MATHEMATICS TEST [ FOR GRADE 11 &12 / UK A & AS - LEVEL / CBSE..]

MATHS TEST { FOR GRADE 11 & 12 } The equation of a circle is x2 + y2 – 2x + 6y +1 = 0.The centre of this circle is[A] ( 1 , 3 ) [B]( -1 , 3 )[C] (1 , -3)[D] (2 , -6)[2] Given y = 3x2 – 12x + 5 . Which of the following points is the turning point for this function . [A] x = 1[B] x = 1.5[C] x = 2[D] x = 3[3] = ……………………..[A] 14[B] 15[C] 17[D] 20[4] If f(x) = 2x3 - 2x2 – 4 , f’’(x) will be equal to[A] 12 x[B] 4(3x – 1)[C] 2(3x + 1)[E] 2x(3x + 1)[5] The centre of a circle is ( -3 , 2) and its radius is 5cm. The equation of this circle is ……………………………[A] (x + 3)2 + (y - 2)2 = 25[B] (x + 3)2 + (y + 2)2 = 25[C] (x – 3)2 + (y - 2)2 = 25 [C] (x - 3)2 - (y - 2)2 = 25 [6] Given f(x) = 1 + 2x - 2x2 . The maximum value of this function is [A] 1 [B] 1.5[C] 2[ D] 2.5[7] If , the sum of the constants A and B will be equal to[A] 0[B] 1[C] 2[D] 3[8] The coordinates of the end points of the diameter of a circle are ( 3 , 4) and (-3 , -4 ) . The equation of this circle is[A] x2 + y2 = 9[B] x2 + y2 = 25[C] x2 + y2 = 64[D] x2 + y2 = 100[9] The area enclosed by the curve y = 3 + 2x – x2 and the x-axis is equal to …………………. square units.[A] 11/3[B] 23/3[C] 32/3 [D] 41/3[10] The value of [A] 4[B] 6[C] 9[D] 12[11] The line y = 2x and the curve y = 6x –x2 intersects at the points P and Q. The coordinates of P and Q are[A] ( 0 , 0) and ( 2 , 5)[B] ( 0 , 2) and ( 6 , 0)[C] (3 ,0) and ( 0 , 6)[D] (0 , 0) and ( 4 , 8 )[12] Given the function, y = The following table shows the corresponding y-values for some x-values chosen from 0 to 1 at equal intervals . Which of the following options gives the approximate value of [A] 3.212[B] 4.345[C] 4.196[D] 5.899[13] The curve y = 10 + 8x + x2 - x3 has a maximum turning point A. The x-coordinate of A is ……………….[A] 1[B] 2[C] 3[D] 4[14] The area of the region bounded by the curve y2 = 2y –x and the y- axis is ---------------------- square units[A] 3/2[B] ¾[C] 4/3 [D] 5/2 [15] Splitting into partial fractions we get[A] [B] [C] [D] [16]AB is the chord of a circle with centre O. The coordinates of the end points of AB are ( 3 , 2) and (- 5, 8). The coordinates of the circle centre are (-2 , 7). The equation of the line passing through the circle centre and the midpoint of the chord is[A] y = 3x – 2[B] y = 2 - 3x[C] y + 2x = 3[D] y = x + 3[17] The area enclosed between the curve y = (1 + x)(4 – x) and the x-axis is…………………….. square units[A] 83/18[B] 92/15[C] 117/30[D] 125/6[18] PR is the diameter of the given circle. The coordinates of P , Q and R are (-3 , 2) , ( 9 , 10 ) and ( a , 4). The value of a , the x coordinate of R is …………..[A] 3[B] 7[C] 9[E] 13[19] The Volume V of a right circular cylinder with a given total surface area is given as V = 400r - r3 . Kim uses calculus to find the maximum possible value for the volume of this cylinder. His answer to the nearest cubic unit will be ………………..[A] 1234[B] 1526[C] 1737[D] 2019[20] The value of is equal to[A] 29 [B] 34[C] 37[D] 41[21] The equation of the circle with centre ( -3 , 1 ) and passing through ( 0 , 5) is…………………………………….[A](x + 3)2+(y -1 )2 = 25[B] (x - 3)2+(y + 1 )2 = 25[C] (x + 3)2+(y - 1 )2+ 25 = 0[d] (x + 3)2- (y - 1 )2- 25 = 0[22] The turning point of the curve y = 12 - - 10 is …………………….[A] x = 2[B] x = 3[C] x = 4[D] x = 5[23]The equation of the circle with centre (3 , 0 ) and touching the y-axis is …………………[A] x2- 6x + y2 = 0[B] x2 - 6y + y2 = 0[C] x2 + y2 - 6x + 2y + 9 = 0 [C] x2 + y2 = 9[24] The circle C has centre ( 3 , 1 ) and it passes through the point P ( 8 , 3). The equation of the tangent to C at the point P is[A] 2x – 7y + 11 = 0[B] 5x + 2y – 46 = 0[C] x + 9y + 58 = 0[C] 7x – 2y + 33 = 0