Math topic中文

Linear one variable

solving linear equations in one variable

Practice questions

  1. 1某商品提价25%后，欲恢复原价，则应降价（ ） A. 40% B. 25% C. 20% D. 15%
  2. 2解方程：14％x−9％(x+10)=7％x+0.214％x-9％(x+10)=7％x+0.2
  3. 3The difference of the two roots of the equation 3x2+9x−k=03x^2 + 9x - k = 0 is 13 units, where kk is a constant. Find the value…
  4. 4央行决定：从2007年12月21日起调整金融机构人民币存贷款基准利率，一年期存款基准利率由现行3.87%提高到4.14%，上调0.27个百分点；所得利息要交纳5%的利息税．例如，存入一年期100元，到期储户纳税后得利息的计算公式为：税后利息…
  5. 5The diagram (not drawn to scale) shows the speed-time graph of a vehicle. The vehicle starts from rest and accelerates u…
  6. 6在平面直角坐标系xOy中，已知A（2，-2），在y轴上确定点P，使△AOP为等腰三角形，则符合条件的点有 ( ) A. 2个 B. 3个 C. 4个 D. 5个
  7. 7解方程 7x+2.5=8.87x+2.5=8.8； 4×(x−2.8)=26.44×(x-2.8)=26.4； 7.2÷(x+0.38)=8.7.2÷(x+0.38)=8.
  8. 8方程(x－1)(x＋2)＝0的两根分别是( ) A. x1＝－1，x2＝2 B. x1＝1，x2＝2 C. x1＝－1，x2＝－2 D. x1＝1，x2＝－2
  9. 9y is inversely proportional to the square of x, x>0x > 0. If x is increased by 25%, find the percentage change in y. Answ…
  10. 10若x=-2是关于x的方程3x-k+1=0的解，则k的值为___．
  11. 11The diagram below shows the speed-time graph of a bus journey. The bus accelerated from rest at 1.25 m/s^2 to a speed of…
  12. 12有三个数5，x，9，它们的平均数为6，则x为 ．
  13. 13分式方程13x−6=34x−8 \dfrac {1}{3x-6} = \dfrac {3}{4x-8}的解的情况为___．
  14. 14Using factorisation, solve 9x2+6x−8=09x^2 + 6x - 8 = 0. Answer x = ... or ... Hence solve 9(y−1)2+6y−14=09(y-1)^2 + 6y - 14 = 0. Answer y = .…
  15. 15方程3x+1=x-3的解是x= ．
  16. 16Adam has some 50-cent and 20-cent coins in his wallet. Given that he has a total of 73 coins adding up to a value of $2…
  17. 17一种商品售价为进价的1.1倍，现每件又降价10元，现售价为每件210元，该商品的进价为 元．
  18. 18已知△ABC\triangle ABC中，∠B∠B是∠A∠A的22倍，∠C∠C比∠A∠A大20∘20^{\circ}，则∠A∠A等于()() A. 40∘40^{\circ} B. 60∘60^{\circ}…
  19. 19数学迷小虎在解关于字母xx的一元一次方程2x−53=x+a3−1\dfrac{2x-5}{3}=\dfrac{x+a}{3}-1去分母时，方程右边的−1-1漏乘了33，因而求得方程的解为x=1x=1，请你帮助小虎求出aa的值，并求出…
  20. 20购买甲、乙两种糖果共100斤，花了1280元，其中甲糖果每斤11元，乙糖果每斤13元，则甲糖果够买的斤数为（ ） A. 586 B. 90 C. 10 D. 无法确定
  21. 21若正多边形的内角和是540°，那么这个多边形一定是正 边形．
  22. 22如果∠A∠A的补角与∠A∠A的余角互补，那么2∠A2∠A是()() A. 锐角 B. 直角 C. 钝角 D. 以上三种都可能
  23. 23《九章算术》中《均输》卷记载了一道有趣的数学问题：“今有凫((野鸭))起南海，七日至北海；雁起北海，九日至南海．今凫雁俱起，问何日相逢？” 大意为：野鸭从南海起飞，77天飞到北海；大雁从北海起飞，99天飞到南海．现野…
  24. 24分式方程2x+1x−1=3\dfrac{2x+1}{x-1}=3的解是()() A. x=−45x=-\dfrac{4}{5} B. x=45x=\dfrac{4}{5} C. x=−4x=-4 D. x=−4x=-4
  25. 25The diagrams show the speed-time graph and the corresponding distance-time graph of a car. The car travelled from a poin…
  26. 26The marked price of a mobile phone is $1288. After selling the mobile phone at 15% discount, the shop owner still makes…
  27. 27若关于xx、yy的多项式x2−2kxy+y2+6xy−6x^{2}-2kxy+y^{2}+6xy-6中不含xyxy项，则k=k=___.
  28. 28已知∣a→∣=∣b→∣=1| \overrightarrow{a}|=| \overrightarrow{b}|=1，a→ \overrightarrow{a}与b→ \overrightarrow{b}夹角是90∘90^{\circ}，c→=2a→+3b→ \overrightarrow{c}=2 \overrightarrow{a}+3 \overrightarrow{b}…
  29. 29设方程3（x+4）-4=2a+1的解是x=3，则a的值是（ ） A. 7 B. 6 C. 8 D. 9
  30. 30请在方程2x+5=x+ 的右边添上一项，使它的解是x=1．
  31. 31A bag contains 12 balls. 2 of the balls are red, n are green balls and the rest are blue balls. Eunice takes two balls f…
  32. 32解方程组： (1){x+2y=52x+y=4(2){3x−2y=52x+3y=12(1) \begin{cases} \overset{2x+y=4}{x+2y=5}\end{cases}(2) \begin{cases} \overset{2x+3y=12}{3x-2y=5}\end{cases}．
  33. 33解方程：5(x-2)=4-(2-x)
  34. 34解下列方程 (1)6x−2=1x+3(1) \dfrac {6}{x-2}= \dfrac {1}{x+3}； (2)x+1x−1−4x2−1=1(2) \dfrac {x+1}{x-1}- \dfrac {4}{x^{2}-1}=1．
  35. 35The solution of the inequality −1<1−x2≤k+1-1 < \frac{1 - x}{2} \le k + 1, where k is a constant, is represented on the number lin…
  36. 36已知在△ABC中，∠A=2∠C，∠B=3∠C，求各内角的度数，并判断△ABC的形状．
  37. 37The equation of a curve is given by y=ln⁡3x32x−1y = \ln \sqrt{\dfrac{3x^3}{2x-1}}, where x>12x > \tfrac{1}{2}. Find the coordinates…
  38. 38The approximate mass of the earth is 5.976×10245.976 \times 10^{24} kg. How many times is the earth heavier than an average male…
  39. 39一件服装标价500元，若以6折销售，仍可获利20%，则这件服装进价为 元．
  40. 40一次数学竞赛共有 20 道题．做对一道题得5分，做错一题倒扣2分，刘冬考了72分，你知道刘冬做对（ ）道题． A. 6 B. 12 C. 14 D. 16
  41. 41一个多边形的每个内角都相等，且它们的每个内角比其相邻的外角大60°，求这个多边形的边数．
  42. 42A chess club currently has 37 male members and 16 female members. The club hosted a Valentine's Day event to attract mar…
  43. 43某生产车间有6060名工人生产太阳镜，11名工人每天可生产镜片200200片或镜架5050个.应如何分配工人生产镜片和镜架，才能使每天生产的产品配套？
  44. 44Given that 464x=1\frac{4}{64^x} = 1, find the value of x. Answer x = ___
  45. 45若3xm+5y23x^{m+5}y^{2}与x3ynx^{3}y^{n}的和是单项式，则mn=m^{n}= ___ ．
  46. 46AA，BB两站间的距离为448km448km，一列慢车从AA站出发，每小时行驶60km60km，一列快车从BB站出发，每小时行驶80km80km，问： (1)两车同时开出，相向而行，出发后多少小时相遇？ (2)两车相向…
  47. 47The first four terms in a sequence of numbers are 3+k, 1+k, −1+k, −3+k, …3 + k,\ 1 + k,\ -1 + k,\ -3 + k,\ \dots where kk is a constant. Fin…
  48. 48若|m|=|-4|，则m= ；方程-x-1=0的解是 ．
  49. 49田圆圆的妈妈给她买了一套服装共花了150元钱，上衣的价格是裤子的1.5倍，上衣和裤子各花了多少钱？（建议你用方程解）
  50. 50A bag contains some green counters, some orange counters and some yellow counters. The probability of picking a green co…
  51. 51下列变形正确的是()(\quad) A. 若3x−1=2x+13x-1=2x+1，则3x+2x=1+13x+2x=1+1 B. 若3(x+1)−5(1−x)=03\left({x+1}\right)-5\left({1-x}\right)=0，则3x+3−5−5x=03x+3-5-5x=0…
  52. 52Solve the equation 2cosec⁡(x−π3)=−42\cosec\left(x-\dfrac{\pi}{3}\right)=-4 for 0≤x≤2π0\le x\le 2\pi. Solve the equation cot⁡(2x+10∘)=tan⁡70∘\cot(2x+10^\circ)=\tan70^\circ…
  53. 53A composite solid is made from a cylinder and two hemispheres. The cylinder has radius pp and length 2p2p, while the he…
  54. 54下列方程的变形正确的是( ) A. 将方程x−23−1=x+52\dfrac{x-2}{3}-1=\dfrac{x+5}{2}去分母，得2(x−2)−1=3(x+5)2(x-2)-1=3(x+5) B. 将方程3(x−5)−4(x−1)=33(x-5)-4(x-1)=3去括号，得3x−15−4x−4=33x-15-4x-4=3…
  55. 55某影碟出租店开设两种租碟方式：一种是零星租碟，每张收费11元；另一种是会员卡租碟，会员每月交会员费1212元，租碟费每张0.40.4元.小彬经常来该店租碟，若小彬每月租碟数量为xx张． (1)分别写出两种租碟方式下小彬应付…
  56. 56Solve the equation 33x×125x=2253^{3x} \times 125^{x} = 225.
  57. 57The graphs of y=x32−4x−1y = \frac{x^3}{2} - 4x - 1 and y=1−xy = 1 - x are drawn on the grid. The points of intersection of the curv…
  58. 58Solve the equation 3−2x7=13(2x−1).\displaystyle \frac{3-2x}{7} = \frac{1}{3}(2x-1). Answer x = ... Simplify 25a2−9b215a−10ab+6b2−9b\displaystyle \frac{25a^{2}-9b^{2}}{15a-10ab+6b^{2}-9b}…
  59. 59The diagram shows the speed-time graph of two cars, A and B. Car A, starting from rest, accelerates uniformly for 2 seco…
  60. 60如果关于xx的不等式2(x−1)<a+22(x-1) < a+2与2x<42x < 4的解集相同，则aa的值为___．