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《算法的含义与流程图》测试 1

《算法的含义与流程图》测试 1
《算法的含义与流程图》测试 1

必修③1.1—1.2(算法的含义与流程图)测试题

1.下面的结论正确的是()

A.一个程序的算法步骤是可逆的B、一个算法可以无止境地运算下去的

C、完成一件事情的算法有且只有一种

D、设计算法要本着简单方便的原则

2、早上从起床到出门需要洗脸刷牙(5 min)、刷水壶(2 min)、烧水(8 min)、泡面

(3 min)、吃饭(10 min)、听广播(8 min)几个步骤、从下列选项中选最好的一种

算法 ( )

A、S1 洗脸刷牙、S2刷水壶、S3 烧水、S4 泡面、S5 吃饭、S6 听广播

B、S1刷水壶、S2烧水同时洗脸刷牙、S3泡面、S4吃饭、S5 听广播

C、S1刷水壶、S2烧水同时洗脸刷牙、S3泡面、S4吃饭同时听广播

D、S1吃饭同时听广播、S2泡面、S3烧水同时洗脸刷牙、S4刷水壶

3、著名数学家华罗庚“烧水泡茶的两个算法、

算法一:

第一步烧水;第二步水烧开后,洗刷茶具;第三步沏茶

算法二:

第一步烧水:第二步烧水过程中,洗刷茶具第三步水烧开后沏茶

这两个算法的区别在哪里?哪个算法更高效?为什么?

4、写出求 1+2+3+4+5+6……+100 的一个算法。可运用公式 1+2+3+……+ n=

2)1

(

n

n

直接计算、

第一步①第二步②第三步输出计算结果

5、已知一个学生的语文成绩为89,数学成绩为96,外语成绩为99。求他的总分和平均成绩的一个算法为:

第一步取A=89 , B =96 C=99 ;

第二步①;

第三步②

第四步输出计算的结果

6、“鸡兔同笼“是我国隋朝时期的数学著作《孙子算经》中的一个有趣而具有深远影响的题目:

“今有雉兔同笼,上有三十五头,下有九十四足,问雉兔各几何。

用方程组的思想不难解决这一问题,请你设计一个这类问题的通用算法。

7、已知直角坐标系的两点A(-1,0),B(3,2),写出直线AB的方程的一个算法。

8.写出交换两个大小相同的杯子中的液体(A 水、 B 酒) 的两个算法。

9. 写出1×2×3×4×5×6的一个算法。

10. 已知一个三角形的三边边长分别为2、3、4, 设计一个算法,求也它的面积。

( B) 流程图

1、 算法的三种基本结构是 ( )

A 、 顺序结构、 选择结构、循环结构

B 、顺序结构、流程结构、循环结构

C 、 顺序结构、 分支结构、流程结构、

D 、流程结构、循环结构、分支结构 2、 流程图中表示判断框的是 ( )

A . 矩形框

B 、菱形框

C 、 圆形框

D 、椭圆形框 3、 下面是求解一元二次方程)0(02≠=++a c bx ax 的流程图,请在空和缺的地方填上适当的标注。

4、下面流图表示了什么样的算法?

5、下面流程图是当型循环还是直到型循环?它表示是一个什么样的算法?

6、已知梯形的上底、下底和高分别为5、8、9,写出求梯形的面积的算法,画现流程图。

7. 设计算法流程图,输出2000以内除以剩1的正整数。

8.某学生五门功课成绩为80、95、78、87、65。写出求平均成绩的算法,画出流程图。

9.假设超市购物标价不超过100时按九折付款,如标价超过100元,则超过部分按七折收费,写出超市收费的算法,并画出流程图。

10、写出求1×3×5×7×9×11的算法,并画出流程图。

11、《中华人民共和国个人所得税法》规定,公民月工资,薪金所得不超过800元的部分不必纳税,超过800元的部分为全月应纳税所得额,此项税款按下表分段累进

试写出工资x (x 5000 元)与税收 y的函数关系式,给出计算应纳税所得额的算法和流程图。

12、根椐下面的算法画出相应的流程图。

算法: S1 T 0 S2 I 2 S3 T T+I S4 I I+2 S5 如果I不大于200,转S3

S6 输出T,结束

13、一个三位数,各位数字互不相同,十位数字比个位,百位数字之和还要大,且十位、百位数字不是素数,设计算法,找出所有符合条件的三位数,要求画出流程图

14. 已知算法:①指出其功能(用算式表示)。②将该算法用流程图描述之。

S1、输入 X

S2 、若X<0,执行 S3. 否则执行S6

S3 、 Y X+1;

S4、输出 Y

S5、结束

S6、若X=0 ,执行S7;否则执行S10;

S7 Y 0

S8 输出Y

S9 结束

S10 Y X

S11 输出Y

S12 结束

15、下面流程图表示了一个什么样的算法?试用当型循环写出它的算法及流程图

参考答案;

A、组算法的含义

1、D

2、C 、

3、第二个算法更高效。因为节约时间。

4、①取n=100 ②计算2

)

1(+n n 5、①计算总分D=A+B+C ②计算平均成绩E=

3

D

6、解析: 鸡兔同笼,设鸡兔总头数为H ,总脚数为F ,求鸡兔各有多少只。算法如下: 第一步 输入总头数H ,总脚数F ; 第二步 计算鸡的个数 x=(4*H -F)/ 2

第三步 计算兔的个数 y=(F -2*H)/2; 第四步 输出 x y 7、解析; 可以运用公式

1

21

121x x x x y y y y --=--直接求解。 第一步 取;2,3,0,12211===-=y x y x 第二步 代入公式

1

21

121x x x x y y y y --=--得直线AB 的方程 第三步 输出AB 的方程 8、解析 算法1

1、 找一个大小与A 相同的空杯子C

2、 将A 中的水倒入C 中

3、 将B 中的酒精倒入A 中

4、 将C 中的水倒入B 中,结束。 算法2

1、 再找两个空杯子C 和D

2、 将A 中的水倒入C 中,将B 中的酒倒入D 中;

3、 将C 中的水倒入B 中,将D 中的酒倒入A 中,结束

注意: 一个算法往往具有代表性,能解决一类问题,如,例一可以 引申为:交换两个变量的值。

9、解析 按照逐一相乘的程序进行 第一步 计算1×2 ,得到2

第二步 将第一步中的运算的结果2与3相乘,得到6; 第三步 将第二步中的运算结果6与4相乘,得到24 第四步 将第三步中的运算结果24与5相乘,得到120; 第五步 将第四步中的运算结果120与6相乘,得到720 第六步 输出结果 10、解析 可利用公式

S=求解,))()((c p b p a p p --- 第一步 取;4,3,2===c b a 第二步 计算 2

c

b a p ++=

第三步 计算三角形的面积S=,))()((c p b p a p p --- 第四步 输出S 的值

B组流程图

1、A

2、 B

3、⑴△

a

b

x

2

2

?

-

-

←⑶输出

2

1

,x

x

4

5的算法。

6、解算法如下

S1 a 5

S2 b 8

S3 h 9

S4 S (a+b)×h/2;

S5 输出S

流程图如下

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