{"id":4780,"date":"2015-09-18T11:49:34","date_gmt":"2015-09-18T11:49:34","guid":{"rendered":"http:\/\/dientoan.julia.us\/?p=4780"},"modified":"2015-09-26T11:47:09","modified_gmt":"2015-09-26T11:47:09","slug":"sat-practice-math-test-set-1","status":"publish","type":"post","link":"http:\/\/www.dientoan.us\/?p=4780","title":{"rendered":"SAT Practice Math Test Set 1"},"content":{"rendered":"<p><script type=\"text\/javascript\" src=\"\/php\/jsxgraphcore.js\"><\/script><script type=\"text\/x-mathjax-config\">MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'], ['\\\\(','\\\\)']]}});<\/script><script\ntype=\"text\/javascript\" src=\"\/php\/mathjax\/MathJax.js?config=TeX-AMS-MML_HTMLorMML\"><\/script><\/p>\n<style>\n.myfont {border: 0px solid black;padding: 0px;border-radius:0px;\nfont-family: Bitstream Charter,Verdana;font-weight:bold;font-style:normal;\nfont-size:20pt}\n.copyright {color:#C0C0C0;\nfont-weight:bold;font-style:italic;font-size:9pt;\nfont-family:Bitstream Charter,Verdana}\n.label {color:#656535;\nfont-weight:bold;font-style:normal;font-size:9pt;\nfont-family:Bitstream Charter,Verdana}\n<\/style>\n<div id=container>\n<div id=left style=\"width:50%;float:left;margin-right:10px;\">\n<div align=center><div align=center vAlign=middle style=\"background:#EEE;border:solid 1px #AAA;padding:3px;\">SAT Math Review Set 1 Key<\/div><\/div>\n<div style=\"border:solid 1px;padding:3px;\">1. Each term of a certain sequence is greater than the term before it. The <u>difference<\/u> between any two consecutive terms in the sequence is always the <u>same number<\/u>. If the fourth and sixth terms of the sequence are 61 and 93, respectively, what is the ninth term ? (<u>Answer<\/u>: 141)<\/div>\n<p><u>Key<\/u>: Let $a$ is the difference between two consecutive terms.<br \/>\nFourth term: $61$<br \/>\nFifth term: $61+a$<br \/>\nSixth term: $61+2a$, therefore, $61+2a=93$. Solve for $a$ to get $a=\\dfrac{93-61}{2}=16$<br \/>\n<u>Ninth term<\/u>: $61+5a=61+5&times;{16}=141$<\/p>\n<div style=\"border:solid 1px;padding:3px;\">2. The square of $x$ is equal to 9 times the square of $y$. If $x$ is 5 more than three times $y$, what is the value of $x$ ? (<u>Answer<\/u>: $\\dfrac{5}{2}$)<\/div>\n<p><u>Key<\/u>: $x^2 = 9y^2$. Take the square root of both sides yields  $x=\\pm{3y}$. Taking the positive solution gives $3y=5+3y$, which is a contradiction (no solution). Substituting the negative solution to $x=5+3y$ yields $-3y=5+3y$. Solve for $y$ gives $y=-\\dfrac{5}{6}$. Finally, solve for $x$ gives $x=5+3\\left(-\\dfrac{5}{6}\\right)=\\dfrac{5}{2}$.<\/p>\n<div style=\"border:solid 1px;padding:3px;\">3. In the following figure, the circle with center O is inscribed in square ABCD. What is the area of the shaded portion of the square ? (<u>Answer<\/u>: $\\dfrac{3\\pi}{4}$)<\/p>\n<div id=\"q3\" align=center class=\"jxgbox\" style=\"width:120px;height:120px;\nbackground-color:'white';border-color:'transparent';border-radius:0px;margin-left:25%;font-family:'Bitstream Charter',Verdana;\"><\/div>\n<\/div>\n<p><script type=\"text\/javascript\">\n     JXG.Options.text.useMathJax=true;\n     JXG.Options.text.cssClass='myfont';\n     b=JXG.JSXGraph.initBoard('q3',\n{boundingbox:[-0.5,4.50,4.50,-0.5],\naxis:false,grid:false,keepAspectRatio:false,\nshowCopyright:false,showNavigation:false});\n     prop=eval({strokeWidth:1,strokeColor:'black',strokeOpacity:0.90,\nfixed:true,highlight:false});\n     b.create('segment',[[0,0],[0,4]],prop);\n     b.create('segment',[[0,4],[4,4]],prop);\n     b.create('segment',[[4,4],[4,0]],prop);\n     b.create('segment',[[4,0],[0,0]],prop);\n     radius=2;x0=2;y0=2;\n     b.create('circle',[[x0,y0],radius],prop);\n     cosx=radius*Math.cos(Math.PI\/4);\n     sinx=radius*Math.sin(Math.PI\/4);\n     b.create('sector',[[x0,y0],[x0+cosx,y0+sinx],[x0+cosx,y0-sinx]],\n{strokeWidth:1,strokeColor:'black',strokeOpacity:0.80,fillColor:'black',\nfixed:true,highlight:false});\n     b.create('segment',[[x0,y0],[4,4]],prop);\n     b.create('segment',[[x0,y0],[4,0]],prop);\n     b.create('text',[2.25,2,\"O\"],{fontsize:14,strokeColor:'black'});\n     b.create('text',[-.40,4.25,\"A\"],{fontsize:14,strokeColor:'black'});\n     b.create('text',[4.10,4.25,\"B\"],{fontsize:14,strokeColor:'black'});\n     b.create('text',[4.10,-.10,\"C\"],{fontsize:14,strokeColor:'black'});\n     b.create('text',[-.40,-.10,\"D\"],{fontsize:14,strokeColor:'black'});\n     b.create('text',[-.40,2.00,\"2\"],{fontsize:14,strokeColor:'black'});\n<\/script><u>Key<\/u>: The square has length of 2. Since the circle is inscribed in the square, its diameter is equal to the side of the square. The radius is 1. The area of the square is $\\pi{r^2}=\\pi$. The shaded area is $\\dfrac{3}{4}$ of the square or $\\dfrac{3\\pi}{4}$.<\/p>\n<div style=\"border:solid 1px;padding:3px;\">4. The following triangle is isosceles and $AB > AC$. Which of the following must be FALSE ?<br \/>\n(A) $AB = BC$   (B) $BC = AC$<br \/>\n(C) $x=y$   (D) $x=z$   (E) $y=z$<br \/>\n(<u>Answer<\/u>: (E))<\/p>\n<div id=\"q4\" class=\"jxgbox\" style=\"width:120px;height:120px;\nbackground-color:'white';border-color:'transparent';border-radius:0px;\nmargin-left:25%;font-family:'Bitstream Charter',Verdana;\"><\/div>\n<\/div>\n<p><script type=\"text\/javascript\">\n     JXG.Options.text.useMathJax=true;\n     JXG.Options.text.cssClass='myfont';\n     b=JXG.JSXGraph.initBoard('q4',\n{boundingbox:[-0.5,4.10,4.50,-0.5],\naxis:false,grid:false,keepAspectRatio:false,\nshowCopyright:false,showNavigation:false});\n     prop=eval({strokeWidth:1,strokeColor:'black',strokeOpacity:0.90,\nfixed:true,highlight:false});\n     x0=2;\n     y0=Math.sqrt(3)*x0;\n     b.create('segment',[[0,0],[x0,y0]],prop);\n     b.create('segment',[[4,0],[x0,y0]],prop);\n     b.create('segment',[[0,0],[4,0]],prop);\n     prop=eval({fontsize:14,strokeColor:'black'});\n     b.create('text',[-.40,-.10,\"A\"],prop);\n     b.create('text',[4.10,-.10,\"C\"],prop);\n     b.create('text',[x0-.10,y0+0.25,\"B\"],prop);\n     b.create('text',[0.30,0.30,\"$x$&deg;\"],prop);\n     b.create('text',[3.20,0.30,\"$z$&deg;\"],prop);\n     b.create('text',[x0-.30,y0-0.60,\"$y$&deg;\"],prop);\n<\/script><u>Note<\/u>: Figure not drawn to scale.<br \/>\n<u>Key<\/u>: Since the triangle is isosceles and $AB > AC$, therefore either $AB = BC$ ((A) is true) or $BC = AC$ ((B) is true). If $AB = BC$, then $x=z$ ((D) is true). If $BC = AC$, then $x=y$ ((C) is true). Since $AB > AC$, $z>y$ ((E) is <u>FALSE<\/u>).\n<\/div>\n<div id=right style=\"margin-left:52%;\">\n<div style=\"border:solid 1px;padding:3px;\">5. <u>Algebra graph<\/u>.<\/p>\n<div id=\"q5\" class=\"jxgbox\" style=\"width:150px;height:100px;\nbackground-color:'white';border-color:'transparent';border-radius:0px;\nmargin-left:20%;font-family:'Bitstream Charter',Verdana;\"><\/div>\n<p><script type=\"text\/javascript\">\n     JXG.Options.text.useMathJax=true;\n     JXG.Options.text.cssClass='myfont';\n     b=JXG.JSXGraph.initBoard('q5',\n{boundingbox:[-5.5,5.10,5.5,-1.5],\naxis:false,grid:false,keepAspectRatio:true,\nshowCopyright:false,showNavigation:false});\n     prop=eval({strokeWidth:1,strokeColor:'black',strokeOpacity:0.90,\nfixed:true,highlight:false});\n     xAxis=b.create('axis',[[-5,0],[5,0]],{\nname:'\\\\(x\\\\)',withLabel:true, \nlabel:{position:'rt',offset:[0,-5],highlight:false},\nfirstArrow:false,lastArrow:true,strokeColor:'black',highlight:false});\n     xAxis.removeAllTicks();\n     b.create('ticks',[xAxis,1],\n{majorHeight:6,minorHeight:2,minorTicks:0,drawZero:true,\ndrawLabels:false,strokeColor:'black',highlight:false});\n     yAxis=b.create('axis',[[0,-1],[0,5]],{\nname:'\\\\(y\\\\)',withLabel: true, \nlabel:{position:'urt',offset:[-15,0],highlight:false},\nfirstArrow:false,lastArrow:true,strokeColor:'black',highlight:false});\n     yAxis.removeAllTicks();\n     b.create('ticks',[yAxis,1],\n{majorHeight:6,minorHeight:2,minorTicks:0,drawZero:true,\ndrawLabels:false,strokeColor:'black',highlight:false});\n     f=b.create('functiongraph',\n[function(x){return (-2*x+4);},-0.5,2.5],\n{strokeColor:'black',highlight:false});\n<\/script>The equation of the line above is $y=-2x+4$. Which of the following is the graph of $y=|-2x+4|$ ?<br \/>\n(<u>Answer<\/u>: )<\/div>\n<p><u>Key<\/u>:<\/p>\n<div style=\"border:solid 1px;padding:3px;\">6. <u>Algebra functions<\/u>. A certain function $f$ has the property that $f(x+y)=f(x)+f(y)$ for all values of $x$ and $y$. Which of the following statements must be true when $a=b$ ?<br \/>\nI. $f(a+b)=2f(b)$<br \/>\nII. $f(a+b)=f(a)\\cdot{f(b)}$<br \/>\nIII. $f(a)+f(a)=f(2b)$<br \/>\n(<u>Answer<\/u>: I and III only)<\/div>\n<p><u>Key<\/u>:<br \/>\nIf $a=b$, then $f(a+b)=f(b+b)=f(b)+f(b)=2f(b)$. Choice I is true. Also, $f(a)+f(a)=f(2a)=f(2b)$, choice III is also true.<\/p>\n<div style=\"border:solid 1px;padding:3px;\">7. <u>Permutations<\/u>.<br \/>\nIf the following 5 cards are placed in a row so that the card number 3 is never at either end, how many different arrangements are possible ?<\/p>\n<div id=\"q7\" class=\"jxgbox\" style=\"width:150px;height:30px;\nbackground-color:'white';border-color:'transparent';border-radius:0px;\nmargin-left:20%;font-family:'Bitstream Charter',Verdana;\"><\/div>\n<p><script type=\"text\/javascript\">\n     JXG.Options.text.useMathJax=true;\n     JXG.Options.text.cssClass='myfont';\n     b=JXG.JSXGraph.initBoard('q7',\n{boundingbox:[-0.1,1.10,5.1,-0.1],\naxis:false,grid:false,keepAspectRatio:true,\nshowCopyright:false,showNavigation:false});\n     prop=eval({strokeWidth:1,strokeColor:'black',fontsize:16,\nfixed:true,highlight:false});\n     x=y=0;\n     s=0.80;\n     for(n=0;n<5;n++){\n     b.create('segment',[[x,y],[x,y+s]],prop);\n     b.create('segment',[[x,y+s],[x+s,y+s]],prop);\n     b.create('segment',[[x+s,y+s],[x+s,y]],prop);\n     b.create('segment',[[x+s,y],[x,y]],prop);\n     b.create('text',[x+.25,y+.35,(n+1).toString()],prop);\n     x+=1.0;}\n<\/script>(<u>Answer<\/u>: 72)<\/div>\n<p><u>Key<\/u>:<br \/>\nThe number of arrangements for 4 cards 1, 2, 4, 5 is $4!=4&times;3&times;2&times;1=24$. Since card number 3 can be placed only after the first, second, and third positions (1, 2, or, 4), the number of possible arrangements are $24&times;3=72$.\n<\/div>\n<\/div>\n<p>Sau m\u1ed9t th\u1eddi gian, c\u00f4 \u1ea5y kh\u00f4ng c\u00f2n \u1edf \u0111\u00f3 <\/p>\n","protected":false},"excerpt":{"rendered":"<p>1. Each term of a certain sequence is greater than the term before it. The difference between any two consecutive terms in the sequence is always the same number. If the fourth and sixth terms of the sequence are 61 &hellip; <a href=\"http:\/\/www.dientoan.us\/?p=4780\">\u0110\u1ecdc ti\u1ebfp <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[2],"tags":[],"_links":{"self":[{"href":"http:\/\/www.dientoan.us\/index.php?rest_route=\/wp\/v2\/posts\/4780"}],"collection":[{"href":"http:\/\/www.dientoan.us\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.dientoan.us\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.dientoan.us\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.dientoan.us\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4780"}],"version-history":[{"count":0,"href":"http:\/\/www.dientoan.us\/index.php?rest_route=\/wp\/v2\/posts\/4780\/revisions"}],"wp:attachment":[{"href":"http:\/\/www.dientoan.us\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4780"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.dientoan.us\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4780"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.dientoan.us\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4780"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}