Math topic中文

Simplification linear

simplification of linear expressions such as: −2(3x−5)+4x-2(3x - 5) + 4x; 2x3−3(x−5)2\quad \dfrac{2x}{3} - \dfrac{3(x - 5)}{2}

Practice questions

  1. 1Factorise completely 9b2−6ab+a2−x29b^{2} - 6ab + a^{2} - x^{2}. Simplify 52x2−7x−4−84−x\dfrac{5}{2x^{2} - 7x - 4} - \dfrac{8}{4 - x}.
  2. 2设(5a+3b)2=(5a−3b)2+A(5a+3b)^{2}=(5a-3b)^{2}+A，则A=()A=() A. 30ab30ab B. 60ab60ab C. 15ab15ab D. 12ab12ab
  3. 3解方程：14％x−9％(x+10)=7％x+0.214％x-9％(x+10)=7％x+0.2
  4. 4n is a positive integer. Explain whether, for all n, (7n+2)2−(7n−1)2(7n+2)^{2}-(7n-1)^{2} is a multiple of 3. Answer ___
  5. 5一艘轮船在静水中的速度为aa千米//小时，水流的速度为1010千米//小时，轮船顺水航行33小时的航程与逆水航行22小时的航程相差 ___ 千米((用含aa的式子表示).).
  6. 6Using 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 = .…
  7. 7Simplify 3x2×4y53x^2 \times 4y^5. Answer ... 3(2x−1)−53(2x-1)-5. Answer ...
  8. 8Simplify −2(−3x−4)+5-2(-3x-4)+5. Answer ...
  9. 9Simplify 3a25b3+(12c25ab)2\frac{3a^2}{5b^3} + \left(\frac{12c}{25ab}\right)^2. nn is a positive integer. Show that, for all nn, (3n+2)2−(3n−2)2(3n+2)^2 - (3n-2)^2…
  10. 10若x<2x < 2，化简(X−2)2+∣3−x∣ \sqrt{(X-2{)}^{2}} +|3-x|的正确结果是 ．
  11. 11It is given that y=xsin⁡x+cos⁡2(x2).y = x\sin x + \cos^2\left(\tfrac{x}{2}\right). Obtain an expression for dydx\dfrac{dy}{dx} in the form…
  12. 12The 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…
  13. 13Factorise the following completely. 45b−18ab−2a2+5a45b - 18ab - 2a^2 + 5a 2p2−23p−162p^2 - \dfrac{2}{3}p - \dfrac{1}{6}
  14. 14The 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…
  15. 15In the diagram, AB is a tangent to the circle with centre O, ∠CAB = 58° and CDE is a straight line. Find, stating your r…
  16. 16Expand and simplify (2x+5)(3+4x)(2x+5)(3+4x).
  17. 17李老师退休后，在社区开了个小店，第一次进货，他以每件aa元的价格购进了 3030件甲种小商品，以每件bb元的价格购进了4040件乙种小商品，且 a<ba < b ． (1)若李师傅将甲种商品提价40％40％，乙种商品…
  18. 18A composite solid is made from a cylinder and two hemispheres. The cylinder has radius pp and length 2p2p, while the he…
  19. 19下列计算正确的是()(\quad) A. x2+x2=x4x^{2}+x^{2}=x^{4} B. x2⋅x3=x5x^{2}\boldsymbol{⋅}x^{3}=x^{5} C. (xy)3=x3y(xy)^{3}=x^{3}y D. (x4)3=x7(x^{4})^{3}=x^{7}…
  20. 20The 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…
  21. 21Solve 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}…
  22. 22Solve x/5+(2x−3)/4=−6x/5 + (2x-3)/4 = -6. Answer x = ... Simplify 2(p−3q)/(10r)+(3q−p)2/r2(p-3q)/(10r) + (3q-p)^2/r. Answer ... Solve the inequality x+1≤7x−24<5x+195x+1 \le \dfrac{7x-2}{4} < \dfrac{5x+19}{5}…
  23. 23解方程：1−x3−x=3−x+22.\dfrac{1-x}{3}-x=3-\dfrac{x+2}{2}.
  24. 24丁丁家五月份支付水费与电费共140元，其中水费为a元，而六月份丁丁家的水费比五月份增加了10%，电费比五月份增加了20%． （1）试用a的代数式表示丁丁家六月份的水电费； （2）当a=40元时，问丁丁家五、六两个月水电费共多少元？
  25. 25Solve the inequality 4x+13>3−2x5\frac{4x+1}{3} > \frac{3-2x}{5}. Simplify (16a12b8)−14\left(\dfrac{16a^{12}}{b^8}\right)^{-\tfrac{1}{4}}, l…
  26. 26Town P and Town Q are 40 km apart. A car is travelling from Town P to Town Q at an average speed of x km/h. During its r…
  27. 27Solve the inequality −3x+42<5−x7\frac{-3x+4}{2} < \frac{5-x}{7}. Answer ... Simplify (64a6b−15)−13\left(\dfrac{64a^{6}}{b^{-15}}\right)^{-\tfrac{1}{3}}…
  28. 28求下列函数的导数 (1)y=x2ln⁡x(1)y={{x}^{2}}\ln x； (2)y=sin⁡x−xx2(2)y=\dfrac{\sin x-x}{{{x}^{2}}} ； (3)y=e−x2x−1(3)y={{e}^{-x}}\sqrt{2x-1}
  29. 29已知当1<a<21 < a < 2时，代数式(a−2)2−∣1−a∣ \sqrt {(a-2)^{2}}- |1-a|的值是___．
  30. 30The variables x and y are connected by the equation y=x35−2x+1y = \frac{x^3}{5} - 2x + 1. Some corresponding values of x and y a…
  31. 31若点P(a+2,3−a)P(a+2,3-a)在第二象限，则(a−3)33−a2+4a+4=\sqrt[3]{(a-3)^{3}}-\sqrt{a^{2}+4a+4}=___.
  32. 32下列运算正确的是()() A. a10+a5=a2a^{10}+a^{5}=a^{2} B. (a3)4=a7(a^{3})^{4}=a^{7} C. (x−y)2=x2−y2(x-y)^{2}=x^{2}-y^{2} D. x3⋅(−x3)=−x6x^{3}⋅(-x^{3})=-x^{6}…
  33. 33已知f(x)f(x)是一次函数，且满足3f(x+1)−2f(x−1)=2x+173f(x+1)-2f(x-1)=2x+17，则函数f(x)f(x)的解析式 ___ ．
  34. 34Simplify Simplify 5−2(6x−1)5-2(6x-1). Simplify (27b9a6)−1/3\left(\dfrac{27b^9}{a^6}\right)^{-1/3}.
  35. 35Factorise 9x2+24xy+16y29x^2 + 24xy + 16y^2 completely. Answer ... Hence factorise 144a8−(9a8+24a4y+16y2)144a^8 - (9a^8 + 24a^4 y + 16y^2) completely. A…
  36. 36将(5x−2)−2(3x−1)(5x-2)-2(3x-1)去括号正确的是()(\quad) A. 5x−2−6x+15x-2-6x+1 B. 5x−2−6x−15x-2-6x-1 C. 5x−2−6x+25x-2-6x+2 D. 5x−2−6x−25x-2-6x-2
  37. 37The table shows some values for y=310x3−x+1y = \frac{3}{10}x^3 - x + 1 for −3≤x≤3-3 \le x \le 3. | x | -3 | -2 | -1 | 0 | 1 | 2 | 3 |…
  38. 38Factorise completely. 24a2b+12ab2−ab24a^2b + 12ab^2 - ab Answer ... mn−18−9m+2nmn - 18 - 9m + 2n Answer ... Expand and simplify (−2x+3q)(x−2q)(-2x+3q)(x-2q)…
  39. 39在等式2a+1=3a的两边都加-2a得 ．
  40. 40The first four terms in a sequence of numbers are given below. Find T5T_5. Answer ... Find an expression, in terms of n,…
  41. 41方程ax-4y=x-1是二元一次方程，则a的取值为（ ） A. a≠0 B. a≠-1 C. a≠1 D. a≠2
  42. 42Answer all the questions A curve has an equation y=2x2x+1y = 2x\sqrt{2x+1}. Show that dydx=ax+b2x+1\frac{dy}{dx} = \frac{ax+b}{\sqrt{2x+1}}…
  43. 43Write down, and simplify the terms in the expansion of (2+x)5(2 + x)^5 in ascending powers of xx. Hence find the coefficien…
  44. 44Show that (3n+1)2+2(3n + 1)^2 + 2 is always divisible by 3 for all integer values of nn. Answer
  45. 45The variables x and y are connected by the equation y=x35−2x+2y=\frac{x^3}{5}-2x+2. Some corresponding values of x and y are giv…
  46. 46下列计算正确的是()(\quad) A. (a3)2=a5(a^{3})^{2}=a^{5} B. (2a)2=2a3(2a)^{2}=2a^{3} C. a⋅a3=a4a\boldsymbol{⋅}a^{3}=a^{4} D. 2a−a=22a-a=2
  47. 47化简：-2（y+x）-（5x-2y）
  48. 48把下列方程改写成用含xx的式子表示yy的形式： (1)32x+2y=1(1)\dfrac{{3}}{{2}}x+{2}y={1}； (2)14x+74y=2(2)\dfrac{{1}}{{4}}x+\dfrac{{7}}{{4}}y={2}； (3)5x−3y=x+2y(3)5x-3y=x+2y…
  49. 49Express x2−6x−2x^2-6x-2 in the form (x−a)2+b(x-a)^2 + b where aa and bb are constants. Answer ___ Hence, state the minimum value…
  50. 50Expand and simplify (3x−y)(y+x).(3x - y)(y + x). Factorise completely 3−12a23 - 12a^2.
  51. 51小博表演扑克牌游戏，她将两副牌分别交给观众AA和观众BB，然后背过脸去，请他们各自按照她的口令操作： bb从第22堆拿出44张牌放到第11堆里； cc从第33堆牌中拿出88张牌放在第11…
  52. 52ABCD is a parallelogram. A is the point (−6,−2)(-6,-2) and B is the point (−4,−7)(-4,-7). BC→=(8−2)\overrightarrow{BC} = \begin{pmatrix}8\\-2\end{pmatrix}…
  53. 53A company sells chocolate muffins and banana muffins. These muffins are sold across three different outlets, which are O…
  54. 54计算： (1)(12)−1−(−8)0+22018×(−12)2017(2)(2a2)2⋅a4−(−5a4)2(1){{(\dfrac{1}{2})}^{-1}}-{{(-8)}^{0}}+{{2}^{2018}}\times {{(-\dfrac{1}{2})}^{2017}}(2){{(2{{a}^{2}})}^{2}}\cdot {{a}^{4}}-{{(-5{{a}^{4}})}^{2}}…
  55. 55“十一”黄金周期间，小刚拿着妈妈给的800元钱到重百商场购买运动服和运动鞋，他来到自己喜欢的“阿迪、达斯”专柜前看到该品牌打出的优惠条件：标价200元以内（含200元）不打折；标价200元以上的按如下方式打折：（1）200～500元（含50…
  56. 56Factorise a2b4−ab2.Answer...Expandandsimplifya^2b^4 - ab^2. Answer ... Expand and simplify (3x + 2)^2 + 4x(2 - x). Answer ...
  57. 57若a<1a < 1，化简(1−a)2−1=\sqrt{{(1-a)}^{2}−1}=___．
  58. 58John and Peter took part in a marathon race. They each ran 42 km. (a) John ran at a constant speed of x kilometres per h…
  59. 59In the following sequence, (1×2)−2=0(1\times2)-2=0 (2×3)−4=2(2\times3)-4=2 (3×4)−6=6(3\times4)-6=6 (4×5)−8=12(4\times5)-8=12 ... (a×12)−b=c(a\times12)-b=c ..…
  60. 60Factorise 3x2−14x−53x^2-14x-5. Answer ... Hence, factorise completely 3(y+1)2−14y−193(y+1)^2-14y-19. Answer ...