初三培优班练习
初三数学培优专题试卷
一、选择题（每题5分，共25分）1. 下列选项中，不是二次方程的是（）A. x^2 - 5x + 6 = 0B. 2x^2 + 3x - 1 = 0C. x^3 - 2x^2 + 3x - 6 = 0D. 4x^2 - 4x + 1 = 02. 已知一元二次方程 ax^2 + bx + c = 0（a ≠ 0）的两根为 x1 和 x2，那么下列选项中，正确的是（）A. x1 + x2 = -b/aB. x1 x2 = c/aC. x1^2 + x2^2 = b^2 - 4ac/aD. x1^2 - x2^2 = (x1 + x2)^2 - 4x1x23. 下列函数中，为反比例函数的是（）A. y = x^2 + 1B. y = 2x + 3C. y = 1/xD. y = 2/x^24. 已知等差数列 {an} 的首项为 a1，公差为 d，那么下列选项中，正确的是（）A. a1 + a2 + a3 = 3a1 + 3dB. a1 + a2 + a3 = 3a1 + 2dC. a1 + a2 + a3 = 3a1 + dD. a1 + a2 + a3 = 3a15. 下列选项中，不是等比数列的是（）A. 2, 4, 8, 16, ...B. 1, 2, 4, 8, ...C. 1, 3, 9, 27, ...D. 1, 3, 6, 9, ...二、填空题（每题5分，共25分）6. 已知一元二次方程 x^2 - 4x + 3 = 0，则其两根之和为 __________，两根之积为 __________。
7. 若反比例函数 y = k/x（k ≠ 0）的图象经过点（2，3），则 k = __________。
8. 等差数列 {an} 的首项为 2，公差为 3，那么第 10 项 an = __________。
9. 等比数列 {an} 的首项为 3，公比为 2，那么第 6 项 an = __________。
初三培优数学测试卷
一、选择题（每题5分，共50分）1. 若a，b是方程x²-3x+2=0的两个根，则a+b的值为（）A. 2B. 3C. 4D. 52. 下列各数中，有理数是（）A. √3B. √2+√3C. πD. 3.143. 已知一元二次方程x²-5x+6=0的两个根为x₁，x₂，则（x₁+x₂）²-4x₁x₂的值为（）A. 1B. 4C. 9D. 164. 在△ABC中，∠A=60°，∠B=45°，则∠C的度数为（）A. 60°B. 75°C. 75°D. 120°5. 已知一次函数y=kx+b的图象经过点A（1，2），B（-2，3），则该函数的解析式为（）A. y=2x+1B. y=3x+1C. y=2x-1D. y=3x-16. 已知函数y=2x+1在x=2时的函数值为5，则该函数的图象（）A. 经过点（1，5）B. 经过点（2，5）C. 经过点（3，5）D. 经过点（4，5）7. 若a，b是方程x²-4x+4=0的两个根，则a²+b²的值为（）A. 4B. 8C. 12D. 168. 在△ABC中，若a²+b²=5²，c²=4²，则△ABC是（）A. 直角三角形B. 等腰三角形C. 等边三角形D. 梯形9. 已知函数y=x²+2x+1的图象的顶点坐标为（-1，0），则该函数的对称轴为（）A. x=-1B. y=-1C. x=1D. y=110. 已知一次函数y=kx+b的图象与x轴、y轴分别相交于点A、B，若OA=3，OB=2，则该函数的解析式为（）A. y=2x+3B. y=3x+2C. y=2x-3D. y=3x-2二、填空题（每题5分，共50分）11. 若a，b是方程x²-4x+4=0的两个根，则a²+2ab+b²的值为______。
初三数学培优试卷及答案
一、选择题（每题5分，共50分）1. 已知一元二次方程x^2 - 5x + 6 = 0，则方程的解为：A. x = 2，x = 3B. x = 1，x = 6C. x = 2，x = 4D. x = 3，x = 52. 下列函数中，是奇函数的是：A. y = x^2B. y = x^3C. y = |x|D. y = x^43. 在等腰三角形ABC中，AB = AC，若∠BAC = 40°，则∠B = ∠C = °。
4. 下列命题中，正确的是：A. 平行四边形的对角线互相平分B. 等腰三角形的底角相等C. 直角三角形的两条直角边相等D. 矩形的对边平行且相等5. 若a、b、c是等差数列，且a + b + c = 12，则a^2 + b^2 + c^2的值为：6. 已知二次函数y = ax^2 + bx + c的图象开口向上，且顶点坐标为(1, -2)，则a、b、c的值分别为：7. 在直角坐标系中，点A(2, 3)关于x轴的对称点为B，则点B的坐标为：8. 已知等腰三角形ABC中，AB = AC，且BC = 6，AD是BC边上的高，则AD的长度为：9. 下列不等式中，正确的是：A. 3x > 2x + 1B. 2x < 3x - 1C. 3x ≥ 2x + 1D. 2x ≤ 3x - 110. 若a、b、c是等比数列，且a + b + c = 27，b^2 = ac，则a、b、c的值分别为：二、填空题（每题5分，共50分）11. 已知一元二次方程x^2 - 4x + 3 = 0的解为x1和x2，则x1 + x2 = ，x1x2 = 。
12. 函数y = 2x - 3的图象与x轴、y轴的交点坐标分别为（），（）。
13. 在等腰三角形ABC中，AB = AC，若∠BAC = 45°，则∠B = ∠C = °。
14. 下列命题中，正确的是：平行四边形的对角线互相平分，等腰三角形的底角相等，矩形的对边平行且相等。
初三数学培优练习题
初三数学培优练习题1. 用选项中的数字填空，并简要说明推理过程：(1) 已知一元二次方程 $2x^2 - 5x - 3 = 0$ 的两个根是 $x_1$ 和$x_2$，则 $x_1 + x_2$ 的值是 ____。
(2) 若正数 $a$ 满足 $\frac{1}{a} + a = 2$，则 $a$ 的值是 ____。
(3) 若函数 $f(x) = 2x - 3$，则 $f(4) + f(-4)$ 的值是 ____。
2. 解答下列方程组，并写出结果的解释：(1)$\begin{cases}2x + 3y = 7 \\3x - y = 1 \\\end{cases}$(2)$\begin{cases}x^2 + y^2 = 25 \\x + y = -4 \\\end{cases}$3. 股票价格涨跌问题：假设某股票的初始价格为 $P_0$ 元，经过一段时间后价格涨到$P_1$ 元，再经过一段时间后价格涨到 $P_2$ 元。
已知 $P_1$ 比$P_0$ 增长了 25%，$P_2$ 比 $P_1$ 降低了 20%。
求：(1) $P_1$ 和 $P_2$ 之间的比值；(2) 经过涨跌后，$P_2$ 相对于初始价格 $P_0$ 的涨跌幅。
4. 几何问题：在平面直角坐标系中，已知点 $A(2, 4)$，点 $B$ 在 $x$ 轴上，点$C$ 在 $y$ 轴上。
若三角形 $ABC$ 的周长是 10，求三角形 $ABC$ 的面积。
5. 概率问题：一个标准的52张扑克牌组中，红心和方块的牌各有 13 张，黑桃和梅花的牌各有 13 张。
从一个标准的扑克牌组中随机抽取 5 张牌，求：(1) 这 5 张牌全是红心的概率；(2) 这 5 张牌全是红心或全是黑桃的概率。
以上就是初三数学培优练习题，希望对你的学习有所帮助！。
初三上册培优数学试卷答案
1. 已知a > 0，b < 0，则下列不等式中正确的是（）A. a + b > 0B. a - b > 0C. -a - b > 0D. -a + b > 0答案：C2. 若x^2 - 2x - 3 = 0，则x的值为（）A. 3B. -1C. 3 或 -1D. 3 或 1答案：C3. 在△ABC中，∠A = 60°，∠B = 45°，则∠C的度数为（）A. 75°B. 90°C. 105°D. 120°答案：D4. 已知一元二次方程ax^2 + bx + c = 0（a ≠ 0）的判别式为Δ = b^2 - 4ac，若Δ = 0，则该方程有两个（）A. 相等的实数根B. 不相等的实数根C. 无实数根D. 有两个复数根答案：A5. 已知x + y = 5，xy = 6，则x^2 + y^2的值为（）A. 11B. 21C. 25D. 36答案：B二、填空题（每题5分，共50分）6. 若x^2 - 5x + 6 = 0，则x的值为______。
答案：2 或 37. 在△ABC中，∠A = 30°，∠B = 45°，则∠C的度数为______。
答案：105°8. 若一元二次方程ax^2 + bx + c = 0（a ≠ 0）的判别式为Δ = 0，则该方程有两个______。
答案：相等的实数根9. 已知x + y = 5，xy = 6，则x^2 + y^2的值为______。
答案：2110. 若x^2 - 4x + 3 = 0，则x的值为______。
答案：1 或 3三、解答题（每题10分，共30分）11. 解方程：2x^2 - 3x - 2 = 0。
解答：将方程因式分解得：(2x + 1)(x - 2) = 0，解得x = -1/2 或 x = 2。
12. 在△ABC中，∠A = 60°，∠B = 45°，求∠C的度数。
初三培优班选拔数学测试卷
竞赛辅导班选拔考试卷数 学一、选择题（共8小题，每小题5分，满分40分．） 1．若实数a 满足|a|=－a ，则|a －2a |等于（ ）. （A ） 2a （B ）0 （C ）－2a （D ）－a 2．设,2002200120012002,2001200020002001==N M 则N M 与的关系是（ ）（A ）N M ＝ （B ）N M 〉 （C ）N M 〈 （D ）1＝MN 3．已知a ，b 为正整数.满足ab-2b-a-24=0,则a+b 的最大值是（ ） （A ） 7 （B ）18 （C ）29 （D ）304．已知M （3，2）、N （1，-1），点P 在y 轴上，使PM+PN 最短，则点P 的坐标是（ ）A ．（0，21-） B. （0，0） C. （0，611） D.（0，41-）5．已知312=-y x ，则xy xy xyy x 3652-+--的值 （ ） A ．71 B ． 71- C ． 72 D ． 72- 6.多项式x 2-4xy-2y+x+4y 2有一个因式是x-2y ，另一个因式是（ ） A .x+2y+1 B.x+2y-1 C.x-2y+1 D.x-2y-1 7.已知分式1||)1)(8(-+-x x x 的值为0，则x 的值为 （ ）A. ±1B.-1C.8D.-1或8 8.设a ＞b ＞0,a 2+b 2=4ab,则ba ba -+的值为 （ ） A.3 B. 6 C.2 D.3二、填空题（共6小题，每小题5分，满分30分）9. 在平面直角坐标系中，m 为实数，点P(m 2＋m ，m －1)不可能在第 象限. 10．已知20082006,20082007,20082008a x b x c x =+=+=+，则多项式222a b c ab bc ca ++---的值 ．11．在△ABC 中，AB ＝15cm ，AC ＝13cm ，BC 边上高A D ＝12cm ，则三角形ABC 的面积为 ．12．已知1-a +（ab-2）2=0,则ab 1+)1)(1(1++b a +…+)2007)(2007(1++b a的值为13.如下左图，已知AB ∥CD,MF ⊥FG,∠AEM=500,∠NHC=550，则∠FGH 的度数为_____________.14．如图，直线l 上摆放着两块大小相同的直角三角形△ABC 和△ECD ，∠ACB=∠DCE=90°，且BC=CE=3，AC=CD=4，将△ECD 绕点C 逆时针旋转到△E 1CD 1位置，且D 1E 1∥l ，则B 、E 1两点之间的距离为_____________.三、解答题（共4题，分值依次为8分、8分、8分、12分和14分，满分50分） 15.已知x+1是f(x)=2x 3-3x+k 的一个因式，试求k 的值.16． 已知，y x xy +=1，zy yz+=2，x z zx +=3，求x 的值。
初三培优班课外练习测试卷23章旋转(1)
初三培优班课外练习测试卷23章旋转(1)——人教实验版九年级数学（上）第23章旋转（1）命题教师徐联君一、选择题（4分×10=40分）1.下列说法：（1）图形在平移过程中，图形上的每一点都移动了相同的距离；（2）•图形在旋转过程中，图形上的每一点都绕旋转中心转了相同的路程；（3）•中心对称图形的对称中心只有一个，而轴对称图形的对称轴可能不只一条；（4）•等边三角形既是对称图形，又是旋转对称图形，但它不是中心对称图形，其中正确的说法有（）A．1个 B．2个 C．3个 D．4个2.五环旗中五环图案中看作是（）A．由一个圆通过平移得到的; B．由两个圆通过平移得到的C．由两个圆通过旋转得到的; D．由两个圆通过对称得到的3.下列现象属于旋转的是（）A．摩托车在急刹车时向前滑动; B．拧开自来水水龙头C．雪橇在雪地里滑动; D．空中下落的物体4．如图所示是某房间木地板图案，该图案旋转后能与自身重合，那么至少旋转的角度是（） A．45° B．30° C．60° D．90°5．用一副扑克牌做实验，选其中的黑桃5和方块4，其中是中心对称图形的有（）A．方块4 B．黑桃5 C．方块4或黑桃5 D．以上都不对6．如图，△ABC与△A′B′C′是成中心对称的，下列说法不正确的是（）A.S△ACB=S△A`B`C`； B．AB=A′B，A′C′=AC，BC=B′C′B.AB∥A′B′，A′C′∥AC，BC∥B′C′C.S△A`B`O=S△ACO D．以上答案都不对7．将六个全等的正三角形密铺成一个六边形，下列说法正确的是（） A．正六边形可看作是其中一个正三角形依次旋转60°、120°、180•°、•240•°，300°得到的。
B．正六边形可看作是三个相邻正三角形绕中心旋转60°得到的。
C．正六边形可看作是其中一个正三角形通过平移得到的；D．以上说法都不正确8．时钟钟面上的秒针绕中心旋转180°，则下列说法正确的是（）A．时针不动，分针旋转了6° B．时针不动，分针旋转了3°C．时针和分针都没有旋转 D．分针旋转了3°，现在时针旋转角度专门小9．如图所示的四组图形中，左边图形与右边图形成中心对称的有（）A．1组 B．2组C．3组D．4组10．如图所示，其中是中心对称图形的是（）二、填空题（4分×7=28分）11．旋转对称是指一个图形绕旋转中心旋转一定的角度后，与图形自身重合，•对应点到旋转中心的距离_______以及对应线段________，对应角________．将等边△ABC绕点B旋转60°后，使得AB与BC能够重合，得到△BCD，则△ABC•与△BCD的位置关系是________．如图，将△ABC绕点A顺时针旋转60°至△ADE位置，假如∠BAC=120°，连结BD、• CE，则△BAD与△ACE是_________三角形．将图形a绕形外一点O按逆时针方向旋转80°得到图形b，则对应点A，A•′与旋转中心连线所成的角为________．12．中心对称是专门的_______对称，是指一个图形绕对称中心________后，与图形自身重合，连结对称点的线段_________，且被__________．13．如图，下列各组图形中，由左边变成右边的图形，分别进行了平移、旋转、轴对称、•• 中心对称等变换，••其中进行平移变换的是_______，••进行旋转变换的是________组,进行轴对称变换的是________组，进行中心对称变换的是________组．14．一条长度为20cm的线段，当它绕线段的________旋转一周时，•线段“扫描”过的圆面积最大，现在最大面积为________，当它绕线段的_________旋转一周时，线段“扫描”通过的圆面积最小，现在最小面积为__________．15．如图，边长为3的正方形ABCD绕点C按顺时针旋转30°后得到正方形EFCG，•EF交AD 于点H，则DH的长为________．16．图（1）中的梯形符合_________条件时，能够通过旋转和翻折成图案（2）．(第15题) (第16题) (第17题) 17．某综合性大学拟建校园局域网络，将大学本部A和所属专业学院B、C、D、•E、F、G 之间用网线连接起来，通过测算，网线费用如图所示（单位：万元），每个数字表示对应网线（线段）的费用．实际建网时，部分网线能够省略不建，•但本部及部属专业学院之间能够传递信息，那么建网所需最少网线费用为_________万元．三、解答题（52分）18．（6分）如图，图中的图案是风车的示意图，试分析图中的旋转现象．•你能仿此设计一种具有旋转现象的图案吗？并说明你的设计意图．（18）（19）19．（8分）如图，将ABCD绕O点按顺时针方向旋转60°，作出旋转后的图形．20．（8分）观看分析图（1）、（2）、（3），回答问题：每个图形各是什么对称图形？假如是轴对称图形，说出有多少条对称轴？•假如是旋转对称图形，指出需要旋转多少度能与自身重合？21．（6分）如图所示，把一个直角三角形ACB绕着30°角的顶点B顺时针旋转，使得得点A与CB的延长线上的点E重合．（1）三角尺旋转了多少度？（2）连接CD，试判定△CBD的形状；（3）求∠BDC的度数．22．（8分）P为正方形ABCD内一点，且AP=2，将△APB绕点A按顺时针方向旋转60•°得到△AP′B′，（1）作出旋转后的图形；（2）试求△APP′的周长和面积．23．（8分）已知：如图在△ABC中，AB=AC，若将△ABC绕点C顺时针旋转180°得到△FEC.（1）试猜想AE与BF有何关系？说明理由．（2）若△ABC的面积为3cm2，求四边形ABFE的面积；（3）当∠ACB为多少度时，四边形ABFE为矩形？说明理由．24．（8分）假如将点P绕定点M旋转180°后与点Q重合，那么点P与点Q关于点M对称，定点M叫做对称中心．现在点M是线段PQ的中点．如图，在直角坐标系中，△ABO的顶点A、B、O的坐标分别为（1，0）、（0，1）、（0，0）．点到P1、P2、P3…中的相邻两点都关于△ABO的一个顶点对称．点P1与点P2关于点A对称，点P2与点P3关于点B对称，点P3与点P4关于点O对称，点P4与点P5关于点A对称，点P5与P6关于点B对称，点P6与点P7关于点O对称…，对称中心分别是A，•B，O，A，B，O，…，且这些对称中心依次循环，已知P1的坐标是（1，1），试写出点P2，P7，P100•的坐标．初三培优班课外练习测试题答案——人教实验版九年级数学（上）第23章旋转(1)1．C 2．A 3．B 4．D 5．A 6．D 7．A 8．D 9．C 10．B11．相等相等相等关于BC对称等边80°；12．旋转旋转180°过对称中心对称中心平分；13．C AD组 B D ；14．某一端点400πcm2中点100πcm2；15．3；16．底角为60•°的等腰梯形；17.9 ；18.能够看作“1”绕中心依次旋转60°、120°、180°、240°、•270°得到的；也能够看作“1”绕中心依次旋转120°、240°得到的；还能够看作“1”绕中心旋转180°得到的，图案略．19．略20．图（1）是轴对称图形，有4条对称轴，也是旋转对称图形，绕中心顺（或逆）时针方向旋转90°、180°、270°图（2）是旋转对称图形，顺（或逆）•时针方向旋转120°、240°图（3）是轴对称图形，有两条对称轴，也是中心对称21．（1）由旋转的性质知旋转角度是∠ABE度数，△ACB≌△EDC，∴∠ABE=180•°-30°=150°（2）由△ACB≌△EDB知，BC=BD，∴△CBD是等腰三角形．∠EBD=15°（3）∵BC=BD，∴∠BCD=∠BDC，∴∠BDC=12×222．（1）略（2）△APP′周长为6，面积为223．（1）AE与BF平行且相等.∵ABC绕点C顺时针旋转180°得到△FEC，∴△ABC•与△FEC关于C点中心对称，∴AC=CF，BC=CE，∴四边形ABFE为平行四边形，•∴AE•平行于BF；（2）∵AC=CF，∴S△BCF=S△ABC=3，∵BC=CE，∴S△ABC=S△ACE=3，∴S △CEF=S△BCF=3，∴S ABFE=3×4=12（cm2）．（3）•当∠ACB=60°时，四边形ABFE为矩形，∵AB=AC，∴∠ABC=∠ACB=60°，∴AB=BC=CA24．P2（1，-1），P7（1，1），P100（1，-3）。
初三数学培优练习
初三数学培优练习1．已知：正方形ABCD 中，45M AN ∠= ，MAN ∠绕点A 顺时针旋转，它的两边分别交CB DC ，（或它们的延长线）于点M N ，．当MAN ∠绕点A 旋转到BM DN =时（如图1），易证BM DN MN +=．（1）当MAN ∠绕点A 旋转到BM DN ≠时（如图2），线段BM DN ，和MN 之间有怎样的数量关系？写出猜想，并加以证明．（2）当MAN ∠绕点A 旋转到如图3的位置时，线段BM DN ，和MN 之间又有怎样的数量关系？请直接写出你的猜想．2．如图，在梯形ABCD 中，AD BC ∥，AB AC ⊥，45B ∠=，AD =，BC =求DC 的长．B B M BC N C N M C N M 图1 图2 图3 A A AD D D A B CD3．已知等边三角形纸片ABC 的边长为8，D 为A B 边上的点，过点D 作DG BC ∥交AC 于点G ．DE BC ⊥于点E ，过点G 作GF BC ⊥于点F ，把三角形纸片ABC 分别沿DG DE GF ，，按图1所示方式折叠，点A B C ，，分别落在点A '，B '，C '处．若点A '，B '，C '在矩形DEFG 内或其边上，且互不重合，此时我们称A B C '''△（即图中阴影部分）为“重叠三角形”．（1）若把三角形纸片ABC 放在等边三角形网格中（图中每个小三角形都是边长为1的等边三角形），点A B C D ，，，恰好落在网格图中的格点上．如图2所示，请直接写出此时重叠三角形A B C '''的面积；（2）实验探究：设A D 的长为m ，若重叠三角形A B C '''存在．试用含m 的代数式表示重叠三角形A B C '''的面积，并写出m 的取值范围（直接写出结果，备用图供实验，探究使用）．4．如图，在矩形ABCD 中，AB=2，AD=3。
初三中考数学培优试卷
1. 下列各数中，绝对值最小的是（）A. -3B. 2C. -2D. 32. 已知a=2，b=-3，那么下列各式中，正确的是（）A. a+b=5B. a-b=-1C. a×b=-6D. a÷b=-23. 如果m和n是方程2x+3=7的解，那么m+n的值是（）A. 4B. 5C. 6D. 74. 在下列各式中，正确的是（）A. (a+b)²=a²+2ab+b²B. (a-b)²=a²-2ab+b²C. (a+b)²=a²-2ab+b²D. (a-b)²=a²+2ab-b²5. 下列各数中，能被3整除的是（）A. 123B. 124C. 125D. 1266. 下列各式中，正确的是（）A. (x+y)²=x²+y²B. (x+y)²=x²+2xy+y²C. (x-y)²=x²-2xy+y²D. (x-y)²=x²+2xy-y²7. 如果a=3，b=4，那么下列各式中，正确的是（）A. a²+b²=25B. a²-b²=7C. a²-b²=9D. a²+b²=78. 在下列各式中，正确的是（）A. (a+b)³=a³+b³B. (a+b)³=a³+3a²b+3ab²+b³C. (a-b)³=a³-3a²b+3ab²-b³D. (a-b)³=a³-3a²b-3ab²-b³9. 下列各数中，能被5整除的是（）A. 123B. 124C. 125D. 12610. 在下列各式中，正确的是（）A. (x+y)³=x³+y³B. (x+y)³=x³+3x²y+3xy²+y³C. (x-y)³=x³-3x²y+3xy²-y³D. (x-y)³=x³-3x²y-3xy²-y³11. 如果a=2，b=-3，那么a²+b²的值是______。
初三数学培优新方法练习题
初三数学培优新方法练习题1. 填空题：a) 3.14是圆周率的近似值，它是一个________数。
b) 7的负数是_________。
c) 38÷2的余数是_________。
d) 在数轴上，-2和2之间有________个整数。
e) 4/5是一个_________数。
2. 选择题：a) 下列哪个数是无理数？1) √22) 1.53) -54) 0.25b) 计算：(2 + 3) × 4 ÷ 2 =1) 82) 113) 64) 10c) 下列哪个数是正数？1) -92) 03) 54) -2d) 定义域是实数的函数图像是一条_________。
1) 直线2) 抛物线3) 高尔夫球杆4) 温度计3. 解答题：a) 用计算器验证下列方程是否成立：(2 + 3) × 4 ÷ 2 = 5b) 请列举2个无理数的例子，并说明它们的性质。
c) 如果一个数的绝对值是9，它可能是什么数？d) 请你举例说明正数与负数相加的规律。
4. 应用题：题干：一张圆形纸片的直径为14厘米，如图所示，将此圆形纸片剪成一个扇形，剪掉那一部份，使剩余的部份在对称轴上折上后叠起来刚好封闭形成一个圆锥形纸帽，问剪掉部分的圆心角是多少？(π取近似值3.14)图片部分省略，仅文字描述。
5. 拓展题：某商场进行打折促销，某商品原价100元。
第一天打9折出售，第二天再对折出售，以后每天都再对折出售。
请计算经过多少天后这个商品的售价低于10元？6. 相关题：题干：小明和小华合计有48个糖果，两人约定，将糖果分成若干份，每份4块。
剩下的2块，如果不够每份都分一块，就交给妈妈。
询问：小明和小华最多可得到多少个糖果，妈妈最多可能得到几块糖果？7. 推理题：a) 下列哪个数不是整数？1) -102) -√253) 04) 1/2b) 如果a是一个正数，那么a的相反数是__________。
8. 综合题：题干：某公司在一年内举办了两次员工聚餐，第一次聚餐花费了总预算的3/5，第二次聚餐花费了剩下预算的2/3。
初三数学培优试题及答案
初三数学培优试题及答案一、选择题（每题2分，共10分）1. 下列哪个数不是实数？A. πB. -3C. √2D. i2. 如果一个圆的半径是5，那么它的面积是多少？A. 25πB. 50πC. 100πD. 125π3. 已知a=3，b=2，求下列表达式的值：a^2 + b^2A. 13B. 17C. 19D. 214. 一个数的平方根等于它本身，这个数是：A. 0B. 1C. -1D. 45. 下列哪个是二次方程的解？A. x = 1B. x = -1C. x = 2D. x = 3（方程为：x^2 - 4x + 4 = 0）二、填空题（每题2分，共10分）6. 一个直角三角形的两条直角边分别为3和4，斜边的长度是______。
7. 一个正数的倒数是1/8，这个数是______。
8. 如果一个数的立方等于-27，那么这个数是______。
9. 一个数的绝对值是5，这个数可以是______或______。
10. 一个二次方程的判别式是36，那么这个方程的根的情况是______。
三、解答题（每题10分，共30分）11. 解方程：2x^2 - 5x - 3 = 0。
12. 证明：如果一个三角形的两边长度分别为a和b，且a < b，那么这个三角形的周长P满足P > 2a。
13. 一个工厂每天可以生产x个产品，每个产品的成本是c元，销售价格是p元。
如果工厂每天的利润是y元，写出y关于x的函数表达式。
四、综合题（每题15分，共20分）14. 一个圆的半径是7，圆心到一个点A的距离是5。
如果点A在圆内，求点A到圆上任意一点B的距离的最大值和最小值。
15. 一个班级有50名学生，其中30名学生喜欢数学，20名学生喜欢英语。
如果一个学生至少喜欢一门科目，求这个班级中同时喜欢数学和英语的学生人数的范围。
答案：一、选择题1. D2. B3. C4. A5. D二、填空题6. 5（根据勾股定理）7. 8（倒数的定义）8. -3（立方根的定义）9. 5，-5（绝对值的定义）10. 有两个不相等的实数根（判别式的定义）三、解答题11. 解：2x^2 - 5x - 3 = 0，使用求根公式，得到x1 = (5 + √41) / 4，x2 = (5 - √41) / 4。
初三数学培优测试卷
一、选择题（每题5分，共25分）1. 下列各数中，属于有理数的是（）A. √3B. πC. 0.1010010001…（循环小数）D. √-12. 已知 a > 0，b < 0，则下列不等式中正确的是（）A. a + b > 0B. a - b < 0C. -a - b > 0D. a - b > 03. 下列函数中，图象为一条直线的是（）A. y = x^2B. y = 2x + 1C. y = 3x - 4D. y = x^34. 已知 a，b，c 是三角形的三边，且 a + b = c，则下列结论正确的是（）A. 三角形是直角三角形B. 三角形是等腰三角形C. 三角形是等边三角形D. 三角形是钝角三角形5. 下列命题中，正确的是（）A. 两个平行四边形面积相等B. 两个矩形面积相等C. 两个菱形面积相等D. 两个正方形面积相等二、填空题（每题5分，共25分）6. 若 a = 3，b = -2，则 a^2 + b^2 的值为 ________。
7. 在直角坐标系中，点 A（2，3）关于 x 轴的对称点坐标为 ________。
8. 若一个数加上它的倒数等于 3，则这个数是 ________。
9. 已知等差数列的前三项分别是 2，5，8，则该数列的公差是 ________。
10. 一个长方形的长是 8cm，宽是 3cm，则它的面积是 ________cm^2。
三、解答题（每题15分，共45分）11. （15分）已知 a，b 是方程 x^2 - 3x + 2 = 0 的两个根，求 a + b 的值。
12. （15分）已知等腰三角形的底边长为 6cm，腰长为 8cm，求该三角形的周长。
13. （15分）已知函数 y = 2x - 1，求该函数的图象与 x 轴的交点坐标。
四、附加题（共20分）14. （10分）已知正方形 ABCD 的边长为 4cm，求对角线 AC 的长度。
2024年福建上杭三中 培优班九年级中考重难题型专练(2)
2024届第九周培优班练习一、完型填空I had a very special teacher in high school. Her husband unexpectedly died of a heart disease. About a week after his 1 , she shared some of her thoughts with a classroom of students.As the late afternoon sunlight came in 2 the classroom windows and the class was nearly over, she moved some things aside on her desk and sat down there. With a gentle look of reflection (沉思) , she said, “Before class is over, I’d like to share with you a thought that has3 to do with our class today, but I think it’s very important. Each of us is put here on earth to learn, share, love and enjoy. None of us knows4 this fantastic experience will end. It can be taken away at any moment.”Her eyes beginning to water, she went on: “So I’d like you all to5 . From now on, on your way to school, or home, find something beautiful to6 . It doesn’t have to be something you see, it could be a scent (气味) — perhaps of newly baked (烘焙) bread coming out of someone’s7 , or it could be the sound of the soft wind slightly touching the leaves in the trees ...”The class was completely quiet. We all picked up our books and went out of the room one by one 8 . That afternoon, I noticed more things on my way home from school than I had in a whole term.Take notice of something 9 on your lunch hour today. Go barefoot (赤脚) or walk on the beach at sunset. For as we get older, it is not the things we did that we often 10 , but the things we didn’t do.1．A．illness B．death C．accident 2．A．over B．across C．through 3．A．nothing B．something C．everything 4．A．where B．when C．what 5．A．make a promise B．take a breath C．have a meeting6．A．see B．enjoy C．notice 7．A．study B．kitchen C．bedroom 8．A．silently B．rapidly C．exactly 9．A．proper B．delicious C．special 10．A．remember B．forget C．regret二、阅读理解Sean Kachmarski knew he would come in last place even before he started the Edmonton Marathon (马拉松). He had only tried one full marathon before, and he had to stop before the end because he ran too slowly. With his family’s support, he decided to try one more time. He started his run at 5: 55 a.m; friends and family came out to cheer him on from a safe distance throughout the morning.But running is a battle against Sean’s body and mind. By mile 10, he was out of breath and already very tired. Rene Wache was volunteering at a water stand when he noticed Sean struggling. Thinking the runner just needed some motivation (动力) to get moving again, Rene began to run slowly with him.“You can do this, Sean!” he said, “Someone is so proud of you! You’ve got this.”The volunteer never planned to run all the way to the finish line with Sean, but that’s exacly what he did. For the next 4 miles, Rene encouraged him to keep going. By the end of the marathon, even the race announcers (播音员) and the local police had joined in to keep Sean moving forward!When Sean crossed the finish line with a time of 7: 07: 23, the first thing that he did was to give his personal cheerleader a huge hug! Sometimes we all need a litle encouragement to help us on our way! 11．It was ________ time for Sean to join in the full marathon.A．the first B．the second C．the third D．the last 12．Which picture shows Rene’s work in the text?A．B．C．D．13．What did Rene do to help Sean on the way?A．He ran with Sean.B．He gave Sean a hug.C．He asked others to help Sean.D．He provided Sean with more water.14．It took Sean about ________ to finish the full Marathon.A．4 hours.B．6 hours C．7 hours D．10 hours 15．What’s the main idea of the text?A．Marathon is a challenge.B．Never give up on the way. C．Encouragement is important.D．Always work together in sports.三、补全短文5选5You’re doing homework for a science class. There is a question: Do new born human babies see the world in black and white? You don’t know the answer.____16___.Searching online for the answer may get you a better grade on the homework. But it won’t help you learn. Guessing is better way to learn, a new study says.“____17．It will help you do better in the exam.” says scientist Amold Glass. If you just copy（抄）the answer, you’ll forget it easily in the future.Glass found this from analyzing (分析) the grades on homework and tests from 2008 to 2017. ___18．But by the late 2010s, many students were doing more poorly in the exam than in the homework.Glass thought something else was going on. ___19．Now almost everyone has one. So it would be easier today to quickly go online and find the answer to just about any homework question. ____20．And that might explain why they aren’t doing so well in the tests.A．But students can’t use phones during an exam.B．Always think about the question on your own first.C．For many years, students had done well in homework and the exam. D．One big thing was the rise of mobile phones.E. Do you guess or look for it online?四、语法填空阅读下面短文，根据语境、音标或所给单词的提示，在每个空格内填入一个适当的词，要求所填的词意义准确、形式正确，使短文意思完整、行文连贯。
初三数学培优试卷
初三数学培优试卷（1） 一、选择题1．下列图形，不是中心对称的图形是（ ）A.圆B.菱形C.矩形D.等边三角形 2．如果x 32-是二次根式，则x 的取值范围是（ ）． A ．32≠x B ．23≠x C ．23≥x D ．32≤x 3．下列计算正确的是（ ）． A ．228=- B ．14931227=-=-C ．()()15252=+- D ．23226=-4. 若关于x 的一元二次方程()0235122=+-++-m m x x m 的常数项为0，则m 的值等于（ ）．A ．1B ．2C ．1或2D ．05．当b>0时，b a 3-=（ ）．A ． ab a -B ．ab a --C ．ab aD ．ab a -6．如右图所示，一只蚂蚁从长、宽都是4，高是6的长方体纸箱的A 点沿纸箱爬 到B 点，那么它所行的最短路线的长是( ) ． A ．9 B ．10 C ．24 D ．2927．已知一个三角形两边长分别为3和6，若第三边长是方程2680x x -+=的解，则这个三角形的周长是（ ）．A ．11B ．13C ．11或13D ．以上答案都不对8. 如果关于x 的一元二次方程()011222=++-x k x k 有两个不相等的实数根，那么k 的取值范围是（ ）．A.41->kB. 41->k 且k ≠0C. 41-<kD. 41-≥k 且k ≠0二、填空题9．计算：()()6556-+= ．10. 关于x 的一元二次方程022=+-m mx x 的一个根为1，则方程的另一根为 ． 11．已知x 1，x 2是方程0362=++x x 的两实数根，则2112x x x x +的值为 . 12.从上午7点25到7点45分，时针旋转了 °，分针旋转了 °。
13.已知点A （ｘ，1）与点AO （4,ｙ）是关于原点O 的对称点，则ｘ＋ｙ= 。
B三、解答题 14．计算 （1）21223222330÷⨯； （2）32137a aa a a +-．15．解方程（1）x 2＋2x －35=0 （2）()()1231=+-x x （3）()222596x x x -=+-16．如图，实数a 、b 在数轴上的位置，化简()222b a b a ---.17．如图，已知△ABC ，画出△ABC 绕点C 顺时针旋转90° 后所得到的图形。
2024年福建上杭三中 培优班九年级中考重难题型专练
2024届培优班练习一、完型填空A Small Act Of Kindness Makes A Big DifferenceLast month I went through a very hard time, because my dear mom 1 . I flew to my hometown to pay my respects and say my goodbyes. Having spent 2 with my family, I had to head back.After boarding the plane, I found my window seat 3 by a young man. Usually it’s not a big deal to me, but I really wanted to sit there. 4 , he was asked to move.My mom was no longer there... I almost lost 5 of my emotions (情绪) when the plane taxied to the runway. Tears filled my eyes. Suddenly I felt a tap on my elbow. It was that young man checking on me. He asked me if I was OK and said he was there 6 I needed to talk. After all, we had a three-hour 7 sitting in the same row.I assured (使确信) him know that I wasn’t ready to talk, but his words had made me feel better. Although I didn’t take him up on his offer, I was 8 that a stranger knew I might need someone at that moment. People on planes 9 do everything they can not to talk to someone, I mean. But here this man was willing to give me all of his time.That moment last month has made me 10 look for ways to serve and help others. They may not be big things, but they may be big to that person.1．A．set off B．woke up C．passed away 2．A．days B．months C．years3．A．stolen B．taken C．kept4．A．As a result B．By the way C．From now on 5．A．ability B．memory C．control 6．A．unless B．if C．since7．A．flight B．walk C．drive 8．A．discouraged B．frightened C．touched9．A．never B．often C．seldom 10．A．actively B．casually C．lightly二、阅读理解The post-1990s generation is often described as self-centered and always asking for help. However, research results have painted a rather different picture: Thepost-1990s generation is independent, strong- minded and hard-working, according to a Peking University report.When it comes to learning and working, over 60 percent think their own interests are more important than others’ opinions. Most of them see successful businessmen as their idols (偶像). But it’s not because they are rich. “Their strong belief in themselves and never-give-up spirit have won the hearts of the generation.” said the report.In addition, the post-1990s generation has a strong sense of social responsibility. Many of them have taken part in volunteer work. They also try to be responsible by studying hard and behaving well.In the UK, many of the post-1990s generation have given up the drinking habits that the past generations had, The Telegraph noted. Most of them now have healthier hobbies, such as gardening and cooking.It’s hard to find time for a hobby if you are going out drinking, Kate Payne, author of The Hip Girl’s Guide to Homemaking, told The Telegraph.Changes in their hobbies have also helped them learn good manners. The Youth Justice Statistics report in the UK showed that young people are less rude and noisy in public.However, a generation’s trails (轨迹) don’t belong to every single person in it. “It’s what you do that can make you the kind of person you want to be.” said Cheng Dongfeng, director of West Anhui University.11．People thought the post-1990s generation was ______ according to Paragraph 1. A．self-centered and dependent B．independent and strong mindedC．strong-minded and hard-working D．responsible and hard-working 12．The post-1990s generation admires successful businessmen for their ________. A．experience B．devotion C．wealth D．will 13．Which of the following best describes young people in the UK?A．They are sociable.B．They are hard-drinking.C．They have healthier hobbies.D．They behave more impolitely. 14．What can we infer (推断) according to the text?A．The post-1990s generations behaved gently in public.B．Each post-1990s generation gets good education.C．The post-1990s generation is successful in business.D．Be yourself, and everyone can make a difference.15．What’s the text mainly about?A．What the post-1990s generation is really like.B．How the post-1990s generation learns good manners.C．Why the post-1990s generation likes successful businessmen.D．When the post-1990s generation has a strong sense of social responsibility.三、短文还原On Feb 15th this year, a cat named Larry celebrated its 10 years as Britain’s mouse-catcher in chief (主管). 16．And he is still working at London’s 10 Downing Street (唐宁街) now.Larry used to be homeless and was adopted (收养) by Dogs and Cats Home in London. 17．Brave and talented cats were badly needed to help out with the problem. 18．He has done a great job since then.Now Larry has become a national star. 19．People like to see him sleeping or greeting guests when he is not catching mice. Larry’s life story from a common cat to a popular star is an inspiration to us all. 20．And maybe normal as Larry used to be, we can also do great things one day.A．The photos taken in his free time attract a lot of attention online.B．His experience tells us why all animals are worth another chance.C．Famous for his mouse-catching skill and bravery, Larry was called in.D．In his time as a mouse-catcher, Larry has served three prime ministers.E.The chance came in 2011, some mice were seen in the prime minister's house.四、短文填词English and Chinese are totally different language. However, some proverbs (谚语) in English seem to have a “twin” in Chinese. Here are three of them.Double-edged sword (双刃剑). / Water can carry a boat, and it can also overturn it.The Chinese proverb was ___21．(one) used by Confucius. He reminded a ruler that his power was ___22．(base) on people who supported him. If the people were dissatisfied, they could easily fight ___23．the ruler. Similarly, double-edged sword reminds us that what brings us power can bring us harm, too.These days, both expressions are used to point out how our tools can___24．help or harm us. It all depends on how we use these tools.Think before you act. / Think three times, and act after.Both cultures are wise enough ____25_____ include this proverb. It is a good phrase to use when any friend is going to make a big ___26．(decide).Stands head and shoulders above the rest. / A crane standing among a group of chickens.A crane is a large bird with long ____27_____(leg) and a long neck. Just imagine such an animal ___28．(stand) among many chickens. The crane will naturally stand out, won’t it?So these two expressions now refer to someone ____29_____ stands out from the rest. You may use them to describe ___30．talented artist, an excellent job candidate, and so on.21_________ 22_________ 23__________ 24___________ 25___________ 26_________ 27_________ 28__________ 29___________ 30___________【答案】1．C 2．A 3．B 4．A 5．C 6．B 7．A 8．C 9．B 10．A 11．A 12．D 13．C 14．D 15．A16．D 17．E 18．C 19．A 20．B21．first 22．based 23．against 24．either 25．to 26．decision 27．legs 28．standing 9．who 30．a。
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1.His grandfather joined the Red Army in 1934.2.She got here this time last month. and she is still here.3.My father began to work in the factory in 1982. And he still works there.4.Jack got up fifteen minutes ago.5.The soldier joined the Party in 1996.6.How long have you kept the book borrowed from the library？7.My brother does homework after supper ．（否定句）8.I think the boys are from England ．（否定句）9.There is something wrong with my computer ．10.He wasn’t old enough to join the army.11.The box is too heavy for us to carry. The box is so heavy that nobody can lift it.rade Wu is so careless that he can’t do the job well.13.She was vary excited at the news. She couldn’t say a word.14.He went to school at the age of seven.He spent three days going over his lessons.15.It took him quite a long time to get the work done.18．My little brother asked me. “Does the earth move around the sun?”19. The policeman said to the boy, “Don’t play on the road.”20. “Don´t lose your key.” she said to her son.21. We noticed that he was standing at the school gate.22. Lin Tao runs faster than the other two boys.23. This coat fits me. That coat fits me. too.24. If you are strict in your study, you'll catch up with your classmates.25. My mother doesn’t go to work by bus any longer.1. He _______( stay) her since last year.2. They ______( learn) English for ten years.3. --- __________ you ever ___________ (read) the book? ---No, not yet.4. How many times _____ he ______________ ( take part in) the sports meeting?5. We ________________ (be) to the Great Wall twice, so he goes to school himself.6. His father ______________ ( go) to Shanghai, so he goes to school himself.7. ---Where is Jim? --- He __________________ ( go)to the office.8. Look! The twins _________________ ( dance) over there.9. ________ your teacher __________________ ( get) back yesterday?10. Sometimes our school __________________ ( have) a school trip in spring.11. I study English by ___________( listen) to tapes.12. What about ____________ ( read) aloud to practice pronunciation? 13. It’s never too young ______ ( study).14. _________( take) notes in class is _______(help).15. I think it’s a good way _____________ ( watch) English movies.16. _____( join) the English club was the best way _____( improve) her English.17. We were __________(interest) in the ________( interest) story that he told us.18. They always end up _________ ( speak) in Chinese.19. My mother doesn’t know how _____________( drive) a car.20. The little girl has to practice __________( play) the piano an hour every day.21. Why not _________( ask) me to his welcome party?22. I want to find a pen pal __________( practice) English.23. It’s not easy _____________ ( understand) what he said.24. One of them _______( be ) from Tibet. 25. Do you enjoy _____( play) the violin?26. They decided ____________( swim) across Zhujiang River.27. Her dream is _____( become) a pilot. 28. This kind of fruit _____( taste) delicious29. Our school ________( have) a sports meeting next week unless it _______( rain).30. We should try our best _____________( help) the poor girl.31 Let’s _____________( not) worry about our problems.32. The lady can _____( easy) become angry33. Did you use _____( have) long hair?34. Please ____________ ( not open) the window. It’s too noisy outside.35. He is _____________( terrify) of the dog.36. The old woman is used to ___________( live) alone.37. Let us go shopping, _______? 38. I heard a _________ ( fun) joke last night.39. His mother looked after her as _______( good) as she could.40. The little boy _______( use) to be shy. He is afraid of _______( speak) in public.41. His mother’s love helped hime _______( feel) _______( good) about himself.42. He has worked since his father _________( die).43. Try to make the students _______( pay) attention to _______( watch) the match.44. The TV set ________________( make) in Japan.45. The trees in our school ___________( water) twice a week.46. English ____________ in Canada. 47. The factory __________( build) in 1958.48. Who is ______________( popular) in your city?49. It is reported that more new teaching buildings __________ ( build) in our schoolnext term.50. I ________( tell) to get there before seven tomorrow, so I’ll have to get up early.13. It’s never too young ______ ( study).14. _________( take) notes in class is _______(help).15. I think it’s a good way _____________ ( watch) English movies.16. _____( join) the English club was the best way _____( improve) her English.17. We were __________(interest) in the ________( interest) story that he told us.18. They always end up _________ ( speak) in Chinese.19. My mother doesn’t know how _____________( drive) a car.20. The little girl has to practice __________( play) the piano an hour every day.21. Why not _________( ask) me to his welcome party?22. I want to find a pen pal __________( practice) English.23. It’s not easy _____________ ( understand) what he said.24. One of them _______( be ) from Tibet. 25. Do you enjoy _____( play) the violin?26. They decided ____________( swim) across Zhujiang River.27. Her dream is _____( become) a pilot. 28. This kind of fruit _____( taste) delicious29. Our school ________( have) a sports meeting next week unless it _______( rain).30. We should try our best _____________( help) the poor girl.31 Let’s _____________( not) worry about our problems.32. The lady can _____( easy) become angry33. Did you use _____( have) long hair?34. Please ____________ ( not open) the window. It’s too noisy outside.35. He is _____________( terrify) of the dog.36. The old woman is used to ___________( live) alone.37. Let us go shopping, _______? 38. I heard a _________ ( fun) joke last night.39. His mother looked after her as _______( good) as she could.40. The little boy _______( use) to be shy. He is afraid of _______( speak) in public.41. His mother’s love helped hime _______( feel) _______( good) about himself.42. He has worked since his father _________( die).43. Try to make the students _______( pay) attention to _______( watch) the match.44. The TV set ________________( make) in Japan.45. The trees in our school ___________( water) twice a week.46. English ____________ in Canada. 47. The factory __________( build) in 1958.48. Who is ______________( popular) in your city?49. It is reported that more new teaching buildings __________ ( build) in our schoolnext term.50. I ________( tell) to get there before seven tomorrow, so I’ll have to get up early. 16.His grandfather joined the Red Army in 1934.17.She got here this time last month. and she is still here.18.My father began to work in the factory in 1982. And he still works there.19.Jack got up fifteen minutes ago.20.The soldier joined the Party in 1996.21.How long have you kept the book borrowed from the library？22.My brother does homework after supper ．（否定句）23.I think the boys are from England ．（否定句）24.There is something wrong with my computer ．25.He wasn’t old enough to join the army.26.The box is too heavy for us to carry. The box is so heavy that nobody can lift it.rade Wu is so careless that he can’t do the job well.28.She was vary excited at the news. She couldn’t say a word.29.He went to school at the age of seven.He spent three days going over his lessons.30.It took him quite a long time to get the work done.18．My little brother asked me. “Does the earth move around the sun?”19. The policeman said to the boy, “Don’t play on the road.”20. “Don´t lose your key.” she said to her son.21. We noticed that he was standing at the school gate.22. Lin Tao runs faster than the other two boys.23. This coat fits me. That coat fits me. too.24. If you are strict in your study, you'll catch up with your classmates.25. My mother doesn’t go to work by bus any longer.1. He _______( stay) her since last year.2. They ______( learn) English for ten years.3. --- __________ you ever ___________ (read) the book? ---No, not yet.4. How many times _____ he ______________ ( take part in) the sports meeting?5. We ________________ (be) to the Great Wall twice, so he goes to school himself.6. His father ______________ ( go) to Shanghai, so he goes to school himself.7. ---Where is Jim? --- He __________________ ( go)to the office.8. Look! The twins _________________ ( dance) over there.9. ________ your teacher __________________ ( get) back yesterday?10. Sometimes our school __________________ ( have) a school trip in spring.11. I study English by ___________( listen) to tapes.12. What about ____________ ( read) aloud to practice pronunciation?。