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第五期 跟踪反馈 挑战自我一、1.C 2.C 3.B 4.D 5.A 6.A 7.D 8.D二、1.4,- 12 ,116 2.相等,互为相反数3.5.4 × 1011 4.百万;1,3,85.3 6. - 2,5 7.64 8.29三、1.(1)1.5 × 108千米;(2)1.3 × 105万人或 1.3 × 109人.2.由于 1.5 ×102cm 是近似数,所以其范围是145cm 耀 154cm.若小亮的身高是154cm,小满的身高是145cm,则相差9cm,故有可能.3.(1)- 15 ;(2)- 25;(3)- 12.四、1.第 1 次剩下原长的 12 ,第 2 次剩下原长的? ?122,…,第 6 次剩下原长的? ?126,即剩下的木条长为 3 × 164 = 364(m).2.13+23+33+ … + n3= 14 n2(n +1)2,13+23+ … +1003= 14 ×1002×1012= 25502500 >( -5000)2.提升能力 超越自我 (1)< ,<,>,>,> ;(2)当 n = 1,2 时,nn+1<(n + 1)n;当 n为大于等于 3 的整数时,nn+1>(n + 1)n;(3)20082 009> 2 0092 008.
第7期 跟踪反馈 挑战自我一、1.B 2.D 3.A 4.D 5.D 6.A 7.C 8.A二、1. 13 a - 5,12 x - 13 y 2.答案不惟一,如 2 009x2y3.1,- 2x,- 13 x2,14 x3 4.四,四,- 165.1.5(S - 3)+ 6 6.(a + b)(a - b)7.( - 2)nxn+1 8.〔(1 + 25% )m × 90% - m〕三、1.(1)(a - b + 3);(2)(4x - 1);(3)(300 + 10n);(4)x + y2 .2.不对,问题出在 ①.正确解法:由原多项式可知,最高次项是 - 5xmy3,于是可得 m + 3 = 6,m = 3.所以原多项式为 - 5x3y3+104x3- 4xy2.3.(1) 13 m + 23 m × 15 ;(2)56.四、1.(1)7;(2)10;(3)13;(4)3n + 1.2.第(1)种方法的绳子长为 4a +4b +8c,第(2)种方法的绳子长为 4a +4b +4c,第(3)种方法的绳子长为 6a +6b +4c,从而可知第(3)种方法绳子最长,第(2)种方法绳子最短.提升能力 超越自我 1.这个多项式最多有五项.如一个符合要求的多项式为 a3+ a2b + ab2+ b3+ 1.若 a、b满足 a + b +(b - 1)2= 0,可知 a + b= 0,b - 1 = 0,解得 a = - 1,b = 1.a3+ a2b + ab2+ b3+1 =( -1)3+( - 1)2×1 +( - 1)×1 +13+1 =( -1)+1 +( - 1)+ 1 + 1 = 1.2.(1)设甲报的数为 a,游戏过程用整式描述为(a + 1)2- 1;(2)399;(3)a = 5 或 - 7.
第8期 跟踪反馈 挑战自我一、1.B 2.B 3.D 4.C 5.A 6.B 7.C 8.D二、1.8a + 10b 2.5,4 3. - 1 4.m - n5.x3- 6x2 6. - 19 7. - 188.x2- 15x + 9,- 29x + 15三、1.(1)4x - 3y;(2)a2- 92 a + 1.2.化简结果:- 3x2+ 12;求值结果:0.3.(1)0.5n + 0.6;(2)4.1 元.四、1.理由:原式 = 2a3- 3a2b - 2ab2- a3+ 2ab2+ b3+ 3a2b - a3- b3= 0,与 a、b的值无关,所以他俩的运算结果都是正确的.2.(1)50,5 050;(2)a +(a + d)+(a + 2d)+ … +(a + 99d)= a + a + d + a + 2d + … + a + 99d =(a + a + … + a)+(0 + d + 2d + … +99d)= 100a + 99d × 50 = 100a + 4 950d.提升能力 超越自我 1.5(2n + 2)- 1010= 10n + 10 - 1010= n.2.阴影部分的面积等于大长方形面积减去 3 个空白三角形的面积,即 S = 4x × 4y - 12 × 4y × x - 12 × 3x × 3y - 12 × 3x × 3y= 5xy.该单项式的系数为 5,次数为 2.
第11期 跟踪反馈 挑战自我一、1.C 2.A 3.D 4.A 5.B 6.B 7.C 8.B二、1.②③④,②④ 2.x = 2,x = 1 3. ± 3 4. - 15.0.7x = 1 000 6.48 7.208.6x + 6 × 32 x + 120 = 720三、1.根据题意,得 3m - 3 = 1,解得 m = 43 ,当 m = 43 时,代入原方程中,得 2x + 4 × 43 = 0,解得 x = - 83 .2.由于 3 = 3, - 3 = 3,所以 1 - 2x = 3 或 1 - 2x = - 3,解分别为 x = - 1 和 x = 2,所以方程 1 - 2x = 3 的解为 x = - 1或 x = 2.3.(1)(1 + 20% )x,2(x - 10);(3)把 x = 25分别代入方程的左边和右边,得左边 =(1 + 20% )× 25 = 30,右边 = 2 ×(25 - 10)= 30.因为左边 = 右边,所以 x = 25 是方程(1 + 20% )x = 2(x - 10)的解.这就是说乙班植树的棵数的确是 25 棵,从上面检验过程可以看出甲班植树棵数应是 30 棵,而不是 35 棵.四、1.猜想:关于 x的方程 x + mx = c+ mc 的解是 x1= c,x2= mc .验证:当 x1= c时,x + mx = c+ mc ,所以 x1= c是方程的解.同理 x2= mc 也是原方程的解.2.(3x -1),x +(3x -1)= 47.正确,由于小明的年龄变为此时的 2倍时,有 x + x = 2x,小明爸爸的年龄变为(3x -1)+ x = 4x -1,而4x -1 = 2 ×2x -1,所以题目中的说法正确.提升能力 超越自我 1.(1)设 x小时后两车相距 660 千米,则 72x + 96x = 660 - 408;(2)设快车开出 x小时后两车相遇,则 72 + 72x + 96x = 408;(3)设 x小时后快车与慢车相距 60 千米,则 408 + 72x - 60 = 96x,或 408 + 72x = 96x - 60.2.等式两边都减去(3a + 2b),得 3b + 2a - 1 -(3a + 2b)= 3a + 2b -(3a + 2b),所以 b - a - 1 = 0,即 b - a = 1,因为 b - a >0,所以 b > a.
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