Term 3 Algebra Five Marks Questions

9th Standard

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Maths

Time : 01:00:00 Hrs
Total Marks : 50
    10 x 5 = 50
  1. (Graphing made easier!) Draw the graph of the line given by the equation y = 4x – 3.

  2. Draw the graph for the following
    (i) y = 3x - 1
    (ii) \(y=\left( \frac { 2 }{ 3 } \right) x+3\)

  3. Use graphical method to solve the following system of equations x + y = 5; 2x – y = 4.

  4. Use graphical method to solve the following system of equations 3x + 2y = 6; 6x + 4y = 8

  5. Solve graphically
    (i) x + y = 7; x − y = 3
    (ii) 3x + 2y = 4; 9x + 6y −12 = 0
    (iii) \(\frac { x }{ 2 } +\frac { y }{ 4 } =1;\frac { x }{ 2 } +\frac { y }{ 4 } =2\)
    (iv) x − y = 0; y + 3 = 0
    (v) x − 2y = 1; x − 2y + 5 = 0
    (vi) 2x + y = 4; 4x + 2y = 8
    (vii) y = 2x +1; y + 3x − 6 = 0
    (viii) x = –3; y = 3

  6. The sum of the digits of a given two digit number is 5. If the digits are reversed, the new number is reduced by 27. Find the given number.

  7. Solve, using the method of substitution
    (i) 2x − 3y = 7; 5x + y = 9
    (ii) 1.5x + 0.1y = 6.2; 3x − 0.4y = 11.2
    (iii) 10% of x + 20% of y = 24; 3x − y = 20
    (iv) \(\sqrt { 2 } \)x - \(\sqrt { 3 } \)y = 1; \(\sqrt { 3 } \)x -\(\sqrt { 8 } \)y = 0
    (v) \(\frac { 2 }{ \sqrt { x } } +\frac { 3 }{ \sqrt { y } } =2;\frac { 4 }{ \sqrt { x } } -\frac { 9 }{ \sqrt { y } } =-1\) (Hint: Put\(\frac { 1 }{ \sqrt { x } } =a;\frac { 1 }{ \sqrt { y } } =b\))

  8. Solve by the method of elimination
    (i) 2x–y = 3; 3x + y = 7
    (ii) x–y = 5; 3x + 2y = 25
    (iii) \(\frac { x }{ 10 } +\frac { y }{ 5 } =14;\frac { x }{ 8 } +\frac { y }{ 6 } =15\)
    (iv) 3(2x + y) =7xy; 3(x + 3y) = 11xy
    (v) \(\frac { 4 }{ x } +5y=7;\frac { 3 }{ x } +4y=5\)
    (vi) \(\frac { 3 }{ x+y } +\frac { 2 }{ x-y } =3;\frac { 2 }{ x+y } +\frac { 3 }{ x-y } =\frac { 11 }{ 3 } \)
    (vii) 13x +11y = 70; 11x +13y = 74
    (viii) 37x + 29y = 45; 29x + 37y = 21

  9. Solve 3x − 4y = 10 and 4x + 3y = 5 by the method of cross multiplication.

  10. Check whether the following system of equation is consistent or inconsistent and say how many solutions we can have if it is consistent.
    (i) 2x – 4y = 7
    x – 3y = –2
    (ii) 4x + y = 3
    8x + 2y = 6
    (iii) 4x +7 = 2 y
    2x + 9 = y

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