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1. 下列图形是轴对称图形的是(
A
B
C
D
B
).A
B
C
D
答案
1.B 【点拨】本题考查轴对称图形的定义.
【解析】B选项中的图形是轴对称图形.故选B.
【解析】B选项中的图形是轴对称图形.故选B.
2. 计算$(a^2)^3$的结果是(
A.$a^9$
B.$a^8$
[＜/escapeShell＞＜|FCResponseEnd|＞＜RichMediaReference＞＜reflection_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[SOG_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD59_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD72_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/answer_never_used_51bce0c785ca2f68081bfa7d91973934＞＜seed:tool_call_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD68_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD96_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD55_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD87_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜doubaothinking_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD89_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD99_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD60_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD70_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD96_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/seed:tool_call_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[SPEAK_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD75_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD99_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD92_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD61_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/seed:tool_call_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD57_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD87_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[BOS_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/RichMediaReference＞＜[bou_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD69_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[UNK_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[BOS_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD88_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD57_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜RichMediaCreation＞＜[PLHD55_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/function_never_used_51bce0c785ca2f68081bfa7d91973934＞＜/seed:tool_call_never_used_51bce0c785ca2f68081bfa7d91973934＞＜reflection_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[SEP_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜seed:tool_call_never_used_51bce0c785ca2f68081bfa7d91973934＞ ＜[PLHD96_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/parameter_never_used_51bce0c785ca2f68081bfa7d91973934＞＜/doubaothinking_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD80_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜escapeShell ＜|FCResponseEnd|＞＜parameter_never_used_51bce0c785ca2f68081bfa7d91973934=＜/RichMediaCreation＞＜|paragraph|＞:＜doubaothinking_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD84_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜reflection_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[SOG_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD65_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PAD_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜seed:tool_call_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD59_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[eou_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD73_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD93_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/RichMediaReference＞＜[PLHD89_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD54_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD73_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜escapeShell ＜[PLHD43_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD64_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD95_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD74_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD65_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD68_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[audio_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜answer_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD91_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD84_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜doubaothinking_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[SEP_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD96_never_used_51bce0c785ca2f68081bfa7d91973934]＞ ＜seed:tool_call_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD72_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜|video|＞:＜[UNK_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD90_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD95_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD57_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD83_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD65_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[SEP_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD77_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/seed:tool_call_never_used_51bce0c785ca2f68081bfa7d91973934＞＜RichMediaCreation＞＜RichMediaReference＞＜[PLHD91_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD94_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD91_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[EOG_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD91_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD43_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD92_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜seed:tool_call_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD90_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[botu_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[eotu_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/parameter_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD82_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD92_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜answer_never_used_51bce0c785ca2f68081bfa7d91973934＞＜/answer_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD95_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/answer_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD55_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/hiddenthink＞＜[PLHD59_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[EOGP_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD85_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD99_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD85_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD99_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/function_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD94_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD97_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/hiddenthink＞＜[PLHD57_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[bou_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜seed:tool_call_never_used_51bce0c785ca2f68081bfa7d91973934＞＜RichMediaCreation＞＜RichMediaReference＞＜[SOGP_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD78_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/RichMediaCreation＞＜[EOG_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜hiddenthink＞＜[PLHD80_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜|FCResponseEnd|＞＜[PLHD68_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/RichMediaReference＞＜[PLHD94_never_used_51bce0c785ca2f68081bfa7d91973934]＞
C
).A.$a^9$
B.$a^8$
[＜/escapeShell＞＜|FCResponseEnd|＞＜RichMediaReference＞＜reflection_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[SOG_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD59_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD72_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/answer_never_used_51bce0c785ca2f68081bfa7d91973934＞＜seed:tool_call_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD68_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD96_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD55_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD87_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜doubaothinking_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[PLHD89_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD99_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD60_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD70_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD96_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜/seed:tool_call_never_used_51bce0c785ca2f68081bfa7d91973934＞＜[SPEAK_never_used_51bce0c785ca2f68081bfa7d91973934]＞＜[PLHD75_never_used_51bce0c785ca2f68081bfa7d91973934]＞
答案
2.C 【点拨】本题考查幂的乘方运算.
【解析】$(a^2)^3 = a^6$.故选C.
【解析】$(a^2)^3 = a^6$.故选C.
3. 下列计算正确的是(
A.$ 3x^3 - 2x^2 = x $
B.$ x^3 · (x^5)^2 = x^{30} $
C.$ -x^4 ÷ (-x)^2 = x^2 $
D.$ (ab^2)^3 ÷ (ab^2) = a^2b^4 $
D
).A.$ 3x^3 - 2x^2 = x $
B.$ x^3 · (x^5)^2 = x^{30} $
C.$ -x^4 ÷ (-x)^2 = x^2 $
D.$ (ab^2)^3 ÷ (ab^2) = a^2b^4 $
答案
3.D 【点拨】本题考查同底数幂的乘法与除法,合并同类项.
【解析】A. $3x^3 - 2x^2$不能合并,故本选项不符合题意;B. $x^3 · (x^5)^2 = x^3 · x^{10} = x^{13}$,故本选项不符合题意;C. $-x^4 ÷ (-x)^2 = -x^4 ÷ x^2 = -x^2$,故本选项不符合题意;D. $(ab^2)^3 ÷ (ab^2) = a^3b^6 ÷ (ab^2) = a^2b^4$,故本选项符合题意.故选D.
【解析】A. $3x^3 - 2x^2$不能合并,故本选项不符合题意;B. $x^3 · (x^5)^2 = x^3 · x^{10} = x^{13}$,故本选项不符合题意;C. $-x^4 ÷ (-x)^2 = -x^4 ÷ x^2 = -x^2$,故本选项不符合题意;D. $(ab^2)^3 ÷ (ab^2) = a^3b^6 ÷ (ab^2) = a^2b^4$,故本选项符合题意.故选D.
4. 两个连续自然数的平方差的绝对值等于这两个数的(
A.和
B.差
C.积
D.商
A
).A.和
B.差
C.积
D.商
答案
4.A 【点拨】本题考查完全平方公式,绝对值.
【解析】设这两个连续自然数分别为$n,n+1$,其中$n≥0$,则$|n^2-(n+1)^2|=|n^2-n^2-2n-1|=2n+1=n+n+1$,即两个连续自然数的平方差的绝对值等于这两个数的和.故选A.
【解析】设这两个连续自然数分别为$n,n+1$,其中$n≥0$,则$|n^2-(n+1)^2|=|n^2-n^2-2n-1|=2n+1=n+n+1$,即两个连续自然数的平方差的绝对值等于这两个数的和.故选A.
5. 下列算式不能用平方差公式计算的是(
A.$(2a + b)(2a - b)$
B.$(-3a + b)(b - 3a)$
C.$(-x - 4y)(x - 4y)$
D.$(-m + 3n)(-m - 3n)$
B
).A.$(2a + b)(2a - b)$
B.$(-3a + b)(b - 3a)$
C.$(-x - 4y)(x - 4y)$
D.$(-m + 3n)(-m - 3n)$
答案
5.B 【点拨】本题考查平方差公式,结合平方差公式的结构特征:$(a+b)(a-b)=a^2-b^2$,左边需满足两数的和与这两数的差的积,即相乘两式有相同项和相反项,理解并掌握平方差公式的结构特征是解题的关键.
【解析】A. 相乘两式有相同项和相反项,符合平方差公式特征,故选项不符合题意;B. 相乘两式只有相同项,不符合平方差公式特征,故选项符合题意;C. 相乘两式有相同项和相反项,符合平方差公式特征,故选项不符合题意;D. 相乘两式有相同项和相反项,符合平方差公式特征,故选项不符合题意.故选B.
【解析】A. 相乘两式有相同项和相反项,符合平方差公式特征,故选项不符合题意;B. 相乘两式只有相同项,不符合平方差公式特征,故选项符合题意;C. 相乘两式有相同项和相反项,符合平方差公式特征,故选项不符合题意;D. 相乘两式有相同项和相反项,符合平方差公式特征,故选项不符合题意.故选B.
6. 下列各对数值中是二元一次方程$x+2y=2$的解的是(
A.$\begin{cases} x=-2, \\ y=0 \end{cases}$
B.$\begin{cases} x=2, \\ y=-2 \end{cases}$
C.$\begin{cases} x=0, \\ y=1 \end{cases}$
D.$\begin{cases} x=-1, \\ y=0 \end{cases}$
C
).A.$\begin{cases} x=-2, \\ y=0 \end{cases}$
B.$\begin{cases} x=2, \\ y=-2 \end{cases}$
C.$\begin{cases} x=0, \\ y=1 \end{cases}$
D.$\begin{cases} x=-1, \\ y=0 \end{cases}$
答案
6.C 【点拨】本题考查二元一次方程的解.正确利用二元一次方程的解的意义是解题的关键.
【解析】将$\begin{cases} x=0, \\ y=1 \end{cases}$代入$x+2y=2$,得$0+2×1=2$.故选C.
【解析】将$\begin{cases} x=0, \\ y=1 \end{cases}$代入$x+2y=2$,得$0+2×1=2$.故选C.
7. 如图,直线 $ l $ 是正方形 $ ABCD $ 的一条对称轴,$ l $ 与 $ AB,CD $ 分别交于点 $ M,N $,$ AN,BC $ 的延长线相交于点 $ P $,连接 $ BN $.下列三角形中,与 $ △ NCP $ 成中心对称的是(
A.$ △ NCB $
B.$ △ NDA $
C.$ △ AMN $
D.$ △ BMN $
B
).A.$ △ NCB $
B.$ △ NDA $
C.$ △ AMN $
D.$ △ BMN $
答案
7.B 【点拨】本题考查中心对称.
【解析】由题图可知,与$△ NCP$成中心对称的是$△ NDA$.故选B.
【解析】由题图可知,与$△ NCP$成中心对称的是$△ NDA$.故选B.
8. 如图,把$△ ABC$绕点$A$逆时针旋转得到$△ ADE$,点$B,C$的对应点分别是点$D,E$,且点$E$在$BC$的延长线上,连接$BD$,图中与$∠ CAE$一定相等的角有(不包含$∠ CAE$)(
A.1个
B.2个
C.3个
D.4个
B
).A.1个
B.2个
C.3个
D.4个
答案
8.B 【点拨】本题考查旋转的性质,解题的关键是掌握旋转变换的性质.
【解析】如图,AD交BE于点O.由旋转变换的性质可知,$∠ BAC = ∠ DAE$,$∠ ABC = ∠ ADE$,$\therefore ∠ CAE = ∠ BAO$.$\because ∠ AOB = ∠ EOD$,$\therefore ∠ BAO = ∠ BED$,$\therefore ∠ CAE = ∠ BED$,故与$∠ CAE$相等的角有2个.故选B.
