radical equations
 * Equations of lines
 * Direct and inverse variation
 * Basic concepts of algebraic functions
 * Newly defined symbols based on commonly used operations
 * Solutions of linear equations and inequalities
 * Quadratic equations
 * Simplifying algebraic expressions

Geometry and measurement

 * Area and perimeter of a polygon
 * Area and circumference of a circle
 * Volume of a box, cube, and cylinder
 * Pythagorean Theorem and special properties of isosceles, equilateral, and right triangles
 * Properties of parallel and perpendicular lines
 * Coordinate geometry
 * Geometric visualization
 * Slope
 * Similarity

Data analysis, statistics, and probability

 * Data interpretation
 * Statistics (mean, median, and mode)
 * Probability

Here are some general hints for answering Regular Multiple Choice questions.
 * __ Method __**
 * 1) Look at the answer choices before you begin to work on each question.
 * 2) Read each question carefully, even if it looks like a question you don't think you can answer. Don't let the form of the question keep you from trying to answer it.
 * 3) If your answer isn't among the choices, try writing it in a different form. You may have the same answer in a different mathematical format.

Samples:

(a) If //m// and //p// are positive integers and (//m// + //p//) x //m// is even, which of the following must be true?
 * (A) **If //m// is odd, then //p// is odd.** CORRECT ANSWER
 * (B) If //m// is odd, then //p// is even.
 * (C) If //m// is even, then //p// is even.
 * (D) If //m// is even, then //p// is odd.
 * (E) //m// must be even.

Explanation:
If //m// is even, then the expression (//m// + //p//) x //m// will always be even and it cannot be determined whether //p// is even or odd. This eliminates choices (C) and (D). If //m// is odd, then (//m// + //p//) x //m// will be even only when //m// + //p// is even and //m// + //p// will be even only when //p// is odd. The correct answer is (A) since the truth of statement (A) also eliminates choices (B) and (E).

(b) If //n// is an odd integer, which of the following must be an odd integer?
 * (A) //n// - 1
 * (B) //n// + 1
 * (C) 2//n//
 * (D) 3//n// + 1
 * (E) **4//n// + 1** CORRECT ANSWER

Explanation:
If //n// is an odd integer, both one more and one less than //n// will be even integers, eliminating choices (A) and (B). Any even multiple of //n// will be an even integer, eliminating choice (C). However, 4//n// is even, making 4//n// +1 an odd integer. The answer to this problem is (E). Note that 3//n// + 1 is even if //n// is odd and it is odd if //n// is even. Since the question asks, "Which of the following MUST be an odd integer," (D) cannot be the correct answer.

(c) If //a// and //b// are integers greater than 100 such that //a// + //b// = 300, which of the following could be the exact ratio of //a// to //b// ?
 * (A) 9 to 1
 * (B) 5 to 2
 * (C) 5 to 3
 * (D) 4 to 1
 * (E) **3 to 2** CORRECT ANSWER

Explanation:
To solve this question, you need to look at the answer choices. For any of the answer choices to be the ratio of //a// to //b//, some multiple of the sum of the two numbers must evenly divide 300. For example, if the ratio of //a// to //b// equaled 9 to 1, then //a// would equal 9//x// and //b// would equal //x// for some number //x//. Furthermore, 9//x// + //x// would have to equal 300. This is possible since 10//x// = 300 yields an integer solution, namely //x// = 30. However, if //x// = 30, then //a// would equal 270 and //b// would equal 30. Although the sum of these numbers equals 300, they do not satisfy the other condition in the problem. That is, both of these numbers are not greater than 100. Therefore, choice (A) can be eliminated. Answer choices (B) and (C) can be eliminated since neither the sum of the two numbers in (B) nor the sum of the two numbers in (C) evenly divided 300. (5//x// + 2//x// = 300 does not yield an integer solution, nor does 5//x// + 3//x// = 300.) Although answer choices (D) and (E) are possible ratios of //a// to //b// (both 4//x// + //x// = 300 and 3//x// + 2//x// = 300 yield integer solutions), (D) results in //a// = 240 and //b// = 60 and can be eliminated since 60 is not greater than 100. Only choice (E) gives a correct ratio of //a// to //b// that satisfies all of the conditions in the problem. For (E), //a// = 180 and //b// = 120, and both integers are greater than 100.

__**2009 Practice Test, sections 2 & 4**__