1. "Because the exponential function y = ax is increasing function (major premise) and y = () x is exponential function (minor premise), y = () x is increasing function (conclusion)", the above reasoning is wrong.

A. Major premise errors lead to wrong conclusions B. Minor premise errors lead to wrong conclusions.

C. the wrong form of reasoning leads to the wrong conclusion D. both the major premise and the minor premise lead to the wrong conclusion.

Analysis: The premise that Y = AX is increasing function is wrong, and a wrong conclusion is drawn. Answer: a.

2. In order to ensure the safe transmission of information, there is a cryptographic system called secret key, and its encryption and decryption principle is as follows.

Now the encryption key is y = loga (x+2). As shown above, plaintext "6" is encrypted to obtain ciphertext "3" and then sent. The receiver decrypts the plaintext "6" with the decryption key. Q: If the ciphertext received by the receiver is "4", the decrypted plaintext is ().

12 b . 13 c . 14d . 15

Analysis: ∫loga(6+2)= 3, ∴ a = 2, that is, the encryption key is y = log2 (x+2).

When the received ciphertext is 4, that is, log2 (x+2) = 4, ∴ x+2 = 24, ∴ x = 14. Answer: C.

3 Prove to absurdity that if the quadratic equation AX2+BX+C = 0 (A ≠ 0) has a rational root, then when there is at least one even number in A, B and C, the following assumption is correct ().

A. suppose a, b and c are even numbers. B. suppose a, b and c are not even numbers.

C suppose a, b and c have at most one even number d suppose a, b and c have at most two even numbers.

Analysis: The negation of "at least one" is "none". Answer: B.

4 If the radius of the inscribed circle of a triangle is R and the lengths of three sides are A, B and C respectively, the area of the triangle is S = R (A+B+C). By analogy, if the radius of the inscribed sphere of a tetrahedron is R and the areas of its four faces are S 1, S2, S3 and S4, then the volume of this tetrahedron is V = _ _ _ _ _ _.

Analysis: If the spherical center of the inscribed spherical surface of a tetrahedron is O, then the distance from the spherical center O to the four surfaces is R, then the volume of the tetrahedron is equal to the sum of the volumes of four triangular pyramids with O as the vertex and four surfaces as the bottom respectively.

Answer: 1/3 R (S 1+S2+S3+S4)

5 In △ABC, the projective theorem can be expressed as a = BCOSC+CCCOSB, where A, B and C are the opposite sides of angles A, B and C in turn. By analogy with the above theorem, the conjecture of spatial tetrahedron properties is given.

Solution: As shown in the figure, in tetrahedron P-ABC, S 1, S2, S3 and S are displayed respectively.

Represents the area of △PAB, △PBC, △PCA and △ABC, and α, β and γ depend on.

Sub represents the size of the angle formed by surface PAB, surface PBC, surface PCA and bottom ABC.

Small, we suspect that the projective theorem can be analogized to three-dimensional space, and its expression should be S = S 1cosα+S2cosβ+S3cosγ.

Is this ok?