Executing the program flowchart shown, the output value of $k$ is

5. The three views of a certain triangular pyramid are shown in the figure. The surface area of this triangular pyramid is
[Figure]
Front (Main) View
[Figure]
Top View
[Figure]
Side (Left) View
A. $2 + \sqrt { 5 }$
B. $4 + \sqrt { 5 }$
C. $2 + 2 \sqrt { 5 }$
D. $5$

The three views of a certain solid are shown in the figure. The volume of this solid is
(A) $\frac { 1 } { 3 } + 2 \pi$
(B) $\frac { 13 \pi } { 6 }$
(C) $\frac { 7 \pi } { 3 }$
(D) $\frac { 5 \pi } { 2 }$

5. The three-view drawing of a certain solid is shown in the figure. The volume of this solid is
[Figure]
Front view
[Figure]
Left view
[Figure]
Top view
A. $\frac { 1 } { 3 } + \pi$
B. $\frac { 2 } { 3 } + \pi$
C. $\frac { 1 } { 3 } + 2 \pi$
D. $\frac { 2 } { 3 } + 2 \pi$

5. Let $l _ { 1 } , l _ { 2 }$ denote two lines in space. If $\mathrm { p } : l _ { 1 } , l _ { 2 }$ are skew lines, $\mathrm { q } : l _ { 1 } , l _ { 2 }$ do not intersect, then
A. p is a sufficient condition for q, but not a necessary condition
B. p is a necessary condition for q, but not a sufficient condition
C. p is a sufficient and necessary condition for q
D. p is neither a sufficient condition nor a necessary condition for q

5. The three views of a solid are shown in the figure. The surface area of this solid is
A. $3 \pi$
B. $4 \pi$
C. $2 \pi + 4$
D. $3 \pi + 4$ [Figure]
6. ``$\sin \alpha = \cos \alpha$'' is ``$\cos 2 \alpha = 0$'' a
A. sufficient but not necessary condition
B. necessary but not sufficient condition
C. necessary and sufficient condition
D. neither sufficient nor necessary condition

6. By reading the flowchart shown in the figure and running the corresponding program, the output result is
A. 2
B. 1
C. 0
D. $- 1$

6. A cube is cut by a plane, and the three-view drawing of the remaining part is shown on the right. The ratio of the volume of the cut-off part to the volume of the remaining part is [Figure]
A. $\frac { 1 } { 8 }$
B. $\frac { 1 } { 7 }$
C. $\frac { 1 } { 6 }$
D. $\frac { 1 } { 5 }$

A cube is cut by a plane, and the orthogonal projections of the remaining part are shown in the figure on the right. The ratio of the volume of the cut-off part to the volume of the remaining part is
(A) $\frac { 1 } { 8 }$
(B) $\frac { 1 } { 7 }$
(C) $\frac { 1 } { 6 }$
(D) $\frac { 1 } { 5 }$

6. Executing the flowchart shown in the figure, the output value of $S$ is
(A) $- \frac { \sqrt { 3 } } { 2 }$
(B) $\frac { \sqrt { 3 } } { 2 }$
(C) $- \frac { 1 } { 2 }$
(D) $\frac { 1 } { 2 }$

6. Let $A , B$ be finite sets, and define $d ( A , B ) = \operatorname { card } ( A \cup B ) - \operatorname { card } ( A \cap B )$ , where $\operatorname { card } ( A )$ denotes the number of elements in the finite set $A$.
Proposition (1): For any finite sets $A , B$, ``$A \neq B$'' is a [Figure]
necessary and sufficient condition for ``$d ( A , B ) > 0$'';
Proposition (2): For any finite sets $A , B , C$, $d ( A , C ) \leq d ( A , B ) + d ( B , C )$.
A. Both Proposition (1) and Proposition (2) are true
B. Both Proposition (1) and Proposition (2) are false
C. Proposition (1) is true, Proposition (2) is false
D. Proposition (1) is false, Proposition (2) is true

7. Execute the program flowchart shown in the figure. The output value of $n$ is [Figure]
(A) $3$
(B) $4$
(C) $5$
(D) $6$

The three-view drawing of a certain quadrangular pyramid is shown in the figure. The length of the longest edge of this quadrangular pyramid is

7. Executing the flowchart shown in question (7), if the input value of K is 8, then the condition that can be filled in the decision box is
A. $\mathrm { s } \leq \frac { 3 } { 4 }$
B. $\mathrm { s } \leq \frac { 5 } { 6 }$
C. $\mathrm { s } \leq \frac { 11 } { 12 }$
D. $\mathrm { s } \leq \frac { 15 } { 24 }$ [Figure]

7. If $l$ and $m$ are two different lines, and $m$ is perpendicular to plane $\alpha$, then ``$l \perp m$'' is ``$l \parallel \alpha$'' a [Figure]
A. sufficient but not necessary condition
B. necessary but not sufficient condition
C. sufficient and necessary condition
D. neither sufficient nor necessary condition

8. The ``fuel efficiency'' of a car refers to the distance a car can travel per liter of gasoline consumed. The figure below describes the fuel efficiency of three cars, A, B, and C, at different speeds. The correct statement is [Figure]
A. Consuming 1 liter of gasoline, car B can travel at most 5 kilometers
B. Traveling at the same speed for the same distance, among the three cars, car A consumes the most gasoline
C. Car A travels at 80 kilometers per hour for 1 hour, consuming 10 liters of gasoline
D. A certain city has a maximum speed limit of 80 kilometers per hour. Under the same conditions, using car C in this city is more fuel-efficient than using car B

Part Two (Non-Multiple Choice Questions, 110 points)

II. Fill-in-the-Blank Questions: There are 6 questions in total, each worth 5 points, for a total of 30 points.

Executing the flowchart shown in figure (8), the output value of $s$ is
(A) $\frac { 3 } { 4 }$
(B) $\frac { 5 } { 6 }$
(C) $\frac { 11 } { 12 }$
(D) $\frac { 25 } { 24 }$

8. The algorithm idea of the flowchart on the right comes from the ``Mutual Subtraction Method'' in the ancient Chinese mathematical classic ``The Nine Chapters on the Mathematical Art''. When executing this flowchart, if the input values of $a$ and $b$ are 14 and 18 respectively, then the output value of $a$ is ( )
A. $0$
B. $2$
C. $4$
D. $14$

The algorithm flowchart on the right is based on the ``Mutual Subtraction for Reduction'' method from the ancient Chinese mathematical classic ``The Nine Chapters on the Mathematical Art''. When executing this flowchart with inputs $a, b$ equal to 14 and 18 respectively, the output value of $a$ is
A. $0$
B. $2$
C. $4$
D. $14$

8. Based on the flowchart on the right, when the input $x$ is 2005, the output $y =$
A. 28
B. 10
C. 4
D. 2

8. Let real numbers $a , b , t$ satisfy $| a + 1 | = | \sin b | = t$
[Figure]
(Figure for Question 7)
A. If $t$ is determined, then $b ^ { 2 }$ is uniquely determined
B. If $t$ is determined, then $a ^ { 2 } + 2 a$ is uniquely determined
C. If $t$ is determined, then $\sin \frac { b } { 2 }$ is uniquely determined
D. If $t$ is determined, then $a ^ { 2 } + a$ is uniquely determined

II. Fill-in-the-Blank Questions (This section contains 7 questions. Multi-blank questions are worth 6 points each, single-blank questions are worth 4 points each, 36 points total.)

8. As shown in the figure, in $\triangle ABC$, $D$ is the midpoint of $AB$. Fold $\triangle ACD$ along line $CD$ to form $\triangle A'CD$. The dihedral angle $A' - CD - B$ has plane angle $\alpha$. Then
A. $\angle A' D B \leq \alpha$
B. $\angle A' D B \geq \alpha$
C. $\angle A' C B \leq \alpha$
D. $\angle A' C B \geq \alpha$
II. Fill-in-the-Blank Questions: This section contains 7 questions. Multi-blank questions are worth 6 points each, single-blank questions are worth 4 points each, for a total of
[Figure]
36 points.

9. The three-view drawing of a tetrahedron is shown in the figure. Then the surface area of the tetrahedron is [Figure]
(A) $1 + \sqrt { 3 }$
(B) $1 + 2 \sqrt { 2 }$
(C) $2 + \sqrt { 3 }$
(D) $2 \sqrt { 2 }$

9. There is one cone made of plasticine with base radius 5 and height 4, and one cylinder with base radius 2 and height 8. If they are remade into a new cone and cylinder, each with the same total volume and height as before, but with the same base radius, then the new base radius is $\_\_\_\_$.

Points $A$ and $B$ are on the surface of sphere $O$, with $\angle A O B = 90°$. Point $C$ is a moving point on the sphere surface. If the maximum volume of tetrahedron $O-ABC$ is 36, then the surface area of sphere $O$ is
A. $36 \pi$
B. $64 \pi$
C. $144 \pi$
D. $256 \pi$