(English Medium) ICSE Class 9 - CISCE Question Bank Solutions for Mathematics

Draw a graph of the equation 2x + 3y + 5 = 0, from the graph find the value of:
(i) x, when y = -3
(ii) y, when x = 8

Draw a graph of the equation 5x - 3y = 1. From the graph find the value of:
(i) x, when y = 8
(ii) y, when x = 2

Draw the graph of the lines y = x + 2, y = 2x - 1 and y = 2 from x = -3 to 4, on the same graph paper. Check whether the lines drawn are parallel to each other.

Draw the graph of the lines represented by the equations x + y = 4 and 2x - y = 2 on the same graph. Find the coordinates of the point where they intersect

Draw the graph of the lines represented by the equations 3x - 2y = 4 and x + y = 3 on the same graph. Find the coordinates of the point where they intersect. State, whether the lines are perpendicular to each other.

Draw the graph of the lines represented by the equations 2x - y = 8 and 4x + 3y = 6 on the same graph. Find the co-ordinates of the point where they intersect.

Draw the graph of the lines represented by the equations 5y = 3x + 1 and y = 2x + 3 on the same graph. Find the coordinates of the point where they intersect.

If `3/2 log a + 2/3` log b - 1 = 0, find the value of a⁹.b⁴ .

If x = 1 + log 2 - log 5, y = 2 log3 and z = log a - log 5; find the value of a if x + y = 2z.

Evaluate :`1/( log_a bc + 1) + 1/(log_b ca + 1) + 1/ ( log_c ab + 1 )`

If x = log 0.6; y = log 1.25 and z = log 3 - 2 log 2, find the values of :
(i) x+y- z       
(ii) 5^{x + y - z}

If a² = log x, b³ = log y and 3a² - 2b³ = 6 log z, express y in terms of x and z .

If log`( a - b )/2 = 1/2( log a + log b )`, Show that : a² + b² = 6ab. 

If a² + b² = 23ab, show that:

log `(a + b)/5 = 1/2`(log a + log b).

If log_√27x = 2 `(2)/(3)` , find x.

If m = log 20 and n = log 25, find the value of x, so that :
2 log (x - 4) = 2 m - n.

Solve for x and y ; if x > 0 and y > 0 ; log xy = log `x/y` + 2 log 2 = 2.

Find x, if :  log_x 625 = - 4

Find x, if : log_x (5x - 6) = 2

Show that : log_a m ÷ log_ab m + 1 + log _ab