Mathematics subject examination includes multiple-choice questions, true or false questions, fill-in-the-blank questions and solution questions.

The knowledge content of the test paper is as follows: number and algebra are about 75 points, space and graphics are about 15 points, and statistics and probability are about 10 points;

The distribution of test paper difficulty is: easy test is about 60 points, senior high school entrance examination is about 25 points, and difficult test is about 15 points.

The following analysis is only for students' reference when reviewing, and the graduation thesis shall prevail.

There is no answer to this question, for reference only.

First, fill in the blanks. (Mandatory and easy to test)

1, approximate value, rewrite the unit with "10,000" and "100 million" or omit the mantissa or "rounding" after "10,000" and "100 million" and the composition of numbers (there must be one).

Typical problem

(0) Write 70.304 million (), rewrite the number () with "ten thousand" as the unit, and the mantissa after omitting "ten thousand" is ().

(1) The number composed of five 1,161100 is ().

(2) According to the results of the fifth national census, the total population of the whole country is1295.33 million, which is recorded as (), rounded to several hundred million or so ().

(3)0.375 is pronounced as (), and its counting unit is ().

(4) The investment of Fuhe Bridge is about 362.5 million yuan, and the figure is rewritten as "100 million" which is () billion.

(5) Compared with the divisor of 50,000, the exact number of 50,000 is at most different in ten thousand ().

(6) The decimal consisting of three hundred, six ones, seven tenths and eight ten thousandths is (), and the two decimal places are about ().

It is possible to find a rule.

Typical problem

Pattern found: 1, 3, 2, 6, 4, (), (), 12, ...

3. Median, mode or average (required)

Typical problem

(1) The weight of students in Class 6 (3) is as follows.

Weight/kg

30

33

36

39

Forty two.

45

48

number of people

2

four

five

12

10

four

three

In the above data set, the average is (), the median is (), and the mode is ().

(2) The average of the three even numbers A, B and C is 16, and the ratio of the three numbers is 3: 4: 5. The three even numbers of A, B and C are (), () and () respectively.

(3) There are three numbers, the average of A and B is 28.5, the average of B and C is 32, and the average of A and C is 2 1, so A is ().

4. You can test negative numbers and positive numbers.

Typical problem

Of the seven numbers (1) 0,0.9,1,-1, 4, 103 and -320, () is a natural number and () is an integer.

(2) The average temperature on the surface of the moon during the day is above zero 126 degrees Celsius, which is recorded as () degrees Celsius, and the average temperature at night is below zero 150 degrees Celsius, which is recorded as () degrees Celsius.

5. Countdown test is possible.

Typical problem

(1) The smallest prime whose reciprocal is ().

The reciprocal of 265/7 is (),

The reciprocal of () is the smallest prime number.

6, the simplest ratio and testable ratio

Typical problem

The simplest integer ratio of (1)3/4 to 0. 125 is (), and the ratio is ().

(2) The diameter of the small circle and the radius of the big circle are both 4cm, the simplest integer ratio of the circumference of the big circle to the circumference of the small circle is (), and the simplest integer ratio of the area is ().

7. Factor multiples must be tested (focusing on prime number, composite number, even number, odd number, prime number, greatest common factor and least common multiple).

Typical problem

(1)5 162 needs at least () to be divisible by 3.

(2) The least common multiple of two prime numbers is 390. If both numbers are composite numbers, they are () and () respectively.

(3) Both numbers are composite numbers and prime numbers, and their least common multiple is 120, which are () and () respectively.

(4) 145□ so that it can be divisible by 3, and the number () is filled in □.

(5) The product of three prime numbers is 273, and the sum of these three prime numbers is ().

(6) Among the natural numbers 1 ~ 30, the number () is neither a multiple of 3 nor a multiple of 4.

(7) In the number 1, 2, 4, 9, 1 1 6, there are () in odd numbers, () in even numbers, () in prime numbers and () in composite numbers. The number that is both odd and composite is (), which is both even and even.

(8) The greatest common factor of 24 and 30 is (), and the smallest common multiple is ().

(9) If A and B are prime numbers, the greatest common factor of A and B is () and the smallest common multiple is ().

The integer part of (10) fraction is a number that is neither prime nor composite among natural numbers, the numerator of the fraction is prime in even numbers, and the denominator is composite in odd numbers within 10. This number is ().

(1 1)8752 needs at least () to be divisible by 2, 3 and 5.

8, quantity and measurement (mutual) required questions.

Typical problem

(1) 2.5m = () cm1080kg = () tons 4800ml = () liters = () cubic decimeter.

(2)3.6 kg = () g 5 km 90 m = () km

(3)6 tons = 500 kg () kg

(4)4.3 hours = () hours () minutes

(5) When 45 points = ()

1.05 cubic decimeter = () ml

9, number (decimal, fraction) comparison size.

Typical problem

Among the numbers 1/6, 4 /25, 16 and 16.7%, () is the smallest.

10, the reciprocity of fraction, decimal, percentage and ratio must be tested.

Typical problem

( 1)()÷32= 15/( )=0.625=()%=():().

(2)12.5% = 2/() =1:() = 3 ÷ () = () decimal.

1 1, the nature of triangle, trilateral relationship, perimeter and area calculation may be tested together.

(triangle key test: 1. Triangles with equal bases and equal heights have equal areas; 2. Equal bottom, high multiple, area multiple or high, bottom multiple, area multiple; 3. When the bases of two triangles are equal, the sum of their areas is equal to the base times the sum of their heights divided by 2; When two triangles are equal in height, the sum of their areas is equal to the sum of the height times the bottom divided by 2. )

Typical problem

(1) The lengths of the three sides of a right triangle are 5cm, 4cm and 3cm respectively, and its area is ().

(2) As shown in the figure, ABFE and CDEF are both rectangles, AB is 6 cm, BC is 4 cm, so the area of the shaded part on the figure is ().

(3) In the triangle, the degrees of the three angles are 45 degrees, 44 degrees and 9 1 degree respectively, which is a triangle.

12, graphic counting is required.

Typical problem

* * in the (1) graph has a () triangle.

(2) A fixed point in acute AOB emits five rays (as shown in the figure), and there are () angles in the figure.

13, chickens and rabbits in the same cage must be measured.

Typical problem

(1) In an environmental knowledge contest, if you answer a question correctly according to regulations, add 10, and if you answer a question incorrectly, deduct 6 points. A player answered 16 in a hurry, and finally got 16. He answered the question correctly ().

(2) There are 28 spiders and dragonflies, each spider has 8 legs, each dragonfly has 6 legs, * * has 194 legs, and spiders have ().

14. Calculation of circle

Typical problem

(1) If the radius of a small circle is half the radius of a big circle, then the area of the small circle is ()% of the area of the big circle.

(2) After welding three sections of round steel with a cross-sectional radius of 2cm into one section, its surface area is reduced by () cm2.

(3) If the circumference of a circle is 2πr, then the circumference of the semi-circle of this circle is ().

15. scale. You must take the exam.

Typical problem

(1) The scale of the numbers in the picture is 1: 4000000. With linear scale, 1 cm is equivalent to the actual distance () km.

(2) On the plan with the scale of 5: 1, the length of a part is measured as 15cm, and the actual length of the part is () mm ... (WeChat official account: Ark Jingbo Liu).

16. Cut the figure.

Typical problem

16, a piece of iron sheet with a length of 1.20 cm and a width of 90 cm, cut into a disc with a diameter of 30 cm, and can be cut into at most () pieces.

17. Thoughts on equations.

Typical problem

The company plans to charter a bus to send foreign employees home for the New Year. The charter fee is fixed. According to the statistics of the number of foreign employees, each person needs to pay 15 yuan. Later, I learned that six people didn't go, and everyone had to pay 3 yuan more, and the charter fare was () yuan.

18. On the principle of double average score

Typical problem

Xiao Ming, Xiao Jun and Xiao Honghua bought some apples with the same money. Xiao Ming and Xiao Jun each got 6 extra points, and Xiaohong got 14 yuan. RMB () per kilogram of apples.

19. The pigeon coop principle must be tested.

Typical problem

(1) A deck of playing cards has four suits (except king size), and each suit has 13 cards. You can randomly draw at least () cards to ensure that the four cards are of the same suit.