Math topic中文

Add subtract linear

addition and subtraction of linear expressions

Practice questions

  1. 1n 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 ___
  2. 2Factorise completely. abc−3c−6+2ababc - 3c - 6 + 2ab Answer ... 80x4−580x^{4} - 5 Answer ...
  3. 3下列运箅正确的是()() A. 2a2−a=a2a^{2}-a=a B. (a+2)2=a2+4(a+2)^{2}=a^{2}+4 C. (a2)3=a6(a^{2})^{3}=a^{6} D. (−3)2=−3 \sqrt {(-3)^{2}}=-3
  4. 4一个长方形长为70厘米，剪去一个最大的正方形后，剩下的是一个小长方形，则这个小长方形周长是 厘米．
  5. 5下列各组是同类项的是( )(\text{ }) A. 2x32x^{3}与3x23x^{2} B. 12ax12ax与8bx8bx C. x4x^{4}与a4a^{4} D. π\pi与−3-3
  6. 6哥哥存的零花钱比妹妹的2倍少20元，比弟弟的2倍多10元，弟弟和妹妹谁存的零花钱多？多多少？
  7. 7已知代数式xa−by2x ^{a-b} y ^{2}与xy2a+bxy ^{2a+b}是同类项，则aa与bb的值分别是(    )(\:\:\:\:) A. a=0a=0，b=1b=1 B. a=2a=2，b=1b=1 C. a=1a=1…
  8. 8六年级和七年级分别有192192人和133133人，现在需要从两个年级选出133133人参加“读书节”活动，并且要使六年级，七年级剩余学生数之比为22：11，问应从六年级，七年级各选出多少人？
  9. 9两辆车分别同时从两地出发，相向而行，甲车每时行35千米，乙车每时行65千米，t时后相遇，相遇时甲车行了 千米，乙车行了 千米，乙车比甲车多行 千米，两地相距 千米．
  10. 10Write down, and simplify the terms in the expansion of (2+x)5(2 + x)^5 in ascending powers of xx. Hence find the coefficien…
  11. 11Expand and simplify (3x−y)(y+x).(3x - y)(y + x). Factorise completely 3−12a23 - 12a^2.
  12. 12y=x34−2x+3y = \dfrac{x^3}{4} - 2x + 3. Complete the table of values for y=x34−2x+3y = \dfrac{x^3}{4} - 2x + 3. On the grid opposite, dra…
  13. 13Express 2x2−6x−122x^2 - 6x - 12 in the form k(x−a)2−bk(x - a)^2 - b, where kk is an integer. Answer: ... Hence, solve 2x2−6x−12=02x^2 - 6x - 12 = 0…
  14. 14计算：t−3t=t-3t= ___ .
  15. 15计算：−2a+7a=-2a+7a=；3a2−(−2a2)=3a^{2}-(-2a^{2})=；−(a−2b+c)=-(a-2b+c)=___.
  16. 16O is the centre of the circle passing through B, E, D and C. Angle DOC=84∘DOC = 84^\circ and angle CBO=54∘CBO = 54^\circ. PQPQ is…
  17. 17已知甲组数据11，22，33，44，55，66，77，88，99，1010，1111，1212，乙组数据a1a_{1}，a2a_{2}，a3a_{3}…a6a_{6}…
  18. 18Complete the table of values for y=2x2−2x.Valuesaregiventoonedecimalplacewhereappropriate.Onthegridopposite,drawthegraphofy=\dfrac{2}{x^{2}}-2x. Values are given to one decimal place where appropriate. On the grid opposite, draw the graph of …
  19. 19Let p=12x2−3yx2p = \frac{1}{2} \sqrt{\dfrac{x^2 - 3y}{x^2}} (a) Evaluate pp when x=−12x = -12 and y=4y = 4, giving your answer corre…
  20. 20The table of values for y=x+5x−7y = x + \dfrac{5}{x} - 7 is given below. | x | 0.5 | 1 | 1.5 | 2 | 3 | 4 | 5 | 6 | 7 | |---|--…
  21. 21小明今年a岁，爸爸今年（a+27）岁，3年后爸爸比小明大 岁．
  22. 22Express x2−4x+8x^2-4x+8 in the form (x+p)2+q(x+p)^2+q. Answer ... Hence explain why there is no solution for x2−4x+8=0x^2-4x+8=0. Answer .…
  23. 23Express 9−8x+x29 - 8x + x^2 in the form a+(x+b)2a + (x + b)^2. Find the value of aa and of bb. Answer a = ... b = ... Explain why…
  24. 24The sequence T1,T2,T3,T4,…T_1, T_2, T_3, T_4,\dots has the following first four terms. T1=22−1=3T_1 = 2^2 - 1 = 3 T2=32−2=7T_2 = 3^2 - 2 = 7 T3=42−3=13T_3 = 4^2 - 3 = 13…
  25. 25Simplify 5a2−(3a−2b)25a^2 - (3a - 2b)^2. Answer ...
  26. 26A bag contains 150 chips. There are 60 blue chips, x red chips and y green chips in the bag. The probability of drawing…
  27. 27下列计算正确的是()(\quad) A. x2y+2xy2=3xy2x^{2}y+2xy^{2}=3xy^{2} B. 3a+b=3ab3a+b=3ab C. a2+a3=a5a^{2}+a^{3}=a^{5} D. −3ab+3ab=0-3ab+3ab=0
  28. 28三个连续整数中，n是最大的一个，这三个数的和为 ．
  29. 29已知A=3a-2b+c，B=a+4b-2c，C=a-3c，求：A-（B+C）．
  30. 30The diagram shows a triangle ABC with AB produced to D. AB=18 cmAB = 18\,\mathrm{cm}, BC=20 cmBC = 20\,\mathrm{cm}, AC=22 cmAC = 22\,\mathrm{cm}…
  31. 31Simplify 25m2−44−4m−15m2\dfrac{25m^2-4}{4-4m-15m^2}. Given that r=3−p24−qr = 3 - \sqrt{\dfrac{p^2}{4} - q}, evaluate rr when p=−8p = -8 and q=7q = 7…
  32. 32刘谦的魔术风靡全国，现刘谦背对小亮，让小亮按下列四个步骤操作：第一步分发左、中、右三堆牌，每堆牌不少于两张，且各堆牌的张数相同；第二步从左边一堆拿出两张，放入中间一堆；第三步从右边一堆拿出一张，放入中间一堆；第四步左边一堆有几张牌，就从中间…
  33. 332c+b=b−ca2c + b = \frac{b - c}{a} Rearrange the formula to make b the subject. Answer b = ...
  34. 34一个多项式与a-2b的和是2a-b，则这个多项式是 ．
  35. 35Simplify −4(2a+b)+7(b−3a)-4(2a + b) + 7(b - 3a). Factorise completely 12xy+6x2−2y−x12xy + 6x^2 - 2y - x.
  36. 36The variables x and y are connected by the equation y=32x+5x−7y = \frac{3}{2}x + \frac{5}{x} - 7. Some corresponding values of x…
  37. 37Leanne says that the equation of the line AB is 2y=−4x+12y = -4x + 1 and the equation of the line PQ is 4y=−9x+24y = -9x + 2. Is she…
  38. 38Solve the equation 2(x−5)=3x−12(x-5)=3x-1. Answer xx = ... Solve the inequality 7−4y>3(y+2)7-4y>3(y+2). Answer ... Given that 1p−12q=13r\dfrac{1}{p}-\dfrac{1}{2q}=\dfrac{1}{3r}…
  39. 39某三角形的第一条边长(2a−b)(2a-b)厘米，第二条边比第一条边长(a+b)(a+b)厘米，第三条边是第一条边的22倍少bb厘米，那么这个三角形的周长是 ___ 厘米．
  40. 40Given that 3v=25−x23v=\sqrt{25-x^2}, find the value of vv when x=−3x=-3. make xx the subject of 3v=25−x23v=\sqrt{25-x^2}.
  41. 41在一张挂历上，任意圈出同一列上的三个数的和不可能是()(\quad) A. 1414 B. 7272 C. 3333 D. 6969
  42. 42下列计算正确的是 A. 2+4=6\sqrt{2}+\sqrt{4}=\sqrt{6} B. a+2a=3aa+2a=3a C. (2a)3=2a3(2a)^{3}=2a^{3} D. a6÷a3=a2a^{6}÷a^{3}=a^{2}
  43. 43Factorise completely 9b2−6ab+a2−x29b^{2}-6ab+a^{2}-x^{2}. Simplify 52x2−7x−4−84−x\displaystyle\frac{5}{2x^{2}-7x-4}-\frac{8}{4-x}.
  44. 44The numbers 1 to 100 are arranged in a table as shown below. A L-shaped shaded frame can be placed around various number…
  45. 45The first four terms in a sequence of numbers are given below. T1=32+5=14T_1 = 3^2 + 5 = 14 T2=42+8=24T_2 = 4^2 + 8 = 24 T3=52+11=36T_3 = 5^2 + 11 = 36…
  46. 46Express 12xy215÷2xy3(3x)2\frac{12xy^2}{15} \div \frac{2xy^3}{(3x)^2} as a single fraction in its simplest form. Given that v3=2s+vs−33\dfrac{v}{3} = \sqrt[3]{\dfrac{2s+v}{s-3}}…
  47. 47The diagram shows the first three of a sequence of figures that are formed by squares of the same size. The number of ve…
  48. 48The diagram above shows a solid structure that is formed from two identical cones and a cylinder. The cylinder is attach…
  49. 49解方程． 7x-2x=135 6.4x-16=3.2 8x÷4=32 4x-0.8×5=6．
  50. 50Write as a single fraction in its simplest form 4−xx+2  −  23−x\displaystyle \frac{4 - x}{x + 2} \; - \; \frac{2}{3 - x}. Answer ...
  51. 51Solid A shows a solid formed by joining a hemisphere of radius rr to one end of a cylinder of height rr. The other end…
  52. 52若x⩽0x\leqslant 0，则化简∣1−x∣−x2\left| 1-x \right|-\sqrt{{{x}^{2}}}的结果是 ．
  53. 53Solve 2x−7=3(1−3x).\n\nAnswerx=...Solvetheinequalities2x-7=3(1-3x).\n\nAnswer x = ... Solve the inequalities 7x-1<13andand\frac{x+1}{2}\ge -2(x-2).\n\nAnswer ... Rea…
  54. 54下列计算正确的是()() A. (a−b)2=a2−b2(a-b)^{2}=a^{2}-b^{2} B. a2⋅a3=a5a^{2}⋅a^{3}=a^{5} C. 2a+3b=5ab2a+3b=5ab D. 33−22=13 \sqrt {3}-2 \sqrt {2}=1
  55. 55Complete the table of values for y=2x+1x2−4y = 2x + \dfrac{1}{x^{2}} - 4. Values are given to two decimal places where appropria…
  56. 56Simplify -9(5x+2y)-3(2x-y). Answer ___ Factorise completely 6ap+9aq-12bq-8bp. Answer ___
  57. 57有5个连续的自然数，中间的一个数是n，求出这5个数的和．
  58. 58Simplify (a+2b)(a−2b)−a2(a+2b)(a-2b)-a^2. Answer ... Hence evaluate 12 349×12 341−12 345212\,349\times12\,341-12\,345^2. Answer ...
  59. 59The first four terms in a sequence of numbers are given below. T1=52−18=7T_1 = 5^2 - 18 = 7 T2=62−22=14T_2 = 6^2 - 22 = 14 T3=72−26=23T_3 = 7^2 - 26 = 23…
  60. 60Simplify (4x+3y)2+(3x−4y)2.Answer...Itisgiventhat(4x+3y)^2 + (3x-4y)^2. Answer ... It is given that x^2 + y^2 = 1.Usingyouranswerinpart(i),explainwhythemaximumvalueof. Using your answer in part (i), explain why the maximum value of …