2026年河北省中考麒麟卷数学试题及答案（一）

一、选择题（本大题共12小题，每小题3分，共36分）1-5ADBCD6-10BDCAB11-12CC二、填空题（本大题共4小题，每小题3分，共12分）【解析】连接AC，交BD于点O，过点E作EG⊥OD于点G∵四边形ABCD是菱形∴AO＝AD2-OD2＝4，EG∥AO∵E是AD的中点 1DEEG 1==2三、解答题（本大题共8小题，共72分.解答应写出文字说明、证明过程或演算步骤） （2）设□为x，则：6－2x－5＜-13∴指针应指向8所在区域 7分 2分正确解答：①×2，得：2x－4y＝8③③-②,得：-y＝7把y＝-7代入①,得：x－2×（-7）＝4解得：x＝-10·····························································································4分∴原方程组的解为···········································································5分（2）联立得：······························································································6分解得：〈ly=8·······································································································（2）∵△ABC≌△ADE∵F为BD的中点∴AF⊥BD···········································································································8分20.（1）5036····································································································2分解23（元）························································4分众数为10元···································································································5分学生人数为50人，从小到大排列后位于第25第26名捐款为15元所以中位数是15元··························································································6分（3）设李老师的捐款金额为x，目前捐款总人数为51人，中位数位于第26位，捐款数仍是15元则15··································································································7分李老师的捐款金额为115元····················································································8分21.解1）30°·········································································································2分（2）方法一：如下图，点M即为所求5分5分提示：∵∠CMD＝2∠CED∴作出DE的垂直平分线交CE于点M即可方法二：如下图，点M即为所求5分提示：∵∠CMD＝2∠CED＝60°∴过点D作CD的垂线交CE于点M即可（答案不唯一，作法正确即可）（3）如图1，若⊙O与CD，DE两边相切，则点O在∠CDE的平分线上如图2，若⊙O与BC，DE两边相切∴C是⊙O与BC边的切点∴D是⊙O与DE边的切点综上，OE的长为33或43··················································································9分34J······················································3分3J/（kg·℃)·······················································································5分34，解得m∴冷冻的猪肉的质量为1.68kg·················································································9分23.解1）90°·········································································································3分（2）由题知点A'在以B为圆心，以BA长为半径的圆上，当B，A'，D共线时，DA'的值最小····4分∴DA'的值最小为10－6＝4·····················································································5分∴DF＝5·············································································································8分 1 1若A'在直线BC上方，α=90°-30°=60°,则边BA扫过区域的面积为若A'在直线BC下方，α=90°+30°=120°,则边BA扫过区域的面积为24.解1）将A（3，1B（0，-2代入y＝x2＋bx＋c 4分（2）①把x＝5代入y＝x2－2x－2中，y＝13≠6∴点P（5，6）不在图象C1上 6分②根据平移规律可得新抛物线解析式为：yx－1－n）2－3当C2经过点P（5，6）时，则有65－1－n）2－3解得：n＝1或n＝7····························································································8分（3）①设直线AB的解析式为y＝kx＋a将A（3，1B（0，-2）代入得1解得∴直线AB的解析式为y＝x－2设直线GG'的解析式为y＝x＋d，过G（1，-3）∴直线GG'的解析式为y＝x－4，G'在x轴上，G'的坐标为（4，0）∴G移动的距离GG'为··································································10分②G