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Answers and analysis of the first grade mathematics test
1
...
The number of sides of this polygon is ( )
A
...
10
【Answer】 A
【Analysis】 Omitted
2
...
It is known that straight line a , b is intercepted by
straight line c , and a ∥ b , ∠1＝48°, then the degree of ∠2 is ( )
A
...
48°
C
...
132°
[Answer] B
[Analysis] Omitted
3
...
As a result, each piece of clothing still made a profit
of 15 yuan
...
120 yuan;
B
...
135 yuan;
D．140 yuan
...
Solve the inequality system or equation
(1)
[Answer] (1)
(2)
(2)
[Analysis] Omitted
5
...
Prove: (1) △ABC≌△DEF; (2) GF＝GC
...
The mascot of the 2010 Guangzhou Asian Games is named "Happy Sheep"
...
There is 1 sheep in the picture,
3 sheep in the picture, and so on
...
A
...
56
【Answer】 C
【Analysis】 Omitted
7
...
-3
B
...
D
...
Given point A (4, 3), AB∥y axis, and AB=3, then the coordinates of point B
are
．
【Answer】 (4,0) or (4,6)
...
According to the
distance of AB, we can get the vertical coordinate of point B
...
【Test point】 The coordinates of point
...
In order to understand the physical test results of ninth grade students, a school
took the physical test scores of ninth grade (1) students as samples, and
statistically analyzed them according to four levels: A, B, C, and D
...
Please answer the following
questions based on the information given in the chart:
(Explanation: Grade A: 90 to 100 points; Grade B: 75 to 89 points; Grade C: 60
to 74 points; Grade D: less than 60 points)
(1) How many students in the ninth grade (1) class took the physical test?
;
(2) Please complete the bar chart; (3) The central angle of the sector where level A
is located in the pie chart is
;
(4) If there are 500 students in the ninth grade of the school, please use this
sample to estimate the number of students in grades A and B in the physical
education test
...
(2) See the analysis for the supplementary graph
...
[Analysis] (1) Calculate by dividing the number of students in grade A by the
corresponding percentage
...
(3) Multiply the percentage of students in grade D by 360° to find the
answer
...
Question analysis: (1) The number of students in the PE test of Grade 9 (1)
class is 10÷20%=50 (people), (2) The number of students in Grade D is 50×(146%-24%-20%)=5 (people) Complete the statistical chart,
(3) The central angle of the sector where Grade A is located in the pie chart is
360°×20%=72°,
(4) The number of students in Grade A and Grade B in the PE test is
500×((46%+20%))=330 (people)
...
[Test points] 1
...
Using a sample to estimate a population; 3
...
10
...
【Test point】 Calculation of rational numbers
...
The figure below is a calendar table for a certain month
...
Also, ∵
, ∴8≤x≤23, ∴24≤3x≤69
...
【Test points】 1
...
Algebraic expressions
...
(This question is 4 points) There is a question like this: " At that time , find
the value of the polynomial
...
Is her statement reasonable? Why?
[Answer] -3
[Analysis] According to the rule of removing brackets and combining the rule of
like terms, simplify the integer, and then we can judge
...
The taxi fare standards in China vary from place to place
...
5 yuan; City B is: the starting price is 10 yuan, and the price per
kilometer after 3 kilometers is 1
...
(1) What is the difference in the price of taking a taxi for s (s>3) kilometers in City
A and City B? (2) If the distance of taking a taxi in City A and City B is 10
kilometers, which city has a higher fare standard? How much higher?
[Answer] (1) (0
...
9) yuan; (2) The taxi fare in City B is higher, 1
...
[Analysis] (1) According to the taxi fare: starting price + fee for the distance
beyond the starting point, you can list the algebraic formula;
(2) Substitute the result into the formula in (1) to find the answer
...
5
(s-3)] yuan; the price of taking a taxi for s (s>3) kilometers in City B is: [10+1
...
Therefore, the price difference of taking a taxi for s (s＞3) kilometers
in the two cities is: [6+1
...
2 (s-3)]=(0
...
9) yuan; (2) Taxi fare in
City A: when x=10, 6+1
...
5=16
...
2 (s-3)=10+7×1
...
4 (yuan), 18
...
5=1
...
Answer: The
taxi fare in City B is higher, 1
...
[Test points] 1
...
Evaluate the algebraic expression
...
(2014 Spring • Laizhou City Midterm) The image of the light emitted by the
flashlight is ( )
A
...
Rays
C
...
Broken line
【Answer】 B
【Analysis】 According to the figure formed by a point on a straight line and the
part beside it, it is called a ray, which can be infinitely extended in one direction
...
Therefore, the answer is B
...
15
...
The selling price is 270 yuan
...
[Answer] 250
[Analysis] According to the question, the price is x×(1+20%), and then according to
the relationship: price×9% off=270, the equation can be: (1+20%)x×0
...
[Test point] Linear equation of one variable
16
...
[Answer] 1
...
[Test points] 1
...
Find the value of the algebraic expression
17
...
5
C．﹣5
D．6
【Answer】 D
【Analysis】 Since the input value of x is known to be -5, we can get y=-x+1 from
the diagram
...
Solution: Given x=-5＜0, y=-x+1=-(-5)+1=6
...
【Test Point】 Evaluate algebraic expressions
...
The solution of the equation 3x-1=x is
．
【Answer】 x=
【Analysis】 Transfer the idea, combine like terms, reduce the coefficient to 1, and
find the value of x
...
19
...
101001,
numbers is ( )
,
, -π, the number of irrational
A
...
3
C．4
D
...
Comment: This is an irrational number question
...
20
...
15
B
...
D
...
[Test point] Definition of opposite numbers
21
...
If B works alone for 22 days, and A completes the rest
...
C
...
【Answer】 A
【Analysis】 According to the question, ① the work efficiency of A and B is
respectively
; ② the total amount of work completed by A + the total
amount of work completed by B = 1 (total amount of work = work efficiency ╳
working time); ③ In the question, it is assumed that A and B took x days to
complete the work, so A took (x-22) days; Based on the above three points, an
equation can be written
, that is
; so
A is the correct answer
...
Given a ﹣ b = 1, then the value of
a ﹣ b ﹣2 b is ___ 【Answer】 1
2
2
【Analysis】 Analysis: This question tests the use of whole substitution to find the
value of the integer
...
23
...
Guess what is the quantitative relationship between ∠DPC and α, β? And explain
the reason;
[Question migration] As shown in Figure 2, DF∥CE, point P slides on the edge AB
of the triangle, ∠PCE=∠α, ∠PDF=∠β
...
(2) If point P moves outside points E and F (point P does not coincide with points
A, B, E, and F), write the quantitative relationship between ∠DPC and α and β,
and explain the reason
...
[Analysis] (1) Draw PE∥AD through P and intersect CD at E, and deduce that
AD∥PE∥BC
...
【Problem Exploration】Solution: ∠DPC=α+β As shown in the figure,
draw PH ∥ DF
through P
...
∴∠ DPC = "β" -α
As shown in Figure 2, ∠ DPC = α - β
∵ DF ∥ CE,
∴∠ PDF =∠1="α"
∵∠ DPC =∠1-∠ACE=∠1-β．
∴∠ DPC = "α" - β
24
...
A said: "It seems that the conditions of this question are not enough, and it cannot
be solved"; B said: "Their coefficients have a certain pattern, you can try"; C said:
"Can we divide both sides of the two equations of the second system of equations
by 4 and solve it by substitution?" Please find the solution of the second system of
equations based on their discussion
...
Question analysis: Divide both sides of the two equations in the second system by 4
to get:
∴
The answer is:
...
The key to solving the problem is to use the method of variable
substitution to solve it
...
As shown in the figure, in △ABC, points D, E, and F are the midpoints of BC,
AD, and EC respectively
...
4 B
...
8 D
...
∴
Therefore, choose A
...
Calculation:
[Answer] -2
[Analysis] According to the operation rules of rational numbers, the operation can
be performed in sequence
...
Given Ax
[Answer] x
n+1
=x
2n+1
=-2
...
n
[Analysis] According to the division of powers with the same base, the base
remains unchanged, and the exponents are subtracted, we can get A=x
n
2n+1
÷x
n+1 =
x
...
The counting sticks in "Nine Chapters on the Mathematical Art" are arranged
vertically
...
The number of counting sticks listed from left
to right in each row in the figure represents the coefficients of the unknown
numbers x and y and the corresponding constant terms
...
We can express it as ()
Figure 1 Figure 2
A．
B
...
D
...
Therefore, A is the correct answer
...
Which of the following events is a necessary event? ( )
A
...
B
...
C
...
Among the thirteen Chinese students, there must be one with the same Chinese
zodiac sign
...
30
...
Then how many people
are there at most?
A
...
12
C
...
14
【Answer】 C
【Analysis】 Solution: According to the question, suppose there are n people, and
the number of apples is 1, 2,
...
1+2+3+
...
So choose C
...
100 apples are divided into several
people with a common difference of 1
...
31
...
A
...
2
C
...
① If ∠B=∠B′ is added, prove: In △ABC
and △A′B′C′,
∴△ABC≌△A′B′C′ (ASA); ② If ∠C=∠C′ is added, prove: In △ABC and △A′B′C′,
∴△ABC≌△A′B′C′ (AAS); ③ If AC=A′C′ is added, prove: In △ABC and △A′B′C′,
∴△ABC≌△A′B′C′ (SAS)
...
32
...
If " ASA " is used to explain △ ABE ≌△
ACD , the additional condition is ________; if " AAS " is used to explain △ ABE ≌△
ACD , the additional condition is ________
...
Therefore, the answer is: (1)
...
∠AEB=∠ADC
...
The product of
a polynomial and is
, then this
polynomial is
...
It mainly tests students' mastery
of polynomial calculation knowledge points in polynomial operation
...
34
...
35
...
65°
B
...
85°
D
...
Then
add or subtract the angles to get the answer
...
A combination of
45° and 30° is enough
...
Comments: This question
mainly tests the use of triangles to draw special angles directly
...
36
...
15
...
15
...
15
...
15
...
6÷60）°=15
...
2
8
means ( )
A
...
8+8
C
...
D
...
If ∠α and ∠β are adjacent supplementary angles, and ∠α>∠β, then the
complementary angle of ∠β is ( )
A
...
C
...
Unsure
∠α
[Answer] C
[Analysis] Because ∠α and ∠β are adjacent supplementary angles, ∠α+∠β=180°,
(∠α+∠β)=90°
...
39
...
A
...
2
C
...
4
【Answer】 B
【Analysis】 ① Wrong, for example
, the sign changes; ③ Wrong, for
example, 0×0, the product is 0; ②④ Correct
...
(2014 Fujian Fuzhou) If
, then the value of m+n is ( )
A
...
1
D
...
41
...
If each box is 25 kg, 40 kg
cannot be packed; if each box is 30 kg, except for the remaining 20 empty boxes,
the rest of the boxes are full
...
2760 kg
B
...
112 kg
D
...
According to the question,
the solution is
42
...
10
years later, Xiao Ming's mother's age was 2 times that of Xiao Ming
...
[Answer] 15 years old, 40 years old
[Analysis] Let Xiao Ming's mother's current age be x years old, and Xiao Ming's
current age be y years old
...
As shown in the figure, straight lines AB and CD intersect EF at G and M
respectively , and straight lines GH and MN intersect AB and CD at G and M
respectively
...
The correct conclusions are ( )
A
...
3
C
...
1
【Answer】 B
【Analysis】 The two sides of a pair of angles in ② have no relationship, so there is
no relationship
...
44
...
20×10
5
obtained by rounding , which of the following statements is correct? ( )
A
...
There are six significant figures, accurate to the unit place
C
...
There are three significant figures, accurate to thousands
【Answer】 D
【Analysis】 In the standard form a×10 , there are three significant figures in the
n
a part, starting from the first non-zero digit on the left, which are 1, 2, and 0,
and after expanding, it can be seen that it is accurate to the thousandth place
...
20×10
5
has three significant figures, which are 1, 2, and 0, accurate
to the thousandth place
...
Comments: This question tests the expression
method of scientific notation and the method of determining the significant figures
of numbers expressed in scientific notation
...
If x=1 is the root of the equation 2x-3n+4=0, then the value of n is ( )
A
...
﹣2
C
...
-
【Answer】 A
【Analysis】 According to the definition of the solution of an equation, substituting
the solution of the equation into the equation gives a linear equation with a
coefficient of n
...
Solution: Substituting x=1 into the equation 2x-3n+4=0 gives 2-3n+4=0, and
solving it gives n=2
...
46
...
Integer
B
...
Irrational
numbers
D
...
Solution: According to the one-to-one correspondence between real numbers and
points on the number axis, we can conclude that
...
Calculate: (x
A
...
x 4n
2
n
) ﹣1 The result is ( )
C．x
﹣1
4n
D
...
Solution: (x
n+1
)
2
• (x
2
n
) -1 = x
2n+2
•x
2n
-2 = x
4n
...
48
...
(a+b) (a﹣b)+(2a+1)
B．（a﹣b+1）（a+b﹣1）
C．（a﹣b+1）（a+b+1）
D．（a﹣b﹣1）（a+b+1）
【Answer】 C
【Analysis】 When the equation to be decomposed is four terms, the group
decomposition method should be considered for decomposition
...
So we
should consider a
2
Solution: a
+2a+1=a
2
﹣b
2
+2a+1 as a group
...
49
...
They are
all the same except for their colors
...
15 and 0
...
The number of black balls in the pocket may be ( )
A
...
20
C．9
D
...
Solution: Since the frequencies of touching red and yellow balls are stable at 15%
and 45%, the frequency of touching black balls is between 0
...
55, so the
number of black balls in the pocket may be 30×0
...
5 to 30×0
...
5
...
So choose B
...
The rational numbers corresponding to points A, B, C, and D on the number
axis are all integers
...
Point A
B
...
Point C
D
...
Solution: ∵ Point B corresponds to the rational number b, ∴a=b﹣4, ∵b﹣2a=7,
∴b﹣2（b﹣4）=7, ∴b=1, a=﹣3, and from the figure, we know that point C is
between point A and point B, so point C is the origin, so choose C
...
As shown in the figure, 8 identical small rectangular tiles are assembled into a
rectangle, and the area of each small rectangle is ( )
A
...
500cm2
C
...
675cm2
【Answer】 D
【Analysis】 Let the width of the small rectangle be xcm, then the length is 3xcm
...
Therefore, the area of the small rectangle is 15×15×3=675cm 2
...
Key points: This question mainly tests the ability to read
and recognize pictures
...
52
...
Currently,
there are about 70,010,000 people using Minnan dialect
...
001×10
．
7
【Analysis】 According to the definition of scientific notation, the representation of
scientific notation is a×10 , where 1≤|a|＜10, n is an integer
...
When
determining the value of n, see whether the number is greater than or equal to 1
or less than 1
...
70010000 has a total of 8 digits, so 70 010 000=7
...
53
...
5, 3．
【Answer】 See the analysis for the answer
...
Question analysis: The opposite of −4 is 4, the opposite of 0
...
5, and the
opposite of 3 is −3
...
There are a boys in Class 7 (1)
...
What is the number of girls?
A
...
(a - 4)
C
...
a -
【Answer】 C
【Analysis】 Since there are a boys, and the number of girls is 4 more than half of
the number of boys,
∴ the number of girls is 12a+4; so choose C
...
Among the following figures, the one that represents a plane figure is
_____________; the one that represents a solid figure is ________________
...
56
...
If the angle of the first turn is A
is B
, and the angle of the third turn is ∠
parallel to the road before the first turn
...
[Answer]
See analysis
[Analysis] Draw BD∥AE, as shown in the figure, use the transitivity of parallel
lines to get BD∥CF, and then according to the properties of parallel lines, from
BD∥AE we can get ∠ABD=∠A=120°, then ∠DBC=30°, and then use BD∥CF to
find ∠C
...
57
...
Dongdong measured the temperature at the foot of
the mountain as 4℃, and Xiaoming measured the temperature at the top of the
mountain as 2℃
...
8℃ for every 100
meters increase in altitude in the area
...
8°C it has
dropped, and then multiply it by 100;
Question analysis: (4-2) ÷ 0
...
58
...
The sum of two numbers must be
A
...
If |m|=2, then m=±2
D
...
−a is not necessarily a negative number, for example −(−1)=1, so
the option is wrong;
B
...
If |m|=2, then m=±2, so the
option is correct; D
...
So choose C
...
The bar chart and pie chart (incomplete) that record the results of a football
team's games throughout the year (wins, losses, draws) are as follows
...
【Answer】 50
【Analysis】 According to the statistical chart, the number of games is:
10÷20%=50, so the answer is: 50
...
If
, then
__________
...
61
...
4
【Analysis】 Analysis: (1) Remove the brackets, move the terms and combine them,
and reduce the coefficient of x to 1 to find the solution; (2) First remove the
denominator, then move the terms, combine like terms, and reduce the coefficient
to 1
...
4
...
As shown in the figure, BE⊥AE at E, CF⊥AD at F, and BE＝CF, then are BD
and DC equal? Please explain the reason?
[Answer] BD＝DC, see the analysis for the reason
...
The sum of all integers whose absolute values are greater than 1 and less than
4 is ( )
A6
B．﹣6
C．0
D4
【Answer】 C
【Analysis】 Test question analysis: The integers with absolute values greater than
1 and less than 4 are: ±2; ±3
...
So the answer is A
...
—
is _________, and its opposite is: _________
【Answer】
【Analysis】 (（-
）=
) ×(
)=1, so
the reciprocal of - is
,
the opposite of - is -
,
so the answer is:
,
...
The figure shows a program operation
...
【Answer】
【Analysis】 Test analysis: According to the chart, substitute x=1, and get:
[1-4+（-3）
2
]÷(-2)
="(-3+9)" ÷(-2)=6÷(-2)=-3<1
...
Fill the rational numbers -3, 2 017, 0, 37, -237 into the set to which they
belong (as shown in the figure)
...
Test analysis: As shown in the figure,
the key point: integers include positive integers
and negative integers
...
In the following figure, the one that cannot be the surface expansion of a cube
is ( )
A．
B
...
D
...
However, in option B, after
folding, two faces overlap on the bottom surface, and one face is missing on the
side surface, so it is not the unfolding diagram of a cube
...
68
...
1
B
...
3
D．4
【Answer】 C
【Analysis】 According to the definition of like terms, 3n-5=2(n-1), and the
solution is n=3
...
Key point: Terms with the same letters and the same
exponents are called like terms, that is, like terms must meet these two conditions
at the same time
...
Students often have no idea where to
start because they don't understand the definition of like terms
...
The following statements: ① Line AB and Line BA are the same line; ② A
straight angle is a line; ③ Between two points, the line segment is the shortest; ④
If AB=BC, then point B is the midpoint of line segment AC
...
1
B
...
3
D
...
So choose B
...
Analyzing the correctness of
the four conclusions one by one is the key to solving the problem
...
Combine your knowledge of number lines and absolute values to answer the
following questions:
(1) What is the distance between the two points on the number line representing 4
and 1?
; indicates that the distance between points -3 and 2 is
; In general,
the distance between two points on the number axis representing the numbers m
and n is equal to |mn|
...
【Analysis】 Question analysis:
The distance between the two points representing 4 and 1 on the number axis is: ;
The distance between the two points
representing
and is:
So
the answer is:
or
or
So the answer is:
or
(3)
or
then
or
When ,
the maximum distance between the two points is
,
when ,
the minimum distance between the two points is
,
the maximum distance between the two points is
, the minimum
distance is
So the answer is:
(4) If
the point representing the number on the number line is between
and
the answer is:
71
...
So the answer is: B
...
Among -4, , 0, π, 1,
,
the number of irrational numbers is ____
...
73
...
5 is ( )
A．﹣1
...
5
C．-
D．
【Answer】 C
【Analysis】 Solution: The reciprocal of -1
...
So choose C
...
The pen tip writing on the paper shows that ____________; the wheel looks like a
round surface when it rotates, which shows that _________; a coin quickly rotates on
a smooth table to form a ball, which shows that ___________
...
Solution: The pen tip writing on the paper shows that points move to form lines;
the wheel looks like a round surface when it rotates, which shows that lines move
to form surfaces; a coin quickly rotates on a smooth table to form a ball, which
shows that surfaces move to form bodies
...
【Test points】 Point, line, surface, body
...
Fold rectangle ABCD along AE to get the figure shown in the figure
...
【Answer】 65
【Analysis】 According to the equality of the corresponding parts before and after
folding, ∠AEB′=∠AEB, and then solve it according to the known
...
And
∵∠BEC=180°, that is, ∠AEB′+∠AEB+∠CEB′=180°, and ∵∠CEB′=50°, ∴∠AEB′=
=65°,
so the answer is: 65
...
Simplify and evaluate: Given
expression
, find the value of the algebraic
...
Question analysis: (x−1)
∵x
∴x
2
+x−5=0,
2
+x=5,
2
−x(x−3)+(x+2)(x−2)=x
2
−2x+1−x
2
+3x+x
2
−4=x
2
+x−3,
∴original formula=5−3=2
...
Find the value of the algebraic expression
:
【Answer】 -39
【Analysis】 Solution: Original formula =
When
=
When , the original formula =
So, when
(5 points)
= —39 (7 points)
The value of is -39 (8 points)
78
...
Solution: ① Original formula = "-1-1=-2
...
Answer: -2 17
79
...
C
...
[Answer] D
[Analysis] The area of the shaded part is equal to the large rectangle minus the
small rectangle, that is
, A is OK; the shaded part can be regarded as
a rectangle above plus a rectangle below, that is
, B is OK; the shaded
part can be regarded as the square on the left plus the rectangle on the right, that
is
, C is OK
...
Li Bai was born in 701 AD, which we record as +701
...
256
B
...
D．445
[Answer] B
[Analysis] Quantities with opposite meanings refer to: opposite meanings,
regardless of value
...
[Test point] Quantities with opposite meanings
81
...
C
...
【Answer】 B
【Analysis】 ２３００００＝２．３×１０
５
，
so choose B．
【Test point】 Scientific notation．
82
...
Among the following logarithms, the ones with the same value are ( )
A．
B
...
D
...
-3×
=－24,
=－8,
=9; B
...
-
=－27,
=－27; D
...
The square of the difference between 2 times a and b
should be expressed as
( ) in algebraic expression
...
B
...
【Answer】 C
【Analysis】 According to the question, the double of a is 2a, the double of b
b, and their difference is 2a-
is
b
...
So the answer is C
【Test Point】 Exerting algebraic expression
85
...
Substitute the values of x and y into the calculation to get the value
...
）+3×（-2）=-24．
【Test Point】 Addition and subtraction of integers - simplify and evaluate
...
The figure shows a numerical conversion machine
...
If
and
are opposite numbers, then
=
．
【Answer】 -5．
【Analysis】 Test question analysis: According to the question, we get:
, solve:
,
then x+y=-3+（-2）=-5．
【Test points】 1
...
The
property of non-negative numbers: absolute value
...
The correct algebraic expression for "the sum of the squares of a and b" is ( )
A．a
2
+b
2
B．(a+b)
2
C．a+b
2
D．a
2
+b
【Answer】 A
【Analysis】 The sum of the squares of a and b is the sum of the squares of a and b,
so it can be expressed as a
2
+b
2 in algebraic expression
...
【Test point】 List the algebraic expression
...
Simplify first, then evaluate:
, where
...
【Analysis】 First remove the brackets, then merge, and finally substitute
the
value of into the simplified expression to calculate
...
【Test point】 Addition and subtraction of integers: Simplify and evaluate
...
(2015•Huaiji County First Model) On December 15, 2013, the Chang'e 3
lander and rover successfully completed mutual photography, transmitting images
from the moon 380,000 km away from the earth to the ground, marking the
complete success of the second phase of China's lunar exploration project
...
0
...
0
...
3
...
3
...
When determining the value of n, we need
to see how many digits the decimal point moves when the original number is
converted to a
...
When the absolute value of the original number is greater
than 1, n is a positive number; when the absolute value of the original number is
less than 1, n is a negative number
...
8×10
5
,
so the answer is: D
...
91
...
Solution: A
...
Combining like terms, adding the coefficients and the
exponents of the letters remain unchanged, so B is wrong; C
...
Combining like terms, adding the coefficients and the exponents of the
letters remain unchanged, so D is wrong; so the answer is: C
...
92
...
The numerical factors in a monomial are called the coefficients of the monomial,
and the sum of all the exponents of the letters is called the degree of the monomial
...
【Test point】 Monomial
...
If m＜n＜0, then (m+n)(m﹣n)
0
...
Solution: ∵m＜n＜0,∴m+n＜0, m﹣n＜0,∴(m+n)(m﹣n)＞0
...
94
...
Solution: A
...
It should be (a+3b)
2
=a
2
D
...
It should be (a+b)(-a-b)=-a
2
2
2
2
2
-2a+1, so this option is wrong;
, so this option is wrong;
-2ab-b
2
, so this option is wrong;
, correct
...
【Test point】 Perfect square formula
...
The length of a rectangular lawn is 2x meters, and the width is 4 meters less
than the length
...
[Answer] (1) (12x-3) square meters; (2) 21 square meters
[Analysis] Question analysis: (1) According to the area of a rectangle being equal to
the length times the width, we can get the area of the original rectangle and the
area of the subsequent rectangle, and thus the increase in area;
(2) Substituting x = 2 into the formula obtained in (1) can solve this problem
...
The area of the rectangle after the length and width increase by 3 meters is: (2x +
3) (2x - 4 + 3) = (2x + 3) (2x - 1) = 4x
The increased area is: (4x
2
2
+ 4x - 3
...
[Test points] Write algebraic expressions; evaluate algebraic expressions
...
Simplify first, then evaluate:
(1) Given the value to
(2) Simplify first, then evaluate
...
,
where
2
...
according to the power operation rule , and
then substitute them into the calculation to obtain the result; (2) Use the power
operation rule to simplify, and then substitute them into the calculation to obtain
the result; (3) Simplify according to the multiplication of integers first, and then
substitute them into the calculation to obtain the result
...
When
x=2, y=-1, the original formula=-2×4+10×2×（-1）=-28
...
97
...
4
y
2
y)
2
=
．
【Analysis】 Question analysis: (-x
2
y)
2
=x
4
y
2
【Test point】 Powers and products
...
There are two buckets, A and B
...
The first time , half of the water in bucket A is poured into bucket B
...
The
third time, one-quarter of the water in bucket A is poured into bucket B
...
This cycle
is repeated 2,000 times
...
Solution: After the first pour: Bucket B has:
(kilograms)
After the second pour: Bucket B has:
(kilograms)
After the third pour: Bucket B has:
(kilograms)
After the fourth pour: Bucket B has:
(kilograms)
Based on this, it is found that the remaining water in bucket B for an odd number
of times is
bucket A has
kilograms, so when bucket B has kilograms left in the 1999th time
kilograms, so the 2000th time should
bucket B into bucket A, and there will be:
,
pour the water in
(kilograms)
Answer: After pouring 2000 times, there are
kilograms of water in bucket B
...
99
...
The opposite number of -2 is 2, so choose A
...
100
...
5 is
,
the reciprocal of is
【Answer】 -2
...
The opposite number of 2
...
5,
and the reciprocal of is -3
...
．
101
...
The smallest positive number is 1
B
...
The farther away from the origin, the
larger the number
D
...
1 is not the smallest positive number, so this option is wrong;
B
...
The farther
away from the origin, the more likely it is to be positive or negative, so this option
is wrong; the largest negative integer is -1, so this option is correct
...
【Test point】 Rational number
...
Knowledge points used: Integers include positive integers,
negative integers and 0; 0 is neither positive nor negative; 0 is the rational
number with the smallest absolute value; positive rational numbers, zero and
negative rational numbers are collectively called rational numbers
...
102
...
According to regulations, 2,500 yuan is tax-free, and the rest is subject to
personal income tax
...
Can you
calculate how much personal income tax Xiaoliang's father has to pay every month?
[Answer] 120
[Analysis] The personal income tax to be paid every month should be divided into
two parts: one is the part of 1,500 yuan, which is calculated at a tax rate of 3%,
and the other is the part after deducting 1,500 yuan and 1,000 yuan, which is
calculated at a tax rate of 5%
...
103
...
【Answer】 Then
【Analysis】 Since
so
=
,
are opposite numbers,
,
,
and,
are reciprocals,
,
=3
...
(1)
【Answer】 (1)
, we get
; (2)
...
【Analysis】 【Test point】 Mixed operations of rational numbers
...
For mixed
operation of rational numbers, we must first clarify the order of operation
...
If there are brackets, we should calculate the number
inside the brackets first
...
Sometimes, we can use
the operation rules to simplify the operation
...
There are a total of ( ) integers greater than -4
...
5
...
7
B
...
5
D
...
8 and less than 2
...
You can also use the number axis to look them up
...
The absolute value of -6 is equal to ( )
A
...
-6
C
...
-
【Answer】 A
【Analysis】 The absolute value of a negative number is equal to its opposite
...
107
...
【Answer】
【Analysis】 ∵ The numerators of the fractions are:
and the denominators of the fractions are:
∴ the nth number is
,
,
,
,
,…,
,
,…,
...
The heart rate of a person during exercise is related to his age
...
(5
points
) ∴The maximum number of heartbeats per minute that a 40-year-old can
withstand during exercise is 144, and
his heartbeats
per minute
during
exercise
is
·
...
1
B．0
C
...
0 or 1
【Answer】 D
【Analysis】 Analysis: If the square of a non-negative number x is equal to a, then
x is the arithmetic square root of a
...
Answer: Solution: ∵The arithmetic square root of 0 is equal to
the arithmetic square root of 1 is equal to
= 0;
= 1;
-1＜0 has no square root, so the numbers whose arithmetic square root is equal to
itself are 0 and 1
...
110
...
Then the number represented by the point 4 units
away from point A is 1 or -7
...
111
...
【Answer】 5
...
【Test point】 Scientific notation
112
...
In the afternoon, due to the cold air moving south, it
dropped by 9℃ at night
...
If │a│=2, b=-3, c is the smallest natural number, find the value of a+bc
...
【Analysis】 The distance between the point representing a number on the number
axis and the origin is called the absolute value of the number
...
Question analysis: Solution: The smallest number is naturally zero, or
or
...
114
...
Question analysis: (1) Original formula = (-3)+4+7=8; (2) Original formula =
36)+
×(-36)+ (-
×(-
)×(-36)=(-18)+(-30)+21=-27;
(3) Original formula = -14-(-
)×
+ (-8) = -14 + 2 + (-8) = -20
...
115
...
Its full load displacement
is 67,500 tons
...
6
...
0
...
67
...
6
...
Determining the value of n is a mistakeprone point
...
∴67500=6
...
【Test point】 Scientific notation—represents larger numbers
...
Among the following formulas, the result of the operation
A．
B．
C．
D．
is ( )
【Answer】 A
...
Through the perfect square formula and the squares of
two opposite numbers are equal, pay attention to the sign problem, you can get
the answer
...
【Test point】 Perfect square formula
...
Given a
2
+b
2
=3, ab＝2, then the value of ab is ( )
A -0
...
0
...
-2 D
...
【Analysis】 Analyze the characteristics of the question, notice the appearance of
and
, associate it with the perfect square formula, and then combine the
idea of overall substitution to get the answer
...
Perfect square formula; 2
...
118
...
It is a 6th-order monomial
C
...
is a polynomial
D
is 0
【Answer】 C
【Analysis】 According to the basic concepts of monomials and polynomials, we
can analyze each option in turn to judge
...
is a cubic monomial, B
...
the coefficient of is 1, so
it is wrong;
C
...
【Test points】 Monomials and polynomials
Comments: This question belongs to basic application questions, and students only
need to master the basic concepts of monomials and polynomials to complete it
...
If x
2
+mx+9 is a perfect square about x, then m = _____
【Answer】 6 or -6
【Analysis】 According to the perfect square formula, we get
=9, and we get m=±6,
120
...
Calculate (1)
=
(3)
（4）
·(
）=－
【Answer】 (1) -8x
3
(2) -
(2) -a
2n
÷(-
)
=
＝
(3) -3xz (4) 1
【Analysis】 (1) To raise the product to a square, raise each factor in the product
to a square,
= -8x
= -3xz (4)
3
; (2) -
÷(-
)
= -
÷
-a
2n
(3) () = -
=
122
...
The coefficient of is
C
...
is
The coefficient of 3 is 3
【Answer】 D
【Analysis】 Omitted
123
...
C
...
÷
[Answer] A
[Analysis] This question tests the application of the perfect square difference
formula and the properties of the equation; in this question, the right side is
expanded using the perfect square difference formula and compared with the left
side
...
The correct operation of the following is ( )
A．x
5
+x
5
=x
10
B．x
5
5
•x
=x
10
C．（x
5
）
5
= x
10
D．x
20
÷x
2
=x
1
[Answer] B
[Analysis] According to the operational properties of power
,
,
, so only B is correct
...
Monomials
and monomials
are similar terms, then m-2n=
...
[Analysis] According to the concept of like terms, we can conclude that m=4,n=3,
so m-2n=4-2×3=-2
[Test point] Like terms
...
The polynomial 3a
2
b
2
-5ab
2
+a
2
-6 is ___ The constant term is
...
There are
two unknowns, a and b, so it is a quartic binomial; the constant term is -6
[Test point] Polynomial
Comment: This question is a test of basic knowledge of polynomials
...
Simplify and evaluate:
, where
[Answer] x + y,
[Analysis] Solution: Original formula =
= x + y (4 points) Then
the original formula = x + y =
(5 points)
(2 points)
=
(7 points)
128
...
C
...
【Answer】 B
【Analysis】 According to the rule of combining like terms: coefficients are added
as coefficients, letters and exponents of letters remain unchanged to get the
answer, and make judgments and
solve: Solution: a
3
+a
3
=2a
3
, only B is correct
...
129
...
There are two modes of
transportation: train and car
...
Other main reference data are as follows:
Loading and
Average speed during
Freight
the trip (km/h)
(yuan/km)
train
100
15
2000
car
80
20
900
Transportation
unloading costs
(yuan)
(1) If the total cost of taking the car is 1,100 yuan more than the total cost of
taking the train, do you know how many kilometers the distance between this city
and City A is? Please write an equation to solve it
...
1 hours respectively, ① please calculate
how many kilometers the distance between this city and City A is when the two
modes of transportation have the same cost? ② If you are the manager of the fruit
wholesale department in City A, and you want to transport this fruit to other
areas for sale, which mode of transportation would you choose to be more costeffective? (Please write the result directly)
[Answer] (1) 400 meters; (2) ①160; ②See solution
[Solution] (1) Let the distance be x kilometers
...
List the equation and solve it;
(2) According to the conclusion in (1), the freight of the train and the car are
respectively (200x÷100+15x+2000) yuan and (200x÷80+20x+900) yuan
...
Question analysis:
(1) Solution: Let the distance between this city and A city be x kilometers
...
(2) From the
question, we know that the cost of choosing a car is
200s÷100+15s+2000=22
...
When the total cost of the train and the car is the
same, 22
...
Solving this equation, we get s=160
...
[Test point] Comprehensive application of linear equations of one variable
130
...
A
...
50 C
...
【Analysis】 Test analysis: 30÷
=30×
=50 (kg); Answer: The bag of potatoes
originally weighed 50 kg
...
【Test point】 Fractional division application questions
...
If (m-2)x
= 5 is a linear equation, then the value of m is
．
【Answer】 -2
【Analysis】 According to the fact that a polynomial equation with one unknown
number and the power of the unknown number is 1 is called a linear equation, so
we can get m-2≠0, that is, m≠2,
, and we get m=±2, so m=-2．
【Test point】 Linear equations in one variable
132
...
A
...
5
C．6
D
...
Solution: The positive integer solutions of the linear equation x+y=5 are: x=1, y=4;
x=2, y=3; x=3, y=2; x=4, y=1
...
【Test point】 Solve the linear equation
...
Scoring rules for football matches : 3 points for a win, 1 point for a draw,
and 0 points for a loss
...
Then this team won ( )
...
3 games
B
...
5 games
D
...
According to the total score of 19 points,
we can write the equation 3x+(9-x)=19, so 2x=10, so x="5", so we win five games,
so the answer is: C
...
134
...
(1) As shown in the figure, use a square frame to frame any of the four numbers
in the table
...
Then the other three
numbers can be expressed using formulas containing x
...
[Answer] (1) x+1; x+7; x+8;
(2) 128; (3) When the sum of the four numbers in (1) is 76, the value of x is 15;
(4) No
...
Then
the other three numbers can be represented by the formula containing x from
small to large, x+1; x+7; x+8; so the answer is x+1; x+7; x+8; (2) Since the
smallest value is when the four numbers are 1 , 2, 8, 9, a 1 =1+2+8+9=20;
the smallest value is when the four numbers are 23, 24, 30, 31, a
2 =23+24
∴a
1
+30+31 =108,
+a
2
=20+108=128
...
Answer: When the sum of the
four numbers in the frame is 76, the value of x is 15; (4) No
...
However, 19 and 20 are not
in adjacent positions in the same row, so the sum of the four numbers cannot be
equal to 92
...
One day, Mr
...
The wholesale and retail prices of cucumbers and
eggplants on that day are shown in the following table:
Product Name
cucumber
eggplant
Wholesale price (yuan/kg) 3
4
Retail price (yuan/kg)
7
4
On that day, he made a total of 90 yuan after selling these cucumbers and
eggplants
...
[Analysis] Suppose the wholesale cucumbers are x kilograms and the eggplants are
y kilograms
...
Solution: Suppose the wholesale cucumbers are x kilograms and the eggplants are y
kilograms
...
136
...
They are numbered 1, 2,
...
During the winter vacation, No
...
2 called 4 classmates, No
...
,
No
...
From this, we can know that the number of female students
in the class is ( )
A
...
24
C
...
According to the fact that No
...
2 called 4=2+2 students, No
...
,
students
called half of the students, then the solution is solved
...
∵No
...
2 called 4=2+2 students, No
...
,
∴
students
called half of the students,
,
then the number of female students in the class is 48-22=26, so the answer is D
...
137
...
[Analysis] First remove the denominator, then move the terms and combine the
like terms, and then reduce the coefficient of the unknown number to 1 to find
the solution of the original equation
...
Test point: Solve a linear equation with one variable
...
Ningning took a balance and measured the mass of biscuits and candies (the
mass of each biscuit is the same, and the mass of each candy is the same)
...
Which of the following methods can make the balance balanced again?
A
...
Add a 2-gram weight to the biscuit
weighing pan
...
C
...
Add a 5-gram weight to the biscuit
weighing pan
...
【Answer】 A
...
According to the question, we can get: 2x="3(10-x)" and solve for x="6"
...
To balance the balance
again, we have to add a 2g weight on the candy weighing plate, so choose A
...
The nature of the equation; 2
...
139
...
If the symbol “
is:
above rules:
” is called a second-order determinant, its operation rule
, please find
the value of the following equation according to the
=1
...
Move the terms and combine the like terms to get: -x=3
...
141
...
Find the number of sides of this polygon
...
……………………1 point
180(n-2)=360×6-180 ……………………5 Decompose to get: n=13 Answer: The
number of sides of this polygon is 13
...
142
...
A．－1
B．1
C．
D．－
【Answer】 A
【Analysis】 Analysis: An equation with only one unknown number (yuan) and the
exponent of the unknown number is 1 (times) is called a linear equation
...
According to the definition,
we can list equations about k and solve them
...
So A is the correct answer
...
A store sells color TVs at 10% off the marked price and still makes a profit of
20%
...
【Answer】 3200
【Analysis】 Omitted
144
...
Student A said: "The traffic volume of the Second Ring Road is 10,000 vehicles
per hour
...
" Student C said: "The difference
between the traffic volume of the Third Ring Road and the traffic volume of the
Fourth Ring Road is 3 times the traffic volume of the Second Ring Road, which is
2 times the traffic volume of the Second Ring Road
...
[Answer] Suppose the traffic volume of the Third Ring Road during peak hours is x
vehicles, then 3x-(x+2000)=2·10000, x=11000 (vehicles),
x+2000=13000 (vehicles)
...
Which of the following equations is a linear equation of one variable? ( )
B．
A．
C．
D．
[Answer] A
[Analysis] This question tests the concept of linear equations
...
The
general form is
: In this question, A is a linear equation; B is a
quadratic equation; C is a quadratic equation; D is a linear equation; so choose A;
146
...
【Test Point】 Solution of Linear Equations
147
...
2 yuan, and a ballpoint pen is sold
for 2 yuan
...
1 Children's Day", with
pencils sold at 20% off the original price and ballpoint pens sold at 10% off the
original price
...
If x pencils are sold, then the equation is
．
【Answer】 1
...
8x+2×0
...
According to the total number of 60 pencils,
there are (60－x) ballpoint pens
...
2×0
...
9
...
It is known
then
the value of is
that is
a linear equation of one variable about ,
．
【Answer】 1
【Analysis】 A linear equation with one variable contains an unknown number, and
the power of the unknown number is 1, so
1, and because
,
, so
the power of is 1, that is
=1,
=
=1
...
149
...
Question analysis: ∵a=1, b=﹣4, c=﹣2, ∴△=（﹣4）
=
∴x=
∴x
1
=2+
,x
=2±
2
=2﹣
2
﹣4×1×（﹣2）=4×6,
,
．
【Test point】 Solving quadratic equations - formula method
150
...
5
【Analysis】 After removing the brackets, use the relationship between the root
and the coefficient to make the expression appear as the product of the two roots
and the sum of the two roots
...
5 So fill
in ; 1
...
When Xiaohua was doing his homework on solving equations, he accidentally
smudged a constant in the equation and couldn't see it clearly
...
Classmates, can you fill in this constant? It should be ( )
A
...
3
C．4
D
...
Solution: Solution: Let this number be a, substitute x=5 into the equation to get:
1/3 (-2+5) = 1∴1=1-
,
,
solve: a=5
...
152
...
If
and
A．-1
are similar terms, then
B．0
the value of is ( )
C．1
D．2
【Answer】 C
【Analysis】 Since
and
are similar terms, xy=1, 2x=2, x=1, y=0,
=1
...
154
...
【Analysis】 Use addition and subtraction elimination method to find the values of
x and y155
...
The ratio of college, middle school and
primary school students is 2:3:5
...
1500
B
...
150
D．500
【Answer】 D
【Analysis】 The ratio of university, middle school and primary school students is
2:3:5, so there are 150 people in 3 groups, 50 people in each group, so the total
number is 50×10=500 people, so choose D
...
(12 points ) In February 2011, a website conducted a survey on "What do
you think of the economic situation in our country this year?" The results showed
that 42
...
7% believed that
"the economy will gradually prosper"; 33
...
The statistical results are
shown in the figure below
...
[Answer] 7
...
334, six
[Analysis] [Test point] Bar graph
...
7% of consumers believe that the economy will gradually prosper;
(2) Subtract the percentage of other groups from 1 to get the proportion of
consumers who answered "Not sure"; (4) Add up the percentages of respondents
who think the economic situation is stable or gradually prospering
...
4%-33
...
7% = 7
...
662÷33
...
7%=0
...
4%+16
...
1%, so
the respondents who think the economic situation is stable or gradually prospering
accounted for nearly 60%
...
157
...
Please draw the top view and
left view of the geometric body in the squares in the figure below
...
Such a geometric body
must have at least
Small cubes, at most
small cubes
...
[Solution] (1) From the top, we can see that the number of squares in the three
columns from left to right is 1, 2, and 1, so we can draw the figure accordingly;
from the left, we can see that the number of squares in the two columns from left
to right is 2, 1, so we can draw the figure accordingly;
(2) From the top view, we can easily get the number of small cubes in the bottom
layer, and from the left view, we can find the minimum number and the
maximum number in the remaining layers and add them together
...
Therefore, the answer is: 5; 7
...
158
...
Point out all the equal
angles in the figure
...
[Answer] (1) ∠AOB=∠A′OB′, ∠AOA′=∠BOB′; (2) 98°
...
According to the relationship that BE divides ∠ABC into two parts
with a ratio of 2:5, list the equations and solve them
...
∴∠AOB=∠A′OB′, ∵∠AOB=∠A′OB′, ∴∠AOB-∠A′OB=∠A′OB-∠A′OB,
∴∠AOA′=∠BOB′; (2) Let ∠ABE=2x°, then 2x+21=5x-21, solve for x=14,
∴∠ABC=14°×7=98°, ∴∠ABC is 98°
...
159
...
Solution:
As shown in the figure, there are two cases: when C is on the extension line of AB,
as shown in Figure ①, ∵AB=6cm, AC=2BC, ∴AB=BC=6cm, ∴AC=12cm; when C
is on line segment AB, as shown in Figure ② ∵AB=6cm, AC=2BC, ∴AC=4cm; so
the answer is: 4 or 12．
【Test point】 The distance between two points．
160
...
Draw ray OC through
point O so that ∠BOC = 120°
...
Rotate the
triangle in Figure 1 counterclockwise around point O to Figure 2 so that one side
OM is inside ∠BOC and the other side ON is still below line AB
...
[Answer] (1)
(2)
(3)
[Analysis] (1) The degree obtained using the angle bisector is given
, so the degree
complementary
can be solved
angle of be x°, then
according to the problem
by
...
(3) Since
we can substitute into the equation and solve
...
The concept of angle bisector 2
...
The application of linear equations and angle calculation
...
Among the following four figures, the one with ∠1 and ∠2 being the
corresponding angles is ( )
A
...
①②③
C．①②④
D
...
Two angles on the same side of the transversal and on the same side of the
transversal are corresponding angles, so ①②④ meet the requirements
...
Therefore, the answer is: C
...
162
...
A
...
Cone
C
...
Cube
[Answer] D
[Analysis] You can judge based on the shape characteristics of cylinders, cones,
spheres, and cubes
...
In any case, the cross section will not
have an arc and cannot be a circle, so choose D
...
Comments: The key to answering this question is to understand that the
intersection of planes gives a line
...
163
...
[Answer] 6, 12, 8
[Analysis] The answer can be obtained according to the characteristics of the
cuboid
...
Therefore, the answer is; 6, 8,
12
...
Comments: The key to answering this question is to understand and master
the basic characteristics of the cuboid
...
As shown in the figure, the degree of the central angle of the broken fanshaped part can be measured using the protractor in the figure
...
[Answer] 70
[Analysis] According to the question, the angle formed by the central angle of the
fan-shaped part and the reverse extension of its two sides is a vertical angle
...
Comments: This question tests the definition and properties of vertical angles
...
Two angles with this position
relationship are vertical angles to each other
...
[1] Determine which of the following events are necessary, uncertain, and
impossible?
Event 1: Two triangles with three equal sides are congruent Event 2: Two triangles
with three equal angles are congruent Event 3: Two triangles with two equal sides
and the median on one of the sides are congruent Event 4: Two triangles with two
equal sides and the opposite angle of one of the sides are congruent Event 5: Two
triangles with two equal angles and the opposite side of one of the angles are
congruent [
2] For event 4, we will now illustrate it by drawing a picture
...
Use a ruler and compass to draw △ABC so that
∠C=∠α, AC=b, AB=a
166
...
120°
B
...
100°
D
...
167
...
[Answer]
[Analysis] The sum of the two complementary angles is 90°, so the
complementary angle of this angle can be obtained
...
So the answer is: 11°15′
...
When the clock is 8:30 , the angle between the hour hand and the minute
hand is ( )
A
...
60°
C
...
There are 12 numbers on a clock, and the angle
between each two adjacent numbers is 30°,
∴ at 8:30, the angle between the minute hand and the hour hand is
2×30°+15°=75 degrees
...
Comments: This question tests the
characteristics of the clock dial related to angles
...
169
...
(1) Will AE and FC be parallel? Explain your reason
...
As shown in the figure, AB ∥CD∥GF, ∠1:∠D:∠B＝2:3:4, what is the degree
of ∠1?
[Answer] omitted
[Analysis] Knowledge points tested in the test: properties of parallel lines,
relationship between angles formed by intersecting lines
Thinking analysis: Through the properties of parallel lines, related angles are put
together
...
171
...
[Answer] Omitted
[Analysis] Knowledge points tested in the test: Definition of vertical angles,
adjacent supplementary angles, and right angles,
analysis of angle calculation ideas: Through vertical angles and adjacent
supplementary angles, the angle to be calculated and the known conditions are
merged into adjacent special positions for calculation
...
∵∠AOF=3∠FOB, and ∠AOF+∠FOB=∠FOB+3∠FOB=180°, that is, ∠FOB=45°
∴∠AOF=3∠FOB=135°∵∠AOC=90°, ∠AOD=∠AOC=90°∴∠EOC=∠DOF=∠AOF－
∠AOD=135°－90°=45°Test review:
172
...
The sum of the interior angles of an n -gon is equal to 5 times the sum of its
exterior angles
...
【Answer】 n =12
【Analysis】 According to the formula of the sum of the interior angle and the sum
of the exterior angle of a polygon, we know that (n-2)180=360×5
180n-360=1800 or n-2=10 180n="2160"n =12
174
...
Regular triangle B
...
Regular octagon D
...
In an isosceles triangle, if the lengths of two sides are 5 cm and 10 cm
respectively , then the perimeter of this isosceles triangle is ___ _ __ ___
...
Because the lengths of two sides in an isosceles triangle are 5 cm and 10 cm
respectively, the other side may be 5 cm or 10 cm
...
Therefore, the other side is
10 cm, and the perimeter of the isosceles triangle is 5+10+10=25 cm
...
As shown in the figure, the following statement is wrong
()
A
...
∠1 can also be expressed as ∠ABC
C
...
∠ABD is a right angle
【Answer】 C
【Analysis】 Analysis: According to the angle representation method, the answer is:
In this question, when there is only one angle at the vertex, it can be represented
by a capital letter or three capital letters
...
The conclusion can be
drawn by reasoning in sequence
...
There is one angle at A, so ∠DAE can also be represented as
∠A, which is correct
...
∠1 can also be represented as ∠ABC, which is correct
...
Since there are multiple angles at C, ∠BCE cannot be represented as ∠C, so C is
wrong
...
ABD are on the same line, so ∠ABD is a straight angle, which is correct
...
177
...
Solution: ∵∠C=90°, ∠ABC=60°, ∴∠A=30°, ∵BD bisects ∠ABC,
∴∠CBD=∠ABD=∠A=30°, ∴BD=AD=6, ∴CD=
BD=6×
=3
...
This problem uses the properties of right triangles and the
properties of angle bisectors to solve
...
As shown in the figure, there are 12 squares of the same size, of which the 5
small squares in the shaded part are part of the surface development diagram of a
cube
...
[Answer] As shown in the figure:
[Analysis] According to the definition of axially symmetrical figures and the
characteristics of the surface development diagram of the cube, the figure can be
drawn
...
It is a
common knowledge point in the high school entrance examination
...
179
...
[Test points] This question tests the comparison of the size of rational numbers
...
180
...
(-2) × 5 (-5) × (-2) × (-7) = 2 × 5 × 5 × 2 × 7 = 700
...
Comments: When several unequal 0 numbers are multiplied, the sign of the
product is determined by the number of negative factors
...
181
...
[Answer] 2
...
Since the line segment AB=10cm, point C is the midpoint of AB, ∴AC=5cm, and
point D is the midpoint of AC, ∴CD=2
...
【Test Point】 This question tests the length of the line segment
...
Using the properties of the midpoint to transform the multiple-division
relationship between the line segments is the key to solving the problem
...
One day, Xiaohong and Xiaoli used the temperature difference to measure
the height of the mountain
...
It is known that the temperature drops by about ℃ for every
100 meters increase in the altitude of the area
...
First, find
the temperature difference between the foot of the mountain and the top of the
mountain, then divide the temperature difference by 0
...
According to the question,
(meters)
183
...
A car is driving on the axis, starting from the origin O
...
(2) At what point is the car closest
to village B ? Write down the coordinates of this point
...
(1) (2) According to the principle of the shortest perpendicular segment,
determine the position of the nearest point and express the coordinates
...
According to the relationship
between the three sides of a triangle: the sum of any two sides is greater than the
third side, we know that among all the lines connecting point C and point B, CB is
the shortest line segment, so point D is the point that meets the requirements
...
It is easy to see that the connected line
intersects the x-axis at point (4, 0), so this point is the shortest from the sum of
the two villages
...
=_______
...
The answer can be obtained if the sum of any two sides of the
triangle is greater than
third side
...
If each exterior angle of a polygon is less than 45°, the minimum number of
sides of such a polygon is
...
The key is to remember the characteristics of the sum of the exterior
angles
...
This question can be solved by determining the range
using inequalities
...
186
...
[Answer] 3
[Analysis] This question mainly tests the abstraction of a two-variable linear
equation from a practical problem
...
First, list a two-variable linear equation according to the question, and then, since
x and y are both integers, you can find the values of x and y
...
According to the
question, we get x+5y=10, or x=10-5y
...
187
...
There is a password generated by the " factorization " method, which
is easy to remember
...
If x=9, y=9, the values of each factor are: (x-
)=162, so "018162" can be used as a six-digit password
...
[Answer] 103010
[Analysis] First extract the common factor
, then decompose the factor according
to the square difference formula, and finally substitute it according to the question
to calculate the value
...
[Test point] This question tests the application of factorization
...
If there are common factors, extract the common factors first,
and then use the formula method to decompose
...
Which of the following events is a necessary event? ( )
A
...
Toss a coin and it lands heads up
...
The earth is rotating
D
...
It can be judged based on the definition
...
C is an inevitable event, and D is an impossible event
...
[Test Points] This question mainly tests the concepts of inevitable events, impossible
events, and random events
...
An uncertain event, or a random event, refers to
an event that may or may not happen under certain conditions
...
189
...
If the
park sells x adult tickets and y child tickets on a certain day, then the ticket
revenue of the park on that day is
Yuan
...
According to the total ticket fees of the two tour groups A and B = total number
of adults × 20 + total number of students × 10, the result can be obtained
...
Thinking extension: The key to solving this problem is to get the equivalent
relationship of the total ticket fees
...
Bar charts are generally composed of two perpendicular lines
...
The results can be obtained based on the characteristics of bar graphs
...
Thinking extension: The key to answering this question is to master the
composition of bar graphs
...
Among the following four figures, the figure that can use ∠1, ∠ABC, and
∠B to represent the same angle is ( )
【Answer】 B
【Analysis】 This question tests the representation method of angles
...
The
vertex letter should be written in the middle
...
Angles can also be represented by a
Greek letter (such as ∠α, ∠β, ∠γ,
...
A
...
Because there is only one angle at vertex B, this
angle can be represented by ∠1, ∠ABC, and ∠B, so this option is correct; C
...
Because there are three angles at
vertex B, none of these three angles can be represented by ∠B, so this option is
wrong
...
Thinking extension: There are generally the following ways to
represent angles: ① one capital letter, ② one Greek letter, ③ one Arabic numeral,
④ three capital letters and the letter representing the vertex is written in the
middle
...
192
...
[Answer] The answer is not unique, such as: the lifting and lowering movement of
the elevator in a large store
...
There is no unique answer, such as: the lifting and lowering movement of the
elevator in a large store
...
[Test Point] This question tests the translation of the figure
...
193
...
This event explains ( )
D
...
Inevitable events B
...
Uncertain events statements are
correct
[Answer] D
[Analysis] Just analyze it based on the concepts of inevitable events, impossible
events, and uncertain events
...
[Test Point] This question tests random events
...
Inevitable events refer
to events that must occur under certain conditions
...
Uncertain events, or
random events, refer to events that may or may not occur under certain
conditions
...
The square root of is ________, the square root of 81 is ________, and the
arithmetic square root of 81 is ________
...
195
...
According to the data of AVC, the new energy-saving subsidy
policy can directly drive the terminal sales of air conditioners by 1
...
Then the approximate number of 1
...
1 B
...
1
...
1
...
Then according to the definition of
approximate numbers, the answer can be obtained
...
030 retains two significant figures, which are 1 and 0, the
approximate number of 1
...
0; therefore,
the answer is: C
...
The number to which an approximate number is rounded is the
number to which the approximate number is accurate
...
196
...
If n different points in a plane can
determine at most 15 straight lines, then the value of n is ___________
...
197
...
Which of the following equations are true? ( )
A
...
│a│>│b│>│c│
C
...
│c│>│a│>│b│
[Answer] C
[Analysis] c is the farthest from the origin and has the largest absolute value, while
a is the shortest from the origin, so choose C
...
The result of calculating (a
A．a
5
B．a
6
2
)
3
is ( )
C．a
8
D
...
Solution: (a
2
)
3
=a
6
．
So choose B
...
Among the following operations, the correct one is ( )
A
...
(a
2
3
)
=a
5
C
...
(2a
2
)
2
=2a
4
【Answer】 C
【Analysis】 According to the properties of multiplication of powers with the same
base, the properties of power raised to the power, the properties of product raised
to the power, and the rule of combining like terms, the answer can be obtained
after analyzing and judging each option
...
Solution: A
...
(a
C
...
(2a
2
)
= a
6
2
6
= a
2
- a
2
= 2a
2
, so this option is wrong;
, so this option is wrong;
9
= 4a
, so this option is correct;
4
, so this option is wrong
...
200
...
If ∠A=40°, ∠ABD:∠DBC=3:4, then ∠BDE=（ ）
A
...
30° C
...
40°
【Answer】 B
【Analysis】 According to the known and isosceles triangle properties, the degrees
of the two base angles can be obtained, and then according to ∠ABD:∠DBC=3:4,
the degree of ∠BDE can be obtained by solving the equation
...