Grade 9
1) In which quadrant does (4,-5) lie?
2) Find the point whose ordinate is -4 and abscissa is 0. Also state it's location.
3) Plot the given points in graph : (-3,6) ; (-2,-2) and (0,0) Join them and name the shape obtained. Also
find its area.
4) Find image of (-5,-6) In x axis.
5) Find image of (-3,-2) In y axis.
6) If polynomial f(x) = 5x^5 -3x^3 +2x ^2 -k gives remainder 1 when divided by x+1 then find k.
7) If p(x) = x ^2 -4x + 3 then find value of p(2) -p(-1) + p(1/2)
8) Is x + 9 a factor of x^3 +13x^2 + 31 x -45 ?
9) Using factor theorem Factorize x^3 -10x ^2 -53 x -42
10) Show that (x -2) is factor of f(x) = 2x^3 -3x^2 -17x +30. Hence factorize f(x).
11) Find value of m so that 2x -1 be a factor of 8x^4 + 4x ^3 -16x^2 +10x +m
12) For what value of m is x ^3 -2mx^2 +16 is divisible by (x +2)?
13) Show that (x -2) , ( x +3) and (x -4) are factors of x^3 -3x^2 -10x +24
14) The polynomials ax^3 + 3x^2 -3 and 2x^3 -5x + a when divided by x -4 leaves remainder R1 and R2
respectively. Find value of a for (i) R1 =R2 (ii) R1 + R2 =0 (iii) 2R1 -R2 =0
15) If ax^3 +4x^2 +3x -4 and x^3 -4x + a leaves same reminder when divided by x -3 then find a
16) If x =-1/2 is zero of p(x) = 8x^3 -ax^2 -x +2 find a
17) If x =0 and x =-1 find a and b for 2x^3 -3x^2 +ax +b
18) Find zero of 2x
19) Find zero of 2x +5
20) Find value of (1/2)^3 +(1/3) ^3 -(5/6) ^3
21) Find value of 30 ^3 +20^3 -50^3
22) If a^2 + b^2 + c^2 = 250 and ab + bc + ca = 3 find a + b + c
23) If a + b + c =0 then find value of a^3 + b ^3 + c ^3
24) Find value of x^3 +y^3 -12xy +64 If x + y = -4
25) Find value of (0.2)^3 -(0.3)^3 +(0.1)^3
26) Factorize 8x ^3 +27y^3 +z ^3 -18xyz
27) Find value of [1.2 x 1.2 x 1.2 - 0.2 x 0.2 x0.2]/ 1.2 x 1.2 + 1.2 x 0.2 + 0.2 x0.2
28) Factorize a^6 - b^6
29) ( 2a-3b -2c) ( 4a^2 +9b^2 +4c^2 +6ab -6bc +4ca)
30) If x + y + z =1 , xy + yz + zx = -1 and xyz =-1 find value of x^3 + y^3 + z^3
31) If a+b+c =6 and ab +bc +ca = 11 find value of a^3 + b^3 +c^3 -3abc
32) If (a -b) =6 and ab =20 find value of a^3 -b^3
33) If x^2 +1/x^2 =83 find value of x^3 -1/x^3
34) If x^4 +1/x^4 =47 find value of x^3 +1/x3
35) If 2x +3y =13 and xy =6 find value of 8x^3 +27y3
36) If 3x -4y =10 and xy =-1 find value of 9x^2 +49y^2
37) If x+1/x =5 find value of x^2+1/x^2 and x^4 +1/x^4
38) If root 11 -root 7/ root 11 + root 7 = a -b root 77 find a and b
39) Simplify (root5 +root3/ root 5-root 3) + (root 5-root3/ root 5+ root 3)
40) If x = root 3 + root2 /root 4-root 2 and y =root 3-root2 / root3 + root 2 find x^2 +y^2
41) Locate root 6 on number line
42) Locate root 7.2 on number line
43) Write p/q form of 0.999....
44) Write p/q form of 1.234( bar is on 34)
45) Find two rational and two irrational numbers between 2/3 and 2/7
