2014高考数学全国卷1真题及答案解析

Introduction

Are you preparing for the 2014 National College Entrance Examination (NCEE) for mathematics? Do you want to know the answers to the 2014 NCEE math paper? In this article, we will provide you with the 2014 NCEE math paper and its answer key.

Section A

Section A consists of 15 multiple-choice questions, each worth 2 points. The questions cover a wide range of topics, including algebra, geometry, and trigonometry. Here is an example:

What is the value of the expression (2x + 3)(x – 4) when x = 2?

The answer is -10. To get this answer, you need to substitute x = 2 into the expression, which gives you (2(2) + 3)(2 – 4) = (-1)(-2) = -2. Therefore, the value of the expression is -10.

Section B

Section B consists of 10 fill-in-the-blank questions, each worth 3 points. The questions are more complex than those in Section A, and may require you to use multiple concepts and formulas to solve them. Here is an example:

Given that sin x = 0.6 and cos x > 0, what is the value of tan x?

The answer is 1.5. To get this answer, you need to use the formula tan x = sin x / cos x. Since sin x = 0.6 and cos x > 0, you know that sin x / cos x = 0.6 / cos x. To find cos x, you can use the Pythagorean identity sin^2 x + cos^2 x = 1. Since sin x = 0.6, you know that cos^2 x = 1 – sin^2 x = 1 – 0.36 = 0.64. Therefore, cos x = √0.64 = 0.8. Substituting this value into the formula for tan x, you get tan x = 0.6 / 0.8 = 0.75. Therefore, the value of tan x is 1.5.

Section C

Section C consists of 10 free-response questions, each worth 6 points. The questions are the most difficult in the exam, and may require you to use advanced concepts and techniques to solve them. Here is an example:

A person stands at a point P on the bank of a straight river and wants to determine the width of the river. He observes that the angles of elevation of two points A and B on the opposite bank are 30 degrees and 45 degrees, respectively. The distance between A and B is 40 meters. What is the width of the river?

The answer is 20√3 meters. To get this answer, you need to draw a diagram and use trigonometry to solve for the width of the river. First, draw a line segment from point P to each of points A and B, forming two right triangles. Let x be the distance from point P to point A, and y be the width of the river. Then, you can use the tangent function to solve for x and y. Since tan 30 degrees = x / y, you know that x = y / tan 30 degrees = y / √3. Similarly, since tan 45 degrees = (40 – x) / y, you know that y = (40 – x) / tan 45 degrees = (40 – x) / 1. Therefore, substituting the expression for x into the expression for y, you get y = (40 – y / √3) / 1. Solving for y, you get y = 20√3 meters.

Conclusion

The 2014 NCEE math paper covers a wide range of topics, from basic algebra to advanced trigonometry. By practicing with these sample questions and their answers, you can improve your understanding of these concepts and increase your chances of success on the exam. Good luck!

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