Teacher education 20 1 1-20 12 school year entrance examination for private schools.
Mathematics subject test paper
Total score: 120 minutes Time: 90 minutes
TestNo.: Name: Result:
I. Fill in the blanks (2 points for each question, 20 points for * * *)
1.() ÷15 = = 20: () = ()% = () (decimal)
There are 4 kilograms of oil in a barrel. If you pour the oil for the first time and then pour it for the second time, there are () kilograms of oil left in the barrel.
3. Make a cube model with a 36 cm long iron wire. If you enclose it with paper, you need at least () square centimeters of paper. The volume of this cube is () cubic centimeters. (Ignore the thickness of the paper)
4. If x and y are reciprocal and =, then 8a = ().
5. Tapered sand pile, with a bottom diameter of 4m and a height of 3m, covers an area of () m2 and a volume of () m3.
6. Water is composed of hydrogen and oxygen in the weight ratio of 1: 8, and 8 1 kg of water contains () kg of oxygen.
Class 7.6 (1) actually arrived at school yesterday, and 49 people 1 didn't come on leave. The attendance rate of this class was ()% yesterday.
8. Draw the largest semicircle in a rectangle with a length of 12 cm and a width of 8 cm, and the circumference of the semicircle is () cm.
9. Xiaohong's father works 8 days off 1 day, and her mother works 5 days off 1 day. On May 28th this year, mom and dad have a rest at the same time, so we will have a rest at the same time in () month next time.
10. The picture on the right consists of two squares with sides a and b respectively. The area () of the shaded part in the figure is expressed by the letter formula.
Second, the judgment (65438+ 0 points for each question, ***5 points)
1. The circumference is fixed, and the diameter is proportional to pi. ( )
2. As the volume of water ice increases, the volume of water ice decreases. ( )
3.6 When people meet each other, they shake hands once and shake hands 12 times. ( )
4.A is more than B, so the ratio of A to B is 5: 4. ( )
5. The radius of the cone bottom surface is doubled, the height is reduced to the original, and the volume of the cone remains unchanged. ( )
Three. Selection (65438+ 0 point for each question, ***5 points)
1. Among the following four formulas, the biggest result is ().
a、a× B、a× C、a
2. Fill a conical container with 24cm high with water, and pour all the water into a cylindrical container with equal bottom. The height of water is ().
A, 72cm b, 24cm c,16cm d, 8cm
3. On the map with the scale of 1: 3000000, the distance from A to B is measured to be 5.6 cm. A car will complete the journey in two days according to the ratio of 3: 2, and the distance difference between the two days is () kilometers.
a、672 B、 1008 C、336 D、 1680
4. A bag of 50 balls, 1, 2,3,4,5 each 10. Take out at least () balls at a time and ensure that at least 4 balls have the same number.
a、6 B、 1 1 C、 16 D、2 1
With the increasingly fierce competition in the communication market, the local telephone tariff of a communication company is reduced by one yuan per minute according to the original standard, and then reduced by 25% again. The current charging standard is B yuan per minute, while the original charging standard is () yuan per minute.
a、b-a B、b+a C、b+aD、B+a
Four, calculation (***30 points)
1. Solve the equation (3 points for each question, ***6 points)
( 1)0.4:0.25 =(2)60% X+X-0.2 = 1
2. Simply calculate the following questions (4 points for each question).
( 1)4+3-5+ 1+ 1 (2)2008×
(3)2-÷- (4)0.25× 1.25×320
(5)0.6×47+52×+0.6 (6)9.75+99.75+999.75+9999.75
Five, solve the problem (5 points per question, ***40 points)
1. Dongfeng primary school teachers and students donated 3450 yuan for the disabled, including teachers' donation of 1050 yuan, and the proportion of donations for junior, middle and senior grades was 3:4:5. How much did the seniors donate?
There are 360 workers in one workshop, including women workers. Later, a group of women workers were recruited. At this time, the proportion of female workers to the total number of workshop workers, how many female workers were recruited?
A cylindrical glass is filled with water, and the water level is 15cm. Measured from the inside, the bottom area of the glass is 50 cm. A cuboid iron block with a bottom area of 10cm and a height of 17cm is vertically placed in the glass. How high is it at the moment? (Water will not overflow)
On the map with the scale of 1: 2500000, Peng Liang measured the distance between the two cities as 8 cm. How many centimeters should he draw on the map with the scale of 1: 8000000?
Bind the same exercise book with a batch of paper. If each book has 30 pages, you can bind 80 books. If the number of pages per page is reduced by 20%, how many copies can this batch of paper be bound? (Use proportional solution)
6. Grade 5 and Grade 6 ***3 10 people participated in the competition. If it is known that the number of participants in grade six and grade five is equal, how many people will participate in the competition in grade five and grade six respectively?
7. A batch of fruit weighed 9000 kilograms when it was sent from the place of origin, and the water content of this fruit was 99%. When they were transported to the local market, the water content dropped to 98.5% due to water evaporation. How much does this batch of fruit weigh at this time?
8. Cut a rectangular piece of iron sheet according to the following figure, which can be made into an iron sheet oil drum, and find the surface area of the iron sheet oil drum. (Unit: decimeter)
Six, additional questions (20 points)
A brand of toothpaste, after market research, found that: under normal circumstances, every time people brush their teeth, it is about squeezing.
1cm long paste, so that a toothpaste can be used for 36 times. In order to increase the sales of toothpaste, it is suggested to change the outlet diameter from 5 mm to 6 mm.
How many times can a toothpaste be used after improvement? (assuming that people are still extruded once 1cm long)
According to this calculation, if each person brushes his teeth twice a day, how many pieces of improved toothpaste will one person use a year (calculated by 360 days)? (Numbers are reserved as integers)
Suppose a city has 50,000 regular customers who use this brand of toothpaste. The retail price of toothpaste is 2.5 yuan, and the cost is 1.2 yuan. After the improvement, the annual profit increased by several percentage points.