Worksheets12 Maths vol I Tm
Total questions: 130
Worksheet time: 1hrs 5mins
π-x
x-π/2
π/2-x
x-π
2π/3
π/3
π/6
π
2Π
Π
0
tan 12/65
|α|≤1/√2
|α|≤1/√2
|α|<1/√2
|α|>1/√2
-π≤x≤0
0≤x≤π
-π/2≤x≤π/2
π≤0≤x
0
1
2
3
-π/10
π/5
π/10
-π/5
[1,2]
[-1,1]
[0,1]
[-1,0]
-√24/25
√24/25
1/5
-1/5
1/2cos-1(3/5)
1/2sin-1(3/5)
1/2tan-1(3/5)
tan-1(1/2)
[-1,1]
[√2,2]
[-2,-√2]∪[√2,2]
[-2,-√2]
x2-x-6=0
x2-x-12=0
x2+x-12=0
x2+x-6=0
π/4
3π/4
π/6
π/3
π/2
π/3
π/4
π/6
tan2α
0
-1
tan2α
tan-1x
sin-1x
0
π
1/2
1/√5
2/√5
√3/2
2
3
4
5
x/√1-x2
1/√1-x2
1/√1+x2
x/√1+x2
0
4
4i
-4
mn
m+n
mn
nm
-q/r
-p/r
q/r
-q/p
-1
5/4
4/5
5
|K|≤6
K=0
|K|>6
|K|≥6
2
4
1
0
a≥0
a>0
a<0
a≤0
0
n
<n
r
3
4
2
5
A
B
I3
BT
1/3
1/9
1/4
1
A-1
A--1/2
3A-1
2A-1
-40
-80
-60
-20
15
12
14
11
0
-2
-3
-1
adj A = |A| A-1
adj(AB) = (adjA)(adjB)
det A-1= (detA)-1
(ABC)-1= C-1B-1A-1
A-1
(AT)2
AT
(A-1)2
-4/5
-3/5
3/5
4/5
0
sinθ
cosθ
1
17
14
19
21
1
2
4
3
e(Δ2/Δ1),e(Δ3/Δ1)
log(Δ1/Δ3),log(Δ2/Δ3)
log(Δ2/Δ1),log(Δ3/Δ1)
e(Δ1/Δ3),e(Δ2/Δ3)
1only
2and3
3and4
1,2,and4
2π/3
3π/4
5π/6
π/4
λ=7,μ≠-5
λ=-7,μ=5
λ≠7,μ≠-5
λ=7,μ=-5
1
2
3
4
0,-40/9
0
40/9
-40/9
15<m<65
35<m<85
-85<m<-35
-35<m<15
4/3
4/√3
2/√3
3/2
6/5
5/3
10/3
3/5
1
3
√10
√11
(4,7)
(7,4)
(9,4)
(4,9)
x+2y=3
x+2y+3=0
2x+4y+3=0
x-2y+3=0
8
6
10
12
10
2√5
6
4
4(a2+b2)
2(a2+b2)
a2+b2
1/2(a2+b2)
2
3
1
4
3
1
-1
9
√2/2
√3/2
1/2
3/4
(9/2√2,-1/√2)
(-9/2√2,1/√2)
(9/2√2,1/√2)
(3√3,-2√2)
√3/√2
√3/2
1/2
1/4
x2+y2-6y-7=0
x2+y2-6y+7
x2+y2-6y-5=0
x2+y2-6y+5=0
8
32
80
40
2ab
ab
√ab
a/b
1/√2
1/2
1/4
1/√3
√/2
1/3
1/3√2
1/√3
2x+1=0
x= -1
2x-1=0
x=1
(-5,2)
(2,-5)
(5,-2)
(-2,5)
2
4
0
-2
(-5,2)
(-3,2)
(5,-2)
(-2,5)
2
-1
1
0
[α̅,β̅,γ̅]=1
[α̅,β̅.γ]=-1
[α̅,β̅,γ̅]=0
[α̅,β̅,γ̅]=2
|a̅| |b̅| |c̅|
1/3 |a̅| |b̅| |c̅|
1
-1
a̅
b̅
c̅
0̅
π/2
π/3
π
π/4
π/6
π/4
π/3
π/2
1
-1
2
3
0
1
6
3
81
9
27
18
π/2
3π/2
π/4
π
8 cu. units
512 cu. units
62 cu. units
24 cu. units
00
450
600
900
-17i^+21j^-97k^
17i^+21j^-123k^
-17i^-21j^+97k^
-17i^-21j^-97k^
π/6
π/4
π/3
π/2
(-5,5)
(-6,7)
(5,-5)
(6,-7)
00
300
450
90
(2,1,0)
(7,-1,-7)
(1,2,-6)
(5,-1,1)
0
1
2
3
√7/2√2
7/2
√7/2
7/2√2
c = ±3
c = ±√3
c>0
0<c<1
(0,6,-1) and (1,-2,-1)
(0,6,-1) and (-1,-4,-2)
(1,-2,-1) and (1,4,-2)
(1,-2,-1) and (0,-6,1)
±3
±6
-3,9
3,-9
1/2,-2
-1/2,2
-1/2,-2
1/2,2
2√3
3√2
0
1
0
1
-1
i
1+i
i
1
0
1/2|Z|2
|Z|2
3/2|Z|2
2|Z|2
1/i+2
-1/i+2
-1/i-2
1/i-2
0
1
2
3
1/2
1
2
3
√3-2
√3+2
√5-2
√5+2
1
2
3
5
Z
Z̅
1/Z
1
1
2
3
4
1
2
3
4
0
1
2
3
3
2
1
0
1/2
1
2
3
-5π/6
-2π/3
-3π/4
-π/2
-110°
-70°
70°
110°
1
i
x2+y2
1+n2
(1,0)
(-1,1)
(0,1)
(1,1)
2π/3
π/6
5π/6
π/2
1
2
-1
-2
1
-2
-1
2
1
-1
√3i
-√3i
cis2π/3
cis4π/3
-cis2π/3
-cis4π/3
1
2
3
4
