Tiêu đề Quantitative Reasoning 2.pdf ✅

The Quantitative Reasoning domain tests your ability to use numbers and mathematical concepts to solve mathematical problems, as well as your ability to analyze data presented in a variety of ways, such as in table or graph form. Only a basic knowledge of mathematics is required (the material studied up to 9th or 10th grades in most Israeli high schools). All of the Quantitative Reasoning problems take the form of multiple-choice questions, that is, a question followed by four possible responses, only one of which is the correct answer. The Quantitative Reasoning sections consist of two categories of questions – Questions and Problems, and Graph or Table Comprehension. Questions and Problems cover a variety of subjects taken from algebra and geometry. Some of the questions are presented in mathematical terms; others are word problems, which you must translate into mathematical terms before solving. Graph or Table Comprehension questions relate to information appearing in a graph or a table. A graph presents data in graphic form, such as a bar chart, line graph or scatter plot. A table presents data arranged in columns and rows. In general, all questions of a given type are arranged in ascending order of difficulty. The easier questions, requiring relatively less time to solve, appear first, with the questions becoming progressively more difficult and requiring more time to solve. The figures accompanying some of the questions are not necessarily drawn to scale. Do not rely solely on the figure's appearance to deduce line length, angle size, and so forth. However, if a line in a figure appears to be straight, you may assume that it is, in fact, a straight line. A Formula Page appears at the beginning of each Quantitative Reasoning section. This page contains instructions, general comments and mathematical formulas, which you may refer to during the test. The Formula Page also appears in the Guide (on the next page) and in the Quantitative Reasoning sections of the practice test. You should familiarize yourself with its contents prior to taking the test. Pages 38-66 contain a review of basic mathematical concepts, covering much of the material upon which the questions in the Quantitative Reasoning sections are based. The actual test may, however, include some questions involving mathematical concepts and theorems that do not appear on these pages. Pages 67-82 contain examples of different types of questions, each followed by the answer and a detailed explanation. QUANTITATIVE REASONING Guide For Examinees Inter-University Psychometric Entrance Test 37
This section contains 20 questions. FORMULA PAGE The time allotted is 20 minutes. This section consists of questions and problems involving Quantitative Reasoning. Each question is followed by four possible responses. Choose the correct answer and mark its number in the appropriate place on the answer sheet. Note: The words appearing against a gray background are translated into several languages at the bottom of each page. General Comments about the Quantitative Reasoning Section * The figures accompanying some of the problems are provided to help solve the problems, but are not necessarily drawn to scale. Therefore, do not rely on the figures alone to deduce line length, angle size, and so forth. * If a line in a figure appears to be straight, you may assume that it is in fact a straight line. * When a geometric term (side, radius, area, volume, etc.) appears in a problem, it refers to a term whose value is greater than 0, unless stated otherwise. * When a (a > 0) appears in a problem, it refers to the positive root of a. * "0" is neither a positive nor a negative number. * "0" is an even number. * "1" is not a prime number. Formulas 1. Percentages: a% of x is equal to a x 100 $ 2. Exponents: For every a that does not equal 0, and for any two integers n and m - a. a a 1 = n −n b. am + n = am · an c. a a m m n n = _ i (0 < a, 0 < m) d. an · m = (an ) m 3. Contracted Multiplication Formulas: (a ± b) 2 = a2 ± 2ab + b2 (a + b)(a – b) = a2 – b2 4. Distance Problems: distance = speed (rate) time 5. Work Problems: amount of work = output (rate) time 6. Factorials: n! = n(n – 1)(n – 2) · ... · 2 · 1 7. Proportions: If AD||BE||CF then DE AB EF BC = and AC AB DF DE = 8. Triangles: a. The area of a triangle with base of length a and altitude to the base of length h is a h 2 $ b. Pythagorean Theorem: In any right triangle ABC, as in the figure, the following always holds true: AC2 = AB2 + BC2 c. In any right triangle whose angles measure 30°, 60°, 90°, the length of the leg opposite the 30° angle is equal to half the length of the hypotenuse. 9. The area of a rectangle of length a and width b is a · b a b h r r x° c b a A h r B C D E F h a A B C ניצב ניצב יתר A B C قائم قائم وتر A B C hypoténuse côté côté צרפתית משולב A B C hypotenuse leg leg רוסית A B C ubgjntyepf rfntn rfntn ספרדית A B C hipotenusa cateto cateto b a h r a b h r r x° c b a A h r B C D E F h a A B C ניצב ניצב יתר A B C قائم قائم وتر A B C hypoténuse côté côté צרפתית משולב A B C hypotenuse leg leg רוסית A B C ubgjntyepf rfntn rfntn ספרדית A B C hipotenusa cateto cateto b a h r a b h r r x° c b a A h r B C D E F h a A B C ניצב ניצב יתר A B C قائم قائم وتر A B C hypoténuse côté côté צרפתית משולב A B C hypotenuse leg leg רוסית A B C ubgjntyepf rfntn rfntn ספרדית A B C hipotenusa cateto cateto b a h r a b h r r x° c b a A h r B C D E F h a A B C ניצב ניצב יתר A B C قائم قائم وتر A B C hypoténuse côté côté צרפתית משולב A B C hypotenuse leg leg רוסית A B C ubgjntyepf rfntn rfntn ספרדית A B C hipotenusa cateto cateto b a h r 10. The area of a trapezoid with one base length a, the other base length b, and altitude h is a b h 2 ] g + $ 11. The sum of the internal angles of an n-sided polygon is (180n – 360) degrees. In a regular n-sided polygon, each internal angle measures n n n 180 360 180 360 = − a a k k − degrees. 12. Circle: a. The area of a circle with radius r is πr 2 (π = 3.14...) b. The circumference of a circle is 2πr c. The area of a sector of a circle with a central angle of x° is r x 360 2 π $ 13. Box (Rectangular Prism), Cube: a. The volume of a box of length a, width b and height c is a · b · c b. The surface area of the box is 2ab + 2bc + 2ac c. In a cube, a = b = c 14. Cylinder: a. The lateral surface area of a cylinder with base radius r and height h is 2πr · h b. The surface area of the cylinder is 2πr 2 + 2πr · h = 2πr(r + h) c. The volume of the cylinder is πr 2 · h 15. The volume of a cone with base radius r and height h is r h 3 π $ 2 16. The volume of a pyramid with base area S and height h is S h 3 $ a b h r r x° c b a A h r B C D E F h a A B C ניצב ניצב יתר A B C قائم قائم وتر A B C hypoténuse côté côté צרפתית משולב A B C hypotenuse leg leg רוסית A B C ubgjntyepf rfntn rfntn ספרדית A B C hipotenusa cateto cateto b a h r a b h r r x° c b a A h r B C D E F h a A B C ניצב ניצב יתר A B C قائم قائم وتر A B C hypoténuse côté côté צרפתית משולב A B C hypotenuse leg leg רוסית A B C ubgjntyepf rfntn rfntn ספרדית A B C hipotenusa cateto cateto b a h r a b h r r x° c b a A h r B C D E F h a A B C ניצב ניצב יתר A B C قائم قائم وتر A B C hypoténuse côté côté צרפתית משולב A B C hypotenuse leg leg רוסית A B C ubgjntyepf rfntn rfntn ספרדית A B C hipotenusa cateto cateto b a h r a b h r r x° c b a A h r B C D E F h a A B C ניצב ניצב יתר A B C قائم قائم وتر A B C hypoténuse côté côté צרפתית משולב A B C hypotenuse leg leg רוסית A B C ubgjntyepf rfntn rfntn ספרדית A B C hipotenusa cateto cateto b a h r a b h r r x° c b a A h r B C D E F h a A B C ניצב ניצב יתר A B C قائم قائم وتر A B C hypoténuse côté côté צרפתית משולב A B C hypotenuse leg leg רוסית A B C ubgjntyepf rfntn rfntn ספרדית A B C hipotenusa cateto cateto b a h r Quantitative Reasoning 38
REVIEW OF BASIC MATHEMATICAL CONCEPTS SYMBOLS Symbol a || b a ⊥ b a b h r r x° c b a A h r B C D E F h a A B C ניצב ניצב יתר A B C قائم قائم وتر A B C hypoténuse côté côté צרפתית משולב A B C hypotenuse leg leg רוסית A B C ubgjntyepf rfntn rfntn ספרדית A B C hipotenusa cateto cateto b a h r «ABC x = y x ≠ y x < y x ≤ y a < x, y x = + a |x| x : y Meaning of the Symbol lines a and b are parallel line a is perpendicular to straight line b 90o angle (right angle) the angle formed by line segments AB and BC x equals y x does not equal y x is less than y x is less than or equal to y both x and y are greater than a x may be equal to a or to (-a) the absolute value of x the ratio of x to y TYPES OF NUMBERS Integer: An integer, also called a whole number, is a number composed of whole units. An integer may be positive, negative, or 0 (zero). Example: ... , -4 , -3 , -2 , -1 , 0 , 1 , 2 , 3 , 4 , ... Note: 0 (zero) is an integer that is neither positive nor negative. Non-integer: A number that cannot be expressed in whole units. Example: , . 1 2 , , 2 1 2 2 1 - 1 37 Consecutive numbers: Integers that follow in sequence in differences of 1. For example, 4 and 5 are consecutive numbers; 2, 3, and 4 are consecutive numbers; (-3) and (-2) are also consecutive numbers. If n is an integer, then n and (n + 1) are consecutive numbers. This is sometimes expressed as: (n + 1) is the next consecutive integer after n. Even number: An integer which, when divided by 2, produces an integer (in other words, it is evenly divisible by 2). If n is an integer, then 2n is an even number. Note: 0 is an even number. Odd number: An integer which, when divided by 2, produces a non-integer (in other words, when it is divided by 2, a remainder of one is obtained). If n is an integer, then 2n + 1 is an odd number. Guide For Examinees Inter-University Psychometric Entrance Test 39