1. REVISION TEST 1 DUM 3272 MATHEMATICS 3
1. Find the centre and radius of each circle below :
i. 222
1=+yx
ii. 222
3)4()3( =−+− yx
iii. 16)5()6( 22
=+++ yx
iv. 04101222
=++++ yxyx
v. 02122433 22
=+−−+ yxyx
2. Find the vertex and focus of parabola below . Hence sketch every parabola.
i. )5(202
−= yx
ii. )1(4)2( 2
−=+ xy
iii. )8(16)7( 2
+−=− yx
iv. )1(24)2(3 2
−−=+ xy
3. Find centre , vertexs and foci for following ellipse below :
i. 1
25 2
2
2
2
=+
yx
ii.
( ) ( ) 1
100
3
9
2
22
=
−
+
− yx
iii.
( ) ( ) 1
4
1
25
6
22
=
+
+
+ yx
iv.
36)5(4)8(9 22
=++− yx
1

2. V ( 5, 8)
V ( 2, 9)
4. Find centre , vertexs and foci for following hyperbola below . Hence sketch
every hyperbola.
i. 1
25 2
2
2
2
=−
yx
ii.
( ) ( ) 1
25
5
169
2
22
=
−
−
− xy
iii.
( ) ( ) 1
1
9
81
4
22
=
+
−
+ yx
iv. 100)5()8(25 22
=+−− yx
5. Write standard equation and general equation for the circle with centre (2 , –5)
and radius is 3 unit.
6. Write standard form for each of parabola below :
a.
x
Directrix : x = 2
b.
2
x
f ( 2, 5)

3. x
7.
y
X
Diagram 1
a. Find
i. distance between foci and centre
ii. vertexs
b. Write equation of ellipse in standard form .
8. Write standard form for hyperbola below :
9. Evaluate each of the following functions:-
2x
4x
lim)b(
5x2x
6x
lim)a(
2
2x3
2
3x −
−
++
−
→→
( )( )
x7
1x3
lim.f
3x
3x5x2
lim.e
3x
1x2
lim.d1x1x5lim.c
x
2
3x
2x3x
−
+
−
−−
−
+
−+
∞→→
−→→
3
C
F
6
4
F
16
C (8, 5)
10 unit
f (17 , 5)

4. g. 





−
−
→ 4x
16x
lim
2
2x






+∞→→ 1x
x3
lim)i(x5lim)h(
x
2
5x






−
−−
−
−→−→ 5x
5x4x
lim)k(x2xlim)j(
2
2x
3
2x
l. 





+
→
x
x
1
lim 23x
10. Find the derivative of the function given below using the first principle method:-
a. f(x) = 3x2
– 4 b. f(x) = 3x2
c. f(x) = x2
+ 2x
d. f(x) = x2
– 2x 3x4x2y.e 23
−+=
11. Differentiate the following functions:-
6x5xy.a 2
−+= b.
2
2x
y
2
−
= c. 1xy 2
+=
12
xxy.d −
−= ( )3x2lnx2cos5y.e ++=
12. Differentiate the following functions :
a. y = sin 2x x
e5x3siny.b −
+= c. y = sin 2
x3
d. y = ln (4-x) e. y = ln 4x f. y = x
e3
2
g. f(x) = 2 cos ( )2
x31− h. y = 3 cos x2
i. f(x) = ln ( sin x) j. y = 5 ln 3x
k. f(x) = x2
e
1
l. f(x) = 2 cos (3x + 1)
m. f(x) = ln ( tan x) n. f(x) = - 4e4x
o. f(x) = 5x3
– sin 2x p. f(x) = ln ( )xx2 2
− q. y = ecos 2x
( )
( )3x2lnxlny.u
eey.s
8
2x5cos
y.r
4
xx2 3
−+=
+=
−
=
t. xx
eey 53
+= −
v. ( )68lnln4 2
+−= xxy
4