2025年ACT数学填空专项训练卷

2025年ACT数学填空专项训练卷考试时间：______分钟总分：______分姓名：______一If$3x-7=11$,whatisthevalueof$2x+5$?二Arectanglehasalengththatistwiceitswidth.Iftheperimeteroftherectangleis30inches,whatistheareaoftherectangleinsquareinches?三Simplifytheexpression$\frac{6x^3y^2}{3xy^4}$.四Whatistheslopeofthelinepassingthroughthepoints$(4,-3)$and$(-2,5)$?五If$f(x)=x^2-4x+3$,whatisthevalueof$f(2)$?六Solvetheinequality$5-2x>1$.Expressthesolutioninintervalnotation.七Acirclehasacenterat$(2,-1)$andaradiusof5.Whatistheequationofthecircle?八Inatriangle,themeasuresoftwoanglesare45degreesand55degrees.Whatisthemeasureofthethirdangleindegrees?九If$a=\frac{1}{2}$and$b=\frac{1}{3}$,whatisthevalueof$a^2+b^2$?十Astoreishavinga25%offsale.Ashirtthatoriginallycosts$40isonsaleforhowmuch?十一Themeanofasetof8numbersis12.Ifonenumberisremovedfromtheset,thenewmeanis15.Whatwasthevalueofthenumberthatwasremoved?十二If$f(x)=3x-2$and$g(x)=x+4$,whatisthevalueof$f(g(3))$?十三Thevolumeofacubeis64cubiccentimeters.Whatisthelengthofoneedgeofthecubeincentimeters?十四Afunction$h$isdefinedas$h(x)=\sqrt{x+3}$.Forwhatvalueof$x$is$h(x)=5$?十五Inarighttriangle,thelengthsofthetwolegsare6cmand8cm.Whatisthelengthofthehypotenuseincm?试卷答案一解析：解方程$3x-7=11$，得$3x=18$，即$x=6$。将$x=6$代入$2x+5$，得$2(6)+5=12+5=17$。二解析：设rectangle的width为$w$，则length为$2w$。perimeter为$2(length+width)=2(2w+w)=6w=30$。解得$w=5$。所以length为$2(5)=10$。area为$length\timeswidth=10\times5=50$平方英寸。三解析：$\frac{6x^3y^2}{3xy^4}=\frac{6}{3}\times\frac{x^3}{x}\times\frac{y^2}{y^4}=2\timesx^{3-1}\timesy^{2-4}=2x^2y^{-2}=\frac{2x^2}{y^2}$。四解析：slope$m=\frac{y_2-y_1}{x_2-x_1}=\frac{5-(-3)}{-2-4}=\frac{8}{-6}=-\frac{4}{3}$。五解析：$f(2)=(2)^2-4(2)+3=4-8+3=-1$。六解析：解不等式$5-2x>1$，得$-2x>-4$。两边同时除以-2（注意不等号方向改变），得$x<2$。区间表示为$(-\infty,2)$。七解析：圆的标准方程为$(x-h)^2+(y-k)^2=r^2$。其中$(h,k)$是center，$r$是radius。代入$(2,-1)$和$5$，得$(x-2)^2+(y-(-1))^2=5^2$，即$(x-2)^2+(y+1)^2=25$。八解析：三角形内角和为180度。第三角angle$=180-45-55=80$度。九解析：$a=\frac{1}{2}$，$b=\frac{1}{3}$。$a^2=(\frac{1}{2})^2=\frac{1}{4}$。$b^2=(\frac{1}{3})^2=\frac{1}{9}$。$a^2+b^2=\frac{1}{4}+\frac{1}{9}=\frac{9}{36}+\frac{4}{36}=\frac{13}{36}$。十解析：折扣为25%，即0.25。折扣后price$=40\times(1-0.25)=40\times0.75=30$美元。十一解析：设原set的sum为$S$。则$\frac{S}{8}=12$，得$S=96$。设removednumber为$n$。新set的sum为$S-n=96-n$，新的数量为7。新mean为$\frac{96-n}{7}=15$。解得$96-n=105$，即$n=-9$。十二解析：$g(3)=3+4=7$。$f(g(3))=f(7)=3(7)-2=21-2=19$。十三解析：设cube的edgelength为$l$。体积volume$=l^3$。$l^3=64$。解得$l=\sqrt[3]{64}=4$厘米。十四解析：解方程$\sqrt{x+3}=