小升初英语奥数题

小升初英语奥数题
小升初英语奥数题

英语数学题

Part Ⅰ: Questions 1 to 10, 10 marks each

1. At the right is shown a 4 × 4 grid. We wish to fill in the grid such that each row, each

column, and each 2 × 2 square outlined by the thick lines contains the digits 1 through 4. Some grids have already been filled in. Find the number of ways we can complete the rest of the grid. Answer :

2. The areas of the faces of a cuboid are 84 cm 2, 70 cm 2 and 30 cm 2. Find the volume of

the cuboid in cm 3.

Answer : 3. The fraction

3

3

313311331

13333

++

++++++can be wrritten in the form

n

m

where the greatest common divisor of m and n is 1, Find m +n . Answer :

4. Find the sum of all the integers N > 1 with the properties that the each prime factor of N is

either 2, 3, 5 or 7, and N is not divisible by any perfect cube greater than 1. Answer :

5. A large fresh water reservoir has two types of drainage system, small pipes and large pipes. 6

large pipes, on their own, can drain the reservoir in 12 hours. 3 large pipes and 9 small pipes, at the same time, can drain the reservoir in 8 hours. How long will 5 small pipes, on their own, take to drain the reservoir?

Answer : minutes

6. At a local village gala, the entire population turned up, 500 people. The event raised £3,000.

Tickets were priced as follows: £7.48 per man, £7.12 per woman and £0.45 per child. How many children were there?

Answer :

7. Each of the distinct letters in the following addition problem represents a different

digit. If A=4, f ind the number represented by the word “MEET”. Answer :

8. Let two 8×12 rectangles share a common corner and overlap. The distance

A T M E

R E C L O U E P E T A A A A A P M

+

from the bottom right corner of one rectangle to the intersection point along the right edge of that rectangle is 7. What is the area of the shaded region? Answer :

9. A spy had to send the 4-digit code abcd to headquarters. For security reasons, he sent

instead the 9 separate 4-digit codes shown. In each of the 9 codes, at least one of the digits a , b , c , and d occurs in its correct position. What is the value of abcd ? Answer :

10. In how many ways can one arrange the numbers 21, 31, 41, 51, 61, 71 and 81 such that

the sum of every four consecutive numbers is divisible by 3? Answer :

Part Ⅱ: Questions 11 to 14, 20 marks each

11. Town A and town B are connected by a highway, with a service station at the midpoint. Mike

and Sam start from A to B at the same time. When Mike reaches the service station, Sam is 16 km behind. Mike reduces speed by 25% after he passes through the service station. When Sam reaches the service station, Mike is 15 km ahead of Sam. What ’s the distance between A and B ?

Answer :

12. Given: ABCD is a trapezoid, AD ∥BC , AD :BC =1:2, :1:3AOF DOE S S ??=,

224cm BEF S ?=, Find the area of AOF ?.

Answer :

13. In how many different ways can the seven empty circles in the diagram on

the right be filled in with the numbers 2 through 8 such that each number is used once, and each number is either greater than both its neighbors, or less than both its neighbors.

Answer :

14. How many rectangles are there in the diagram on the right such that the sum of the

numbers within the rectangle is a multiple of 4? Answer :

C

B 1 2 3 4 5 6 7 8 10 14

11

15 12

9 16

13

15.What is the sum of the digits of the following product 9999×6666 ? Answer: ________

16. A digit is placed in each empty square in the grid to the right so that each row contains each of the digits 1, 2, 3, 4, 5 and each column (纵队)contains each of the digits 1, 2, 3, 4, 5. What digit is placed in the square at the bottom right corner of the grid?

Answer: ________

17. If you continue the given number pattern, in what row will the number 2009 be? 7 -------------- row 1 14 21 -------------- row 2 28 35 42 -------------- row 3 49 56 63 70 -------------- row 4 Answer: ________

18. Dave can answer each problem on a certain test in 6 minutes. Michael can answer each problem in 1 minute. Suppose Michael rests for two hours in the middle of answering the problems but Dave works straight through the test without stopping. Suppose further that they finish the test at the same time. How long did it take Dave to answer all the problems? Answer: ________ minutes

19. There are eight different 2-digit numbers AD , BA , BG , CE , DB , DH , EF and FC . They are less than 70 and all divisible by 7. Each of the distinct letters represents a different digit. The same letter represents the same digit. Given E =5, what is G ? Answer: ________

20. There are 7 identical circles in the figure and each area is 10. Find the area of shaded region. Answer: ________

21. In a certain class consisting of 54 students, some boys and some girls, exactly 4

7

of the boys and exactly

3

5

of girls walk to school. What is the greatest possible number of students in this class who walk to school? Answer: ________

22. Each of the distinct letters in the following addition problem represents a different

digit. If A=4, find the number represe nted by the word “MEET”.

Answer: ________

23. In how many ways can one arrange the numbers 21, 31, 41, 51, 61, 71 and 81 such that the

A T M E R E C L O U E P E T A A A A A P M

+

sum of every four consecutive numbers is divisible by 3? Answer: ________

24. Balls of the same size and weight are placed in a container. There are red, yellow and blue 3 different colors and 15 balls in each color. If we want to get X red balls, Y yellow balls and Z blue balls from the container, with 133X Y X Z Y ≥-≥-≥,,, then find the number of all possible ways.

Answer: ________

25. Town A and town B are connected by a highway, with a service station at the midpoint. Mike and Sam start from A to B at the same time. When Mike reaches the service station, Sam is 16 km behind. Mike reduces speed by 1

5

after he passes through the service station, and Sam increases speed by

1

4

after he passes through the service station. Finally, they arrive at B at the same time. What ’s the distance between A and B ? Answer: ________

26. Given: ABCD is a trapezoid, AD ∥BC , AD :BC =1:2, :1:3AOF DOE S S ??=, 2

24cm BEF S ?=, Find the area of AOF ??

Answer: ________

27. (1)How many rectangles are there in the diagram on the right such that the sum of the numbers within the rectangle is a multiple of 2?

Answer: ________(请将答案填在答题纸第13题的位置处)

(2) How many rectangles are there in the diagram on the right such that the sum of the numbers within the rectangle is a multiple of 4?

Answer: ________(请将答案填在答题纸第14题的位置处)

C

B 1 2 3 4 5 6 7 8 10 14

11

15 12

9 16

13

小升初常见奥数题简便运算

小升初常见奥数题 简便运算 知识储备: 1. 常见整数的拆解 AAAAA=A ⅹ11111 A0A0A0A0A=A ⅹ1 ABABABABAB=AB ⅹ1 ABCABCABC=ABC ⅹ1001001 =1111111ⅹ1111111 2. 常见公式 1n(n+1) =1n - 1n+1 如:120 =14 - 15 1n(n+k) =( 1n - 1n+k )ⅹ1k 如:124 =( 14 - 16 )ⅹ12 121 =( 13 - 17 )ⅹ14 a+b a ⅹb = a a ⅹb + b a ⅹb = 1b + 1a (a ,b 不等于0) 即:a+b a ⅹb = 1a + 1b 如:1128 = 14 + 17 1663 = 17 + 19 3. 字母代替法 在多个代数式运算时,可以设最短的算式为a ,次短的算式为b 典型考题: 3333333ⅹ5555555 分析 =1111111ⅹ1111111,所以约分后= 13ⅹ5 = 115

121 + 2022121 + 50505212121 + = 121 + 2ⅹ10121ⅹ101 + 5ⅹ1010121ⅹ10101 + 13ⅹ101010121ⅹ1010101 = 121 + 221 + 521 + 1321 = 1 ( 17 + 111 + 113 + 117 )ⅹ( 1+17 + 111 + 113 ) –( 1+ 17 + 111 + 113 + 117 )ⅹ( 17 + 111 + 113 ) 解:设 17 + 111 + 113 = m ,17 + 111 + 113 + 117 = n ,所以 原式= n ⅹ(1 + m )- (1 + n )ⅹ m =n + mn - m – mn =n – m =17 + 111 + 113 + 117 - ( 17 + 111 + 113 ) =117 11ⅹ2 + 12ⅹ3 + 13ⅹ4 + 14ⅹ5 + …… + 12017ⅹ2018 = (1- 12 )+ ( 12 - 13 )+ ( 13 - 14 )+ …… +( 12017 - 12018 ) = 1- 12018

外国语学校小升初入学考试中英文奥数试题库

外国语学校小升初入学考试中英文奥数试题库 Document number:PBGCG-0857-BTDO-0089-PTT1998

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小升初英语单词必须掌握的词汇 1、颜色(colour): 四会: red blue yellow orange green pink black white 红色蓝色黄色橙色绿色粉红色黑色白色 三会: brown grey purple 棕色灰色紫色 2、动物(animal): 四会: cat dog monkey panda rabbit duck pig bird 猫狗猴熊猫兔子鸭子猪鸟 mouse tiger lion snake cow hen bear 老鼠老虎狮子蛇牛母鸡熊 三会: elephant dragon giraffe zebra sheep goat 大象龙长颈鹿斑马绵羊山羊 3、食物(food): 四会: rice meat fish soup cake bread hot—dog Coke tofu 米饭肉鱼汤蛋糕面包热狗可乐豆腐 juice milk water tea cheese egg sweets potato tomato 橙汁牛奶水茶奶酪鸡蛋糖果土豆西红柿三会: hamburger chicken French fries coffee noodles peanut 汉堡包鸡肉炸薯条咖啡面条花生 ice—cream biscuits chocolate 冰淇淋饼干巧克力 4、水果(fruit): 四会: apple banana pear peach orange grape 苹果香蕉梨桃橙子葡萄 三会: strawberry pineapple watermelon mango 草莓菠萝西瓜芒果 5、衣服(clothes): 四会: clothing T—shirt shirt coat hat cap sock sweater

PEP人教版2020年小升初英语模拟检测卷 (含答案)

2020年小升初英语模拟试卷 一、听录音,选择与你所听到的内容 1.听录音,根据问题选择最合适的答句() A. Yes, she is. B. Yes, it is. 2.听录音,选择你所听到的句子() A. Hello! I'm Alice. B. I like singing. C. What about you? 3.听录音,选择合适的答语() A. There is a bed and a desk. B. There is a living room. C. It's beside the plant. 4.听录音,选择你所听到的句子() A. It's got a famous lake in the south. B. It's got a beautiful lake in the south of China. C. It's got a tall mountain in the south. 5.听句子,选择句子含有的信息() A. 283yuan B. 145 yuan C. 582 yuan 6.听录音,根据录音内容把物体放到正确的位置上。 A. B. C. D. E. (1)________ (2)________ 7.听录音,根据所听到的问题,选出最佳答语() A. It's in the desk. B. It's a Chinese book. 8.听录音,选择你所听到的对话

A. —What colour is that robot, Mum? —It's black and blue. B. —What colour is that plane, Mum? —It's brown and blue. 9.What's Mary's favourite festival? A. The Spring Festival. B. The Lantern Festival. C. The Dragon Boat Festival. 10.Is he riding a bike? A. No. He is reading a book. B. No, he isn't. C. Yes, he is. 11.What does Kitty need? A. Some brushes. B. Some glue. C. A pair of scissors. 12. 13.听句子,选择句子中含有的信息() A. jump high B. jump far C. run fast 14. 15. 16. 17.听录音,匹配 ⑴Tom________ A. ⑵John________ B.

小升初常见奥数题集锦(一)

小升初常见奥数题集锦 简便运算 知识储备: 1. 常见整数的拆解 AAAAA=A ⅹ11111 A0A0A0A0A=A ⅹ101010101 ABABABABAB=AB ⅹ101010101 ABCABCABC=ABC ⅹ1001001 1234567654321=1111111ⅹ1111111 2. 常见公式 1n(n+1)=1n - 1n+1如:120=14 - 15 1n(n+k)=( 1n - 1n+k )ⅹ1k 如:124=( 14- 16)ⅹ12 121=( 13- 17)ⅹ14 a+b a ⅹb = a a ⅹb + b a ⅹb = 1b + 1a (a ,b 不等于0) 即:a+b a ⅹb = 1a + 1b 如:1128= 14+ 171663= 17+ 19 3. 字母代替法 在多个代数式运算时,可以设最短的算式为a ,次短的算式为b 典型考题: 12345676543213333333ⅹ5555555 分析 1234567654321=1111111ⅹ1111111,所以约分后= 13ⅹ5= 115

121+ 2022121+ 50505212121+ 1313131321212121 = 121+ 2ⅹ10121ⅹ101+ 5ⅹ1010121ⅹ10101+ 13ⅹ101010121ⅹ1010101 = 121+ 221+ 521+ 1321 = 1 (17+ 111+ 113+ 117)ⅹ( 1+17+ 111+ 113) –( 1+ 17+ 111+ 113+ 117)ⅹ( 17+ 111+ 113 ) 解:设 17 + 111 + 113 = m ,17 + 111 + 113 + 117 = n ,所以 原式= n ⅹ(1 + m )- (1 + n )ⅹ m =n + mn - m –mn =n – m =17 + 111 + 113 + 117 - ( 17+ 111+ 113 ) =117 11ⅹ2 + 12ⅹ3 + 13ⅹ4 + 14ⅹ5 + …… + 12017ⅹ2018 = (1- 12 )+ ( 12 - 13 )+ ( 13 - 14 )+ …… +( 12017 - 12018 ) = 1- 12018 = 20172018

2018年小升初:小学英语复习资料汇总大全

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